grease.lubrication.in.rolling.bearings

GREASE LUBRICATIONIN ROLLING BEARINGS

Tribology Series

Bhushan Introduction to Tribology, 2nd Edition March 2013Bhushan Principles and Applications to Tribology, 2nd

EditionMarch 2013

Lugt Grease Lubrication in Rolling Bearings January 2013Honary and Richter Biobased Lubricants and Greases: Technology

and ProductsApril 2011

Martin and Ohmae Nanolubricants April 2008Khonsari andBooser

Applied Tribology: Bearing Design andLubrication, 2nd Edition

April 2008

Stachowiak (ed) Wear: Materials, Mechanisms and Practice November 2005Lansdown Lubrication and Lubricant Selection: A

Practical Guide, 3rd EditionNovember 2003

Cartier Handbook of Surface Treatment and Coatings May 2003Sherrington, Roweand Wood (eds)

Total Tribology: Towards an IntegratedApproach

December 2002

Kragelsky and Tribology: Lubrication, Friction and Wear April 2001Stolarski and Tobe Rolling Contacts December 2000Neale and Gee Guide to Wear Problems and Testing for

IndustryOctober 2000

GREASE LUBRICATIONIN ROLLING BEARINGS

Piet M. LugtSKF, The Netherlands

A John Wiley & Sons, Ltd., Publication

This edition first published 2013C© 2013 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Lugt, Piet M., author.Grease lubrication in rolling bearings / Piet M. Lugt.pages cm. – (Tribology in practice series)Includes bibliographical references and index.ISBN 978-1-118-35391-2 (hardback) – ISBN 978-1-118-48396-1 (obook) – ISBN 978-1-118-48397-8 (epub)

1. Roller bearings–Lubrication. 2. Lubrication and lubricants. I. Title.TJ1071.L78 2013621.8′9–dc23

2012031584

Cover photograph courtesy of SKF Maintenance Products

A catalogue record for this book is available from the Library of Congress.

ISBN: 978-1-118-35391-2

Typeset in 10/12pt Times by Aptara Inc., New Delhi, India

Dedicated to:Marjo, Michiel and Marijn

Contents

Preface xvii

Series Preface xix

List of Abbreviations xxi

1 Introduction 11.1 Why Lubricate Rolling Bearings? 11.2 History of Grease Lubrication 21.3 Grease Versus Oil Lubrication 3

2 Lubrication Mechanisms 52.1 Introduction 52.2 Definition of Grease 62.3 Operating Conditions 62.4 The Phases in Grease Lubrication 72.5 Film Thickness During the Bleeding Phase 8

2.5.1 Ball Bearings 82.5.2 Roller Bearings 10

2.6 Feed and Loss Mechanisms During the Bleeding Phase 102.7 Film Thickness and Starvation (Side Flow) 112.8 Track Replenishment 122.9 Grease Flow 13

2.9.1 Non-Newtonian Rheology 142.10 Wall-Slip 152.11 Oxidation 162.12 EP Additives 162.13 Dynamic Behaviour 172.14 Grease Life 17

2.14.1 Temperature 182.14.2 Speed 192.14.3 Load 192.14.4 Bearing Type 202.14.5 Grease Type 202.14.6 Environment 21

viii Contents

3 Grease Composition and Properties 233.1 Base Oil 24

3.1.1 Natural Triglyceride and Wax Ester Base Oils 263.1.2 Mineral Oils 263.1.3 Synthetic Oils 30

3.2 Base Oil Viscosity and Density 413.2.1 Viscosity–Temperature 443.2.2 Viscosity–Pressure–Temperature 453.2.3 Density, Compressibility 47

3.3 Thickener 493.3.1 Soap Greases, Simple Greases 503.3.2 Complex Greases 513.3.3 Non-soap Thickeners 523.3.4 Mixed Thickeners 523.3.5 Mechanical Structure 533.3.6 Oil Retention 563.3.7 Properties of Different Types of Grease Thickeners 56

3.4 Additives 613.4.1 Corrosion Inhibitors 623.4.2 Antioxidants 623.4.3 EP/AW Additives 63

3.5 Solid Fillers/Dry Lubricants 663.5.1 MoS2 and Graphite 663.5.2 Nanoparticles 663.5.3 ZnO 663.5.4 Teflon (polytetrafluoroethylene) 663.5.5 Polyethylene 66

3.6 Compatibility 673.7 Polymer Grease 67

4 Grease Life in Rolling Bearings 714.1 Introduction 714.2 Relubrication Intervals and Grease Life 714.3 The Traffic Light Concept 72

4.3.1 Low Temperatures 744.3.2 Extreme Low Temperature 754.3.3 Extreme High Temperature 75

4.4 Grease Life as a Function of Temperature in the Green Zone 754.5 SKF Relubrication and Grease Life 764.6 Comparison Grease Life/Relubrication Models 784.7 Very Low and High Speeds 82

4.7.1 Speed Ratings and Speed Factors 824.7.2 High Speed 824.7.3 Very Low Speeds 85

4.8 Large Rolling Bearings 854.9 Effect of Load 86

Contents ix

4.9.1 Varying Load 864.9.2 Direction of Load 894.9.3 Very Heavy Loads 89

4.10 Effect of Outer-Ring Rotation 904.11 Cage Material 904.12 Bearing Type 91

4.12.1 Roller Bearings 914.12.2 Hybrid Bearings 91

4.13 Temperature and Bearing Material 924.14 Grease Fill 944.15 Vertical Shaft 954.16 Vibrations and Shock Loads 964.17 Grease Shelf Life/Storage Life 97

5 Lubricating Grease Rheology 995.1 Visco-Elastic Behaviour 995.2 Viscometers 102

5.2.1 Parallel Plate and Cone-Plate Viscometers 1035.2.2 Errors in Rheometry Measurements 1035.2.3 Errors in Thin Film Parallel Plate Rheometry Measurements 105

5.3 Oscillatory Shear 1085.3.1 Theory 1085.3.2 Application to Grease 1105.3.3 Effect of Thickener Concentration 112

5.4 Shear Thinning and Yield 1125.4.1 Grease 1125.4.2 Lubricating Oil 116

5.5 Yield Stress 1185.5.1 The Concept 1185.5.2 Influence of Temperature 1195.5.3 Consistency 120

5.6 Wall-Slip Effects 1225.7 Translation Between Oscillatory Shear and Linear Shear Measurements 125

5.7.1 Viscosity 1255.7.2 Yield Stress 126

5.8 Normal stresses 1265.9 Time Dependent Viscosity and Thixotropy 1285.10 Tackiness 133

5.10.1 Introduction 1335.10.2 Tackifiers 1345.10.3 Pull-Off Test 1355.10.4 Other Tests 136

6 Grease and Base Oil Flow 1376.1 Grease Flow in Pipes 137

6.1.1 Approximation Using the Newtonian Pipe Flow Equations 137

x Contents

6.1.2 Non-Newtonian Fluid 1386.1.3 Bingham Rheology 1396.1.4 Sisko Rheology 1406.1.5 Power Law Rheology 1406.1.6 Herschel–Bulkley Rheology 1406.1.7 The Darcy Friction Factor 1426.1.8 Transient Effects 1446.1.9 Air in Grease 1446.1.10 Entrance Length 1456.1.11 Solid Particles in Grease Flow 1456.1.12 Wall-Slip/Slip Layer 1456.1.13 Impact of Roughness 1476.1.14 Grease Aging in Pipes 149

6.2 Grease Flow in Rolling Bearings 1496.2.1 Churning 1496.2.2 Flow Through Bearing Seals 1526.2.3 Relubrication 1526.2.4 Grease Flow Around Discontinuities 1536.2.5 Creep Flow 1536.2.6 Flow Induced by Vibrations 155

7 Grease Bleeding 1577.1 Introduction 1577.2 Ball Versus Roller Bearings 1587.3 Grease Bleeding Measurement Techniques 1587.4 Bleeding from the Covers and Under the Cage 1597.5 A Grease Bleeding Model for Pressurized Grease by Centrifugal Forces 161

7.5.1 Oil Bleeding Model 1627.5.2 Quality of the Model 166

8 Grease Aging 1718.1 Mechanical Aging 172

8.1.1 Softening of Grease in Rolling Bearings 1728.1.2 Hardening of Grease in Rolling Bearings 179

8.2 Grease Oxidation 1798.3 The Chemistry of Base Oil Film Oxidation 181

8.3.1 Chemical Reactions 1818.4 Oxidation of the Thickener 1838.5 A Simple Model for Base Oil Degradation 1858.6 Polymerization 1868.7 Evaporation 1868.8 Simple Models for the Life of Base Oil 187

8.8.1 Booser’s Oil Life Model 1878.8.2 Two Phase Model 188

Contents xi

9 Film Thickness Theory for Single Contacts 1919.1 Elasto-Hydrodynamic Lubrication 192

9.1.1 History 1929.1.2 The Navier–Stokes Equations 1939.1.3 The Reynolds and Thin Film Equation 1949.1.4 Cavitation 198

9.2 Contact Geometry and Deformation 1989.2.1 Rigid Bodies 1999.2.2 Elastic Deformation 200

9.3 EHL Film Thickness, Oil 2029.3.1 Example: 6204 Bearing 205

9.4 EHD Film Thickness, Grease 2059.4.1 Measurements 2059.4.2 Film Thickness Models for Grease Rheology 207

9.5 Starvation 2129.5.1 Starved Oil Lubricated Contacts 2129.5.2 Starved Lubrication EHL Models 2139.5.3 Base Oil Replenishment 2199.5.4 Starved Grease Lubricated Contacts 222

9.6 Spin 225

10 Film Thickness in Grease Lubricated Rolling Bearings 22710.1 Thin Layer Flow on Bearing Surfaces 228

10.1.1 Contact Replenishment in Bearings 22810.1.2 Thin Layer Flow Induced by Centrifugal Forces 23110.1.3 Combining the Thin Layer Flow on the All Bearing Components 233

10.2 Starved EHL for Rolling Bearings 23410.2.1 Central Film Thickness 23410.2.2 Combining Lightly Starved and Severely Starved 237

10.3 Cage Clearance and Film Thickness 23910.4 Full Bearing Film Thickness 241

11 Grease Dynamics 24511.1 Introduction 24511.2 Grease Reservoir Formation 24511.3 Temperature Behaviour 24611.4 Temperature and Film Breakdown 24911.5 Chaotic Behaviour 249

11.5.1 Reconstruction of the Temperature Dynamics Using Time DelayedEmbedding 249

11.5.2 Estimation of the Time Delay τ 25111.5.3 Calculation of the Dimensions d and m 25111.5.4 Calculation of the Lyapunov Exponents 252

11.6 Quantitative Analysis of Grease Tests 25311.7 Discussion 254

xii Contents

12 Reliability 25712.1 Failure Distribution 25812.2 Mean Life and Time Between Failures 26112.3 Percentile Life 26412.4 Point and Interval Estimates 265

12.4.1 Graphical Methods for Point Estimates 26512.4.2 Suspended Tests, Censored Data 26712.4.3 Weibull Parameters η and β: Maximum Likelihood Method 26912.4.4 Bias of Point Estimates 27212.4.5 Confidence Intervals for β 27312.4.6 Confidence Intervals and Unbiased Point Estimates

for Life Percentiles 27312.4.7 Estimate Precision 274

12.5 Sudden Death Testing 27512.5.1 Maximum Likelihood Method for a 3-Parameter Weibull

Distribution 28012.6 System Life Prediction 281

13 Grease Lubrication and Bearing Life 28313.1 Bearing Failure Modes 28313.2 Rated Fatigue Life of Grease Lubricated Rolling Bearings 285

13.2.1 Introduction 28513.2.2 The Lubrication Factor 28713.2.3 The Contamination Factor ηc 28813.2.4 The Stress-Life Modification Factor aslf 289

13.3 Background of the Fatigue Life Ratings of Grease Lubricated Bearings 28913.3.1 Fatigue Life and Endurance Testing in the Period 1940–1960 28913.3.2 Fatigue Life and Endurance Testing After 1960 29113.3.3 The Reliability of Grease Lubricated Bearings 292

13.4 Lubricant Chemistry and Bearing Life 29613.4.1 Anti-Wear Additives 29713.4.2 EP Additives 29713.4.3 The Influence of Lubricant Additives on Bearing Life 297

13.5 Water in Grease 30413.5.1 Introduction 30413.5.2 Film Thickness 30413.5.3 Water in Oil and Bearing Life 30413.5.4 Concentration of Water 30513.5.5 Water in Grease 306

13.6 Surface Finish Aspects Related to Grease Lubrication 306

14 Grease Lubrication Mechanisms in Bearing Seals 30914.1 Introduction 30914.2 Lubrication Mechanisms for Elastomer Contact Seals 30914.3 Sealing Action of Grease 312

14.3.1 Migration of Contaminant Particles in the Pocket 313

Contents xiii

14.3.2 Migration of Contaminant Particles in the Vicinityof the Sealing Contact 316

14.4 Softening and Leakage 31914.5 Compatibility 32014.6 A Film Thickness Model for Bearing Seals 320

14.6.1 Oil Feed 32114.6.2 Oil Loss 321

14.7 Some Examples Showing the Importance of Sealing and Grease 324

15 Condition Monitoring and Maintenance 32715.1 Condition Monitoring 32715.2 Vibrations and Acoustic Emission 32815.3 Lubcheck 33115.4 Consistency Measurement 33115.5 Oil Bleeding Properties 33215.6 Oil Content 33215.7 Particle Contamination 33215.8 Spectroscopy 333

15.8.1 Infrared (IR) Spectroscopy 33315.9 Linear Voltammetry 33415.10 Total Acid Number 33515.11 DSC – Differential Scanning Calorimetry 33515.12 Oxidation Bomb 33615.13 Water 336

16 Grease Qualification Testing 33916.1 Introduction 33916.2 Standard Test Methods 339

16.2.1 Penetration/Grease Consistency 33916.2.2 Worked Penetration 34116.2.3 Shell Roll Stability 34116.2.4 Dropping Point 34316.2.5 Emcor 34416.2.6 Oil Separation 34616.2.7 Water Resistance 34716.2.8 Low Temperature Torque 34816.2.9 Flow Pressure 34916.2.10 4-Ball Weld Load 34916.2.11 4-Ball Wear Scar 35016.2.12 High Speed Grease Life Testing, RHF1 35116.2.13 R0F 35316.2.14 R0F+ 35416.2.15 R2F, Using the Special Spherical Roller Bearing 35616.2.16 R2F, Using Standard Bearings 35716.2.17 V2F 35816.2.18 FE8 359

xiv Contents

16.2.19 FE9 36016.2.20 A-Frame Cycle Test 36016.2.21 Cold Chamber Test 36116.2.22 BeQuiet+ 36216.2.23 Fafnir Friction Oxidation Test 36416.2.24 Copper Corrosion Test 36516.2.25 EP Reaction Test 36616.2.26 Compatibility with Preservatives/Process Fluids 36716.2.27 Compatibility Tests for Polymeric Materials 36716.2.28 Remaining Oil Percentage, or Thickener/Oil Ratio 36816.2.29 ROF/ROF+ 36916.2.30 R2F and FE8 Comparison 37016.2.31 ASTM D 3527 Life Performance of Wheel Bearing Grease 37316.2.32 ASTM D 5483 Oxidation Induction Time of Lubricating Greases by

Pressure Differential Scanning Calometry 37316.2.33 Linear Sweep Voltammmetry 373

16.3 Some Qualification Criteria for Grease Selection 37316.3.1 Low Temperature Limit 37316.3.2 Low Temperature Performance Limit 37416.3.3 High Temperature Performance Limit 37416.3.4 High Temperature Limit 37416.3.5 Minimum Speed 37516.3.6 Maximum Speed 375

16.4 Pumpability 375

17 Lubrication Systems 37717.1 Single Point Lubrication Methods 37917.2 Centralized Grease Lubrication Systems 38017.3 Pumps 382

17.3.1 Shovel Pump for Pumping High Viscous Grease 38217.3.2 Method to Create a Positive Head Pressure by Using a

Follower Plate 38417.4 Valves 38417.5 Distributors 38617.6 Single-Line Centralized Lubrication Systems 386

17.6.1 Single-Line System and Venting 38717.6.2 Prelubrication Distributors 38717.6.3 Relubrication Distributors 39017.6.4 Strengths and Weaknesses of Single-Line Systems 392

17.7 Dual-Line Lubrication Systems 39317.7.1 Description 39317.7.2 Strengths and Weaknesses of the Dual-Line System 394

17.8 Progressive Lubrication Systems 39417.8.1 Description 39417.8.2 Strengths and Weaknesses of Progressive Systems 397

Contents xv

17.9 Multi-Line Lubrication System 39717.10 Cyclic Grease Flow 39717.11 Requirements of the Grease 398

17.11.1 Grease Pumpability 39817.11.2 Venting Pressure for Single-Line Systems 39917.11.3 Oil Separation/Bleeding 40017.11.4 Cleanliness 40017.11.5 Compressibility 40117.11.6 Homogeneity 40117.11.7 Additives 40117.11.8 Compatibility 40217.11.9 Delivery Resistance or Pressure Losses 402

17.12 Grease Pumpability Tests 40217.12.1 Flow Ability 40317.12.2 Delivery Test 408

A Characteristics of Paraffinic Hydrocarbons 413

References 415

Index 439

Preface

Technology development and bearing development have gone hand-in-hand. There are morethan 50 billion bearings operating in the world at any time. They are the most widespreadmachine element after nuts and bolts [412]. The continuous increase in performance is placingvery high demands on bearings in many applications. The load carrying capacity of bearingshas increased enormously over the years and energy losses have been reduced. In practice thismeans that for the same type and size of bearing, the service life has become much longerand the frictional torque has been reduced. Long service life and low friction in bearings canonly be obtained by proper lubrication, that is, by having a lubricating film separating therolling elements from the rings such that roughness interaction is prevented. In the case of oillubrication, the films can easily be calculated using classic Elasto-Hydrodynamic Lubrication(EHL) models. In the case of grease lubrication, this is much more difficult. Several aspectsplay a role here, such as oil bleeding, oil flow and starvation. But mechanical and thermalaging aspects of the grease or its components also have an influence on the ability to form alubricating film.The challenge in grease research is primarily three-fold. The first challenge is to develop

greases that will provide longer life and/or are able to operate under more severe conditions(extreme low and high temperature and speed). The second challenge is the developmentof predictive tools, such as numerical models or expert systems. The third challenge is todesign bearing-systems that will increase grease life by, for example, optimizing the greaseflow. All these aspects require a fundamental understanding of the lubrication mechanisms oflubricating greases.The bearing industry has a particular interest in understanding grease lubrication. More than

90% of all rolling element bearings are greased and sealed for life, effectively making greasea bearing component, similar to rolling elements and seals. In addition, the internal design ofthe bearing has an impact on the performance of the grease. This book gives an overview ofthe existing knowledge on the various aspects of grease lubrication and the state of the artmodels that exist in the public literature today.In other words, this book reviews the physical and chemical aspects of grease lubrication,

primarily directed towards lubrication of rolling bearings. It is intended for researchers andengineers in the petrochemical and bearing industries. It may also be of interest for teachingin postgraduate courses.I have used material and information from various experts in the field of grease lubrication,

rolling bearings, seals and lubrication systems. The following persons contributed to much ofthe material in the various chapters: Dave M. Pallister, Chapter 3, Grease composition and

xviii Preface

Chapter 8, Grease Aging; Pieter Baart, Chapter 7, Grease bleeding and Chapter 14, Sealing;Marco T. van Zoelen and Cornelis (Kees) H. Venner, Chapters 9 and 10, Film thickness; JohnH. Tripp and Slavco Velickov, Chapter 11, Grease dynamics; Antonio Gabelli, Chapter 13,Bearing Life; Raimund Stockhammer and Paul Conley, Chapter 17, Lubrication systems.John H. Tripp is the main author of Chapter 12, Reliability. Much of the text from Chapter

16 originates from documents from Ben Huiskamp.I utilized various experts to review parts of this book: Bas v.d. Vorst (rheology), Sebastien

Blachere (reliability), Rihard Pasaribu (grease aging), John Tripp (grease flow), Pieter Baart(rheology), Brian Murray and Alan Thomson (Condition Monitoring and Maintenance) andDick Meijer (grease composition). Marylou Rood created many of the figures and WalterVerhaert edited the full document.Many thanks to the people of the SKF reference group: Alejandro Sanz, Hakan Lindgren,

Domenico Bosco, Frank Berens, Frank Fiddelaers, Victoria van Camp, Gerwin Preisinger, Fer-dinant Schweitzer, Filip Rosengren, Goran Lindsten, Cornelia Haag, Jurgen Kreutzkaemper,Risto Kuukkanen, Rihard Pasaribu and Steve Lane for their critical review of the documentand constructive comments.I would like to express my sincere thanks to Alejadro Sanz for originating this project and

for his continuous support throughout the writing process.I hereby acknowledge Alexander de Vries, Alan Begg, Edward Holweg and Eva Karlsson

for their permission to commence this work and Alexander de Vries for his approval of thefinal document.

Piet M. LugtSKF Engineering & Research Centre, The Netherlands

Series Preface

There aremore than 20 billion grease lubricated rolling bearingsworking in variousmechanicaldevices across the world. Experience shows that about 80% of premature bearing failures aredue to lubrication problems. This is a long-awaited book addressing the important topic ofrolling contact bearing lubrication by greases.The book opens with a discussion on grease lubrication mechanisms and then follows

by describing grease composition and properties, grease life in rolling bearings, rheologicalproperties, flow characteristics and grease ageing. The text then proceeds to calculations ofgrease film thickness in elastohydrodynamic contacts, beginning with the theory and endingwith the temperature effects on grease dynamics. The next section explaining the theory ofreliability is followed by a description of the effects of grease lubrication on bearing life. Greaselubricated seals are also discussed in a separate chapter. The book finishes with chapters oncondition monitoring, grease testing standards and grease lubrication systems. The interestedreader will be able to find all information relevant to greases and grease lubricated rollingbearings in this book.The strength of this book is its comprehensiveness. The fundamentals of grease properties

and the lubrication of rolling bearings are illustrated through practical applications, with anemphasis on bearing life and reliability. The topic has been thoroughly researched by theauthors and all the relevant areas are meticulously covered. The material is presented in aneasily accessible manner.Based on the contents and the level of detail, this book can be recommended for advanced

undergraduate and postgraduate courses in the subject areas of tribology, machine design,reliability and maintenance. Practicing engineers and designers will also find the book veryuseful as a reference. The book is a valuable addition to Wiley’s Tribology Book Series.

Gwidon StachowiakUniversity of Western Australia

List of Abbreviations

a = Acceleration [m·s−2]a = Constant in the Walther equation Chapter 3 [cSt]a = Radius of spherical particle Chapter 14 [kg m−3]ax ,ay = Half Hertzian contact width [m]a+,a− = Location of the boundary of the pressurized

regionChapter 9 [m]

asl f = Stress-life factor Chapter 13 [-]A = Speed factor A = b f × n × dm Chapter 4 [rev· mm·min−1]A = Surface area [m2]AW = Anti-Wear (additive) Chapter 13 [-]b f = Bearing factor Chapter 4 [-]bbrg = Bearing factor Chapter 13 [-]b = Soap fibre diameter Chapter 7 [m]b1,2 = Lubrication factor constants Chapter 13 [m]b = Lubricant film width in seal contact Chapter 14 [m]B = Bearing width [m]

Bin∗ = Bingham number Bin∗ = τy

K

(D2uav

)nChapter 6 [-]

c = Mutual approach of two spherical bodies incontact

Chapter 9 [m]

c = Stress-life exponent of the rolling contact Chapter 13 [-]c = Constant in the Walther equation Chapter 3 [log10 log10

cSt/log10 K ]c1,2 = Contamination factor constants Chapter 13 [-]C = Correlation function Chapter 11 [-]C = Dynamic capacity of a rolling bearing Chapter 13 [N]C = Concentration Chapter 13 [%]Cs = Concentration at the surface Chapter 13 [%]CEY = Computerized Evaluation of Yield Chapter 5 [Pa]d = Bearing bore diameter [m]d = Dimension of an attractor Chapter 11 [-]dc = Correlation dimension Chapter 11 [-]dd = Drop diameter in a wetting test Chapter 13 [m]de = Elastic deformation Chapter 13 [m]dr = Roller diameter Chapter 10 [m]drr = Distance between two rollers Chapter 10 [m]dm = Pitch diameter Chapter 10 [m]D = Bearing outer diameter or pipe diameter Chapter 6 [m]

xxii List of Abbreviations

D = Diffusion coefficient Chapter 13 [m2s−1]D = Deborah number Chapter 5 [-]e1 = Yielding energy density Chapter 5 [Pa]E = Young’s modulus [Pa]Ec = Complete elliptic integral Chapter 13 [-]EHL = Elasto-Hydrodynamic Lubrication Chapter 9 [-]

E ′ = Reduced elastic modulus 2E ′ = 1−ν21

E1+ 1−ν22

E2Chapter 9 [Pa]

E = Activation energy Chapter 3 [J·mol−1]EP = Extreme Pressure (additive) Chapter 13 [-]f = Specific body force Chapter 9 [N·m−3]f = Fibre volume fraction Chapter 7 [-]f = Darcy friction factor 64/Re Chapter 6 [-]f = Probability density function Chapter 12 [s−1]f0 = Initial fibre-volume fraction Chapter 7 [-]fmax = Maximum fibre-volume fraction Chapter 7 [-]fm0 = Initial fibre volume fraction Chapter 7 [-]fs = fs = ρω2r ∂r

∂s Chapter 9 [N·m−3]F = Load Chapter 9 [N]F = Cumulative distribution function Chapter 12 [-]Fa = Axial load [N]Fr = Radial load [N]Fc,r = Force on particle in radial direction Chapter 14 [N]Fc = Elliptic integral Chapter 13 [-]Fd,r = Drag force on particle in radial direction Chapter 14 [N]Fbody = Body force Chapter 7 [N]Ff riction = Friction force Chapter 7 [N]Flip = Seal lip force Chapter 14 [N]g = Gravitational acceleration Chapter 7 [m·s−2]G = Shear modulus Chapter 5 [Pa]G ′ = Storage modulus Chapter 5 [Pa]G = Duty parameter Chapter 14 [-]G ′′ = Loss modulus Chapter 5 [Pa]G∗ = Complex modulus G∗ = G ′ + iG ′′ Chapter 5 [Pa]G = Bearing mass Chapter 4 [kg]G = Material parameter G = αE ′ Chapter 9 [-]Ga = Factor for pressure drop in pipe with Sisko model Chapter 6 [-]G p = Grease quantity for relubrication Chapter 4 [g]h = Film thickness Chapter 9 [m]h = Gap height Chapter 5 [m]h = Hazard function (=p) Chapter 12 [s−1]k = Permeability Chapter 7 [m2]hcs,0 = Initial starved film thickness Chapter 9 [m]hc = Central film thickness Chapter 9 [m]hm = Minimum film thickness Chapter 9 [m]h = Planck’s constant (6.63×10−34) Chapter 3 [J·s]hd = Drop height in a wetting test Chapter 4 [m]h00 = Parameter in film thickness equation Chapter 9 [m]h = Film thickness Chapter 9 [m]h = Free surface layer thickness Chapter 9 [m]

List of Abbreviations xxiii

h∞ = Average (over the length) layer thickness Chapter 9 [m]h0,∞ = Initial layer thickness at the centerline Chapter 10 [m]hc,0 = Initial central film thickness Chapter 10 [m]hi = Initial layer thickness Chapter 9 [m]hcff = Central fully flooded film thickness Chapter 9 [m]hcs = Central, starved film thickness Chapter 9 [m]hEHL = Hydrodynamic film thickness Chapter 9 [m]hD = Central starved film thickness according to

DamiensChapter 10 [m]

h R = Residual layer film thickness Chapter 9 [m]hT = Total film thickness Chapter 9 [m]hZ = Central starved film thickness according to

Van ZoelenChapter 10 [m]

H = Shannon entropy Chapter 11 [-]H = Cumulative Hazard function Chapter 12 [-]k = Boltzmann’s constant k = 1.38× 10−23J/K or

k = 8.62× 10−5eV/Kk = Permeability Chapter 7 [m2]k = Reaction rate coefficient. Unit depends on

reaction orderk f = Bearing grease life factor (GfT) Chapter 4 [-]K = Load correction factor in the presence of water Chapter 13 [-]K = Grease consistency index τ = τy + K γ n Chapter 5 [Pa·sn]K = Plastic viscosity τ = τy + K γ Chapter 5 [Pa·s]K0 = Grease consistency index at ambient pressure Chapter 9 [Pa·sn]K = Constant in the Walther equation Chapter 3 [log10 log10 cSt]K = Grease consistency index

τ = τy + K γ n + ηbγ

Chapter 5 [Pa·sn]

K ′ = Grease consistency indexτ = [τ n

y + (K ′γ )n]1/n

Chapter 5 [Pa·sn]

lt = Total length of the track Chapter 9 [m]L p = Percentile life for bearing life Chapter 12 [MRevs]L p = Percentile life for grease life Chapter 12 [hour]L pq = Percentile life p at confidence limit percentile

qChapter 12 [hour]

L = Mean life Chapter 12 [hour] or [MRev]L p = Reference life at p ◦C Chapter 4 [hour] or [MRev]L = Dimensionless material parameter

L = αE ′(

E ′ Rxη0us

)− 14

Chapter 9 [-]

L = Length used in various contexts [m]Lentr = Entrance length Chapter 6 [m]L p = Maximum likelihood estimate for L p Chapter 12 [hour] or [MRev]L ′

p = Mean unbiased estimate of L p Chapter 12 [hour] or [MRev]L ′′

p = Median unbiased estimate of L p Chapter 12 [hour] or [MRev]L p = Estimate of L p with sudden death testing Chapter 12 [hour] or [MRev]L = Likelihood Chapter 12 [s−1] or [-]m = Mass [kg]m = Phase space dimension Chapter11 [-]m = Shear thinning parameter m = 1/n Chapter 6 [-]

xxiv List of Abbreviations

m = Normal stress parameter Chapter 5 [-]M = Dimensionless load number

M = FE ′ R2x

(E ′ Rxη0us

) 34

Chapter 9 [-]

M = Torque Chapter 5 [N·m]M = Molecular weight Chapter 3 [-]Moil = Mass of oil Chapter 8 [kg]N = Avogadro’s number (6.02×1023) Chapter 3 [mol−1]NN = Non-Newtonian Chapter 5 [-]N1 = Normal stress difference Chapter 5 [Pa]N2 = Normal stress difference Chapter 5 [Pa]n = Shear thinning parameter

τ = τy + K γ n + ηbγ

Chapter 5 [-]

n = Number of overrollings Chapter 13 [-]n = Rotational speed [rev·min−1]n = Total number of measurements point over a

length LChapter 13 [-]

n = Number of bearings Chapter 12 [-]n0 = Population of test bearings Chapter 12 [-]nc = Number of contacts in a bearings Chapter 10 [-]nmax = Limiting speed with grease lubrication Chapter 4 [rev·min−1]nopt = Speed where droplets detach from inner-ring

surfaceChapter 4 [rev·min−1]

n dm = Speed number n × dm Chapter 4 [mm·min−1]p = Exponent in the life equation Chapter 13 [-]p = Pressure [Pa]p = Instantaneous failure probability rate Chapter 13 [s−1]pbody = External body force per unit volume Chapter 7 [N·m−3]p f riction = Friction force per unit volume Chapter 7 [N·m−3]�p = Pressure difference Chapter 6 [Pa]ph = Maximum Hertzian pressure Chapter 9 [Pa]pr = Constant in Roelands equation

pr = 1.962 · 108Chapter 3 [Pa]

pN N = Pressure in a non-Newtonian fluid Chapter 6 [Pa]P = Equivalent load Chapter 13 [N]

Pe = Peclet number Pe = 6πηa3 γkT Chapter 5 [-]

Pen = Penetration (ISO 2137 test) Chapter 5 [1/10 mm]Pu = Fatigue load limit Chapter 13 [N]qy = Mass flow in y-direction integrated over the

trackChapter 9 [kg·s−1]

q = Fluid velocity Chapter 7 [m·s−1]qx , qy = Volume flow per unit length Chapter 9 [m2·s−1]q = Specific mass flow (mass flow per unit of

length)Chapter 9 [kg·s−1·m−1]

q = Fluid velocity Chapter 7 [m s−1]q = Integrated mass flow flux to the side of the

trackChapter 9 [kg·s−1]

q = Pivotal function for the life percentileconf.interval estmn.

Chapter 12 [-]

Q = Flow rate Chapter 5 [m3· s−1]

List of Abbreviations xxv

r = Ratio combined layer and uncompressed fullyflooded film

Chapter 9 [-]

rev = Revolution [-]r = Radius [m]r = Fibre radius Chapter 7 [m]r = Number of failures Chapter 12 [-]R = Larger radius [m]R = Ideal gas constant (8.31) [J ·mol−1·K−1]R = Reliability Chapter 12 [-]R = Precision ratio for β: R = v0.95(r,n)

v0.05(r,n)Chapter 12 [-]

Roller = Change of penetration (roll stability) Chapter 8 [1/10 mm]

Re = Reynolds number Re = ρu D

ηChapter 6 [-]

Reav = Reynolds number using ηw Chapter 6 [-]

Rq = Roughness parameter Rq =√1

L

∫ L

0z2dx Chapter 13 [m]

Rsk = Roughness parameter Rsk = 1

n R3q

i=n∑i=1

z3i Chapter 13 [-]

Ro = Outer radius, see Figure 7.2 [m]Rc = Radial position of the seal contact Chapter 14 [m]s = Coordinate on axisymmetric surface Chapter 10 [m]S(t) = Probability that a bearing survives a time t Chapter 12 [-]t = Time [s]ttr = Transition time Chapter 10 [s]tc = Characteristic time tc = η/G Chapter 5 [s]T0 = Temperature at which η0 has been measured Chapter 3 [K]T = Temperature [K]Tc = Temperature at the centre of the EHL film Chapter 9 [K]T (◦C) = Temperature with unit Celsius Chapter 3 [◦C]Tg = Glass transition temperature Chapter 3 [K]u = Velocity [m·s−1]u = Pivotal function for the life percentile

conf.interval estmn.Chapter 12 [-]

um = Mean velocity (um = (u1 + u2)/2) Chapter 9 [m·s−1]u p = Velocity of particle Chapter 14 [m·s−1]us = Entrainment velocity (us = u1 + u2) Chapter 9 [m·s−1]us = Slip velocity Chapter 9 [m·s−1]us = Shaft velocity Chapter 14 [m·s−1]uav = Average velocity Chapter 5 [m·s−1]U = Dimensionless number U = η0us

2E ′ R Chapter 9 [-]v = Pivotal function (normalized shape parameter) Chapter 12 [-]V = Volume Chapter 7 [m3]Vp = Percentage free volume in a bearing filled with

greaseChapter 4 [%]

w = Exponent relating load to stress Chapter 13 [-]w = Load per unit width Chapter 9 [N·m−1]W = Dimensionless load number W = F

E ′ R2Chapter 9 [-]

W = Dimensionless wear parameter Chapter 13 [-]W = Width of grease reservoir Chapter 14 [m]

xxvi List of Abbreviations

Wi = Weissenberg number Chapter 14 [-]xcg = Effective thickness of reaction layer Chapter 13 [m]z = Viscosity–pressure coefficient Chapter 3 [-]z p = Half the thickness of the film where plug flow

occursChapter 9 [m]

z = Number of rolling elements Chapter 10 [-]Z = Load cycle number Chapter 8 [-]Z0 = Load cycle reference number Chapter 8 [-]x, y, z = Coordinates (running direction,across the

track, height)[m]

X, Y = Dimensionless co-ordinates X = xax,Y = y

ayChapter 9 [-]

ys = Slip layer thickness Chapter 6 [m]yl = Transition from viscous flow to plug flow Chapter 6 [m]Yt = Reconstruction state vector Chapter 11 [-]Z = Load cycle number Z = 8L/(π D) Chapter 6 [-]ZDDP = Zinc Di-alkyl Di-thio Phosphate Chapter 13 [-]α = Viscosity–pressure coefficient Chapter 3 [Pa−1]α = Surface angle (sometimes also α′) [rad]

α = Relative radius of plug flow α = τy

τw

Chapter 6 [-]

β = Shape parameter in the Weibull distribution Chapter 12 [-]β = Maximum likelihood estimate for β Chapter 12 [-]βW = Value of β for a selected Weibull distribution Chapter 12 [-]β ′′ = Median unbiased estimate of β Chapter 12 [-]β ′ = Mean unbiased estimate of β Chapter 12 [-]↔β = Median value of β.

↔β= v0.50β Chapter 12 [-]

γ = Shear Chapter 5 [-]γm = Shear for Doraiswamy rule Chapter 5 [-]γR = Shear at the outer radius of the plate-plate

rheometerChapter 5 [-]

γ = Resistance to side flow parameter Chapter 9 [-]γ = Shear rate Chapter 5 [s−1]γc = Characteristic shear rate Chapter 5 [s−1]γw = Shear rate at the wall Chapter 6 [s−1]γw,N = Shear rate at the wall for a Newtonian fluid Chapter 6 [s−1]δ = Phase shift G′′

G′ = tan δ Chapter 5 [-]�q = Roughness parameter

�q =√

1L

∫ L0

(θ − θ

)2dx

Chapter 13 [rad]

ε = Roughness on pipe surface Chapter 6 [m]ζ = Lim. shear stress factor τL = τL0 + ζ p;

0.02 < ζ < 0.15Chapter 9 [-]

η = Dynamic viscosity Chapter 3 [Pa s]ηoil = Base oil viscosity Chapter 5 [Pa·s]ηb = Viscosity at γ → ∞ (usually it is assumed

ηb = ηoil )Chapter 5 [Pa s]

ηb = Lubrication penalty factor in the life equation Chapter 13 [-]ηc = Contamination penalty factor in the life

equationChapter 13 [-]

ηg = Viscosity at the glass transition temperature Chapter 3 [Pa·s]

List of Abbreviations xxvii

ηi = Viscosity at γ → 0 Chapter 5 [Pa·s]η0 = Dynamic base oil viscosity at ambient

pressure and T = T0Chapter 3 [Pa s]

ηw = Viscosity at the wall Chapter 5 [Pa·s]η1 = Required viscosity for adequate lubrication Chapter 13 [Pa·s]η∗ = Complex viscosity Chapter 5 [Pa·s]η = Scale parameter Chapter 12 [s]η = Maximum likelihood estimate for η Chapter 12 [s]ηW = Value of η for a selected Weibull distribution Chapter 12 [s]θ = Fractional film content Chapter 9 [-]θ = Fiber tilting angle Chapter 7 [rad]θ = Slope in a roughness profile Chapter 13 [rad]κ = Ratio of contact size in running and transverse

directionChapter 9 [-]

κd = κd = 1.03(

Ry

Rx

)0.63Chapter 9 [-]

κ = Ratio of viscosity and required viscosity Chapter 13 [-]λ = Ratio radii of curvature λ = Rx/Ry Chapter 9 [-]λ = Ratio of film thickness and combined

roughnessChapter 13 [-]

λ1 = Normal stress parameter Chapter 5 [-]λ = Lyapunov exponent Chapter 11 [-]ν = Poisson’s ratio Chapter 12 [-]νcSt = Kinematic viscosity with unit cSt Chapter 3 [cSt]ρ = Density Chapter 3 [kg m−3]ρp = Density of particle Chapter 14 [kg m−3]ρg = Density of grease Chapter 14 [kg m−3]ρ = Ratio compressed and uncompressed density Chapter 9 [-]ρc = Dimensionless density ρc = ρ(ph)/ρ0 Chapter 10 [-]ρ0 = Density at ambient pressure Chapter 3 [kg m−3]σ = Stress [Pa]σ = Surface tension Chapter 9 [N·m−1]τ = Shear stress [Pa]τ = Time delay Chapter 11 [s]τ = Minimum life (L0) Chapter 12 [s][Revs]τy = Yield stress Chapter 5 [Pa]τy0 = Yield stress at T = T0 and ambient pressure Chapter 5 [Pa]τc = Characteristic time τc = η

ρω2 h2iChapter 10 [s]

τL = Limiting shear stress τL = τL0 + ζ p Chapter 5 [Pa]τL0 = Limiting shear stress at ambient pressure Chapter 5 [Pa]τw = Wall shear stress Chapter 5 [Pa]τy,∞ = Yield stress after severe aging Chapter 8 [Pa]τy,0 = Yield stress of fresh grease Chapter 8 [Pa]τy = Dimensionless yield stress τ = τy hc

2η0umChapter 9 [-]

υ = Correlation exponent Chapter 11 [m]ψ = Normal stress coefficient Chapter 5 [s−1]� = Bearing circumference coordinate (angle) Chapter 10 [rad]ω = Frequency Chapter 5 [s−1]ω = Parameter uav = ωumax Chapter 6 [-]

xxviii List of Abbreviations

ω = Angular speed Chapter 9 [rad · s−1]ωi = Angular speed inner raceway Chapter 9 [rad · s−1]ωo = Angular speed outer raceway Chapter 9 [rad · s−1]ωR = Angular speed rollers Chapter 9 [rad · s−1]

Subscriptsav = Average0 = Reference or startx, y, z = x,y,z directionsr = Radial directionθ = Circumferential directionN = NewtonianN N = Non-Newtonianw = Wall

1Introduction

1.1 Why Lubricate Rolling Bearings?

Rolling motion can be used to carry and transmit load while facilitating movement with verylow friction and low wear rates, even in the absence of lubrication. The best known examplewhere this is used is the wheel, invented by Mesopotamians in ca. 3500 BC. Lubrication ofwheel–road (or later wheel–rail) contact is difficult, but even in the absence of lubrication wearrates are much lower than those of, for example, sledges or sliding shoes. The rolling bearingis based on this principle, although the configuration is more complex since, for carrying asingle load, several rolling elements are used, which have a double contact (with the inner-ringand the outer-ring). Unfortunately, even in the apparently rolling contacts, slip occurs. Thisis partly due to the elastic deformation of the bodies in contact, which flattens the contactsto some extent, and partly due to the kinematics in the bearings. The first effect is usuallyvery small (and can be decreased by using materials with a high elastic modulus). The secondeffect is more severe. The first effect is dominant in the contacts on tapered and cylindricalroller bearing raceways, which can run at very low friction levels (note that this does not applyto the contacts on the flanges in these bearings). For other bearing types, sliding profiles inthe contacts between rolling element and rings typically show just one or two points of purerolling. Positive slip occurs between these points and negative slip outside these points. Thisis shown in Figure 1.1 for a thrust spherical roller bearing.In the absence of lubrication, the surfaces will be in intimate contact, resulting in high

friction and wear at the areas where slip occurs. This will produce high stresses close to thesurface, leading both to reduction of the fatigue life of the bearing and also to wear.The occurrence of wear in the slip zones and the absence of wear in the points of pure

rolling will produce a nonuniform wear profile across the tracks, leading again to high stressesat the zero-sliding points where less wear has taken place, with a corresponding reduction inthe life of the bearing. This does not mean that rolling bearings cannot run in the absence oflubrication, but with no lubrication the service life will be impaired.Full separation of the surfaces in contact, or ‘full film lubrication’, is preferable. In this case

there is virtually no wear and the life of the bearing will be determined by fatigue. If full filmconditions are not possible the materials should preferably be ‘incompatible’, meaning that

Grease Lubrication in Rolling Bearings, First Edition. Piet M. Lugt.© 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.

2 Grease Lubrication in Rolling Bearings

Zero sliding points

Rolling cone

Figure 1.1 Slip in a spherical roller thrust bearing. Reproduced from Olofsson, 1997 C© Elsevier.

adhesion and ‘welding’ can be avoided. This can be done by using ceramic rolling elements,for example, or by applying a suitable coating (or surface treatment) on one or both surfacesin contact. Due to the local sliding conditions a coating will wear and the service life ofthe bearing is determined by the wear rate and thickness of the coating. Nevertheless, therelatively short unlubricated life can be increased substantially by this solution. The advantageof using fluid lubrication is its ability to repair itself after shear in the contacts due to its abilityto replenish the contacts (a self-healing mechanism). If a sufficient quantity of lubricant isavailable, this will happen through churning, splashing or will be flow-induced by the geometryof the bearing (by the pumping effect and centrifugal forces). In the case of grease lubrication,it occurs primarily through oil-bleeding, spin, cage distribution and to some extent through acentrifugal force inducing flow in thin lubricant layers.

1.2 History of Grease Lubrication

Theword ‘grease’ is derived from theLatinword ‘crassus’meaning fat. As far back as 1400BC,bothmutton fat and beef fatwere used as axle greases in chariots (journal bearings). Early formsof grease lubricants before the 19th century were largely based on natural triglycerides, animalfats and oils, commonly known as ‘grease’ (Polishuk [475]).1 Partial rendering of fats withlime or lye would produce simple greases that were effective as lubricants for wooden axles

1 Lard was used for the lubrication of traditional windmills in the Netherlands.

Introduction 3

and simple machinery. Triglycerides are good boundary lubricants that show low coefficientsof friction but they show poor oxidative stability at elevated operating temperatures.After the discovery of oil in the USA (Drake) in 1859, most lubricants were based onmineral

oil [450]. The first ‘modern’ greases were lime soaps or calcium soaps, which today are notmuch used in rolling bearings. They may however be used providing that the temperaturesstay low. Later, aluminium and sodium greases were developed, which could accommodatehigher temperatures. Until the Second World War only these calcium, sodium and aluminiumgreases were used.In the 1930s–1940s new thickeners were discovered for multipurpose greases, based on

calcium, lithium and barium [450]. In 1940 the first calcium complex grease and lithiumgrease patents [182] were issued. Today, over 50% of themarket still consists of lithium grease.Aluminium complex greases were developed in the 1950s and lithium complex greases in the1960s. Polyurea use, started in the 1980s, especially in Japan.In 1992 a new type of grease was invented byMeijer [414], where the thickener comprises a

mixture of a highmolecular and lowmolecularweight polymer of propylene.A grease structurecould be obtained through rapid quenching. This type of grease has been successfully testedand is used today in, for example, paper mill bearings [73]. Another example is nanotubegrease [271,272].Grease lubricants are used in a large variety of environments. Operating temperatures for

grease lubricated applications range from subzero, −70 ◦C to temperatures exceeding 300 ◦Cfor high temperatures applications. They are also used in vacuum atmospheres encounteredby space applications. More often, the operating environment involves wet and humid atmo-spheres, exposure to salt water and many other types of corrosive agents that affect theperformance of rolling bearings and machine elements. The chemical composition of greaselubricants varies considerably to accommodate the large variety of applications and extremesin operating environments. Grease is commonly used for rolling bearing lubrication as acost-effective and convenient source of lubrication.

1.3 Grease Versus Oil Lubrication

Asmentioned above, the longest service life can be obtained if the lubricant film fully separatesthe contacting surfaces. In a rolling bearing this is achieved through hydrodynamic actionwhere the lubricant is sheared inbetween the roller–ring contacts. Once inside these contactsthe viscosity becomes so high, due to the high pressures, that leakage (pressure-driven flow)out of the contact will remain very small. It will be shown later, in Chapter 9, that thisfilm thickness depends on oil viscosity and bearing speed. Obviously, a film can only bemaintained if sufficient oil is available. In oil bath lubrication this is not a problem, but inthe case of grease lubrication this is more difficult. The lubricating grease will generate athick film at the beginning of bearing operation, formed by the combination of thickenerand base oil. Side flow occurs due to the pressure difference inside the bearing contacts andnext to the tracks. There may be very little reflow back into the track and the bearing maysuffer from starvation, with thinner films then expected based on EHL (Elasto-HydrodynamicLubrication) theory.Inside the bearing contacts (micro) slip occurs and heat will be generated. In the case of

oil lubrication, the oil will act as a coolant for the bearing, reducing the temperature rise and


therefore maintaining a sufficiently high viscosity and film thickness. Unfortunately, this isnot possible in grease lubrication. There is generally no flow here and therefore no coolingeffect by the lubricant.High temperatures, mechanical work and the build-up of contaminants cause aging of the

lubricant. In the case of oil lubrication this will be small due to the cooling and replenishmentaction. Unfortunately the effect of aging cannot be neglected in grease lubrication. Aging willprimarily occur through oxidation of the base oil and thickener and through the breakdownof the structure. A long service life therefore often requires periodic replenishment throughactive relubrication (systems). Sometimes, the specific rheological behaviour of grease createsdifficulties in centralized lubrication systems (pumpability).Despite the above mentioned drawbacks, there are also clear advantages in using grease as

a lubricant. Generally, friction levels are lower than in the case of oil lubrication, primarilydue to the absence of churning, apart from the start-up phase. The next advantage is the easeof operation. Sealed and greased-for-life bearings do not require oil baths, which may leak.A well designed bearing with good quality grease requires no maintenance. In addition, thegrease will fulfil a sealing function and form a barrier against entry of contaminants onto theraceway, extending the service life of the bearing.For the selection of oil, the main parameters are: viscosity, boundary lubrication properties

(lubricity) and type of additives. In the selection of grease the properties of the thickenerdominate, but again the oil base stock properties are important. The main parameters are:consistency, operating temperature range, oil bleeding properties, viscosity of the base oil,corrosion inhibiting properties (additives) and load carrying capacity. This makes greaseselection much more complex than oil selection. In this book the various aspects of greaselubrication in rolling bearings will be described, that is the lubrication of the bearing, thelubrication of the seal, lubrication systems, condition monitoring techniques and test methods.In the next chapter (Chapter 2) the lubrication mechanisms will be described. This chapter willtouch uponmany items that will be described in the following chapters, such as ‘film thickness’(Chapters 9 and 10), ‘rheology’ (Chapter 5), ‘flow’ (Chapter 6), ‘oil bleeding’ (Chapter 7),‘aging’ (Chapter 8) and ‘dynamic behaviour’ (Chapter 11). A large chapter in this book isdedicated to grease composition and properties for the various grease types (Chapter 3). A veryimportant topic is bearing service life, which is given by the life of the grease (Chapter 4) andthe life of the bearing (Chapter 13) supported by a separate chapter on reliability (Chapter 12).Finally, separate chapters are dedicated to seal lubrication (Chapter 14), condition moni-

toring (Chapter 15), test methods (Chapter 16) and lubrication systems (Chapter 17).

2Lubrication Mechanisms

2.1 Introduction

Compared to oil lubrication, the physics and chemistry of lubricating grease in a rollingbearing is today not well understood. Howevere, it is certain that grease provides the bearingwith a lubricating film that is initially thick enough to (at least partly) separate the rollingelements from the raceways. Unfortunately, generally the thickness and/or the ‘lubricity’ ofthis film changes over time, leading to a limited period in which the grease is able to lubricatethe bearing, generally denoted as ‘grease life’. This time is preferably much longer than thefatigue life of the bearing. It is still not fully understood how this film is generated or how itdeteriorates over time and leads to bearing damage and ultimately failure.

Although an exact prediction of the film thickness and ‘lubricity’ cannot be made, it iscertain that a number of aspects are very important in the prediction of the performance of thegrease and/or in selecting the optimum grease for the specific bearing application. Examplesare the rheology (flow properties of the grease), the bleeding characteristics, EHL oil filmformation, boundary film formation, starvation, track replenishment, thermal aging (such asoxidation) and mechanical aging [374].

Another important aspect in grease lubrication in rolling bearings is that the ‘grease life’is not deterministic, that is, there is no absolute value for this and it is given by a statisticaldistribution. Even if bearings are running under very well controlled conditions, such as ina laboratory situation, there is the usual significant spread of failures. The ‘grease’ life istherefore usually defined as L10, that is, the time at which 10% of a population of bearingsis expected to have failed [280], similar to bearing life. If a higher reliability is required, acorrection is needed. To prevent grease failures, a bearing may be relubricated. If possible,this should be done well before failure is to be expected. Generally, the relubrication intervalis defined as L01, that is the time at which 1% of a population of bearings is expected to havefailed [280].

All this, and more, will be treated in this book in separate chapters. To give the reader asummary and an introduction to these chapters, the possible mechanisms in combination withthe physical aspects of grease lubrication will first be given in this chapter.



2.2 Definition of Grease

Grease is defined as ‘a solid to semi-fluid product or dispersion of a thickening agent in aliquid lubricant. Other ingredients imparting special properties may also be included’ [450].The base oil is kept inside the thickener structure by a combination of Van der Waals andcapillary forces [70]. Interactions between thickener molecules are dipole-dipole includinghydrogen bonding [282] or ionic and Van der Waals forces [197]. The effectiveness of theseforces depends on how these fibres contact each other. The thickener fibres vary in lengthfrom about 1–100 microns and have a length diameter ratio of 10–100, where this ratio hasbeen correlated with the consistency of the grease for a given concentration of thickener [518].Sometimes grease is called a thickened oil (rather than a thick oil) [226, 230]. Generally, alubricating grease shows visco-elastic semi-plastic flow behaviour giving it a consistency suchthat it does not easily leak out of the bearing.

2.3 Operating Conditions

The lubrication process is different for different speeds and temperatures and even for differentbearing types. At high temperatures, oxidation and loss of consistency play a major role. Atvery low temperatures, the high values for consistency and/or viscosity may lead to too highstart-up friction torque. The temperature window at which a grease can operate is givenby the grease manufacturer or by the bearing manufacturer and is determined by life- andfunctional tests.

At very low speeds, a bearing may be packed with grease because the churning losses willbe minimal. This implies that there will always be sufficient lubricant in the inlets of thecontacts and effects such as starvation may be neglected. At very high speeds the centrifugalforces on the grease inside the bearing will be so high that most of the grease will be lost fromthe contacts very quickly, leading to severe starvation or, in the case of sealed bearings, to anoverfilled outer ring–rolling element contact. The definition of speed range is roughly as givenin Table 2.1.

The lubrication mechanism that will be described below typically applies to bearings runningat medium speed. Other conditions will be described elsewhere in this book.

Table 2.1 Definition of speed ranges. Here n dm is the product of rotationalspeed (r/min) and bearing mean diameter (mm).

Range n dm (mm/min)

Very low < 40 000Low 40 000 – 90 000Medium 90 000 – 500 000High 500 000 – 1 000 000Very high 1 000 000 – 1 500 000Ultra high 1 500 000 – 3 000 000

Lubrication Mechanisms 7

2.4 The Phases in Grease Lubrication

There are roughly two phases for grease lubrication in bearings running under constant con-ditions, see Figure 2.1. After filling the bearing with grease and starting the rotation of thebearing, the grease will start flowing. As a rule of thumb, approximately 30% of the freevolume of the bearing should be filled with grease. The quantity of grease that is availablein this phase is therefore large enough to provide the bearing contacts with a fully floodedlubricant film.

Part of the grease flows next to the running tracks, where it will stay due to its consistencyand part of the grease finds it way inside the bearing, such as under the cage bars or in the cagepocket. During this ‘churning phase’, the grease flow behaviour is governed by the internaldesign of the bearing, the design of the housing and the rheological properties of the grease.The friction torque will be large due to the relatively high ‘viscosity’ of the grease and thetemperature of the bearing will rise. As more and more grease flows out of the swept volumeof the bearing, the friction torque will decrease and so will the temperature, until a quasi steadystate temperature has been reached. The ‘churning phase’ typically takes from a few hours toup to 24 hours, depending on the percentage filling and the speed. Examples will be given inChapter 11. During most of this phase, the contacts will be ‘fully flooded’ with grease andthe film will consist of grease materials, that is, both thickener material and oil. Typical shearrates in the contact are in the order of 107 s−1 and 104 s−1 in the cage pocket. The grease istherefore severely ‘worked’ and the fraction of grease that participates for longer times in theflow process will degrade heavily. The grease behaviour during this phase is determined bythe rheological properties of the grease. Relatively fresh grease will be located on the cagebars or on the seals/shields. Heavily degraded grease can be found on the running tracks [111].The film thickness during this phase may change rapidly as a function of the change of therheological properties of the severely degraded grease on the tracks. Such a change in filmthickness was measured by Wilson in 1979 [616] in cylindrical and spherical roller bearings,where he showed that the lubricant film initially exceeds the value that could be expectedbased on fully flooded base oil lubrication calculation. In his measurements, the film thicknessdecreased below this value almost instantaneously. The thick lubricant films at the beginningindicate that, at least during the initial bearing operation, thickener material enters the contact.

These film thickness measurements were made by measuring the electrical capacitanceof the gap between rolling elements and raceways (see also e.g. Heemskerk et al. [253],Baly et al. [58] and Schrader [519]). This is a rather complex technique where all bearingcontacts are measured simultaneously and where only relatively thick films can be measured.

Reservoir formation: rheology

Churning phase Bleeding phase Severe filmbreakdown

Film thickness: fully flooded

Reservoir consumed

Film thickness: starved EHL, occasionalfilm breakdown and replenishment

Figure 2.1 The phases in grease lubrication of rolling bearings.


Therefore, single contact measurements are often made where a single ball runs on an opticallycoated glass disc and the film thickness is measured using interferometry techniques. Thismakes it possible to measure very thin films down to a few nanometers. Such single contactmeasurements have been made by Åstrom et al. [35], Williamson et al. [614] and Kaneta et al.[309], using a scoop for the grease to provide fully flooded conditions. They have confirmedwith these techniques that the film thickness is higher than the fully flooded base oil filmthickness. The optical set-up also made it possible to show that grease thickener lumps wereentering the contact.

It is only in the initial churning phase that a fully flooded situation exists. Side flow, bothin the inlet of a contact and in the Hertzian contact itself, will reduce the volume of lubricanton the tracks and starvation will occur. This can also be seen in the measurements of Wilson[616], later confirmed by Barz [68], who measured film thickness in cylindrical roller thrustbearings for longer times. The films become so thin that metal-to-metal contact occurs veryregularly, which was shown by Wikstrom and Jacobson [613] who measured the electricalcapacity in a grease lubricated spherical roller bearing.

2.5 Film Thickness During the Bleeding Phase

During the bleeding phase, there are several possible mechanisms for maintaining a lubricantfilm. The grease may release oil by bleeding [97] or by breakdown of the thickener structurein the contacts. It may also simply provide a stiff ‘grease film’ as referred to by Scarlett [518],who called this a ‘high viscosity layer retained within the rolling track’. It is very difficultto investigate this since so little oil is necessary for lubrication. For instance, Booser [93]operated a ball bearing on only two initial drops of oil at 36 000 r/min for two weeks at 100 ◦Cbefore encountering failures! So if ‘grease layers’ are found in experiments, these layers arenot necessarily the lubricant layers. Very small additional quantities of (bled) oil may providesufficient lubrication for relatively long times.

By means of FTIR (Fourier Transform Infra-Red) spectroscopy, Cann et al. [116, 117]observed thickener layers on the surfaces of a ball-on-disc machine and assumed that the filmwas formed by base oil, thickened with broken thickener fibres. This may well be causedby mechanical work on the grease, which is heavily sheared in the highly loaded thin filmcontacts, causing breakdown of the thickener structure, adhesion to the surfaces [113] andrelease of oil, providing free oil for replenishment.

There is a clear consensus in the lubrication and bearing industry that the bleeding propertiesof a lubricating grease are important. For instance Kuhl [347] found that roller bearings needgreases with higher bleeding rates than ball bearings. Also, the work of Azuma et al. [39] andSaita [510] confirms that the grease bleeding properties have a direct impact on grease life.It is likely that both effects (bleeding and breakdown of the grease structure) play a role inproviding the contacts with the lubricant, where the dominating mechanism depends on theoperating conditions and/or bearing design.

2.5.1 Ball Bearings

Cann et al. [111, 112] have investigated the chemical composition of the lubricant in greaselubricated ball bearings taken from R0F (6204-type ball bearings, bore diameter diameter


20 mm)1 and R2F tests (6209-type ball bearings, bore diameter 45 mm). In both cases, theoperating temperature was the same. The small bearings (with a steel cage) were run at n dm =335 000 mm rev/min and 670 000 mm rev/min, C /P = 65 and the larger bearings (witha polymer cage) at n dm = 97 500 mm rev/min, C /P = 3 and C /P = 10. The observeddifferences in lubrication conditions were not only related to bearing size, but more likelycaused by differences in the operating speeds and load. For the lower speed, higher loadR2F test, they write that initially grease is overrolled, releasing free oil through degradation.Simultaneously, grease is pushed to the side, onto the seals. In the next phase, grease is shearedfrom the seal back into the raceway where it again degrades into an oil-like lubricant (althoughpatches of grease were also found). This lubricant moves onto the balls into the pocket. Oilwas found in the cage pockets.

In the higher speed and lower load R0F test, no significant amounts of free oil could befound. This means that under these conditions, grease is sheared into the contacts and intothe cage pockets where it is overrolled and sheared and where oil is released. Hence, contraryto the lower speed, high load R2F test, the grease on the shields may not serve as an oilreservoir.

Scarlett [518] described the flow of grease in a ball bearing (1 3/4 inch bore, n dm =176 000 mm rev/min) with an inner-ring guided brass machined cage and mentions theformation of ‘pads’ of grease adhering to the cage bore (‘under’ the cage). These grease padshad a higher consistency with a higher soap concentration than the original grease. Scarletexplicitly states that this is due to oil loss by bleeding, which occurs during the first 100 hoursof operation and, according to him, does not contribute to feeding oil to the bearing after this.This statement is not based on any experiments in this paper though. In his tests he foundheavily degraded thickener on the tracks but not next to the tracks. Scarlett describes testswhere grease was removed from the covers after the initial churning period. In this case hefound early bearing wear. This means that the grease on the covers plays an important role inlubrication after the initial phase. He investigated this role further by performing experimentsusing a tracer in the base oil of various greases on the covers only. Surprisingly, he found noflow of oil or grease from the covers into the bearing. He carried out his tests with variousgrease types! A similar conclusion was reached by Milne et al. [423]. Scarlett concluded that,after the churning period, there is no grease or base oil flow from the housing recesses intothe bearing and postulates that its function is to form a closely fitting seal to prevent escapeof essential lubricant from the bearing. These results are contrary to what was found by Saita[510] who put tracer material in grease next to the bearing and measured tracer flow from thisgrease reservoir next to the bearing towards the running track, from which he concluded thatthis grease provides oil by bleeding!

Lansdown and Gupta [354] write that there is clear evidence that in ball bearings the wholeof the grease is involved in the lubrication process, not just the bled base oil. They foundequal performance in grease plated ball bearings (a technique where grease is coated on to thebearing surfaces) and in the case of conventional grease lubrication. In their analysis of ballbearings they also write that grease adjacent to the raceways is often softer and has a higher oilcontent then the grease near the outside of the bearing covers. Unfortunately, these statementsare not illustrated with any examples, proofs or references.

1 For a description of grease life tests, see Chapter 16.


Contrary to this, Dalmaz and Nantua [155] indicate again that the base oil provides the film.They tested six lithium greases in angular contact ball bearings, varying base oil viscosityand thickener structure and concentration. In addition, they performed single-contact filmthickness measurements. Similarly to Hurley [282] they report that the initial film thickness isproportional to the thickener concentration and larger than that of the base oil. However, theirbearing life tests show that bearing life is related to base oil viscosity only and not to thickenertype. This suggests that the ‘grease film’ may last only very briefly and after that the film willbe formed by the base oil only for the main part of the life of the bearing. This mechanismis confirmed by Saita [510] who developed a new grease for deep groove ball bearings andcylindrical roller bearings in a traction motor for a high speed train in Japan, where additionalgrease reservoirs were made next to the bearing. Their measurements indicate a flow of baseoil from grease (called oil bleeding) adjacent to the track, feeding the contacts.

2.5.2 Roller Bearings

It seems that greater consensus exists on the lubrication mechanisms in roller bearings. Hereclearly oil bleeding is considered to be a main mechanism providing the lubricant for therolling contacts (e.g. Booster and Wilcock [97]). This was also clearly found in the sphericalroller bearings test from Wilstrom and Hoglund [611, 612] where both grease and base oil wereused and where equal friction torque was measured. Mas and Magnin [402] investigated greasebefore and after running in tapered roller bearings and found an increased viscosity of thegrease and reduced oil content under the cages. This implies that grease bleeding occurs fromgrease located under the cage bar. However, they also show by means of SEM the destructionof fibres in the raceway, confirming once more Cann et al. [116, 117]’s conclusions, that isthat the grease film consists of base oil thickened with broken grease fibres.

2.6 Feed and Loss Mechanisms During the Bleeding Phase

According to Wikstrom and Jacobsson [613], the film thickness during the ‘bleeding phase’is determined by a mass balance of oil feed and loss to the contacts. Such a balance isschematically drawn in Figure 2.2. In their paper they assume a lubricant feed by oil bleeding,by shear, centrifugal forces and capillary forces. The feed by shear takes place through, forexample, the cage shearing action on the volume of grease located on the bearing shoulders orseals (see e.g. Cann et al. [111, 112]). Inside the EHL contact, the contact pressure will drivelubricant out from the contact. The fraction that is driven out in the running direction can beused to lubricate the following contacts and is therefore not lost. The fraction that flows outof the track, however, does not easily flow back and may be considered as lost. Oxidation andpolymerization may not necessarily be considered as part of the ‘loss mechanisms’. Theseprocesses may also change the properties of the lubricant and have an indirect effect on filmformation. Evaporation will be relevant in the case of air going through the bearing. In somebearing types the centrifugal forces on lubricant layers may be so high that these forces induceflow either towards or away from the contact. Capillary forces, surface tension driven forces or‘Marangoni’ effects (thin layer flow due to temperature gradients), may replenish the contact[327]. This may be especially relevant in the case of low starvation or occasional starts andstops. Finally, the cage may be scraping off or redistributing the lubricant on the tracks [157].


Pressure induced side flow

Oil bleeding

Bleeding due to shear

Capillary forces

Centrifugal force driven lubricant flow

Oxidation

Polymerization

Replenishment

Roller/ball–racewaycontact

Centrifugal force inducedside flow

Evaporation

Cage scraping

Figure 2.2 Balance between feed and loss of lubricant ultimately determining the lubricant filmthickness.

The above described mechanism does not always apply. In the case of slow rotation, outer-ringrotation, large bearings, vibrations, shock loads and so on other mechanisms also play a role.

2.7 Film Thickness and Starvation (Side Flow)

During the ‘churning phase’ and at the beginning of the ‘bleeding phase’ the bearing contactswill be fully flooded with grease where the initial film thickness is higher than can be expectedbased on the base oil viscosity alone. Both base oil and thickener material will be draggedinto the gap between rolling element and ring raceway. The fully flooded film thickness hasbeen modelled by Dalmaz and Nantua [155] and Hurley [282] by assuming that the initialfilm thickness is proportional to the thickener concentration and larger than that of the baseoil. Others have used grease rheology as input for a model. Jonkisz and Krzeminski-Fredihave[306] and Kauzlarich and Greenwood [315] used a Herschel–Bulkley model. Bordenet et al.[99] used a ‘four parameter rheology model’ which is quite similar to the Herschel–Bulkleyrheology model. They all found slightly higher values of the film thickness compared to thosecalculated using the base oil viscosity alone. Yang and Qian [625] used a Bingham rheologymodel to predict the film thickness. They showed that the film thickness, again for fully floodedconditions, can be calculated by using the conventional EHL formula, whereby the viscosityof the grease at high shear rates should be used, rather than the oil viscosity.

Aihara and Dowson [21] performed an experimental study of the factors affecting filmthickness in a grease lubricated two-disc machine. They suggest that the grease lubricatedstarved film thickness can be estimated by taking 70% of the value of the fully flooded filmthickness using the base oil viscosity. This is in accordance with Saman’s [513] theory, whoassumed that the contacts will ultimately be so starved that the inlet meniscus will move closeto the Hertzian contact, such that zero-reverse flow can be assumed. Theoretically this willlead to a reduction of 71% of the fully flooded film thickness.

The reduction in film thickness after the initial phase may not only arise from classicalstarvation. Kauzlarich and Greenwood [315] show that shear degradation of the grease also


leads to a reduction of film thickness over time and that the fully flooded film thickness ingrease lubricated bearings after some time can simply be calculated using the base oil viscosity.

During the ‘bleeding phase’, the observed decrease of film thickness over time is primarilycaused by side flow of base oil from out of the Hertzian contacts. If the film thickness is assumedto consist mainly of base oil, starvation models for oil lubricated contacts are relevant. Suchmodels have been developed by, for example, Chevalier et al. [124], Damiens [156, 158] andVan Zoelen et al. [584, 586]. The oil will be driven out of the running track by flow in frontof the contacts and inside the Hertzian contacts. The first effect will be relevant at the onsetof starvation. Later, the oil layers on the running tracks will be so thin that the film thicknessinside the contacts will be almost equal to the combined oil layers on the track, howeverreduced, due to the compression of the oil layers by the contact pressures with a maximum ofapproximately 30%. At this point side leakage is primarily caused by side flow from oil insidethe contacts. However, this will be relatively small, due to the very high viscosities caused byhigh contact pressures and the piezo-viscous behaviour of lubricating oils.

At higher temperatures the thin lubricant layers feeding the starved lubricated contacts maybe deteriorated by effects such as evaporation [339] and/or oxidation [494–496].

2.8 Track Replenishment

In the absence of track replenishment, the film thickness decreases very rapidly [586]. Replen-ishment of running tracks has been investigated since the early 1970s when Chiu [125] showed,using a viscous flow model, that replenishment of oil that is pushed to the side by the roller/ball–raceway contact can flow back into the track if a sufficiently thick layer is present next to thetrack and if the bearing speed is not too high. Surface tension driven replenishment is generallytoo slow to be relevant in bearings, but capillary forces may have some effect [298]. Even atmoderate speeds, centrifugal forces may drive the flow in free oil layers in rolling bearings.Gershuni et al. [218] calculated the flow from ridges of oil next to the tracks on the inner-ringand the outer-ring in cylindrical roller bearings and showed that in the case of outer-ringrotation significant replenishment of the tracks takes place, whereas replenishment from theseridges will be very slow in the case of inner-ring rotation. Oil may actually be thrown offthe rings! Farcas and Gafitanu [192] developed a model based on the wetting properties ofthe lubricant only for inner-ring rotation, they calculated the critical speed at which lubricantdroplets are no longer able to adhere to the surface due to the centrifugal forces (in their testsat about n dm = 700 000 mm rev/min). They validated their model using electrical resistancemeasurements over the bearing contacts and showed that metal-to-metal contact occurs abovea critical speed.

Another possible replenishment mechanism is described by Merieux et al. [417] who showthat grease shear degradation in the vicinity of the contacts may cause softening of the greaseuntil the grease has been transformed into plain base oil, with a enough quantity to replenish therunning track and cause film growth. This softening was confirmed in the work of Landsdownand Gupta [354].

Van Zoelen et al. [583] investigated the impact of the tangential component of the centrifugalforces on the thin film flow on tapered and spherical roller bearing inner rings. They showeda significant effect. Such a flow may either replenish the track or shear oil further away fromthe contacts.


The cage also plays a very important role in film replenishment. The cage may store greasefrom which oil bleeding will take place. It will also direct the flow in the cage pocket. The cagemay scrape off the lubricant from the running tracks but it may also redistribute the lubricantand thereby repair the lubricant layers which have become critically thin locally. This wasshown by Damiens et al. [157] who made film thickness measurements on a single contactwhere they mounted a single cage-pocket, cut from a full cage, on their ball-on-disc deviceand were then able to vary the clearance between the cage and ball from 0.05–0.5 mm. Theyshow that the behaviour with oil is very different from that with grease and that the clearancein the cage–ball contact is critical here.

Lubricant replenishment by oil bleeding plays an important role. This bleeding action maytake place from grease which is stored on the cage and is heavily pressurized by centrifugalforces [39, 45] or from stationary grease stored next to the swept volume (e.g. [510]).

2.9 Grease Flow

After the initial filling of the system, the grease is forced to flow by the moving rolling elementsand cage. Most of the grease is pushed sideways but part of it stays close to the contacts or endsup on the cage. For grease lubricated systems, the initial filling is of crucial importance. Toomuch grease will lead to excessive churning and therefore, because of the high consistency ofgrease, too high friction levels, which produce increased operating temperatures [612]. Thiswill cause breakdown of the network structure and oxidation of oil and thickener leadingto a short grease life and leakage out of the system. Too little grease reduces the efficiencyof replenishing the running tracks and therefore also leads to a short lifetime [192, 332]. Inaddition to the amount of grease, the initial position of the grease in the bearing or gearboxbefore churning is also important [379]. Relatively small differences in initial filling may leadto large differences in performance. However, according to Cobb [129] there is no differencein grease performance with respect to start-up torque, temperature and leakage through seals ifball bearings are filled from one side only, provided the same total amount of grease is placedin the bearing under either placement condition. This indicates that often most of the greasein a ball bearing participates in the initial flow phase.

The ultimate aim is to provide the bearing with a grease distribution that is optimal forthe system performance – not too much, preventing the grease from continuously churning/flowing, and not too little, ensuring an optimal supply of oil by bleeding or shear. The amountof grease that can be stored close to the running tracks obviously depends on the internaldesign of the bearing and the flow properties of the grease, that is its rheological behaviour.The temperature distribution in the bearing is also important here. Generally, for practicalreasons, the bearing temperature is measured on the outer-ring and the cage temperature ishardly ever reported. Joshi et al. [307] have performed temperature measurements on the cageof a tapered roller bearing. The bearing was running in an oil bath (75% full). They recordedthe temperature of both housing and cage and showed that the cage temperature responseis much more sensitive to changes in lubrication than the housing temperature. This has animpact on the ‘fluidity’ of the grease and therefore again on the flow.

The operating conditions and also the design of the equipment, have an impact on the flow ofgrease. For instance, in a case of vertical shaft arrangements or where vibrations are present, theamount of grease available for lubrication will be different from ‘standard conditions’. Under


such circumstances, generally a high consistency grease is used to prevent grease falling backinto the track and to maintain a lubricant reservoir adjacent to the row(s) of rolling elements.

Until now the flow of grease in bearings has only been studied experimentally. Visualizationtechniques have revealed flow patterns [518] but most of the work has been indirect, relatingflow to friction torque or temperature measurements. A quantitative model enabling predictionof the formation of the grease reservoir is not available today.

The flow of grease in a bearing is a two-phase system: a mixture of air and grease. Thecrucial free surface effect is missing in all studies that have been done on grease flow so far.Strictly, oil separation takes place as well, adding another phase to the system. In addition,thermal and mechanical aging takes place, continuously changing the mechanical propertiesof the grease. Another complicating factor in the study of grease flow in rolling bearingsis the large variation in scale and shear rates inside the bearing configuration. Between therolling elements, clearly churning takes place with relatively low shear rates. In the inlet ofthe contacts there may be phase separation (similar to what happens with water in emulsionsin the inlet of EHL contacts), so that a jet flow may occur or even droplets formed [356].

2.9.1 Non-Newtonian Rheology

The flow behaviour, but also the volume of grease that can be maintained inside the bearingclose to the tracks, is determined by the flow properties of the grease, that is the grease rheology.This topic has been studied quite extensively. For instance, the possible visco-plastic behaviour,that is the existence of a yield stress for grease, has been the topic of many papers [34, 61,64, 311, 403, 630], where the main conclusion is that this behaviour may be assumed if highaccuracy at low shear rates is not required. Actually, creep occurs and the grease has a very highviscosity at such low shear rates. The solid-like behaviour, or resistance to flow (or leakage)is traditionally characterized through the consistency or penetration, measured using a conepenetrometer (ISO 2137, ASTM D217) which is translated into a NLGI consistency number.A correlation between yield stress and penetration/consistency can be found in Chapter 5 or,for example Couronne et al. [139]. Generally, this is only determined at room temperature,which makes it a good general stiffness classification number but which also makes it uselessas a measure for the stiffness of the grease at the bearing operating temperature.

The grease will be severely worked in the bearing. This applies to the grease that is beingchurned between the rolling elements but also to the fraction that passes the EHL contactswhere shear rates are O(106 s−1). This causes a rapid change in the rheological properties ofthe grease during the initial phase of bearing operation. It is therefore relevant to measure therheology after working the grease. This can be done in a rheometer itself, in a grease worker[9] (Figure 16.1) or in a Shell roll stability tester [10] (Figure 16.2). The ability to maintain itsconsistency when worked is called ‘shear stability’ or ‘mechanical stability’. The yield stressdepends strongly on temperature. Measurements for different types of grease can be foundin Karis et al. [311] and Czarny [148]. For example Karis shows that the yield strength of alithium grease may drop from 500 Pa at 20 ◦C to 100 Pa at 60 ◦C.

At higher shear rates, visco-elastic behaviour is observed (e.g. Forster and Kolfenbach[198]), often in combination with shear thinning. In general the well known non-Newtonianrheology models such as the Cross model, power law, Herschel–Bulkley or Sisko models canbe used to describe the rheological behaviour of grease [630]. Measurements from low to highshear rates can be found in Pavlov and Vinogradov [468].


0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Shear rate (1/s)

She

ar s

tres

s (P

a)

Figure 2.3 Typical shear stress versus shear rate curve.

There are a number of models proposed for low and high shear rates. The best knownare the power law, Rhee–Eyring, Bingham and Herschel–Bulkley models. A definition ofthese models can be found in Yousif [630]. These models assume solid or very high viscousbehaviour at low shear rates and viscous behaviour (with possible shear thinning) at highershear rates. A model that fits the measurements well in a wide range of shear stress is Palaciosand Palacios’s [461]:

τ = τy + K γ n + ηbγ . (2.1)

Here τ is the shear stress, τy the yield stress, K the grease consistency index, γ the shear rate,n the shear thinning exponent and ηb a viscosity for which the value of the base oil is a goodapproximation. Usually 0 ≤ n ≤ 1. At high shear rates the grease behaves like the base oil,at medium shear rates shear thinning takes place and at the onset of shear yield takes place.This is illustrated in Figure 2.3. In addition to this nonlinear shear stress-shear rate behaviour,grease is thixotropic meaning that the measured stress also depends on time. Paszkowski[465] defined thixotropy as an isothermal decrease in structural (apparent) viscosity duringshearing (at both constant and variable shear rates) followed by an increase in the viscosityand the resolidification of the substance once shearing ends.

2.10 Wall-Slip

Wall-slip is known to occur and seriously disturbs the measurements in rheometers [150, 151],even if very rough plates are used [56]. Westerberg et al. [605] developed a simple 1D modelfor the flow of grease but also measured the flow directly (using a micro-PIV technique),clearly showing wall-slip at low flow rates. However, the Herschel–Bulkley model parametersthat were found using the micro-PIV measurements were significantly different from thosemeasured on a plate-plate rheometer. The roughness of the surface and the surface energyproperties have a large impact on wall-slip. This is relevant for the choice of cage roughness


and material. Two mechanisms for wall-slip have been proposed: Forster [197] claims that theflow close to the wall is restricted by the breaking fibre contacts. He reports that at high sliprates, internal slip in the fibres will be responsible for wall-slip. Bramhall and Hutton [100]ascribe wall-slip to a lower concentration of thickener particles at the wall which slips overa layer of oil. Similarly, according to Czarny [150, 151] slip does not occur on the wall butinside a layer very close to the wall. A wall layer is formed by the interaction between theparticles of the grease thickener (which are usually polar) and the wall material, resulting in aconcentration gradient of thickener close to the wall. Slip occurs in the weakest layer, that is,the layer with the highest concentration of base oil.

Wall-slip is very relevant in bearings since it will cause (micro) flow inside the bearing atlocations where the body forces on the grease are apparently too low to exceed the yield stress.

2.11 Oxidation

At high operating temperatures oxidation may take place, which reduces the grease lifesignificantly (e.g. Ito [293]). Oxidation processes take place in the bled base oil but alsoin the grease itself where crust formation may lead to reduced bleeding rates. Antioxidantsin the grease prevent this oxidation process. However, the action of the antioxidants limitsthis for some time and significant oxidation does not take place until a certain ‘inductiontime’ has passed [494]. According to Van den Kommer and Ameye [340], in many cases theantioxidants will be totally consumed after 50% of grease life. The induction time is a functionof temperature, grease properties and material properties. Wear particles may act as catalystsand increase the reaction rate, particularly in the case of brass cage material. The latter doesnot mean that the use of brass cages will reduce grease life. In fact, wear particles containingzinc, lead and copper are good solid lubricants and may well counteract this effect.

2.12 EP Additives

EP/AW (Extreme Pressure/Anti-Wear) additives are generally applied for low speed and/orhigh load and are designed to protect the bearing surfaces from damage in case of film collapse.The effect that these additives have on grease life is not well understood. According to Gow[229] ‘Some 90% of all lubricant additives destroy the thickener structure of grease sincethey are often based on surface-active materials and this leads to what is commonly calledthe “mayonnaise effect” (softening and discoloring)’. He also mentions that of the remaining10% some 90% do not work. He ascribes this to the fact that the thickener material is almostalways very polar (metallic soaps) and the fact that the (also polar) EP additives will adhere tothe soap structure rather than to the metal surface [227]. This is in contradiction to the resultsfound by McClintock [406] who tested the effect of a number of EP greases on lubricantlife and found an increase in life. The EP additives may indeed have an adverse effect onsome grease formulations but they certainly work well for greases specifically designed forhigh load, low speed applications. In an evaluation of the ‘Timken OK Load test’ Kaperick[310] shows that identical EP additives give a different response to EP-action for differentformulated greases and ascribes this to a possible impact of mobility towards the surfacethrough chemical interactions or attractive forces. This is in line with the mechanisms proposedin oil lubrication, such as polarity and solvability (e.g. Tomala et al. [573]). It is well known


that many sulfur/phosphorus EP/AW type additives have an adverse effect on bearing life[449], which means that their protective action is not always appropriate (in rolling bearings).

Today, there is technology under development to replace the sulfur/phosphorous EP/AWadditives. An example is the use of Bismuth as an EP/AW additive, being nontoxic and showingvery good performance [500].

2.13 Dynamic Behaviour

The decrease in film thickness due to starvation and insufficient replenishment may be so severethat occasional relatively mild metal-to-metal contact occurs. Very often, this leads to a localincrease in contact temperature or minute vibrations, which initiates a replenishment action.

This self-healing mechanism has been recognized only in the last two decades. It was in 1996that Mas and Magnin [402] speculated on the release of fresh ‘grease’ after heat developmentcaused by film breakdown. They wrote that a grease lubricated bearing will fail as soon asthis can no longer take place. This would imply a dynamic behaviour of subsequent filmbreakdown and ‘repair’. The fact that grease lubricated bearings run in mixed lubrication forlong time periods can be observed in the work of Wikstrom and Jacobson [613] who measureda dynamic character in film breakdown in spherical roller bearings by measuring the electricalcapacitance across the contacts.

Cann and Lubrecht [114] showed in their ball-on-disc machine that severe starvation can be‘repaired’ by adding additional lubricant to the contact. Very pronounced dynamic behaviourwas observed in the cylindrical roller bearing tests described in [379]. Here, it was shown thatmetal-to-metal contact precedes a temperature rise, shortly after which a lubricating film isrestored. The temperature rise must therefore be caused by metal-to-metal contact (and notby the churning of lumps of grease falling into the raceway), which occurs on a longer timescale. During the time that the temperature is high, film repair takes place, probably becauseof softening of the grease, inducing (micro-) flow. After this, the temperature falls back to itssteady state. Such a film breakdown and repair phenomenon is called an ‘event’. It has beenshown [379] that grease lubrication may exhibit ‘deterministic chaotic’ behaviour.

2.14 Grease Life

Grease life models have been developed by the bearing manufacturers, with the exception ofthe GfT model [222]2 . Compared to fatigue life models [290], the scientific developmentsare still very limited and there is much to be done towards the development of true physicalgrease life models. Despite this, these models do reveal the important parameters and generalbehaviour. Therefore there is much that can be learned about lubrication mechanisms fromthese models.

At the moment of writing, all grease life models are empirical models, that is based onnumerous tests. The test rigs that are used for this are primarily ball bearing test rigs, availableon the market through bearing manufacturers (R0F, FE9). Roller bearing test rigs are alsoavailable (R2F, FE8) but are usually only used for functional testing rather than life testing.For a description of these test rigs, see Chapter 16.

2 GfT = Gesellschaft fur Tribologie, a German/Austrian Tribology Society.


0 1 2 3 4 5 6

x 105

102

104

106

108

1010

1012

ndm

L 10 (

hour

s)

Fatigue lifeGrease life

Figure 2.4 L10 grease life and basic bearing life versus speed for a 6204-2Z bearing running underR0F test conditions at 70 ◦C.

It is generally believed that grease life follows the Weibull probability density function. Themain parameters determining grease life are measures for the circumferential speed (such asn dm), temperature and load. As an approximation [4], grease life is exponentially dependenton speed (n) and temperature (T ):

ln Lgrease ∼ −n, (2.2)

ln Lgrease ∼ −T, (2.3)

whereas bearing fatigue life is proportional to the number of stress cycles and thereforeinversely proportional to speed:

Lbearing ∼ n−1. (2.4)

An example is given in Figure 2.4 representing the load case of small deep groove ballbearings in the R0F test rig. For obvious reasons the fatigue life is much longer than greaselife. There is no consensus in the literature on Eq. 2.2, but there is a general agreement onEq. 2.3.

2.14.1 Temperature

The main reason for speed and temperature being the most important parameters is that thishas a major impact on the hydrodynamic film and the mechanical and thermal aging of thegrease. Oxidation is usually described with first order kinetics and the viscosity–temperaturerelation is described by a more or less exponential relationship. The grease will initially build


up a relatively thick film, but starvation will at some point in time lead to severe metal-to-metal-contact, which will initiate failures. Both the fully flooded film thickness and the rate ofstarvation are a function of the base oil viscosity where, as will be shown later in Chapter 10,the decay rate is inversely proportional to the viscosity. The Arrhenius behaviour (Eq. 2.3)is therefore plausible. This can also be found in many grease life test results, for exampleIto et al. [293], who showed this in their extensive grease life test programme for small deepgroove ball bearings at temperatures exceeding 100 ◦C. Arrhenius behaviour only applies in a(grease type dependent) temperature window, which is called the ‘green temperature window’.At very high temperatures severe degradation takes place and ultimately the grease even losesits consistency. At low temperatures the grease stops bleeding, or it becomes so stiff that thelubricant flow mechanism will be different.

All relubrication/grease life models are developed for this ‘green temperature window’,assuming a general behaviour and a certain lubrication mechanism. This means that the modelsonly apply to those conditions where oxidation is not too severe, that is where the temperatureis not too high. The critical temperature at which a deviation from the models occurs canbe tested quite easily since the grease life will be relatively short at high temperatures. Thistemperature is therefore very often specified and called the ‘high temperature performancelimit (HTPL)’. The lower temperature boundary is more difficult to measure since greaselife is very long at ‘lower’ temperatures, leading to unacceptably long test times. For safetyreasons, the life expectation is usually limited to no more than twice the life at 70 ◦C, that isat temperatures lower than 70 ◦C the life may be maximally twice the life calculated with T =70 ◦C, with the exception of full complement bearings and thrust bearings. Also relubricationintervals in excess of 30 000 hours are not advisable [4].

At extremely high temperatures the grease will lose its consistency. This point is called the‘dropping point’ which is related to the ‘high temperature limit’. Obviously, this temperatureshould never be exceeded.

2.14.2 Speed

Grease life decreases with increasing speed. In the case of fully flooded conditions the filmthickness increases with increasing speed and it is therefore believed that starvation is themechanism behind this effect. In some papers the decreasing time between successive over-rollings with the corresponding decreasing time for replenishment is given as an explanationfor a decreasing film thickness with speed. As described in Chapter 10, this is unlikely to be theonly reason. Important is the increase of centrifugal force and mechanical work with increasingspeed, which has a great impact on the grease flow, structure and bleeding properties.

2.14.3 Load

Another important parameter is load. This is shown in Figure 2.5 where grease life and bearingfatigue life are plotted as a function of load for a specific example. In all models for greaselife (or relubrication intervals) the load P is normalized to the bearing load capacity (C /Por P/C). This capacity C is defined as the load at which the fatigue life L10 is equal to onemillion revolutions. This suggests that there is a relation to fatigue life, which is obviouslynot the case. It is only done for convenience to compare grease life to bearing life. Something


0 2 4 6 8 10

106

105

104

103

102

Load [0.01 P/C]

Life

(ho

urs)

Bearing life

Grease life

Figure 2.5 L50 grease life and bearing life versus load for urea greases. n = 10 000 rpm, T = 150 ◦C(grease life data from [317]).

similar applies to P which is the equivalent load and which is calculated from the combinedradial and axial load representing the same stress-state as in the case of a pure radially loadedbearing. The analogue to bearing life theory is convenient. The magnitude of the bearing loadwill have a relatively small impact on the fully flooded lubricant film thickness (see Eq. 9.48)but will have a larger impact on starvation rate contact size, grease degradation and damageduring metal-to-metal contact.

2.14.4 Bearing Type

Grease life is always normalized to the grease life in deep groove ball bearings, which showthe longest grease life, meaning that this bearing type is ‘easier’ to lubricate than other bearingtypes. This could be related to more pronounced starvation in line contacts [158], to favourablegrease flow due to ball spin and geometry, for example, to possible inherent pumping due tocentrifugal effects [585] or different cage designs. Roller bearings require a grease with ahigher bleeding rate [347], which would confirm that the starvation rate is larger than in deepgroove ball bearings.

2.14.5 Grease Type

Obviously, grease life is not only determined by the operating conditions and bearing type. Thegrease type and grease quality are also very important. A good grease has a good ‘consistency’,good ‘shear stability’, favourable bleeding and flow properties and good boundary lubrication,including lubricity properties. The base oil viscosity should be favourable for the speed andtemperature.

In order to determine grease life, models and tests are necessary, such as the R0F/R0F+ test.


2.14.6 Environment

In addition to operation outside the above mentioned temperature window, other factors mayalso cause a deviation from the standard ‘lubrication mechanism’. In the case of outer-ringrotation, centrifugal forces will throw grease onto the outer-ring where an accumulation ofseverely worked and degraded grease will occur. Also in the case of vertical shaft arrangementsthe life will be different due to a difference in grease flow during the churning phase but alsoduring the bleeding phase where lumps may easily fall into the track.

As mentioned above, the initial filling rate is important. Generally, the models apply toan optimally filled bearing. To the author’s knowledge only Farcas and Gafitanu [192] haveincluded the initial volume of grease inside the bearing as a parameter in a life mode. Theirempirical model is based on a limited dataset though.

The effects of shock loads and vibrations are also often incorporated by means of penaltyfactors. These effects cause grease lumps from the covers/seals to fall into the bearing, resultingin high temperatures and loss of the grease reservoir. The same applies to the effect of airflow through the bearing. Lubricant droplets formed behind the rolling elements [356] will bedragged out of the bearing and will no longer replenish the inlet of the next rolling element.Airflow will also have an impact on the evaporation rate, especially at higher temperatures.Lansdown and Gupta [354] showed that evaporation of base oil not only happens on thin filmsbled out of the grease but may even happen to oil retained in grease.

3Grease Composition and Properties

P.M. Lugt and D.M. Pallister

Grease lubricants serve as a simple and convenient source of lubrication for a wide variety ofrolling bearing applications and operating machinery. The performance of grease lubricantslargely depends on the properties of materials used in their composition. Knowledge andunderstanding of the lubricant is essential for engineering reliable rolling bearing applications.In this chapter, the composition and properties of lubricating greases will be described.

The definition of grease is diverse. Grease is defined by the National Lubricating GreaseInstitute (NLGI) [450] and the American Society for Testing and Materials in ASTM D288[195] as ‘a solid to semi-fluid product or dispersion of a thickening agent in a liquid lubricant.Other ingredients imparting special properties may also be included’. Stepina [560] definesgrease as ‘lubricating greases are colloidal systems (dispersions), mostly gels, rarely sols, inwhich the dispersive (continuous) phase is formed of lubricating oil and the dispersed phase(thickener) is an anisotropic solid which penetrates the liquid phase so that the gel producedacquires properties characteristic of the plastic (solid) state’. The Society of AutomotiveEngineers defines grease lubricants as thickeners added to lubricating oils to acquire theproperties of a pseudoplastic solid capable of providing a local and stationary source oflubrication [15].

The dispersed phase (‘thickener’, 3–30%) may be a soap, solid hydrocarbons, inorganicmatter (fine dispersed silica gells, silicon dioxide, betonies graphite etc.) or organic materials(carbon black, pigments polymers, urea derivatives etc.), [207].

The base oil is kept inside the thickener structure by a combination of Van der Waals andcapillary forces [70]. Interactions between thickener molecules are dipole-dipole includinghydrogen bonding [282] or ionic and Van der Waals forces [197]. The effectiveness of theseforces depends on how these fibres contact each other. The thickener fibers vary in length fromabout 1–100 microns and have a length–diameter ratio of 10–100 where this ratio has beencorrelated with the consistency of the grease for a given concentration of thickener (Scarlett[518]). It is not obvious how to visualize the structure of grease. Figure 3.1 shows scanning



(a) (b)

(c) (d)

Figure 3.1 SEM photographs of different grease soap structures: (a) lithium-12-hydroxy stearate inmineral oil, coarse structure; (b) lithium-12-hydroxy stearate in mineral oil, fine structure; (c) lithium-12-hydroxy stearate in ester oil, very fine structure; (d) modified lithium-12-hydroxy stearate in mineraloil. Courtesy of SKF.

electron microscope pictures of different soap structures. Since grease contains 70–97% oil,one may argue that the thickener structure may collapse if the oil is washed out and that sucha picture is misleading. The low volume fraction of thickener is very visible in AFM (atomicforce microscopy) measurements from, for example, Hurley and Cann [284] and Baart et al.[45]. Figure 3.2 shows an example of such measurements. Another visualization techniquethat is sometimes used is the Freeze-Fracture technique (Magnin and Piau [392], Shuff andClarke [528]), where a replica is made of a frozen grease sample, which can be observed inthe SEM.

3.1 Base Oil

Grease lubricants ‘bleed’ fluids that provide liquid lubricant films for reducing friction ofrolling bearings and machine elements. The fluid viscosity properties of the base oil largelydetermine the performance of grease lubricants. Base oils should remain fluid throughout the

Grease Composition and Properties 25

00 500 1000 1500 2000 2500 3000 3500 4000 4500 nm deg

56545250484644424038363432302826242220181614121086420

500

1000

1500

2000

2500

3000

3500

4000

4500

nm

(a) (b)

Figure 3.2 Atomic force microscope image of unwashed lithium greases. (a) Reproduced from Baartet al., 2010 C© Taylor and Francis Group. (b) Reproduced with permission from Delgado et al., 2009. C©Springer.

range of operating temperatures and Hertzian contact pressures. Preferably, base oil viscosityshould also provide full film lubrication over the range of speeds and temperatures.

The physical properties of base oils that effect lubrication are measured by several criteria.Pour point values measure the minimum temperature where the base oil exhibits fluidity.The Viscosity Index (VI) is a measure of the change in base oil viscosity with temperature.High viscosity index lubricants show the lowest drop in viscosity for increasing temperature.Pressure–viscosity coefficients of base oils provide a measure of the viscosity increase offluids with increasing (Hertzian contact) pressure and largely determine the fluid film formingcapability of a lubricant, [631]. Volatility, thermal stability and oxidative stability of basefluids often determine the effective upper operating temperature limit of an application. Theseparameters are important for maintaining elasto-hydrodynamic lubrication (EHL) in rollingbearings (or more generally machine elements).

Mineral oil and triglycerides are commonly used base oils but synthetic base oils are requiredfor many applications. The most common synthetic oils include poly-alpha-olefins (PAO),synthetic esters, polyalkylene glycols silicones and perfluoropolyalkylether fluids (PFPE).Many of these synthetic base oils are not compatible with soap thickeners and must rely onTeflon, polyurea, clay or fumed silica thickening systems to form grease lubricants. Greaselubrication with synthetic base oils are most often used for extreme environment bearingapplications (NLGI [450]).

Often, the distinction between base oil and additives is not clear. Mixtures of fluids areoften used for the base oil of grease lubricants. Mixtures of esters and mineral oil or PAO oilsare common base oils for rolling bearing grease lubricants. Mixtures of esters and phosphateesters are commonly used for high temperature applications. Lubricants for the gas compressorindustry combine a mixture of silicone fluids and mineral oils to reduce water condensation.Additives are mostly used to enhance the properties of common base oil fluids but may alsofunction as base oils in specialty applications.


Table 3.1 Natural triglycerides [88, 474].

Triglceride Source Properties

Neat’s foot oil Boiled cattle feet Nondrying oilLard oil Animal fat Nondrying oilMenhaden fish oil From menhaden fish Good lubrication and rust preventive properties.

Nondrying oil.Whale oil Whale blubberSperm oil

(Illegal after 1970)Sperm whale blubber Very good lubricant, used for fine machinery.

Good heat stability and good rust preventative.Seal oil Seal blubber Used for tempering steelPorpoise jaw oil Porpoise jaw fat Used for fine machineryLinseed oilCastor oilRosin oilRapeseed oilOlive oilTung oilSoya bean oilCottenseed oilCoconut oilBabassu oilJojoba oil Wax from the jojoba bean

3.1.1 Natural Triglyceride and Wax Ester Base Oils

Centuries ago, greases and lubricants were primarily based on animal fats, plant seed oilsand waxes. There are several types of natural waxes and triglycerides. A list of the mostcommon types and their properties are shown in Table 3.1. Triglyceride based grease andoil lubricants are on the rise again, especially for environmentally sensitive applications.Although very limited in performance, natural triglycerides based grease lubricants showvery good biodegradability and are frequently used for high loss and total loss lubricationapplications used in sensitive environments [475].

3.1.2 Mineral Oils

The most common base oil used for fluid film lubrication and grease lubrication is mineraloil. Mineral oil is an excellent material for lubrication of machine elements. It has a low cost,is readily abundant and available in a large range of viscosities. The viscosity characteristicsof mineral oil hydrocarbons are largely determined by molecular weight, the length of themolecule and branching of molecules.

Mineral oils remain in liquid form over a wide range of temperatures and pressures providinggood fluid film lubrication properties. They are hydrolytically stable and show good oxidationstability at temperatures below about 100 ◦C. They are hydrophobic, repelling water andprotecting metal components from rust and corrosion. Mineral oils are compatible with a widerange of grease thickener and additive systems [471, 480]. Mineral oils used for lubrication


Table 3.2 API (American Petroleum Institute) Group Base Oil Classification [471, 507].

Base oil grade Characteristics Saturates Sulfur content VI

API I Solvent refined <90% >0.03 80–120API II Hydro-treated >90% <0.03 80–120API III Severely hydro-treated >90% <0.03 >120API IV PolyAlphaOlefin (PAO) >99% <0.01 >120API V Esters and other base oils – – –

typically contain hydrocarbons with 25 or more carbon atoms. Assuming that these atomsare connected with single bonds with a covalent bond1 length of 0.154 nm, such a moleculewould be approximately 3 nm long. The Van der Waals radius2 of a carbon atom is 0.17 nm.So the ‘thickness’ of such a molecule would be in the order of magnitude of 0.2 nm. TypicalEHL films are in the order of 500 nm, which means that a maximum of about 2500 moleculeswould fit over the height of such a film.

Mineral oils are produced from the distillation of petroleum crude oils. Three basic cate-gories:

• Paraffinic• Naphthenic• Aromatic

classify base stocks according to chemical composition. Examples of each type of hydrocarbonare shown in Figure 3.4. The true composition of mineral oil depends on the source of crudeoil and consists of varying amounts of paraffins, naphthenes, and aromatic hydrocarbons.Actually simple distillation of crude oil produces a complex mixture of alkenes, aromaticheterocyclics, aromatic hydrocarbons, waxes, linear and branched paraffins and cyclic naph-thenes. Mineral oils from first run crude oil distillation require further refining to removeunwanted aromatics, heterocyclics and waxes. Solvent refining is used to remove waxes andaromatics. Hydrogenation or hydro-refining is used to further reduce the aromatics and olefincontent of first run petroleum hydrocarbons. Severe hydro-treating with hydrogen reformswaxy straight-chain hydrocarbons into lower melting point branched-chain isoparaffins. Thisrestructuring process improves low temperature fluidity while maintaining a high viscosityindex. A simplified diagram of crude oil refining processes is shown in Figure 3.5. The levelof oil refining is defined by the American Petroleum Institute and the grading level is shownin Table 3.2. More often, several sources of crude oil may be combined to maintain consistentsupplies of lubricating oil of specified grade and quality [471, 480].

Paraffinic Oils

Paraffinic oils are the most widely used type of mineral oil base stock. Paraffin oils consistof mixtures of alkanes; ‘hydrocarbons’ that have carbon chains saturated with hydrogen. The

1 A bond made by sharing electrons.2 The radius of an imaginary hard sphere which can be used to model the atom.


Mel

ting

poin

t, vi

scos

ity in

dex

Degree of branching

Figure 3.3 Viscosity Index as a function of branching of the oil molecules. Reproduced from Mortierand Orszulik, 1994 C© Springer.

hydrocarbon chains may be straight or branched. Paraffinic oils are very nonpolar and donot have the solvency power of olefinic oils (alkenes) or naphthenic base oils for some polarlubricating oil additives. However, compared to naphthenic or olefinic oils, paraffinic oils havea better oxidation stability, higher VI index and higher pour point. The degree of branchingdetermines the change of viscosity with temperature, where the best viscosity–temperatureperformance (highest VI-index) is obtained from straight-chain hydrocarbons. High levels ofstraight-chain hydrocarbons in lubricating oil are not favourable, as they have high meltingpoints and form crystalline wax precipitates at low temperatures [480], see Figure 3.3. Lowlevels of branching, especially towards the centre of the linear chains, improve pour pointswhile maintaining a high viscosity index [101]. Examples of branching in paraffin oils andthe effect on physical properties are given in Appendix A, Table A.1 of [101]. Examples ofpressure–viscosity coefficients are provided in Table 3.6.

White Oils and Olefins (Alkenes)

Crude oil distillates often contain alkenes, or unsaturated hydrocarbons. These unsaturatedhydrocarbons, commonly called olefins, are hydrocarbons that have carbon-carbon doublebonds. Olefinic hydrocarbons are better solvents than paraffinic hydrocarbons. They alsoremain fluid to much lower temperatures [450]. The olefinic double bond is chemically reac-tive, resulting in very poor oxidation stability [247]. For this reason, refining processes aredesigned to remove olefinic hydrocarbons from lubricant base stocks. Super-refined naphthenicoils were once commonly used for rolling bearing lubrication. These refined naphthenic ‘whiteoils’ were obtained by oleum treatment of base stocks to remove olefins and aromatics. Thischemical treatment subsequently improved the oxidative stability and temperature–viscositycharacteristics. Oleum and sulfuric acid refining of mineral oils has been prohibited for lubri-cating oil production due to the large amounts of waste generated from this process. Currently,hydro-refining of olefinic mineral oil distillates is used to improve the oxidative stabilityand viscosity properties that are important for lubrication performance. Oleum processing ofmineral oils is still used to produce pharmaceutical grade white mineral oil.


Naphthenes Aromatics

Olefins (alkenes)

Paraffins (alkanes)

Figure 3.4 Structure of the various types of mineral oils: (a) straight paraffins, (b) olefins, (c) naph-thenes, (d) aromatics.

Naphthenic Oils

Naphthenic oils are characterized by one or more saturated cyclic carbon chains consisting offive and six member cyclic hydrocarbon rings, see Figure 3.4. They are better solvents for polaradditives and grease thickeners than paraffinic oils. One of the main reasons for widespread useof naphthenic base oils for grease, is that metal soap thickeners are more soluble in naphthenicthan in paraffinic oils (NLGI [450]). Naphthenic oils produce more mechanically stable metalsoap greases than paraffin oils [474]. Naphthenic oils also have lower pour points and higherdensities than straight-chain hydrocarbons and are generally free of wax. In past applications,naphthenic oils found wide application for low temperature lubrication and low temperaturehydraulic systems [471]. Table 3.6 shows that the pressure–viscosity coefficients of naphthenicoils are generally higher than paraffinic oils. Naphthenic oils have poor viscosity–temperaturecharacteristics and poor oxidative stability that limit its useful upper temperature range [471].

Aromatics

Aromatics are hydrocarbon systems with alternating, or conjugated single bond and doublebond carbons. This conjugated double bond system is the basis of aromaticity. The aromaticcarbon-carbon bonds are stronger than aliphatic hydrocarbon carbon-carbon bonds. Simplearomatic compounds show good thermal stability, oxidation resistance and high density.Aromatic petroleum base stocks from crude oil are generally mixtures of alkylbenzenes,alkylnaphthalenes and other higher order alkylaryl hydrocarbons. The alkyl side groups ofalkyl-aryl hydrocarbons are prone to oxidation. The thermal stability of aromatic base oilis somewhat better than either naphthenic or paraffinic oils. Aromatic petroleum base oilshave lower melting points and good low temperature fluidity because there are no waxesin this base stock. Aromatics also show poor viscosity–temperature characteristics and astronger tendency to dissolve water due to high polarity. Aromatic base oils have excellentsolvent properties and have found widespread use for rubber compounding. Other applicationsinclude subzero diesel engine oils, low temperature hydraulic oils as well as lubricating oilsfor closed-system refrigeration systems. The high thermal stability of aromatic base stocks


Crudeoil

API Ibase oil

API IIIbase oil

API Ibase oil

base oilAPI II

Vacuumdistilliator

Propaneextraction

MEKdew axing

Hydrofinish / hydrotreatment

Severehydrotreating

Furfuralsolvent

extraction

Aromatics

Wax

Figure 3.5 Simplified diagram for crude oil refining leading to the various API group base oils.

has found application for heat transfer fluids. High aromatic content base oils have toxicityassociated with polynuclear aromatic (PNA) content. The need for this type of mineral oil basestock has dwindled as the newer synthetic oils provide better performance with lower toxicityfor these applications [471].

Even with the wide array of performance enhancing additives available for today’s lubri-cants, operating conditions of rolling bearings and other machine elements frequently exceedthe capability of mineral oil and triglyceride base oil greases to provide long-term and lifetimerolling bearing lubrication. Many applications have well established endurance life perfor-mance, established maintenance schedules and relubrication intervals, which far exceed thecapabilities of mineral oil or triglyceride base oil grease to provide lifecycle lubrication. Greaselubricants utilizing synthetic base fluids and oxidation resistant thickeners improve endurancelife and prolong rolling bearing operation at both the high and low temperature extremes ofour environment.

3.1.3 Synthetic Oils

Synthetic oils are lubricants that have been manufactured or ‘synthesized’ from one or morebasic raw material components. Low molecular weight raw materials are combined to formbase oils with desired lubricant properties. Some synthetic base oil components originatefrom natural sources. Fatty acids for synthetic esters originate from seed oils and animal fatrenewable sources. Other synthesis routes use coal and coal gas in Fischer–Tropsch synthesisto produce waxes and other hydrocarbon lubricants. Most synthetic lube stocks are made fromgas and petroleum based materials. Synthetic lubricants, unlike mineral oils derived from crudeoil, have a well defined molecular structure with well defined molecular weight distributions,physical properties and chemical characteristics. Synthetic oils are more expensive than crudeoil based lubricants, but the added performance is often needed for many applications. The mostcommon synthetic base oils used in grease lubricants are organic esters, poly(alpha-olefins)(PAO) synthetic hydrocarbons, perfluoropolyethers (PFPE) and silicones. Synthetics have abroader temperature range than the mineral oils, lower evaporation rates, higher viscosity index,excellent low temperature performance and improved high temperature oxidation resistance.


R″

HO − [ CH2 − CH − O ]n − H

Figure 3.6 General formula of a PAG (polyalkylene glycol). It contains oxygen in the backbone andtherefore has a high affinity to steel surfaces.

Polyalkylene Glycols (PAG)

The general formula for polyalkylene glycols is shown in Figure 3.6. This class of chemicalcompounds have ether linkages in the polymer backbone. They are usually formed commer-cially from the condensation of ethylene oxide (EO), propylene oxide (PO) or butylene oxides(BO) using a catalyst. The ratio of EO, PO and BO monomers used to form polyethers has alarge effect on the water solubility of the polymer [471]. Polyethylene oxides are very watersoluble and are used as surfactants and detergents. Polypropylene and polybutylene glycolsare water insoluble. The terminal end of the polyether polymers may be left as a free hydroxylgroup or may further react with fatty acids to form complex esters that act as lubricants, emul-sifiers or surfactants. PAG lubricants have very low pour points and are suitable for both highand low temperature (−50 to + 200 ◦C) applications. Moreover, they have very high viscosityindexes that range from 140 to values exceeding 200. The pressure–viscosity coefficients arelow, typically 12 GPa−1. PAGs have high thermal stability, somewhat better than highly refinedmineral oils, and show good oxidative resistance. Thermo-oxidation of PAG fluids generallyresults in volatile fragment losses and does not leave varnishes and residues from oxidation.Polyalkylene glycol lubricants provide good lubricity and their high polarity gives them goodboundary lubrication properties. The oxygen-carbon backbones of the polyether polymershave high affinity for steel surfaces providing their excellent lubricity properties. PAG lubri-cants are very hygroscopic (water-seeking) absorbing large quantities of water (1–10%) fromexposure to humid air. The high affinity for water is due to hydrogen bonding to oxygen withinthe structure [188]. Most polyalkylene glycol lubricants are not miscible with mineral oils.Special attention is required for the choice of seals, hoses, gaskets and paints used in contactwith these fluids [400].

Organic Esters

Synthetic esters are an important class of synthetic lubricants, offering good lubricity andoperating performance over a wide range of temperatures. Esters consist of an acid in whichat least one −OH (hydroxyl) group is replaced by an −O-alkyl group (−O(CH2)nCH3). Themolecule is therefore very polar which lowers the volatility and raises the flash point. Thispolarity also has an impact on the efficiency of the EP/AW additives where the ester may coverthe metal surface rather than the additives. Esters can be classified in terms of their polarityusing Van der Waal’s formula [580]:

Non-polarity index = total number of C atoms × molecular weight

number of carboxylic groups × 100. (3.1)


O O

RO − C−[ CH2 ]n − C − OR

Figure 3.7 Dibasic ester. Commonly used is n=4,7,8. The −O-alkyl group makes the molecule verypolar.

The higher this index, the lower the affinity to a metal surface, which translates into a improvedresistance to scuffing and wear [341]. Esters are thermally stable (−60 to + 200 ◦C) [13, 106]and are recommended for high temperatures and speed. Esters are usually miscible withmineral oils, PAOs and most lubricant additives. They are inherently biodegradable.

Organic esters have good metal wetting properties (low interfacial tension) and good shearstability properties [471].

There are two common forms of esters: dibasic acid esters (Figure 3.7) and polyol esters(Figure 3.8). Both types are commonly used in greases. Esters are synthesized from thereaction of alcohols or polyhydric alcohols with either inorganic or organic acids using acatalyst. Alcohols and acids combine at elevated temperatures to form esters with water asa by-product. This reaction is reversible and esters hydrolyse back to acids and alcohols inthe presence of water. There are several common forms of esters, both organic and inorganic.Esters are often used in base oils to dissolve additives.

Dibasic Acid Esters

Dibasic acid esters are synthesized from the reaction with dibasic acids and alcohols. Thealiphatic dibasic acid esters have excellent low temperature fluidity and very good temperatureviscosity characteristics. In addition to a high viscosity index, the diesters have amongstthe lowest pressure–viscosity coefficients of the commonly used synthetic base oils [5, 47,242]. Bair’s paper [47] shows that low pressure–viscosity coefficients of diesters correlateto low traction coefficients. This may be due to the fact that diesters remain fluid at highHertzian contact pressures and low temperatures [47, 242, 557]. A study by Washo [600]compared the friction torque values of grease lubricated 6202 ball bearings. His study showsthat diester-lithium-soap grease consistently demonstrated the lowest frictional torque values

R

O

O

O O

O

O

O R

R

R

Figure 3.8 Polyol ester.


H3C

CH3

CH3P

O

Figure 3.9 Tricresyl phosphate.

as compared to a wide variety of other grease types. Early aircraft turbine engine lubricantsused diester base oil with about 3–5% tricresylphosphate for lubrication (Figure 3.9). Theseturbine oils show good low temperature properties, with pour points as low as −60 ◦C, andgood high temperature performance, showing thermal stability to temperatures as high as200 ◦C [13, 106].

Polyol Esters

Polyol esters are formed from the reaction of saturated mono-carboxylic fatty acids withpolyhydric alcohols. The most common polyols are neopentyl glycol, trimethylol propane,pentaeryithritol and dipentaerythritol. The polyol esters have higher viscosity than the diesters,with very good viscosity–temperature characteristics, providing viscosity indexes greater than140. They have low traction coefficients, low pressure–viscosity coefficients and good lubricity.They also show better high temperature thermal and oxidation stability than the diester baseoils. Polyol esters can operate at temperatures up to 250 ◦C. Polyol ester base oils are commonlyused for high temperature and high speed applications. Advanced turbine engine lubricantscurrently use complex polyol ester base oils which exhibit even higher temperature stabilitythan the diester base oil. The polyol ester fluids also tend to cause seal swell, like diester fluids,and readily remove paint and finishes from metal surfaces.

Phthalate Esters

Aromatic dibasic acid esters are occasionally used in lubrication. The aromatic phthalatediesters (Figure 3.12) have good solvency properties, low cost, and are often used as plas-ticizers. Common aromatic dibasic acid esters are the phthalates and isophthalate esters of2-ethylhexylol and many other types of alcohols. The phthalate esters show low volatility at

O

R − C − OR′

Figure 3.10 A carboxylic acid ester. R and R′ denote any alkyl or aryl group (functional group derivedfrom a simple aromatic ring).


Figure 3.11 1-Hexene, an example of an Alpha-Olefin. A PAO may have a branched backbone.

O

O

OR

OR'

Figure 3.12 Phthalate ester.

high temperatures, good thermal and oxidative stability and low pour points. They have poorviscosity–temperature characteristics but this largely depends on the alcohol component of theester. Phthalate esters generally have slightly higher viscosities than either polyol or diesterbase oils.

Trimellitic Acid Esters

Trimellitic esters are tribasic esters of trimellitic acid (Figure 3.13). Esters of trimellitic acidare manufactured by reactions of the acid anhydride with mono-functional alcohols. Againthis is an ester that is commonly used as a plasticizer because of its solvency properties. Itshows high thermal stability and very good oxidation resistance and minimal high temperature

O

O

OO

O

O

H3C

H3C

CH3

CH3

CH3

CH3

Figure 3.13 Trimellitic ester.


OO

O

n

Figure 3.14 Example of a synthetic polymeric esters: polycaprolactone.

volatility losses. Trimellitic acid esters generally have higher viscosities than polyol or diesterbase oils and can be used to achieve higher ISO viscosity grades than diesters of polyol estersalone can provide [106, 506].

Synthetic Polymeric Esters

Synthetic polymeric esters (Figure 3.14) manufactured from polymerization of acrylic andalkyl-acrylic acids are commonly used to modify the properties of grease and oil lubricants.Common uses of polymeric esters are viscosity index improvers and pour point depressants[92, 471]. The improvement of viscosity index is a function of the molecular weight of theadditive. Grease lubricants commonly use synthetic polymeric esters for thickener modificationand tackiness additives [92]. These types of polymer additives used in grease improve theviscosity index properties of base oils and improve adhesion and cohesive strength of greaselubricants [106].

Phosphate Esters

Phosphate esters can be derived from the reaction of phosphoric acid and alcohols. Com-mercially, they are made from the reaction of phosphorus oxychloride and alkyl substitutedphenols or alcohols using a catalyst [400]. Examples of several phosphate esters are shown inFigure 3.15. The triaryl phosphate esters have good oxidative and thermal stability and exhibitgood low temperature fluidity. Triphenylphosphate (TPP) shows thermo-oxidative stability totemperatures exceeding 340 ◦C. Phosphate esters generally show lower compressibility thanmineral oils, which is an important property for hydraulic fluids. Triaryl-phosphate esters havehigh pressure–viscosity coefficients but they exhibit poor temperature–viscosity characteris-tics. The aromatic phosphate esters commonly have negative viscosity index. Additives areoften necessary to improve the viscosity temperature characteristics. Phosphate esters havelow volatility that provides very good high temperature flame and fire resistance properties.

O

RO − P −OR′

OR

Figure 3.15 Phosphate esters (R can be H or any other organic radical).


O

O

nO

O

Figure 3.16 Polyphenyl ether.

The alkyl-aryl and triaryl phosphate esters are commonly used for fire resistant hydraulicfluids and flame resistant plasticizers. Phosphate esters have poor hydrolytic stability, readilyforming strong acids from exposure to water. The most common phosphate esters additivesused for the lubricants industry are dibutyl phenyl phosphate and isodecyl diphenyl phosphate[400]. These are most often used as additives to provide friction reduction and anti-wearproperties for heavily loaded applications that require boundary lubrication. Phosphate estersrequire special attention to the choice of seals, hoses, gaskets and paints used in contact withthese fluids. Many seal and gasket materials that show compatibility with mineral oils cannotbe used with phosphate ester fluids as they have strong solvency that results in swelling andloss of strength [92, 400]. Many phosphate esters are multifunctional in that many phosphateesters are used as anti-wear (AW) additives.

Synthetic Hydrocarbons, PAO

A poly-α-olefin (PAO), is a polymer made by copolymerizing a low molecular weight α-olefin, which is an alkene where the carbon-carbon double bond is located between the 1st

and 2nd carbon atom in the molecule, derived from petroleum. The product from this poly-merization is treated with hydrogen to produce a fully saturated hydrocarbon. PAO lubricantscharacteristically have very high viscosity indexes (>140), low pressure–viscosity coefficientsand low traction coefficients. They also demonstrate very low pour points and excellent lowtemperature fluidity. They have excellent thermal stability and are very responsive to antioxi-dant additives. Poly α-olefins show superior oxidation stability for fully formulated lubricantformulations. PAO lubricants are very pure hydrocarbons that have good hydrolytic stabilityand are hydrophobic (water-fearing), showing a very low affinity for water. Volatility is muchlower than mineral oil base stocks with similar viscosity characteristics. This is an improve-ment over mineral oils, as they commonly show increases in viscosity due to volatile lossesin high temperature applications [471]. As with mineral oils, the viscosity, low temperaturepour points and viscosity index of PAO lubricants increase with chain length. Branching inPAO base stocks tends to decrease viscosity, decrease pour points and decrease the viscosityindex. The low polarity of PAO lubricants consequently shows poor solvency characteristicsfor additives. PAO lubricants may also cause seal shrinkage and sometimes may extract addi-tives from seal polymers. Addition of ester base oils to PAO lubricant formulations sometimeshelps to improve additive solubility and in some cases improve seal compatibility issues [471].

Alkylated Aromatic Synthetic Hydrocarbons

Alkylbenzene (Figure 3.17) and alkylated naphthalene (Figure 3.18) base oils are producedfrom Friedel–Crafts alkylation of benzene or naphthalene aromatics isolated from crude oil.


CH3

Figure 3.17 Alkylbenzene (dodecylbenzene).

The aromatic carbon-carbon bonds are stronger than aliphatic hydrocarbon carbon-carbonbonds subsequently improving thermal stability of these base fluids. The properties of thealkyl aromatic compounds largely depend on the number of alkyl groups attached to the aro-matic ring and the chain length of the alkyl groups. Alkylated aromatic hydrocarbons offervery good oxidative stability and very low volatility at elevated temperatures. They also offerlow temperature fluidity and low pour points. While the viscosity temperature characteristicsare similar to refined paraffin oils, the pressure–viscosity coefficients of alkylated naphthenesare higher than PAO, esters or paraffin oils. The alkyl aromatics have good solvent proper-ties for polar additives showing low aniline points and good hydrolytic stability. Alkylatednaphthalenes show very good radiation resistance [278, 471]. Listings of typical propertiesare shown in Table 3.3.

Traction Fluids-Cycloaliphatics

Traction fluids came about through the need for lubricants for variable speed traction drivesused in the automobile industry. These synthetic hydrocarbons develop glass-like consistencyat high contact pressures. They are based on cycloaliphatic hydrocarbon with some properties

CH3

CH3

CH3

CH3

CH3

H3C

CH3

CH3H3C

H3C

(a) 1−decylnaphthalene (b) 1 β−didecylnaphtalene

(c) 1,3,5−tris(decyl)naphthalene (d) 2,3,6,7−tetrakis(decyl)naphthalene

Figure 3.18 Alkylated naphthalenes.


Table 3.3 Properties of alkylated aromatics (some of the data was obtained from Hourani [278]).

Visc. Visc. Pour AnilineName 40 ◦C 100 ◦C VI point point ◦C α(1/GPa)

Dialkyl naphthalene 114 13.5 110 −39 94 21 @ 25 ◦C16 @ 45 ◦C13 @ 100 ◦C

Polyalkyl naphthalene 177 18.7 118 −26 103 13 @ 25 ◦C12 @ 45 ◦C11 @ 100 ◦C

Synesstic 5 29 4.7 74 −39 32 18 @ 25 ◦C14 @ 45 ◦C9 @ 100 ◦C

Synesstic 12 109 12.4 105 −36 90 30 @ 25 ◦C25 @ 45 ◦C18 @ 100 ◦C

(2,4,6,8,10-penta- 4 100 −40 n.a. n.a.methylundecyl) benzene

showing similarity to naphthenic oils. They have very high pressure–viscosity coefficients andlow solidification pressures. The pressurized fluids readily transmit shear forces with hightraction coefficients and prevent wear by maintaining EHD fluid films in Hertzian contacts.These fluids are also used in rolling bearing applications where skidding may cause damageto rolling elements [471].

Polybutylene and Polyisobutylenes

Low molecular weight polybutylene and polyisobutylene polymers (often called poly-isobutenes PIBs) are good lubricants and are used in some specialty greases. They have alow viscosity index, between 70 and 110, and are less oxidation stable than either polyal-phaolefins or esters [471]. They are often used for their ability to burn completely withoutleaving deposits [106]. This happens at the decomposition temperature of 290 ◦C [471].

The higher molecular weight PIBs are often used in combination with other base fluids andare often used as VI-improvers. They also improve adhesion and cohesive strength of greaselubricants [106]. They have good wetting properties on metals and they are compatible withmineral oils, PAO oils and most synthetic esters but are incompatible with PAGs and siliconeoils [106].

PIB’s are also used in high temperature greases as carriers for solid lubricants (graphite,MoS2).

PIBs have viscosity indexes between 70 and 110 [471]. The pressure-viscosity coefficientfor polybutenes is typically α = 3.59 × 10−8 Pa−1 (Stepina and Vesely [560] and Table 3.6)much higher than values observed for either PAO or ester lubricants [480].


Table 3.4 Polyphenyl ether. Reproduced from Mahoney et al., 1960 C© Taylor and Franics Group.

Melting PourLubricant Abbreviation point ◦C point ◦C

Bis(p-phenoxyphenyl) ether pp–4P3E 229–231 –Bis(o-phenoxyphenyl) ether 00-4P3E 249–251 –Bis(m-phenoxyphenyl ) ether mm-4P3E 104–106 10m-phenoxyphenyl-p-phenoxyphenyl ether mp–4P3E 118 10m-phenoxyphenyl-o-phenoxyphenyl ether mo-4P3E 165 –p -phenoxyphenyl-o-phenoxyphenyl ether po-4P3E 182 –Bis(mix-phenoxyphenyl) ether mix-4P3E liquid 10p-Bis(p-phenoxyphenoxy)benzene ppp-5P4E 298–300 –m-Bis(m-phenoxyphenoxy)benzene mmm-5P4E liquid 40p-Bis(m-phenoxyphenoxy )benzene mpm-5P4E 171–174 40m-B is(p-phenoxyphenoxy)benzene pmp-5P4E 190–192 –m ix-Bis(mix-phenoxyphen oxy)benzene mix-5P4E liquid 40Bis(p-(p-phenoxyphenoxy)phenyl)ether pppp-6P5E 342–345 –Bis(m-(m-phenoxyphenoxy)phenyl)ether mmmm-6P5E liquid 50m-B is(m-(p-phenoxyphenoxy)phenoxy)benzene pmmmp-7P6E 189–191 85Bis(m-(m-phenoxyphenoxy)phenoxy)benzene mmmmm-7P6E liquid 70

Polyphenyl Ethers

Currently, polyphenyl ethers are one of the most thermally stable and radiation resistanthigh temperature lubricants. They are very expensive, have very low volatility and a flashpoints that exceed 300 ◦C. These ethers are commonly employed as lubricants for nuclearreactor applications. They have been used in high speed aircraft and rocket applications totemperatures exceeding 300 ◦C. Polyphenyl ether 7P6E (pmmmp) has thermal decompositiontemperatures of 460 ◦C, 5P4E (mmm) 466 ◦C, and 4P3E (mm) 446 ◦C. They have excellentoxidation stability and are very radiation-resistant. The aromatic groups of polyphenyl ethersoffer high pressure–viscosity coefficients that improve EHD film forming properties [631]. Butthe aromatic groups of the polyphenyl ethers also contribute to poor viscosity–temperaturecharacteristics. Polyphenyl ethers show poor fluidity at low temperatures, some forms aresolids at room temperature [238, 450]. Meta position aromatic ether linkages provide themost liquid form of polyphenyl ether. Ortho and para linked polyphenyl ethers are solids withhigh melting points. Table 3.4 gives examples of melting points and pour points of severalpolyphenyl ethers [395]. Some modified polyphenyl ethers have been synthesized to exhibitlower pour point properties than pure polyphenyl ethers (−15 to −20 ◦C) [411, 631]. Examplesof polyphenylether lubricants are shown in Figure 3.16.

Silicones

Silicone fluids are one of the truly manmade synthetic materials [364]. Dimethylsiliconefluids are produced from the reaction of dichloro-dimethyl silicone monomers with water.Dimethylsilicone polymers have methyl groups attached to a silicone and oxygen backbone,see Figure 3.20. They are chemically inert and can be used at temperatures ranging from


CH3 CH3 CH2

CH3 − C −[ CH2 − C − CH2 ]n−2 − C

CH3 CH3 CH3

Figure 3.19 Polybutene structure.

−60 to 250 ◦C. They have very low surface tension, low volatility, good thermal stabilityand good oxidation resistance. Silicones are also both water repellent and nontoxic. They arecommonly used on fabrics and textiles to impart water repellency [92]. The viscosity indexof dimethysilicones is among the highest of all base oil lubricants, values can be greater than300 [471]. They also show very good shear resistance; fluids with molecular weights less than1000 show almost no loss of viscosity in high shear applications [92]. Dimethyl silicones arecommonly used for heat transfer fluids, low-temperature brake fluids, ultra-low temperaturelubricants and high temperature greases. Unfortunately, dimethysilicones are poor boundarylubricants showing very low load carrying capacity. Silicones are more compressible thanother organic materials [92]. They have poor anti-wear properties [13] and do not respond toextreme pressure or anti-wear additives [471]. Silicones show a strong tendency towards cagefailure when used for ball bearing lubrication [485]. Several modified silicones, fluorosiliconesand phenyl silicone fluids show somewhat better boundary lubrication and fluid film formingproperties than dimethylsilicones. Silicones are high-cost lubricants and are generally used forspecial applications. Sometimes silicones are used as anti-foam additives. It has been observed[108] that for silicone fluid greases in ball bearings, the clearance should be two to three timesthe radial clearance that is normally used. This is probably caused by the bad ‘lubricity’ ofsilicone fluids.

Perfluoropolyethers

Perfluoropolyethers or PFPE fluids are one of the few base oils designed for very high temper-ature lubrication. There are four different types of perfluoroethers that vary in composition andbranching. The PFPE fluids do not have hydrogen atoms in their structure, these fluids consistof carbon, oxygen and fluorine atoms. An example of the structure of perfluoropolyethers isgiven in Figure 3.21. Perfluoropolyethers (PFPE) fluids are made by the anionic polymeriza-tion of hexafluoropropylene oxide. Molecular weights of these synthetic fluids range from

CH3 CH3

CH3 − Si −[ O − Si ]n − CH3

CH3 CH3

Figure 3.20 Molecular structure of dimethylsilicone.


Table 3.5 Properties important for selecting base oils (Stepina and Vesely [560] and others).

Mineral Dialkyl Siliconesoil PAO benzenes Diesters Polyols Polyglycols Methyl-phenyl

Max.temp. (◦C)Absence of O2 200 200 260 250 300 260 320

Presence of O2 150 150 200 210 240 200 250Comp.elastomers 2 4 2 4 4 3 2Toxicity 3 1 3 2 2 3 1Cost 1 3–10 2–3 5 10 5 50α × 10−8 1.6–5.1 1 – 1–1.5 – 1–1.4 –

2000 to 6800. These fluids are commonly known by their trade names Fomblin Z, FomblinY, Krytox and Demnum [636]. They are very inert and do not react with oxygen and mostchemical agents. The PFPE fluids remain a fluid over a wide temperature range, exhibitingpour points as low as −90 ◦C. They exhibit thermal stability to temperatures exceeding 450 ◦Cand thermo-oxidative stability to temperatures exceeding 400 ◦C in air atmospheres. Theyhave very high pressure–viscosity coefficients as shown in Table 3.6. Temperature–viscositycharacteristics of PFPE fluids vary considerably depending on the amount of branching. Lin-ear PFPE fluids can exhibit viscosity indexes that exceed 200, branched chain PFPE fluidsusually have a viscosity index in the range of 120 to 150 [509]. One of the criteria limiting thehigh temperature performance of PFPE fluids is the chemical reactivity of these fluids towardsmetal surfaces. The chemical reaction of fluorine with metals often limits the upper applicationtemperature [92]. PFPE fluids are stable to 288 ◦C in the presence of 52100 steel. Above thistemperature the formation of metal fluorides limits the use of this fluid for lubrication. PFPEfluids show the highest chemical stability with nickel and cobalt alloys. This combination isstable to temperatures of about 370 ◦C without degradation. Corrosion prevention is difficultwith perfluoropolyether greases.

3.2 Base Oil Viscosity and Density

Fluids in which the shear stress τ is directly proportional to the rate of shear, du/dy or γ areknow as Newtonian fluids, the proportionality constant η being the dynamic viscosity:

τ = ηγ with γ = du

dy. (3.2)

− [ CF2 − CF − O ]n −

CF3

Figure 3.21 Molecular structure of a perfluoropolyether.


Table 3.6 Pressure–viscosity coefficients for fluids at different temperatures. In some cases themeasurements were taken at slightly different temperatures. The values from Roelands [499] wereobtained at 38, 100 and 150 ◦C, from Evans [189] at 40 and 100 ◦C, from Ohno and Kuwano [457] at20, 40 and 100 ◦C, from Gold et al. [225] at 25 and 80 ◦C and from Rahman et al. [485] at 20, 40 and100 ◦C.

Temperature (◦C)

20 38 99 149Fluid Pressure visc. coeff. α × 10−8 (Pa−1)

Ester [225] 1.41 0.96Advanced ester [305] 1.28 0.99 0.85Advanced ester [499] 1.52 1.38 1.34Formulated advanced ester [305] 1.37 1.00 0.87Formulated advanced ester [499] 1.84 1.48 1.22Sebacate ester [189] 1.42 1.16Di (2-ethyl-hexyl) sebacate [5] 1.51 0.99Polyalkyl aromatic [305] 1.58 1.25 1.01Polyalkyl aromatic [499] 2.03 1.74 1.45Paraffinic [225] 2.11 1.59Synthetic paraffinic oil (lot 3) [305] 1.77 1.51 1.09Synthetic paraffinic oil (lot 4) [305] 1.99 1.51 1.29Synthetic paraffinic oil (lot 2) [305] 1.99 1.51 1.29plus anti-wear additive [305]Synthetic paraffinic oil (lot 4) [305] 1.96 1.55 1.25plus anti-wear additiveSynthetic paraffinic oil [499] 2.84 2.69 2.55HVI650 paraffinic oil [189] 2.75 1.75Dewaxed paraffinic oil (ISO 10) [457] 1.63 1.11Dewaxed paraffinic oil (ISO 38) [457] 1.78 1.13Dewaxed paraffinic oil (ISO 46) [457] 1.68 1.12Dewaxed paraffinic oil (ISO 120) [457] 1.95 1.13Paraffinic oil [457] 1.50 1.11Special paraffin oil [5] 2.21 1.39PAO [457] 1.12 0.89PAO [225] 1.53 1.12C-ether [305] 1.80 0.98 0.795C-ether [499] 1.45 0.91 0.74Super-refined naphthenic mineral oil [305] 2.51 1.54 1.27Super-refined naphthenic oil [499] 3.08 1.81 1.34Synthetic hydrocarbon (traction fluid) [305] 3.12 1.71 0.94Synthetic traction fluid [499] 3.15 1.36 1.50Traction fluid (Santotrac 50) [189] 2.87 1.65 1.50Fluorinated polyether [305] 4.17 3.24 3.02Fluorinated polyether [499] 4.46 4.38 4.35Dimethyl Silicone [485] 1.36Silicone [5] 1.79 1.50Fluorosilicone [485] 2.54 1.48 0.21


Table 3.6 (Continued)

Temperature (◦C)

20 38 99 149Fluid Pressure visc. coeff. α × 10−8 (Pa−1)

Fluorolube [5] 4.43 2.84Naphthenic oil [485] 4.31 2.13 0.39Naphthenic oil [485] 5.58 6.06 0.63Naphthenic oil [485] 6.29 3.11 1.21Naphthenic [225] 3.24 2.04Special naphthenic oil [5] 3.02 1.69Polybutene [485] 2.85Polybutene [485] 3.14Polybutene [485] 2.93Polybutene [5] 3.69 1.96Polyglycol [225] 1.36 0.9

The SI unit of dynamic viscosity is N · s · m−2 or Pa · s. A unit that is frequently used inlubrication is the Poise P , or centiPoise cP where

1cP = 0.01 P (3.3)

= 10−3Pa · s.

The industrial standard for measuring the viscosity of lubricants is the ‘kinematic viscosity’,which is the ratio of the dynamic viscosity and the density:

ν = η

ρor η = ρν. (3.4)

This arises from practice where the viscosity is not directly measured by imposing a shearas in a rheometer but where it is commonly measured in a ‘U’-tube viscometer. Here the oilflows vertically though a tube under gravity where the time taken for the oil meniscus to travelbetween two marked lines is measured. The SI unit for the kinematic viscosity is m2 s−1. Theunit that is generally used for the kinematic viscosity is the ‘Stokes’, which is defined as

1St = 1 cm2 s−1 = 10−4m2 s−1. (3.5)

Obviously a very unpractical unit. The more commonly used unit is the centiStokes, cSt:

1 cSt = 0.01 St = 10−6m2 s−1 (= 1 mm2s−1). (3.6)

For example, for water, having a density of ρ = 1000 kg m−3, the conversion would be

1 cSt = 10−3 Pa · s (3.7)


(water has a kinematic viscosity of ν = 1 cSt and a dynamic viscosity of η = 0.001 Pa · s).So if the viscosity is given in cSt, then the dynamic viscosity (in Pa·s) can be calculatedusing

η = 10−6 · ρνcSt. (3.8)

The viscosity of oils varies with the structure of the various compounds they contain. Theresistance to shear, or viscosity, generally increases with molecular weight, branching andboiling point. Also having a dipole moment or being able to form hydrogen bonds increasesthe viscosity.

3.2.1 Viscosity–Temperature

The viscosity of the base oil decreases significantly with increasing temperature. For paraffinicoils this continues until wax crystals start to form which gives an ‘apparent solidification’ [480].This formation of wax will result in high levels of friction.

For the relation between viscosity and temperature at low pressure a number of mod-els/equations exist. These can be classified into models based on fluid theory and on inter-polation of measured viscosity at a number of temperatures. The temperature dependence ofviscosity can be modelled by absolute reaction rate theory from the 1930s [191], described by,for example, Karis and Nagaraj [312] or Bogie and Harris [84]

η = hN

Vexp

(�E

RT

)(3.9)

where

• h = Planck’s constant• N = Avogadro’s number• V = molecular volume (molecular weight/density)• �E = the activation energy of the viscous flow ‘reaction’/molar ‘activation free energy’• R = the gas constant• T = the absolute temperature

This is an example where fluid theory is applied to predict viscosity and is very useful formolecular dynamics simulations, for example.

However, in practice simple equations based on curve fitting viscosity–temperature mea-surements are more often used. These are listed by, amongst others, Crouch and Cameron[146].

A commonly used equation, named after Reynolds, reads:

η

η0= exp (−β (T − T0)) (3.10)


with

β = −1

Tmax − Tminln

ηTmax

ηTmin

(3.11)

where η is the viscosity at temperature T , ηo is the viscosity at a reference temperature T0 andβ is the temperature coefficient to be calculated by interpolation between two reference pointsηTmax and ηTmin . This is usually done at 40 and 100 ◦C. This equation is reasonably accurate andmainly used when simplicity is required, such as for computing intensive calculations.

One of the most widely used equations is the Walther equation [514]. This equation is thebasis for the ASTM, ISO and DIN charts and guidelines and reads:

log10 log10 (νcSt + a) = K − c log10 T . (3.12)

Here a is a constant for a particular fluid. The constants c and K are calculated from theviscosity at two temperatures:

c = log10 log10(νcSt1 + a) − log10 log10(νcSt2 + a)

log10 T2 − log10 T1. (3.13)

K = log10 log10

(νcSt1 + a

)+ c log10 T1. (3.14)

For lubricating oils, a can be chosen as a = 0.7 (Sanchez-Rubio et al. [514]) or a = 0.8(Seeton [521]).

The Vogel equation reads:

η = A exp

(B

T + C

). (3.15)

Here A, B, C are fitting factors and T is the absolute temperature (K). Note that, according tothis equation, there exists a temperature at which η → ∞.

3.2.2 Viscosity–Pressure–Temperature

The lubricant will experience very high pressures in a rolling bearing. In the EHL contacts,pressures of typically 1–3 GPa will occur. The viscosity of the lubricant is strongly pressure-dependent and for the prediction of the lubricant film thickness and friction, the viscosity inrespectively the inlet and the Hertzian contact need to be calculated at these high pressures.Several equations for this are available where, unfortunately, the more accurate ones arealso more complex and require specific viscosity measurement data. A universal equation ofstate for the viscosity–pressure–temperature (and density) is obviously appealing since suchmeasurements are difficult to perform. The balance between required accuracy and complexitywill determine the choice.


Barus

A widely-used relation is the Barus [67] viscosity pressure relation:

η (p) = η0 exp(αp) (3.16)

where

• η0 = viscosity at ambient pressure• α = pressure–viscosity coefficient

For lubricating oils these variables will be approximately:

0.001 ≤ η0 ≤ 0.1 Pa s (3.17)

0 ≤ α ≤ 4.0 × 10−8Pa−1. (3.18)

The advantage of the Barus relation is its simplicity, making it easy to use, especially inanalytical calculations. However, the relation predicts viscosities which are too high at highpressures. Table 3.6 shows the results from high pressure viscometry for some lubricating oils.

In the case that high pressure viscosity data is not available, an engineering approachwould be to obtain the value for α from film thickness measurements using a ball-on-discconfiguration, which has become quite common. The viscosity–pressure coefficient α couldbe obtained by fitting the measured film thickness to one of the EHL film thickness equationswhich will be given later in Section 9.3.

Roelands

A more accurate relation was proposed by Roelands [499] :

η (p, T ) = η0 exp

[{ln (η0) + 9.67}

{(1 + p

pr

)z (T0 − 138

T − 138

)s0

− 1

}](3.19)

with

• pr = 1.962 × 108 Pa• T0: temperature at which η0 has been measured (K)• s0: viscosity–temperature index, typically 1.0 ≤ so ≤ 1.5• z: pressure viscosity index, typically 0 ≤ z ≤ 0.8

By defining α as

α = 1

η

(∂η

∂p

)p=0,T =T0

(3.20)


the relation between z, α, η0 reads:

z = prα

ln(

η0

ηdim

)+ 9.67

, (3.21)

where ηdim=1 Pa·s.A low loaded bearing application will show a pressure of approximately 0.5 GPa. Using

an oil with viscosity η0 =0.009 Pa s and α = 2.0 × 10−8 Pa−1, Barus’ relation predicts aviscosity η =198 Pa s, whereas Roelands’ relation predicts a viscosity η =46 Pa s. Sinceviscosity plays a central role in lubrication, this example shows the significance of the use ofan accurate viscosity–pressure relation.

Yasutomi

Bair [48] has shown that the Roelands relation underestimates the viscosity at higher temper-atures and suggests an equation based on free volume theory [627]:

η = ηg exp

[−2.3C1

(T − Tg

)F

C2 + (T − Tg)

F

], (3.22)

where ηg is the viscosity at the glass transition temperature (O(107) < ηg < O(1012) Pa s[48]. Tg is the glass temperature:

Tg = Tg(p = 0) + A1 ln (1 + A2 p) (3.23)

and the relative free volume expansivity is

F = 1 − B1 ln (1 + B2 p) (3.24)

and A1, A2, B1, B2, C1, C2 and Tg0 are parameters to be fitted using measurements.3

3.2.3 Density, Compressibility

Compared to the changes in viscosity with temperature and pressure, the changes in densityare very small. However, due to the very high pressures in the EHL film, the base oil cannotbe considered incompressible.

The lubricant density is a function of the size of the molecules from which it is composedand typically varies between 860 and 980 kg/m3. The density changes with temperature andpressure. For the temperature dependency the following empirical formula may be used [560]:

ρ = ρT1 + αρ (T1 − T ) . (3.25)

Here αρ=0.65 for 831 < ρ < 950 and αρ=0.60 for 951 < ρ < 1000 kg·m−3.

3 As an example, for Turbine oil T9, ηg = 107 Pa s, Tg(p = 0)=-76 ◦C, A1=228.3 ◦C, A2=0.7645 GPa−1, B1=0.188,B2=25.84 GPa−1, C1=11.45, C2=30.26 ◦C.[48], η0(T=40 ◦C)=0.0088 Pa s, z=0.87,s0=1.2 [368].


When a lubricant is compressed below the solidification pressure, the variation of densitywith pressure is roughly linear up to a compression of approximately 35%. For pressureshigher than the solidification pressure there is little change in density. A widely used formuladescribing this well is the Dowson and Higginson [178] density equation

ρ = ρ00.59 × 109 + 1.34p

0.59 × 109 + p. (3.26)

Figure 3.22 illustrates the change of density with pressure. The formula applies to both mineraland synthetic lubricants, except for silicones for which compressibility is much higher thanfor mineral oils [471].

The rate of pressure increase in an EHL contact is generally so large that there is notime for crystallization, which means that the distance between the molecules will simplybecome smaller with increasing pressure. At pressures higher than the solidification pressurethe distance between the molecules has become so small that further compression will leadto deformation of the molecules [242]. Hamrock et al. [246] found that the solidificationpressure varies considerably for different lubricants and derived an alternative to equation3.26. Their measurements show that the Dowson and Higginson formula applies to mineraloils up to 2 GPa and that a significant deviation may occur for synthetic oils. The latter wasillustrated by measurements using a PAO. Jacobson [296] showed phase changes at value of

1.5

1.45

1.4

1.35

1.3

1.25

ρ/ρ 0

1.2

1.15

1.1

1.05

10 0.5 1 1.5

Dowson and Higginson

Tait/Bain@20C

Tait/Bain@100C

p [GPa]

2 2.5 3

Figure 3.22 Relative density of oil as a function of pressure and temperature.


about 1.2 GPa for PAO (at room temperature). The values for solidification or phase changewere much lower for paraffins and even lower for naphthenics.

The Hamrock et al. [246] equation may be more advanced, but the formula contains fourlubricant type specific constants which need to be determined using high pressure densitymeasurements for which not much data is available. This makes it difficult to use and isthe reason why the Dowson and Higginson relation is still favourable in EHL calculations.For more information on the impact of compressibility on EHL film thickness, the reader isreferred to Venner and Bos [588].

In high pressure physics (and occasional in tribology [463]), the empirical Tait equation iswidely used:

ρ0

ρ= 1 − 1

K ′0

ln

[1 + p

K0

(1 + K ′

0

)]. (3.27)

Other than in the Dowson and Higginson formula, the density is temperature dependent throughthe pressure bulk modulus, which is exponential in temperature:

K0 = K00 exp (−βK T ) . (3.28)

For completeness Bair also gives a relation for the reference ambient pressure density:

ρR

ρ0= 1 + αv (T − TR) . (3.29)

However, this equation is not relevant for the work in this book where the relative densityrelation is primarily used to describe the relation between the highly compressed film thicknessand the nonloaded oil layers on the raceways. Bair [50, 51] has shown that for EHL calculations,in the absence of compressibility data, the Tait equation gives a higher accuracy than theDowson and Higginson relation 3.26. He proposes using K ′

o = 11, αv = 8 × 10−4, K00 =9 GPa and βK = 6.5 × 10−3 K−1.

Figure 3.22 shows the difference between the Dowson and Higginson and the Tait/Bairrelation for two different temperatures. The difference between the Dowson–Higginson andTait/Bair equation becomes significant at higher temperatures. This is very relevant to greaselubrication where the temperatures in the application may be high or where increased testtemperatures are used to accelerate the failure process.

The Dowson and Higginson and Tait relations, 3.26 and 3.27, apply to a uniform compres-sion. It has been shown using molecular dynamics calculations [193] that in (sliding) EHLcontacts the density close to steel walls (so close to the rolling elements and rings) is higherthan in the centre of the film, but that the Dowson and Higginson relation describes the densityin the centre of the film well.

3.3 Thickener

The grease thickener determines the basic properties of greases and is used to classify greasesinto different types. There is a large variety of thickening materials used for lubricating greases.


Froishteter et al. [207] divides the thickener types into three groups depending on their nature,interaction of the dispersing medium and thickening mechanism:

• Polymorphous thickeners: thickeners which do not interact with oils at ambient temperatureor those that form colloid dispersions at high temperatures (e.g. soaps).

• Nondissolvable thickeners: thermally stable thickeners of organic and inorganic origin,which do not dissolve in oil and which show no phase transformations when the temperatureincreases (e.g. silica gels, bentonites, carbon black, pigments).

• Thickeners which do not possess polymorphous properties but which melt at relatively lowtemperatures forming homogeneous solutions in the oil at a temperature level exceedingtheir melting point (e.g. solid hydrocarbons).

This classification shows that there is not a unique type of skeleton which gives grease itssolid-like behaviour at low shear. The type of material and the stiffening ‘mechanism’ can bevery different. This will lead to different chemical and physical properties such as bleedingrates, rheology, oxidation, mechanical stability and so on. This is why the type of thickenerdetermines the basic properties of grease.

In the subsections below the most common types of thickener will be described, includingtheir molecular structure and their specific properties.

3.3.1 Soap Greases, Simple Greases

Soap thickeners are formed by a neutralization reaction of an acid and base to form a saltand water (as a by-product). When the acid is a fatty acid (carboxylic acid often with a longunbranched aliphatic4 tail: CH3(CH2)n−COOH), its salt is called a soap.5

In general a maximum thickening effect is achieved with carboxylic acids having 18 carbonatoms [397]. Figure 3.23 shows the chemical structures from a simple acid to a Ca-di-12-hydroxystearate soap. Increasing and decreasing the chain length increases and decreases thethickening capacity [397]. Increasing the chain length increases the solubility in the baseoil, decreasing it decreases the solubility. The solubility of soap in the base oil also dependssignificantly on the molecular weight of the type of base oil.

If the acidic component has a narrow range of molecular weight, as in fatty acids, a simplesoap is made (e.g. lithium stearate). This means that all thickener molecules will be practicallyequal and have the same structure. Figure 3.23 illustrates some of the notation that is used here.Soaps may be present as crystallites and dissolved molecules but can also form agglomeratesor fibres.

A branched alkyl chain lowers the melting point and decreases its thickening effect. Unsat-urated carboxylic acids (containing double bonds) are more soluble in mineral oils, reducethe dropping point and decrease the thickening effect. They also have a lower oxidation sta-bility. Hydroxyl groups (−OH) generate polarity which increases the melting point and thethickening effect.

4 CH chains which do not contain aromatic rings.5 Domestic soap is the sodium variant where water solubility (Na-end) is combined with fat and dirt on the other end(long hydrocarbon end). The cleaning action is provided by dissolving dirt particles from water by the formation ofmicelles surrounding the dirt particle.


H − R acid

carboxyl group

O

− CHCHH − O − 3

O

CHH − O −

Formic Acid

O

CH− H − O −[ CH2 ]16 − CH3

Stearic Acid

O OH

CLi − O − −[CH2 ]10 − C −[ CH2 ]5 − CH3

Li 12-hydroxystearate

Ca di-12-hydroxystearate

O OH

O − C −[ CH2 ]10 − C−[CH2 ]5 − CH3

Ca

O − C −[CH2]10 − C −[CH2 ]5 − CH3

O OH

Figure 3.23 Different types of acids for forming simples soap grease thickeners.

3.3.2 Complex Greases

There is no clear definition of complex greases. Complex greases can be made by reacting ametallic base with two dissimilar acids of widely different molecular weight forming a complexsoap. According to this, a complex soap grease contains only multivalent anions [474] andwould therefore exclude lithium complex soaps. Complex greases can also be defined as thosesoaps made by a conventional metallic soap in combination with a ‘complexing agent’. Thiscomplexing agent can be inorganic or organic and can even contain another metal. Usually,complex soaps are made by a base (e.g. LiOH) and a fatty acid (e.g. stearic acid) and anonfatty acid (e.g. acetic acid). As an example a calcium complex grease is drawn in Figure3.25. The grease thickener consists of a combination of conventional calcium soap and a lowmolecular weight organic acid as a complexing agent. For calcium, the complexing agent isessentially calcium acetate. Complexes formed from monovalent cations such as Li+ mayin a physical-chemical sense not be called complexes but rather adducts. For Li-complexgrease it is most likely that cross-linking of soap crystals will take place (NLGI [11]). Forlithium the complexing salt is the lithium salt of a dibasic acid (an acid containing two


O O

Li - O - C −[ CH2 ]7 − C − O − Li Li azelaic

OH

Li - O - C −[ CH2 ]7 − CH2 − CH2 − CH2 − CH2 −[ CH2 ]5 − CH3 Li 12-hydroxystearate

O

Figure 3.24 Li-complex (hydroxystearate acid and azelaic acid).

replaceable hydrogen atoms per molecule). Examples of a molecular structure is are given inFigure 3.24.

‘Complex’ soap greases are developed for higher temperatures. The dropping point is 40 ◦Chigher than normal soap thickened greases. (65 ◦C higher according to NLGI [11], 50–100 ◦Chigher according to Mang and Dresel [397], for Al-complex even 140 ◦C [66]). The maximumtemperature is about 180 ◦C, mainly determined by the properties of the base oil.

Complex greases usually have a higher thickener concentration, leading to reduced oilseparation. For this reason, this type of grease is less suitable for low temperature applications.

As an illustration, Figure 3.24 shows an example where the cross-linking agent is an azelaicacid and can therefore be applied at higher temperatures (see Table 3.8 for the various complexgrease types). In 1998 Dresel [179] published a survey on complex greases.

3.3.3 Non-soap Thickeners

Inorganic thickeners do not have a melting point, thus do not show a phase change at hightemperatures. Examples are clay and silica which consist of spherical or plate-like particles.The particles are electrochemically charged and ‘gel’ the oil. The platelets do not breakdownunder shear and these are therefore more stable.

Polyurea, discovered by Swaken [564] in 1954, is commonly used as thickener. It is thename for poly(alkyl-substituted) urea. It is formed by adding hydrocarbon chains onto ureaand linking the resulting molecules. The molecular structure of polyurea is drawn in Figure3.31. Different polyurea types are di-urea, tri-urea and tetra-urea. Three di-urea thickenersare used: aliphatic diurea (see also Figure 3.31), alicyclic di-urea and aromatic di-urea. Thestructure of aliphatic diurea consists of a fibrous network whereas the other types consists offine needle-shaped crystals.

3.3.4 Mixed Thickeners

Mixed soaps are comprised of several cations. As an example, they can be formed by the reac-tion of one type of acid with two different bases, forming, for example, Li-12hydroxistearateand Ca-12hydroxistearate. The properties of these greases can be deduced from the propertiesof their components. By having mixed soaps, unfavourable qualities of specific soap types canbe compensated. An example is the improvement of water resistance of Na and Li-soaps bybuilding in a Ca-soap.


O OH

O - C −[ CH2 ]10 − C −[ CH2 ]5 − CH3

Ca

O - C - CH3

O

Figure 3.25 Calcium complex soap (stearate and acetate).

3.3.5 Mechanical Structure

Grease of the organic thickener type is a mixture of oil and metal salts of fatty acids(CnH2n+1COOH), which is crystalline by nature. It is generally believed that the fatty acidsstick to each other to form a network. Salomonsson et al. [512] have visualized this networkand observed fibres with an average diameter of 30 nm and a length of around 1 μm. Figures3.26 and 3.27 show the probable structure. There are two forces that hold these moleculestogether:

• Ionic: attraction of the negatively charged carboxyl group and the positively charged metalion. F ∝ 1

d , that is the attractive forces are inversely proportional to the distance betweenthe charged particles.

OxygenCarbon C - O distance 1.27Å

MonovalentHydrogen (one on O - C - O angle 125º metaltop of the other)

4Å (for lithium)

Front view

Front view4Å 2.5Å

1.54Å

114º 1.45Å

4.84Å

Figure 3.26 Assumed structure of monovalent metal soap. Reproduced with permission from Forster,Kolfenbach and Leland, 1956 C© NLGI.


Carboxyl

Hydrocarbon

Figure 3.27 Fibre arrangements. The long carbon chains are lined up parallel to the thin section of thesoap fibres rather than normal to it [474, 593].

• Van der Waals: permanent or induced dipole-induced dipole interaction between neighbour-ing methyl and methylene groups. Induced dipole interaction is caused by fluctuations of theelectron density in a molecule which again induces a dipole in a molecule nearby, causing anattractive force. F ∝ 1

d6 , that is, the attractive forces are inversely proportional to the sixthpower of the distance between the interacting groups.

The carboxyl group (COOH) and the metal ion are strongly attracted, forming the structurefrom Figure 3.26 making a row of molecules, forming again layers of double molecules placedend to end, hydrocarbon to hydrocarbon and carboxyl group to carboxyl group [474, 559],as shown in Figures 3.27 and 3.28. Having two of these ‘rows’ parallel to each other willresult in an ionic force between the two pairs, both attracting and repulsing. The rows areorganized in fibres such that the total attractive forces will be stronger in a row than betweenrows. If the rows contact each other then it will be through Van der Waals forces and theseforces will depend on the relative packing of the chains. The strongest forces are obtainedif the molecules are arranged parallel to each other. In that case the adjacent hydrocarbonchains are as close as possible to each other, see Figures 3.27, 3.28. Unfortunately, there is arepulsive force between these chains caused by the adjacent oxygen atoms from parallel rows.However, this repulsive force is reduced by having one oxygen of the carboxyl group aboveand one under the plane formed by the hydrocarbon chains. So the forces in a row inside thefibre are very strong, while only weak forces operate between layers. This crystal structureresembles that of material like graphite and has the tendency to cleavage, or to easily slipalong planes parallel to the rows, which therefore gives the ‘fatty touch’ behaviour of soap(Forster [197]).


1

Tail to tail

2

Tail to side

3

Side to side

Figure 3.28 Three types of soap fibre contacts. Reproduced with permission from Forster, Kolfenbachand Leland, 1956 C© NLGI.

As mentioned above, the soap molecules may be aligned forming fibres. During the for-mation of the fibres they will move in contact. The forces between the fibres are the sameas those inside the fibres, that is, ionic and Van der Waals. The effectiveness of the forcesbetween fibres depends on how they contact each other. Forster [197] assumes three typesof contact as depicted in Figure 3.28. This figure shows the fibres formed by the fatty acidsare connected by the ionic forces. The fibres may be in contact in ‘tail-to-tail’ mode, and theeffective forces will be mainly Van der Waals. In the second mode, ‘tail-to-side’, the attractiveforce is a combination of ionic and Van der Waals where the ionic force contribution willbe small. In the third mode, ‘side-to-side’, both ionic and Van der Waals forces apply wherethe ionic force will dominate.

It is not only the soap itself which determines the shape of the fibres. Salomonsson et al.[512] visualized the structure of various greases and concluded that fibres are more irregularin shape when paraffinic base oil is used compared to naphthenic oil.

At low shear rates it will be mainly the contact points between fibres that will break. Athigher shear rates, the actual fibres may breakdown in height, width or length [276].

The thickener fibres vary in length from about 1–100 microns and a length to diameter ratioof 10–100 (this ratio has been correlated with the consistency of the grease [518]). Table 3.7shows some typical sizes of soap fibres. Large coarse fibres do not adsorb fluid as well asfine fibres. This means that a higher percentage of thickener is required for the coarse fibregrease to give it the same consistency as grease with a fine structure. It has been shown forlithium greases that the finer the particle (or increasing the surface area per unit volume), thestronger its gelling action [277], see Figure 3.29. Very often Li-soap thickener fibres appear tohave a helix structure which may be the consequence of the asymmetric shape of the lithium12-hydroxystearate molecule resulting from the lateral hydroxyl group [402].


Table 3.7 Average soap fibre sizes . Data modified fromPolishuk, 1963 C© STLE.

Grease fibres Diameter (μm) Length (μm)

Ba complex 1 ≈ 100Short fibred Ca 0.15 1.5Long fibred Ca 1 ≈ 100Li 0.2 2-25Ca complex 0.1 1Ca complex 0.1 <1

3.3.6 Oil Retention

There are three ways that oil molecules are retained inside the thickener structure. There canbe attraction between the polar components of the base oil and thickener, there can be capillaryeffects and there can be mechanical retention in the spaces between adjacent fibres [149]. Toremove the oil that is kept by mechanical retention, a large pressure is required! Surprisingly,according to Boner [88], only 25% of the oil can be washed out using a solvent. Additivesalso play a role retaining oil as will be discussed later in Section 3.4.

3.3.7 Properties of Different Types of Grease Thickeners

After the description of the various grease types, in the next sections their properties will bedescribed. For convenience, Table 3.8 summarizes the properties of the greases that are listedhere.

Con

sist

ency

, AS

TM

pen

etra

tion

Surface area/volume, 1/μ

440

400

360

320

280

240

20060 7040 50 30 10 20 0 80

Figure 3.29 Effect of soap fibre surface area/volume on consistency of 12% lithium soap grease.Reproduced from Hotten and Birdsall, 1952 C© Elsevier.

Tabl

e3.

8Si

mpl

ean

dco

mpl

exgr

ease

s(w

itha

min

eral

oila

sba

seoi

l)an

dth

eir

typi

cald

ropp

ing

poin

tand

max

imum

tem

pera

ture

for

oper

atio

n(d

ata

from

NL

GI,

quot

edfr

omPi

rro

and

Wes

sol[

471]

),ap

plic

atio

nm

axte

mpe

ratu

rean

ddr

oppi

ngpo

inti

sal

sogi

ven

bySc

hmid

tin

[66]

.Min

imum

tem

pera

ture

from

Har

ris

[249

].

App

l.D

ropp

ing

Wat

erW

ork

Oxi

datio

nR

ust

Pum

pabi

lity

Oil

Oth

erM

ain

Gre

ase

type

tem

p.po

int

resi

st.

stab

ility

stab

ility

Prot

ectio

nlu

b.sy

stem

sepa

ratio

nA

ppea

ranc

epr

op.

appl

icat

ion

Ca

−93

100

Goo

dto

Fair

Poor

toPo

orto

Goo

dto

Poor

toSm

ooth

and

EP

grad

esG

ener

alus

eex

celle

ntto

good

exce

llent

exce

llent

exce

llent

good

butte

ryav

aila

ble

for

econ

omy

Ca-

anhy

drou

s−1

0–11

014

0E

xcel

lent

Goo

dto

Fair

toPo

orto

Fair

toG

ood

Smoo

than

dE

Pgr

ades

Mili

tary

exce

llent

exce

llent

exce

llent

exce

llent

butte

ryav

aila

ble

mul

tiser

vice

Ca-

com

plex

−20–

177

260+

Fair

toFa

irto

Poor

toFa

irto

Poor

toG

ood

toSm

ooth

and

EP

grad

esM

ulti

serv

ice

exce

llent

good

good

exce

llent

fair

exce

llent

butte

ryav

aila

ble

auto

m./i

nd.

Na

−30–

121

170

Poor

toFa

irPo

orto

Goo

dto

Poor

toFa

irto

Smoo

thto

Adh

esiv

ean

dR

ollin

gfa

irgo

odE

xcel

lent

fair

good

fibro

usco

hesi

vebe

arin

gs

Na-

com

plex

−20–

150

240

Li

−30–

135

180

Goo

dG

ood

toFa

irto

Poor

toFa

irto

Goo

dto

Smoo

than

dE

Pgr

ades

Mul

tise

rvic

eex

celle

ntex

celle

ntex

celle

ntex

celle

ntex

celle

ntbu

ttery

avai

labl

ein

d.

Li-

com

plex

−20–

177

260+

Goo

dto

Goo

dto

Fair

toFa

irto

Goo

dto

Goo

dto

Smoo

than

dE

Pgr

ades

Mul

tise

rvic

eex

celle

ntex

celle

ntex

celle

ntex

celle

ntex

celle

ntex

celle

ntbu

ttery

avai

labl

eau

tom

./ind

.

Al

−79

110

Goo

dto

Poor

Exc

elle

ntG

ood

toPo

orG

ood

Smoo

thT

hrea

dex

celle

ntex

celle

ntan

dcl

ear

lubr

ican

ts

Al-

com

plex

−30–

177

260+

Goo

dto

Goo

dto

Fair

toG

ood

toFa

irto

Goo

dto

Smoo

than

dE

Pgr

ades

Mul

tise

rvic

eex

celle

ntex

celle

ntex

celle

ntex

celle

ntgo

odex

celle

ntbu

ttery

avai

labl

ein

d.

Poly

urea

−30–

177

243

Goo

dto

Poor

toG

ood

toFa

irto

Goo

dto

Goo

dto

Smoo

than

dE

Pgr

ades

Mul

tise

rvic

eex

celle

ntgo

odex

celle

ntex

celle

ntex

celle

ntex

celle

ntbu

ttery

avai

labl

eau

tom

./ind

.

Org

ano

clay

−177

260+

Fair

toFa

irto

Goo

dPo

orto

Goo

dG

ood

toSm

ooth

and

EP

grad

esH

igh

tem

p.ex

celle

ntgo

odex

celle

ntex

celle

ntbu

ttery

avai

labl

e(f

req.

relu

be)


Lithium Soap Greases

Today, Li-soap greases are practically all made from 12-hydroxy stearic acid.6 They can beclassified as multipurpose greases with excellent mechanical stability, good water resistanceand reasonably high temperature performance (up to 120 ◦C [228], 110 ◦C [249]). Schmidt [66]specifies 110 ◦C for lithium stearate and 130 ◦C for lithium-12-hydroxy-stearate. If siliconesare used as the liquid phase, a temperature range of −40 ◦C to 200 ◦C is claimed [248]. Adisadvantage of lithium 12-hydroxy stearate grease is pumpability at low temperatures causedby high elastic properties [228] and loading extremes [249]. The low limit temperature is−30 ◦C.

The fibre size in lithium hydroxystearate is typically between 0.2x2 μm and 0.2x20 μm[397], Table 3.7. For heavy loads a high base oil viscosity (ca. 200–1000 cSt) is chosen. Formultipurpose greases typically a mineral base oil with a viscosity of 60–120 cSt is used. Inhigh speed applications, diesters or polyalphaolefin oils with a viscosity of 15–30 cSt arechosen as base oils. Finally, for gears an oil-insoluble polyalkeneglycols [397] is best.

A variant to Li-soap grease is mixed based lithium–calcium grease, which may have betterwater resistance and better shear stability than pure litium greases [389].

Calcium Soap Greases

Calcium greases are the oldest metal soap greases. The melting point is quite low (100 ◦C) andthe upper temperature limit is only 60 ◦C [66]. In this grease, water is needed to stabilize thestructure. This water evaporates, leading to a loss of consistency and therefore short grease life.Obviously, this is accelerated when running at higher temperatures. Therefore, these greasesare only used in less demanding applications or in wet applications (temperatures up to 60or 80 ◦C). Calcium greases have good adhesion properties [228]. Recently, Ca-soaps havealso been used that are not stabilized by water and which can be used up to temperatures of110 ◦C. They are called ’Anhydrous calcium soap greases’. They have the same good adhesionproperties [228] and a dropping point around 140 ◦C [389].

Calcium sulfonate thickener greases have good EP/AW properties without the use of addi-tives [336]. Moreover, they have inherent good mechanical stability and a high dropping point(>310 ◦C), [388].

Sodium Soap Greases

Sodium soaps are very similar to domestic soaps. They can be used up to 110 ◦C [228], 80 ◦C[249], 100 ◦C [66] and down to −30 ◦C [249]. These soaps are not used much today. Theyare water soluble (like domestic soap) and will show a thin grease-in-water, noncorrosiveemulsion in contact with water. They are not really resistant against water pressure [410] andmay be easily washed out. They should also not be used when the bearing has long periods ofstand-still. In this case the bearing may corrode. Moreover, they have a short shelf life.

Aluminium Soap Greases

Aluminium soap greases are extremely sensitive to shear [88, 228], which means that theyquickly lose their consistency. These greases are not used in rolling bearings. Their maximumtemperature is only 70 ◦C [66].

6 Originally patented by Shell [1].


Lithium Complex Soap Greases

Lithium complex greases have a high melting point and the operating temperature range isbetween −30 ◦C and 140 ◦C [249] or even 150 ◦C [66]. The low temperature limit is −20 ◦Cfor Li.

According to Gow [228] this type of grease can be operated continuously even at 150 ◦Cwith mineral oils and 200 ◦C with synthetic oils. It has excellent resistance against oxidation,excellent pumpability and broad compatibility with other greases.

Calcium Complex Soap Greases

Calcium acetate is used here to modify the simple soap. The grease operating window is muchwider then in the case of a simple calcium soap grease and can be used at −20 ◦C < T <

130 ◦C [249]. According to Schmidt [66] these greases can even be used up to 140–180 ◦C.Thickening during bearing operation may occur [249]. Calcium derivatives are crystallized inthe structure (calcium sulfonate), giving them inherent EP/AW behaviour [228]. The droppingpoint is above 240 ◦C. Pumpability and shelf life are not so good (the grease has a tendencyto harden [389]). Water resistance is excellent. It maintains its consistency even when a greatamount of water is introduced.

In calcium sulfonate complex greases the calcium sulfonate derivatives are crystallized intothe thickener structure, which gives them inherent EP/AW capacity. Moreover this type hasexcellent corrosion protection properties. The high soap content that is needed to give it itsconsistency reduces pumpability and bleeding properties [389].

Sodium Complex Soap Greases

The temperature window of sodium complex soap greases is extended compared to the simplesodium greases: −20 ◦C < T <140◦C [249]. According to Schmidt [66], the maximumoperating temperature is 130 ◦C.

Aluminium Complex Greases

Aluminium complex greases can be used at high temperatures. The dropping point is above240 ◦C. The upper temperature limit is 150–180 ◦C [66]. Furthermore, they are highly waterresistant. Pumpability is excellent (low thickener concentration [389]) and aluminium complexgreases are particularly adopted for use in lubrication systems (Boner [88]). The mechanicalstability is similar to conventional Al-grease, which was poorer than Li-grease.

Polyurea Greases

Polyurea thickeners provide excellent high temperature performance for grease lubrication.The vast majority of polyureas and diureas are manufactured from reactions combiningmethylenediphenyl diisocyanate (MDI) or toluene diisocyanate (TDI) with diamines and/orfatty amines [292, 475]. Structures of the two diisocyanates are shown in Figure 3.30. MDIhas two phenyl groups bridged by a methylene group. This bond forms a rigid structure inurea structures. MDI forms more flexible urea structures. Urea (MDI and TDI) thickeners aregood free radical scavengers produced during high temperature lubrication of rolling bearings.The aromatic structure of urea thickeners acts similarly to substituted phenolic and aromaticdiamine antioxidants [304, 352].


NC

O

NC

O

CH3

NCOOCN

CH2

(a) Toluene diisocyanate TDI. (b) Methylenediphenyl diisocyanate MDI.

Figure 3.30 Urea (MDI and TDI) thickeners.

Polyurea greases show a better adhesion to metal surfaces than metal soap greases [336].In a metal soap grease the metal ion may act as a catalyst for oxidation. The absence of thisin polyurea gives this grease type its extremely good high temperature performance. Polyureathickener shows poor performance at ambient temperatures and the raw materials are toxic. Ithas poor rust preventative properties, but excellent anti-wear and anti-fretting properties [186].Urea thickeners can be classified into diurea and polyurea (see Figure 3.31, where polyurea isan oligomer formed from composite molecules (with a larger number of urea groups). Diureathickeners, which are largely used for rolling bearings, can be classified as aliphatic diurea,alicyclic diurea or aromatic diurea. The molecular attraction between the diurea molecules is

Aliphatic diurea

Alicyclic diureaDiurea

Tetraurea NH C

Aromatic diurea

NH

O

n

O

R C NH R'NH

NH C NH

O O

R C NH R2R1 NH

NH C NH

O O

R C NHNH

NH C NH

O O

R C NHNH

Figure 3.31 Urea thickener classification and molecular structure.


much stronger than those between the polyurea molecules. This gives the polyurea greases arelatively poor shear stability and may lead to thermal softening. Urea greases have excellentanti-wear properties due to the formation of boundary layers. Polyurea greases tend to hardenduring storage.

Clay Greases

The best known clays for lubricating grease are bentonite clays. They are characterized by alaminar structure in a crystalline lattice [224, 473]. Clay greases are not common in bearings.Their advantage is that the clay particles do not melt, so there is no dropping point, resultingin a high upper temperature of 150–200 ◦C [66](160 ◦C and for short periods 200 ◦C [224].The mechanical stability is reasonable. The structure is very sensitive to polar additiveswhich should therefore be avoided (EP/AW but also anti-corrosion additives). Oil oxidationand separation can result in a residue of abrasive clay [228]. Moreover, the protection fromcorrosion is very bad. Pumpability is good though. They also show very good fretting wearprotection due to the structure of the thickener. Typical applications for Bentonite grease arehigh temperature and low speed. They should not be used for high loads and high speeds [224].

Silica Gel Greases

Similar to clay based greases, silica gel greases show excellent pumpability. However, thesegreases are hardly used anymore because of inherent instability of the thickener.

PTFE Greases

PTFE (polytetrafluoropolyethers) thickeners are inert and can be used in combination withinert base oils in aggressive environments. They can be used at extremely high temperatures(continuous temperature of 250 ◦C or higher) and work well at low pressures (space appli-cations). PTFEs are not recommended for high load carrying capacity. Hazardous thermaldecomposition products can be built at temperatures exceeding 300 ◦C (Fluorinated com-pounds).

Polyethylene Greases

Polyethylene can be produced with a similar specific weight as a mineral base oil and doestherefore not separate easily, even if very high (centrifugal) forces are applied to the grease.This grease can be used at very high speeds or at rapid accelerations [228].

3.4 Additives

Additives are chemicals commonly added to lubricating oil and grease to improve lubricatingperformance in application. Mineral oil grease lubricants need oxidation inhibitors to accom-modate high temperature applications. The basic additive package for mineral oil based greaselubricants includes addition of rust and oxidation inhibitors (R&O). Viscosity index improversmay be added, which are aliphatic molecules with different side groups, primarily used toimprove the viscosity characteristics of base oils over a wide range of temperatures. Additives


can be used to improve impact resistance while others are used to lower friction. For thoseapplications operating under more extreme load conditions, anti-wear and extreme-pressureand solid lubricant additives may be necessary to improve lubricant performance [87, 200,456, 507]. Additives may also be used to strengthen grease structure. They act mainly throughinterface modification of the free energy of thickener molecules [111].

3.4.1 Corrosion Inhibitors

Corrosion inhibitors are additives that block reactions that result in the dissolution (corrosion)of metallic elements. They are largely categorized as cathodic or anodic inhibitors. Cathodicinhibitors block cathodic reactions that involve the reduction of oxygen or hydrogen ion(H+). Anodic inhibitors block the anodic dissolution of steel and other metals. Some corrosioninhibitors act as both an anodic and cathodic inhibitors. Amines are common cathodic inhibitorsthat interfere with the reduction of hydrogen ions. Zinc oxide and zinc salts are also a commonlyused cathodic inhibitors [131, 343, 507].

Anodic inhibitors include compounds like phosphates, borates, molybdenates and manyother (oxide) film forming compounds that reduce the dissolution rate of the corroding metal.Sodium nitrite is a commonly used anodic corrosion inhibitor that forms a metal oxide passiva-tion film on steel surfaces [507, 516]). Calcium sulfonates, imidizolines and metal carboxylatesare the most common rust inhibitors used for grease lubrication. Currently, sodium nitrite isnot incorporated into grease formulations due to the formation of nitrosoamines (carcinogenic)from reactions of nitrites with secondary amines (i.e. antioxidants), [507]. Some examples ofcorrosion inhibitors are given in Table 3.9.

3.4.2 Antioxidants

Antioxidants are divided into families with different performance characteristics. Chemicalfamilies include phenolics, metal deactivators, aromatic amine antioxidants, dithiophosphatesand phosphites, thiosynergists and hydroxylamines. The most common antioxidants used ingrease lubrication are the aromatic secondary amines, zinc dialkyl-dithiophosphates, zincdithiocarbamates, thioesters and hindered phenols. More recently organophosphate, thiadia-zoles and phenothiazines have also been used for improving the oxidation stability of lubricants[431, 456, 507]. Blends of antioxidants are often used to provide improved performance [491].

Hindered phenols and aromatic secondary amine antioxidants inhibit the oxidation of baseoil fluids by terminating the free radical chain reactions (radical scavengers) initiated by alkylperoxides. Carbamates, dialkyldithiphosphates, organosulfur or organoselenium compoundsact by decomposing alkyl peroxides or peroxy radicals [431, 487, 507].

The aromatic amines are known to be more effective for providing oxidation inhibitionat elevated temperatures than hindered phenols (>120 ◦C, [431]. Synergisms among metaldeactivators and radical scavengers promote the effectiveness of antioxidants when severaldifferent types are combined for use as mixtures [431, 507]. This often involves the use of metaldeactivators and metal ion chelating agents. Metal ions catalyse hydrocarbon oxidation byaccelerating hydroperoxide decomposition and promoting condensation of oxidation productsto form varnish and sludge [351].


Table 3.9 Common rust inhibitors. Data from the following websites:Chemtura, BASF (formerly Ciba), Angus Chemical, RT Vanderbilt, AkzoNobel, Dover Chemical Company, Huntsman, King Industries, Air Products,Arkema Pilot, Afton Chemicals, Croda, Rhein Chemie, Dow, Syrgis.

Sulfonates Barium sulfonatesCalcium sulfonatesZinc sulfonatesMagnesium sulfonates

Naphthalenesulfonates Lithium dinonylnaphthalenesulfonatesCalcium dinonylnaphthalenesulfonatesBarium dinonylnaphthalenesulfonatesMagnesium dinonylnaphthalenesulfonatesDiethylenetriamine dinonylnaphthalenesulfonates

Metal Carboxylates Zinc CarboxylatesCalcium Carboxylates

Succinates Succinate estersSuccinic acid half esterPolyester succinimidesDodecenylsuccinic acid reaction productsAmine Succinates

Imidazolines ImidazolinesOctyldecyl imidazolineFatty Imidazoline derivativesAmido Imidazolines

Sarcosines N-acyl sarcosinesN-Oleoyl SarcosineN-Acyl sarcosinates

Phosphate Esters Alkyl Phosphate estersC12-C14 alkylamine neutralized phosphate esters

Phosphite Esters Dilauryl hydrogen phosphiteDibutyl hydrogen phosphiteAlkyl phosphites

Amides Fatty AmidesDiethanolamine Oleamide

More recently, greases designed with polymer-bound and thickener-bound antioxidantsshow improved oxidative stability [29, 38, 507]. Covalently bound antioxidants resistvolatilization at elevated temperatures providing more effective oxidation inhibition.

A list of commercial antioxidants is provided in Table 3.10.

3.4.3 EP/AW Additives

Extreme pressure (EP) and anti-wear (AW) additives are commonly used in gear and machin-ery lubricating oils and greases to minimize wear and scuffing in machine applications under


Table 3.10 Some examples of antioxidant additives. Irgamet and NACAP are metal deactivators.Metal deactivators are used in combination with ‘normal antioxidants’ to reduce the effects of metalions on oxidation. CUVAN 303 is an oil-soluble corrosion inhibitor and metal deactivator for greases(data obtained from Rudnick [507] and from supplier data available on the internet).

Trade name Company Chemistry

Ethanox 4740∗ Albemarle Mixed-butylphenols/ Phenylenediamine blendEthanox R© 4705∗ Albemarle N,N-disalicylidene-1,2-diaminopropaneIrganox R© L 57 BASF Octylated/butylated diphenylamineIrganox R© L 153 BASF Liquid, high molecular weight phenolic antioxidantIrganox R© L 06 BASF Octylated n-phenyl-1-naphthylaminesIrganox R© 3114 BASF Butylated hydroxytoluene (BHT).Irganox R© 30∗∗ BASF Triazole derivativeIrgamet 39 BASF Triazole derivativeIrgamet BTZ∗ BASF Benzotriazole, metal deactivatorCuvan R© 303 RT Vanderbilt benzotriazole derivativeCuvan R© 484∗∗∗ TR Vanderbildt 2,5-Dimercapto-1,3,4-thiadiazole derivativeCuvan R© 826∗∗∗ TR Vanderbildt 2,5-Dimercapto-1,3,4-thiadiazole derivativeROKON R© ∗∗∗∗ RT Vanderbildt 2-MercaptobenzothiazoleVanlube R© AZ RT Vanderbildt Zinc diamyldithiocarbamateVanlube R© EZ RT Vanderbildt Zinc and ammonium diamyldithiocarbamateVanlube R© NA RT Vanderbildt Alkylated diphenylamineVanlube R©E 81 RT Vanderbildt Purified dioctyldiphenylamine.Vanlube R© 961 RT Vanderbildt Octylated and butylated diphenylamineVanlube R© 7723 RT Vanderbildt Methylene-bis-dibutyldithiocarbamateVanlube R© BHC RT Vanderbildt Phenolic antioxidantVanlube R© 601 RT Vanderbildt Heterocyclic sulfur–nitrogen compoundVanlube R© 601E RT Vanderbildt Heterocyclic sulfur–nitrogen compoundBenefos 1680 Mayzo Tris(2,4-ditert-butylphenyl) phosphiteIrgafos 168∗∗∗∗∗ BASF Tris(2,4-ditert-butylphenyl) phosphiteIrganox 1135∗∗∗∗∗∗ BASF Octyl-3,5-di-tert-butyl-4-hydroxy-hydrocinnamateIrganox 1093 BASF Distearyl3,5-di-tert-butyl-4-hydroxybenzyl phosphonate

∗Ethanox 4740, used in conjunction with very small amounts of Ethanox 4705. (a chelating agent),proves to be an excellent antioxidant for yellow grease.∗∗Metal Deactivator, synergistic behaviour with Irganox R© L antioxidants, resulting in superior oxidationstability.∗∗∗Ashless oil-soluble corrosion inhibitor and metal deactivator for nonferrous metals, particularly forcopper. CUVAN 484 will also enhance anti-wear and oxidation resistance properties of lubricants.CUVAN 826 is capable of suppressing the corrosive action of hydrogen sulfide.∗∗∗∗copper corrosion inhibitor.∗∗∗∗∗Phosphite antioxidants function by decomposing peroxides and provide protection for greases duringhigh temperature processing but not during end-use at elevated temperatures. Combinations with phenolicantioxidants often show synergistic performance and are widely used.∗∗∗∗∗∗Coumaric acid is a hydroxycinnamic acid, an organic compound that is a hydroxy derivative ofcinnamic acid. There are three isomers, o-coumaric acid, m-coumaric acid and p-coumaric acid, thatdiffer by the position of the hydroxy substitution of the phenyl group. p-coumaric acid is the mostabundant isomer of the three in nature. It can be found in a wide variety of edible plants such as peanuts,tomatoes, carrots and garlic.


heavy load conditions [431]. Modern EP gear oils and greases are formulated with additivesthat contain sulfur, frequently combined with phosphorus additives to achieve thermal sta-bility and heavy load-carrying capacity. Some years ago, it was commonplace for gear oilsformulated for heavy loading to contain sulfurized sperm oil, chlorinated paraffin and leadnaphthenate extreme pressure additives. These combinations allowed smooth, low noise oper-ation of heavily loaded gear sets. The use of chlorinated paraffin, lead soaps and sperm oilderivatives has been outlawed in past years. Sulfurized sperm oil has been largely replaced byother sulfurized fatty oils including sulfurized Jojoba oil [223]. Lead EP additives have largelybeen replaced by bismuth derivatives of similar structure and function [498, 637]). Many sul-furized oils have shown excellent biodegradability and are often used for EP additives in greaselubricants used for environmentally sensitive applications [507]. Several metal carboxylateshave good friction reducing and anti-wear properties when added to lubricants [487].

The most commonly used anti-wear (AW) additive has been zinc dialkyl dithiophosphate[555]. It was used as an additive in automobile engine oils and hydraulic fluids as early asthe 1930s [371]). ZDDP additives function simultaneously as antioxidant, corrosion inhibitorand anti-wear agents [487]. It has been shown that the oxidation inhibition mechanism, ZDDPadditive acts to decompose alky peroxides and destroys peroxy radicals [279]. The anti-wearproperties of ZDDP are complex and are discussed in full detail in the references cited in Ratoiet al. [487].

Phosphate esters and phosphites also function as anti-wear additives and metal deactiva-tors [371]. Additives like tricresyl phosphate have long been used as antiwear additives forlubrication [87]. Some organo-phosphorus additives have been shown to promote fatigue lifein rolling bearings used in lubricating oils [200, 449, 464, 596]). A list of common EP andanti-wear additives are provided in Table 3.11.

Table 3.11 Common EP and anti-wear additives. Data fromthe following websites: BASF, RT Vanderbilt, Dover ChemicalCompany, King Industries, Arkema, Afton Chemicals, RheinChemie, Elco (Division of Detrex), Clariant, Chemtura.

Sulfurized fatty oilsSulfurized terpenesSulfurized olefinsChlorinated paraffinsChlorinated fatty acidsChlorinated fatty oilsSulfurized, chlorinated fatty oilsSulfurized, chlorinated fatty acidsAlkyl/Aryl PhosphitesAlkyl/Aryl PhosphatesAmine Alkyl/Aryl PhosphatesZn, Mo and Sb DialkyldithiophosphatesZn, Mo and Sb DialkyldithiocarbamatesZn, Ca, Sn, Pb, Sb, and Bi Metal NaphthenatesAlkyl triphenyl phosphorothionatesOverbased Calcium Sulfonates


3.5 Solid Fillers/Dry Lubricants

Unlike oil-based lubricants, grease lubricants have the capability of dispersing solid lubricantsand fillers to extend lubricating properties of greases operating under extreme conditions. Manysolid lubricants and fillers can be added to grease to improve load carrying characteristics,improve impact load characteristics and reduce fretting corrosion damage from oscillatoryloads and vibration [87, 475].

3.5.1 MoS2 and Graphite

Molybdenum disulfide and graphite are both lamellar structured solid lubricants. They arecommonly used in EP grease lubricants for slow moving, heavily loaded machinery. Graphiteand ‘moly disulfide’ are also effectively used for thread compound pastes that prevent galling.The additive levels for these pastes are very high, of the order of 60%. Graphite and molyb-denum disulfide are most effective when burnished or used as dry lubricating films. Additivesused in grease and oil interfere with the adhesion to the metal substrate and diminish frictionand load reducing activity [231, 507]. Organomolybdenum additives are often more effectiveeither alone or in combination with molybdenum disulfide solid lubricants additives [624].

3.5.2 Nanoparticles

Greases incorporating nanocrystalline titanium dioxide and nanocrystalline silicone dioxideshow significant reduction in friction and wear [122]. Nano boric acid and potassium tetraboratehave also been used successfully as friction reducing additives in greases [118]. Consumerreports warn that the toxicity effects of nanotechnology have not yet been fully explored [16].

3.5.3 ZnO

Zinc oxide is a commonly used filler for greases and pipe thread pastes. It acts as a brightenerto give the grease product a white colour and is commonly called ’white grease’. Zinc oxideis a commonly used filler for grease used in the food industry as it acts to neutralize foodacids while maintaining grease consistency. Zinc oxide filler is also used in grease lubricantsto prevent impact load damage to machine elements [87, 105, 474].

3.5.4 Teflon (polytetrafluoroethylene)

It is well known that Teflon is commonly used as a universal thickener for many types ofgrease lubricants [87, 474]. Teflon also has friction and wear reducing properties when usedas an additive in grease lubricants [122].

3.5.5 Polyethylene

Polyethylene is used for impact loads and improving EP properties of grease lubricants [523].This is demonstrated by the Ford Engineering Material Specification for grease lubricantsused for power seat units and automobile body hardware applications [2, 3]. Polyethylene is


Table 3.12 Grease compatibility chart. Reproduced from Pirro and Wessol, 2001 C© CRC Press. B,borderline, C, compatible, I, incompatible, X, same grease.

Ca 12- Li 12-Al hydr. Ca hydr. Li poly-

com. Ba Ca st. ac. com. Clay Li st ac. com. urea

Al complex X I I C I I I I C IBa I X I C I I I I I ICa I I X C I C C C C ICa 12-h.st.ac. C C C X B C C C C ICa complex I I I B X I I I C CClay I I C C I X I I I ILi I I C C I I X C C ILi 12-h.st.ac. I I B C I I C X C ILi complex C I C C C I C C X IPolyurea I I I I C I I I I X

also used as a thickener for high speed shaft coupling greases. Teflon and polyethylene arecommon additives for grease lubrication of nylon and plastic gears.

3.6 Compatibility

Mixing greases can change performance. More often, mixing leads to loss of consistency,but for some mixtures hardening may occur. Mixing of greases can also result in lowering ofdropping points and changes in oil bleed rate (ASTM D6185 [8]). Individual grease lubricantsmost often perform better than the grease mixtures. A table demonstrating simple greasecompatibility is shown in Table 3.12.

3.7 Polymer Grease

Polymers may be added to the lubricating grease to improve its properties, such as the shearstability, water resistance and yield [355]. The mechanism behind this is that a polymernetwork and soap network may interpenetrate each other [169], changing the network strengthand stability.

Alternatively, the traditional soap thickener can be totally replaced by a polymer. This isan SKF invention [414] and is called ‘polymer grease’. Such a grease has improved bleedingproperties at low temperatures, oil bleeding characteristics that are less temperature dependent,good lubricating abilities at low temperatures, good mechanical stability and improved greasenoise characteristics.

Originally this grease type was developed for low temperature lubrication. Lubrication atlow temperatures is difficult for conventional greases due to reduced bleeding and adversesurface tension effects between thickener and base oil. A polymer grease has good bleedingproperties at low and medium temperatures. Adding rubber to the grease can optimize thecrystalline–amorphous balance in the system [183].


(a) Prepared with slow cooling (b) Prepared with quenching

Figure 3.32 SEM pictures of a polymer grease. Courtesy of SKF.

The grease is made by heating the oil and (a mixture of) polymer(s) above the meltingpoint of the polymer (190–210 ◦C), also polymers with higher melting points can be chosen200–225 ◦C, [415]) and additives may be added here. Next the mixture is cooled to roomtemperature. Cooling time is approximately 30 seconds. This ‘quenching’ has a major impacton the grease structure, which is dissolved in oil. The result is a three-dimensional net-structure,which works in the same way as a ‘normal’, metal-soap thickened grease. Quenching couldbe done using a cooling plate or by spraying.

Figure 3.32 shows the impact of quenching on the structure. The structure is very irregularin the case of slow cooling and has large and many small pores. After quenching the greaseis worked to the final consistency, for example in a three roll-mill or grease worker. Duringworking additional additives may be added. A conventional grease contains 5–30% metal-based soap thickener (polar) and 70–95% base oil including additive packages. The polymerthickened lubricant contains 10–13% polypropylene (PP), a nonpolar material, and 87–90%oil including the additive package.

The improved oil separation is illustrated in Table 3.13. The table clearly shows thatconventional greases practically stop bleeding at temperatures lower than 20 ◦C, whereas thepolymer grease continues bleeding.

In addition to the improved bleeding at lower temperatures, there is another advantage: thepolymer is nonpolar, which means that the soap does not compete with the metal surface toattract the (also polar) additives.

Table 3.13 Oil separation according to DIN 51817, [414].

NLGI-class 2 grease Test temperature [◦C]

0 20 40 70

Polymer grease 1 3.8 8.5 14EP-lithium soap/mineral oil 0 0.7 5 9Lithium soap/mineral oil 0.4 1.3 6 12


The basic polymer grease and a polymer grease with additives has been tested in the R0Ftest at 10 000 rpm and 120 ◦C (for a description, see Section 16.2.13). This gave L50 =6000 hours and 3500 hours respectively, which is significantly higher than that of a standardgood quality lithium grease. The low temperature performance is excellent. Tests in the coldchamber (Section 16.2.21) with 22310 CC/C3 bearings under conditions analogous to the R2Fmethod (Section 16.2.16) showed no bearing failures at ambient temperatures down to −20 ◦C[414].

Polypropylene is compatible with most greases and therefore hybrid greases can also bemade.

Alternatively, a multiple thickener system may be used comprising a nonpolar and a polarthickener component [413]. This is different from mixing a conventional metal-soap greasewith a polymer grease. Here the mixture of these components is made prior to quenching. Thisimproved the mechanical stability while maintaining the favourable bleeding properties.

4Grease Life in Rolling Bearings

4.1 Introduction

Predictions on grease life, relubrication intervals or reliability of grease lubricated bearings aredone through empirical relations developed mainly by the bearing industry. Physical models,such as those for bearing life [290,380] are not available. This may seem surprising as greaselife is very often shorter than bearing life and therefore dominates service life. Moreover,grease lubrication is known to sometimes cause early bearing failures (e.g. [477]). Clearly,accurate models are needed. However, the physics and chemistry of grease lubrication are socomplex that such models have not yet been published.

Today, grease life predictions are obtained from tests such as the R0F, R2F or FE8, FE9tests. Test results are interpolated and extrapolated to predict life at, for example, varioustemperatures, loads and bearing sizes.

Due to the relatively small number of bearings that are usually tested, the accuracy of thetest results is limited and this is the reason why grease life is usually expressed in L50, that is,the time at which the probability of failure is 50% or, in other words, the time at which 50%of a large population of bearings has failed (see Chapter 12).

Grease life is not only determined by grease properties and operational conditions. The typeof bearing also plays a role. This is generally incorporated in models by so called ‘bearingfactors’. These bearing factors have been derived for what is generally called a ‘good quality’lithium soap grease. Other grease types may deviate from this. As an example, Azuma et al.[39] have shown that an aliphatic diurea grease can increase the life of angular contact ballbearings by a factor of 20 compared to no improvement for deep groove ball bearings.

4.2 Relubrication Intervals and Grease Life

In the case that the bearing can be relubricated, that is, supplied with fresh grease, well beforethe end of grease life, the bearing system life is not determined by grease life. The choiceof the relubrication interval is determined by the grease life where a certain reliability hasto be chosen. Usually, the time at which the probability of failure is 1% is accepted as thecriterion for this, that is the L01 grease life. With an average Weibull slope of β = 2.3, the



relubrication interval is then equal to 16% of the expected L50 grease life (see Section 12.3).This means that grease life tests can be used to determine relubrication intervals. To increasereliability further, even shorter relubrication intervals are chosen rather than the intervals basedon grease life. As an example, in the case that the operating temperature is lower than 70 ◦C,the relubrication intervals of 70 ◦C are recommended to be maintained [57, 454] or increasedby no more than a factor of two [4]. Another example illustrating the difference between greaselife and relubrication intervals is given by the fact that bearing manufacturers recommend notto exceed relubrication intervals of 30 000 hours [4] or 3 years [13]. Obviously, there are manybearings that run well for more than 3 years with high reliability. Relubrication intervals canbe chosen to be much shorter than the L01 grease life if the aged grease cannot be totallyremoved from the bearing. In such a case, the reduction in relubrication interval depends onthe application. As a rule of thumb, the relubrication interval could be reduced by a factorof 0.5–0.7 [13].

There are also many applications in which relubrication intervals are not determined bygrease life at all. Examples are applications where particle ingress or water contamination is sostrong that the grease needs to be replaced frequently to remove moisture and/or contaminants.In these cases, the grease will need to be replaced well before its end of life.

4.3 The Traffic Light Concept

All lubricating greases are designed to operate in a certain temperature window. If the temper-ature is too high, the grease will lose its consistency and/or severe oxidation will take place. Inthe case of too low temperatures, the start-up torque may be too high and/or oil bleeding toolow. This is illustrated in the traffic light concept, Figures 4.1 and 4.2. The low temperaturelimit (LTL) is the lowest temperature at which the grease will enable the bearing to be startedup without difficulty. The high temperature limit (HTL) is determined by the type of thickenerand for soap based greases, and is given by the dropping point. The dropping point indicatesthe temperature at which the grease irreversibly loses its consistency and becomes a fluid.Operation outside the low temperature and high temperature limits is not advised, which isindicated in Figures 4.1 and 4.2.

LTL LTPL

Temperature

HTPL HTL

Forbiddento operate

Unsafefunctioning(only for shortperiods)

Safefunctioningi.e. withpredictablegrease life

Figure 4.1 Traffic light concept, courtesy of SKF [4].

Grease Life in Rolling Bearings 73

100

10

1

0.1

0.01LTL LTPL

Bearing temperature

Starvation process

Nor

mal

ised

Gre

ase

life

Degradation process

HTPL HTL

Forbiddento operate

Unsafefunctioning(only for shortperiods)

Safefunctioningi.e. withpredictablegrease life

Figure 4.2 Grease life versus temperature for ball and roller bearings, where ball bearings have alonger life at low temperatures, courtesy of SKF [4].

In the temperature domain between the low temperature performance limit (LTPL) andhigh temperature performance limit (HTPL), the grease will function reliably and the greaseperformance is given by its ability to build up a film, bleeding properties, oxidation rate andrheology as described in this book. Base oil viscosity, grease viscosity, oxidation and all otherrelevant grease properties show ‘Arrhenius’ behaviour [91], that is these properties show amore-or-less exponential relation with the temperature. Therefore, in this region, the ’greenzone’, grease life shows this ‘Arrhenius behaviour’ as well. This makes grease life reasonablypredictable in this (green) temperature window. Operation in the amber zone, between thehigh temperature performance limit (HTPL) and the high temperature limit (HTL), shouldonly occur for very short periods. An amber zone also exists for low temperatures.

The critical temperatures are grease dependent and are determined by grease testing. Thehigh temperature limit is determined by the dropping point (with a safety margin), see Section16.3.4, p. 375. The low temperature limit is determined by start-up torque (Section 16.3.1,p. 374) and bleeding properties. The green zone may be determined by grease life testing,where the boundaries (LTPL and HTPL) are determined by the points at which a deviation fromthe Arrhenius behaviour becomes significant. McCusker [410] suggests as a rule of thumb thatthe maximum operating temperature that is chosen is at least 55 ◦C lower than the droppingpoint. A guideline for standard greases can be found in Figure 4.3. It is however stronglyadvised to follow the grease specifications for this. Many bearing manufacturers specify thetemperature ranges for specific bearing greases in their catalogues.


10

10

10

10 Log

10 l

ife

[hrs

]

Inverse of absolute temperature [K–1]

Cold Cool Warm Hot

–10 ˚C50 ˚C 200 ˚C

Figure 4.3 Grease life as a function of temperature according to Smith and Wilson [545] and accordingto the traffic light concept for standard greases, courtesy of SKF [4]. Reproduced with permission fromSmith and Wilson, 1980 C© STLE.

Obviously, other methods may also apply, such as those based on measurement of greasebleeding, rheology and oxidation.

4.3.1 Low Temperatures

With decreasing temperature, the tendency of grease to bleed decreases and the stiffness(consistency) of the grease increases. This may ultimately lead to an insufficient supply oflubricant to the contact surfaces of the rolling elements and raceways [55] so the lubricatingaction of the base oil can be neglected for low temperatures. It will be the grease in itstotality that will lubricate [66]. Low temperatures will result in a high torque which maycause slippage of the rolling elements and therefore wear [13, 220]. This point is called thelow temperature limit (LTL). Continuous operation below the low temperature limit should beavoided. However, in many cases, the internal heat development and increasing temperature,will decrease the frictional torque again.

The low temperature limit also depends on bearing type, unlike the high temperature limits.Ball bearings are easier to lubricate and therefore have a lower low temperature performancelimit [4].

Exceeding the low temperature limit is less harmful than exceeding the high temperaturelimit. In many cases, the high torque at low temperature is reduced by heat development duringbearing operation, which will bring the bearing into the green zone.


The low temperature performance limit is around 50 ◦C, see Figure 4.3. Smith and Wilson[545] give an equation for the decrease of life with temperature at low temperatures, that is inthe range from 50 ◦C to −10 ◦C. In this temperature domain, according to Smith and Wilson,the grease life at can be written as:

log10 L = −4700

T+ 20, (4.1)

where T is the temperature in Kelvin. This equation does not contain the bearing speed andsize and is therefore not very practical. However, Booser and Khonsari [96] used the tests fromSmith and Wilson [545] to derive an equation relating the base oil viscosity to grease life atlower temperatures (below 40 ◦C):

L = L40 ×(

η

η40

)2

, (4.2)

where L40 is a reference life at a temperature of 40 ◦C.

4.3.2 Extreme Low Temperature

In general, temperatures of about −40 ◦C and −20 ◦C are regarded as extreme low andlow temperatures respectively. At low temperatures a low viscosity base oil and lithium soapthickener with low stiffness could be used to avoid a high starting torque [13].

Lindenkamp and Kleinlein [366] also recommend a low base oil viscosity (ν < 25 cStat 40 ◦C). They claim that during start-up, the torque is determined by an apparent greaseviscosity at shear rates between 102 and 105 s−1 (depending on the bearing speed), whichshould therefore be low. In addition, they claim that the base oil pour point does not have agreat effect. Similar results are reported by Ewald et al. [190]. Synthetic oil based grease isrecommended for the possibility of choosing a low viscosity and because it tends to have alow viscosity index VI [410].

Wikstrom and Hoglund [611] recommend a high viscosity PAO (poly alpha olefins). Theyargue that a low viscosity base oil may reduce the start-up friction (Wikstrom and Hoglund[612]) but may not separate the surfaces well enough when the temperature rises.

4.3.3 Extreme High Temperature

It is recommended to use synthetic oils since these show a lower evaporation and oxidation rate.Moreover they have a high viscosity index. High temperature greases are typically polyurea,fluorosilicone and PFPE, see Chapter 3 or Sharma et al. [525]. At high temperatures oxidationwill be the rate determining factor in the grease aging process. This will be described later inChapter 8.

4.4 Grease Life as a Function of Temperature in the Green Zone

Extensive testing by the industry and to some extent by academia has resulted in a wide varietyof models. Usually, grease life is specified at a certain temperature and it is generally accepted


that the grease life for a ‘good quality’ lithium soap grease is reduced by a factor of 2 every15 ◦C, so

L = L Ref × 0.5(

T −TRe f15

), (4.3)

or

L

L Ref= exp

[TRef − T

15ln 2

], (4.4)

where L Ref is the life at temperature T = TRef , usually taken as TRef = 70 ◦C. This model isapplied in reference [4] for relubrication intervals for all bearing types and for grease life indeep groove ball bearings. Others, e.g. [454], [454] apply it to relubrication intervals but notto grease life for deep groove ball bearings. In [454], temperature and speed are connected(see e.g. Eq. 4.14).

Urea greases generally have better high temperature performance. However, according toKawamura et al. [317], the life reduction rate is larger: the life of urea greases is reduced by afactor of 2 every 10 ◦C:

L

L Ref= exp

[TRef − T

10ln 2

], (4.5)

which means a factor of 2.8 every 15 ◦C.Ito et al. [293] showed that the base oil type is also important here. They executed an

extensive grease life test programme for small deep groove ball bearings and urea greasesat temperatures exceeding 100 ◦C and showed that this factor again reduces significantly byusing, for example, silicone oils, as illustrated in Figure 4.4.

The Gesellshaft fur Tribologie (GfT [222]) recommends a factor of 2 for every 10–15 ◦C.

4.5 SKF Relubrication and Grease Life

The SKF grease life model is relatively simple and therefore easy and convenient to use.The relationship between life and the product of bearing speed and mean diameter for aconstant load can be plotted on a log-linear scale as a straight line, as shown in Figure 4.5.For the calculation of life/relubrication intervals of bearings other than radial ball bearings, acorrection to the product of mean diameter and speed is made through a bearing factor, b f .Radial ball bearings are the easiest bearings to lubricate with a grease. Other bearing typeswill give a shorter life (b f > 1). The bearing factors are listed in Table 4.1.

Figure 4.5 shows the relubrication intervals for three load levels assuming a smooth transitionbetween the lines. However, for loads lower than C/P=15, a constant grease life is assumed.This means that the model has incorporated a safety margin here. Obviously, this only appliesdown to loads higher than the minimum load on a rolling bearing, which is around C/P=50. Itshould be noted that the length of the lines indicate the domain in which the model is reliable.The model cannot be used for ultra-low and high speeds. Moreover, it is recommended not tohave intervals over 30 000 hours.


10 00010 000

10 000

10000

10000

10000

1000

100180160140120100

100000

3000

3000

3000

3000

3000

Speed : 3000, 10 000 r/minLoad (P/C) : 0.014

Urea-synthetic oil

Urea-mineral oil

Lithium-synthetic oil Lithium-

silicone oilLithium-mineral oil

Gre

ase

life

[ h

]

Temperature [˚C]

Figure 4.4 Effect of temperature on grease life (from Ito et al. [293]).

Example

A 22205E spherical roller bearing operating at a speed of 5000 rev/min at a temperature of100 ◦C under a pure radial load P = 6.12 kN. The bore and outside diameter of this bearingare 25 and 52 mm respectively, so the mean diameter dm = 38.5 mm. The bearing factorb f = 2, so A = b f × n × dm = 385 000. The dynamic capacity of the bearing is C = 49 kN, soC/P = 8. With these numbers, Figure 4.5 gives a relubrication interval (at 70 ◦C) of 1700hours. Since the bearing is running at 100 ◦C, the relubrication interval should be reduced bya factor of 4 giving a relubrication interval of 425 hours.

Based on Figure 4.5, Huiskamp [280] developed a life model for deep groove ball bearings,including the quality of the lubricating grease. This model is shown in Figure 4.6. Here, greaselife is plotted as a function of n × dm , temperature and grease properties. The grease propertiesare reflected in the ‘Grease Performance Factor’ (GPF). The GPF changes the scale of thetemperature, leading to longer lives for higher values of GPF. The GPF is not an inherentgrease property. It may be a function of speed and temperature again. Moreover, as mentionedpreviously, in the case that the bearing is running outside the green zone in the traffic lightplot, the performance deteriorates. This also applies to speed. All lubricating greases have amaximum speed limit. For some greases, already at n × dm >500 000, the life may be lowerthan predicted by this plot.


Table 4.1 Bearing factors and recommended limits for speed factor A [4].

Recommended limitsfor speed factor A for load ratio

Bearing type*

Bearingfactor

b f C/P ≥ 15 C/P ≈ 8 C/P ≈ 4

Ball bearings radial 1 500 000 400 000 300 000Deep groove ball bearing 1 500 000 400 000 300 000Angular contact ball bearing 1 500 000 400 000 300 000Self aligning ball bearings 1 500 000 400 000 300 000CARB toroidal roller bearing 2 350 000 200 000 100 000Cylindrical roller bearings, nonlocating 1.5 450 000 300 000 150 000Cylindrical roller bearings, locating, 2 300 000 200 000 100 000

without external thrust load, orwith small but alternating axial load

Cylindrical roller bearings locating with 4 200 000 120 000 60 000a constantly acting small axial load

Cylindrical roller thrust bearings 10 100 000 60 000 30 000Needle roller bearings 3 350 000Needle roller thrust bearings 10 100 000Spherical roller bearings Fa/Fr<e 2 350 000 200 000 100 000

and dm <800, series 222, 238, 239Spherical roller bearings Fa/Fr<e 2 250 000 150 000 80 000

and dm <800, series 213,223, 230, 231, 232, 240, 248, 249

Spherical roller bearings with 2combined load Fa/Fr<e

Spherical roller bearings with axial load 6 150 000 oil recomm. oil recomm.or combined load. Fa/Fr>e

Spherical roller thrust bearings, 4 200 000 120 000 60 000rotating shaft washer

Taper roller bearings 2 350 000 300 000 200 000Thrust ball bearings 2 200 000 150 000 100 000

∗Only applies to standard design

The impact of temperature in this plot is reflected in the straight line in the semi-log plot inFigure 4.6. The grease aging follows the rule of a factor of 2 per 15 ◦C temperature rise downto a certain temperature, after which it should be taken constant.

Figure 4.6 applies for shielded bearings with inner-ring rotation. With better seals, such as2RS1, 2RSL, 2RZ, and so on, but also with ceramic components (hybrid bearings), grease lifeis extended.

4.6 Comparison Grease Life/Relubrication Models

There are many publications on predictive models/methods for grease life and relubricationintervals, and most originate from the bearing industry. To make a comparison is very difficult,primarily because all models are empirical where the underlying test data is usually not


0100

500

1000

5000

Rel

ubric

atio

n in

terv

al [h

]

10 000

50 000

100 000

200 000 400 000

bf n dm rev mm/min

600 000 800 000

C/P ≈ 4

C/P ≈ 8

C/P ≥ 15

Figure 4.5 Relubrication intervals in hours as a function of the speed factor A (A = b f × n × dm

[mm/min]), for 70 ◦C operating temperature [4]. The bearing factors b f are listed in Table 4.1. Courtesyof SKF.

published. The quality of the models depends on the number and variety of tests, whichshould be huge to derive an accurate model.1 After all, there are many grease types, bearingtypes/variants and bearing sizes. Moreover, the test domain for the operating conditions can bevery wide. The type of test rigs and the number of tests that have been used for the developmentof the models is no doubt different for each model. It is therefore inevitable that the modelswill be different.

Other difficulties in comparing the models are that often only graphs are presented withoutthe underlying equations and that the reliability of the various models (L01, L10, L50 etc.)is different. In this section, it is assumed that grease life can be described with a Weibulldistribution with β = 2.3, which implies that L10 = 2.7L01 and L50 = 6L01 (see Section 12.3,

1 Booser from General Electric mentions that he used 2000 grease life tests [91] to derive his model. This was in1974. The databases with test data have obviously grown since then.


100 000

10 000

1000

L 10

[h]

700 000

600 000

500 000

400 000

300 000

200 000

≤ 20 000n × dm = 100 000

100

GPF = 1

GPF = 2

GPF = 4

35

50

65

40

55

70

45

60

75

50

65

80

55

70

85

60

75

90

65

80

95

70

85

100

75

90

105

80

95

110

85

100

115

90

105

120

95

110

125

100

115

130

105

120

135

110

125

140

115

130

145

120

135

150

n = rotational speed [r/min]dm = mean diameter = 0.5 × (d + D) [mm]

Operating temperature [°C],scale depending on Grease Performance Factor

Figure 4.6 Grease life in lubricated-for-life radial ball bearings running at low loads (C/P ≥ 15). L10

as a function of n × dm , temperature and grease type (from Huiskamp [280]).

p. 264). Figure 4.8 shows a comparison of some models for low load (C/P > 20): [4], Booser[91], Kremer [342], Naka [443] and GfT (Gesellshaft fur Tribologie ) [222] (with a low andhigh band). Grease life is usually plotted as a function of n × dm . Kremer’s model describesgrease life as a function of n × √

d, see Eq. 4.7. In Figure 4.8 this model is plotted for a 6206bearing. The Naka grease life model is expressed in n and the limiting speed. Naka’s model isplotted for a bearing with a speed limit of 15 000 r/min and dm = 33.5 mm. Booser’s model fordeep groove ball bearings (original form in [91] but updated in [323, 324]) is again expressedin n × dm :

log10 L = −2.6 + 2450

T + 273− 9.6 × 10−7 × k f × n × dm . (4.6)

The unit for T is ◦C and the factor k f is a bearing factor adopted from the GfT model (seeFigure 4.7), where k f = 1 for deep groove ball bearings.

The GfT published their model as a log-log plot, as shown in Figure 4.7. To make acomparison possible, this has been translated into the semi-log plot of Figure 4.8. Figure 4.8shows that the Booser and GfT models are quite similar, except for in the low speed regionwhere the GfT and Kremer models predict a much longer life. The GfT model in the semi-log plot clearly shows that the more-or-less linear behaviour is changing at very low speeds,leading to longer lives. The other models [4, 91, 454] do not show this behaviour. Instead,


100 000

50 000

30 000

20 000

10 000

5000

3000

2000

1000

500

300 200

20 30 50 70 100 150 200 300 500 700 1000 1500 2000

Bearing k

Deep groove ball bearing

Angular contact ball bearing

Cylindrical roller bearing

Tapered roller bearing

Spherical roller bearing

Self aligning ball bearing

1.0

1.0

3.3

4.0

8.0

1.5

L 10 li

fe [

h]

k n d 10 [min mm]–3 –1f m

Figure 4.7 Lubrication intervals according to the German Tribology Society, GfT [222]) and based onL10. The diagram applies to NLGI 2-3 lithium soap greases, operating (outer-ring) temperatures of 70 ◦Cand load P/C < 0.1. For a more detailed list of bearing factors k f for this model, the reader is referredto GfT [222] or Mang and Dresel [397]. Reproduced from Gesellschaft fur Tribologie e.v, 2006 C© GFT.

100 000

10 000

1000

L 1 [

oper

atin

g ho

urs]

1000 100 000 200 000 300 000

[4]

GfTh

Booser

GfTi

Naka et al. WideTemperaturegrease

Kremer (d = 20)

Kremer (d = 30)

400 000n * dm

500 000 600 000 700 000 800 000

Figure 4.8 Various relubrication models for bearings running under low load and at a temperature of70 ◦C: [4] (C/P>15), Booser [91], Kremer [342], Naka [443] (C/P=15), GfT [222](C/P>10) (with a lowand high band). To make a comparison possible it is assumed that L10 = 2.7L01 and L50 = 6L01. TheKremer model is plotted for a 6204 and a 6206 bearing. The Naka model is plotted for a bearing with aspeed limit of 15 000 rpm and dm = 33.5 mm. Note that the models were developed for different greasetypes and that the absolute values can therefore not be compared.


these models show the same behaviour throughout the speed-domain in which they may beapplied. In Figure 4.5, the borders of this domain are indicated by dots. The GfT model ismore conservative at the lower speed end of the plot whereas [4] is more conservative at thehigher end of the plot. GfT claims that its model is valid in a wider speed range (up to 2million n × dm) where grease life is predicted to be very short (figure 4.7). The Naka modelshows behaviour similar to the model from reference [4] (for the specific case plotted here).The absolute values depend strongly on the chosen speed limit. As an example, increasing thespeed limit from 15 000 to only 20 000, keeping the mean diameter constant, causes the linesto cross at n × dm = 550 000.

4.7 Very Low and High Speeds

4.7.1 Speed Ratings and Speed Factors

The maximum speed of bearings with grease lubrication is usually determined by heat gen-erated in the bearing, which can at some point no longer be dissipated from the bearing toits surroundings. The reference is set at a temperature increase of 50 ◦C, usually on top ofthe ambient temperature of 20 ◦C leading to a temperature of 70 ◦C. These temperatures aregiven by ISO 15312:2003. This maximum speed in rolling bearings is called the ‘referencespeed’. Catalogue [4] specifies the reference speed for a regular grease with a lithium thickenerand mineral base oil with viscosity 100 < ν < 200 cSt at 40 ◦C and with 30% filling. Thesenumbers can be found in Table 4.1.

If higher viscosity base oils are used, friction and therefore heat generation will be higher,leading to a correction of the permissible speed. The same applies to load. The values inthe [4], according to ISO 15312 are given for P = 0.05C0. At lower loads, a correctionfactor for load also needs to be applied. However, sometimes the minimum load is evenlower [4].

Bearing manufacturers also specify a so-called ‘limiting speed’. The speed limit is deter-mined by criteria that include the form stability or strength of the cage, lubrication of cageguiding surfaces, centrifugal and gyratory forces acting on the rolling elements and otherspeed-limiting factors. The maximum speed at which a bearing can be run safely is deter-mined by the minimums of speed rating and limiting speed.

4.7.2 High Speed

The high speed regime for a grease lubricated bearing depends on the load and bearing typeas listed in Table 4.1. As an example, for deep groove ball bearings running at low load, thisis n × dm = 500 000. At such high speeds, special greases or modified bearing executionsshould be used to achieve a grease life/relubrication interval as predicted by Figure 4.5, forexample, hybrid bearings [4]. At high speed, four problems should be addressed.

• Friction and heat development should be limited.• The lubricant film/layer thickness should not be reduced too much by the centrifugal forces.• Grease lumps should not easily fall back into the track.• The lubricant should be able to withstand high loads due to centrifugal forces.


High speed grease lubrication can be mostly found in smaller bearings, mainly spindlebearings. Bearings with a bore diameter of around 3 mm (bearings for dental spindles) maybe run for long times at n × dm = 1.9 × 106 [442]. For larger bearings (angular contact ballbearings, 20 mm bore) [442] could reach a grease of life of 15 000 hours at n × dm =1.04 × 106 but only a few hours at n × dm = 1.8 × 106 at a temperature of 70 ◦C, which theydefine as the limit for grease lubrication.

However, for bearings with a bore diameter larger than 10 mm, grease lubrication is generallylimited to n dm = 1.8 × 106 [442].

Consistency and Initial Filling

During the churning phase, the heat development is mainly determined by the consistency ofthe grease. Soft grease easily flows back whereas a stiffer grease stays outside the track assoon as it has been ‘pushed’ there. This property of grease is called ‘channeling’. A grease thatstays away from the moving elements in a bearing has good channelling characteristics. Poorchannelling characteristics will result in flow of grease into the track, leading to increasedfriction and heat development.

This was confirmed by the tests from Accinelli [19], who suggests a consistency of at leastNLGI 2 and by Kawamura [316], who suggests a grease with a high resistance to shearing.

With open angular contact ball bearings, Naka [442] found a linear relation between greaselife and initial grease filling volume up to 100% filling of the free internal space if ‘abnormalheat generation did not occur in the early phase’.

Grease Life Models

Most models are limited to moderate speeds. The grease life model developed by theGesellschaft fur Tribologie [222] (Figure 4.7) covers quite a wide speed domain. Here thespeeds are plotted up to n × dm = 2 000 000. This plot is an extension of the early work ofKremer [342] (see also [333]), who published the following grease life model:

L10 = 20

(14 × 106

n√

d− 4d

), (4.7)

derived for bearings with a bore diameter d between 20 and 65 mm. At lower speeds, the firstterm dominates, giving a more-or-less straight line on a log-log plot of L10 versus n × dm . Athigher speeds, the second term dominates causing the line to deviate from this, leading to adeterioration in performance at high speed, see Figure 4.7.

Base Oil Viscosity

The GfT developed a plot, Figure 4.9, showing the limiting speed, again in terms of n × dm , forgrease lubricated bearings as a function of the base oil viscosity, showing that a low viscositybase oil would be favourable for high speed. Also Naka et al. [442], who tested high speedangular contact ball bearings, concluded that a low viscosity base oil is preferable.


Rot

atio

nal

spee

d n

× d

m [

rev

× m

in–1

× m

m]

Base oil viscosity [mm²/s at 40 ˚C]

Bearing temperature: 50 to 70 ˚C

10

9

8

7

6

5

4

3

2

10

0 50 100 150 200 250 300 350 400 450 500

220 320 460

Figure 4.9 Limiting characteristic speeds and base oil viscosity at 40 ◦C for grease lubricated deepgroove ball bearings running between 50 and 70 ◦C. Reproduced from Gesellschaft fur Tribologie e.v,2006 C© GFT.

According to Accinelli [19], part of the problem is described by the challenge of keepingadequate amounts of lubricant against the action of centrifugal force in critical areas. Theconclusions that are drawn from his tests contradict the GfT diagram, Figure 4.9. He concludesthat high speed greases should have a high viscosity to resist possible unbalance in high loadsdue to the high centrifugal forces and low tackiness to reduce heat generation.

Surface Tension and Wetting

Farcas and Gafitanu [192] developed a model that predicts the speed at which oil dropletsare detached from the bearing surfaces due to high centrifugal forces. They assume that thelubricant is spread over the entire inner ring raceway up to a speed, nopt , where droplets of oilwill be detached by centrifugal forces:

nopt = 24.12

√σ (1 + cos αd )

ρ2rir h1.5d

√dd

, (4.8)

where σ is the surface tension. The parameters αd , hd and dd are determined from themeasurement of a droplet of oil on a stationary plate, where dd is the wetting diameter ofthe droplet, hd is the height of the droplet and αd is the contact angle. rir is the inner-ringraceway radius. The unit for nopt is rev/min. Note that this equation is a static force balanceand therefore does not contain the base oil viscosity and that

nopt ∝ 1√2rir

(4.9)


for a given lubricant. This indicates that, according to this formula, not n × dm but n × √dm

(centrifugal acceleration) determines the maximum speed. It should be noted that this work isnot validated. Clearly much more work is needed in this area.

Bleeding Properties

Bleeding properties are important at high speed [202]. It is likely that a high bleeding rate maybe favourable for high speed grease operation [316, 442].

Bearing Design

The critical component in a bearing at high speed is the cage, which should be strong enoughto withstand the high centrifugal forces and light enough to limit these forces. Naka et al.[442] showed through tests that an outer ring guided cage will contribute to longer greaselife at high speed. Scarlett [518] specifically mentions that inner-ring centred cages should beavoided for high speed grease operation and that machined cages are preferred over pressedcages. By using ceramic rolling elements the centrifugal forces will be reduced.

Impact of Load at High Speed

Naka et al. [442] tested open angular contact ball bearings at very high speed and found thatthe effect of load is more pronounced at high speed (n × dm = 1.8 × 106) than at moderatespeed and found a linear relation:

L ∝ P. (4.10)

4.7.3 Very Low Speeds

Bearings operating under very low speeds and very low load call for a grease with lowconsistency. Bearings operating under very low speeds and very high load call for a greasewith high viscosity and if possible with very good EP characteristics [4].

4.8 Large Rolling Bearings

In the model from Figures 4.5, 4.6 and 4.7 grease life is given as a function of n × dm . Thismeans that bearing size has the same weight as speed. However, in the case of large bearings,grease relubrication intervals are sometimes not given by grease life but by the need to removecontaminants from the bearing raceways (see Section 4.2).

The lubrication mechanisms in large bearings may well be different than in small bearings.Differences between small and large bearings that are relevant for grease lubrication are thecontact size, the larger volume for churning, the thicker lubricant layers, the larger greasereservoirs and the different roughness of the functional surfaces.

The contact size has an impact on the Deborah number: the time that the lubricant is shearedgrows with increasing contact size and therefore its rheology. The larger free volume will


generate a different flow type than in the case of small free volumes, which has an impact onthe mechanical work on the grease and side-flow. The layers of grease/oil on the functionalsurfaces will be thicker. This will have an impact on the oxidation rate, ‘thin film flow’ andbulk flow of the grease. Booser [90] recommends NLGI grade 3 greases for larger size bearingsto maintain a large free height against the force of gravitation to prevent flow of higher stacksof grease in the bearing. The impact of a difference in roughness combined with a differencein Hertzian contact size is not obvious. The flattening of roughness is given by its relativecharacteristic wavelength and the lubricant properties. It goes beyond the scope of this bookto described this. The reader is referred to Masen et al. [404].

It is recommended to apply an interactive procedure for relubrication with initially relubri-cating more frequently and to adhere strictly to the regreasing quantities. Also, the appearanceof the used grease and the degree of contamination due to particles and water should bechecked, looking for damage, wear and leaks [4].

4.9 Effect of Load

Bearing load shortens grease life more than would be expected based on EHL film thicknesstheory. The bearing manufacturers have developed various models for this, which are all basedon extensive testing. Some of these models will be described in this section.

4.9.1 Varying Load

Often, bearing manufacturers give penalty factors in their catalogues for specific loads withoutgiving formulae (for instance [4] and [222]). In their catalogues it is assumed that grease lifeis constant at low loads up to a certain point which is for [4] C/P = 15 and for [222] C/P =10. At higher loads grease life/relubrication intervals are calculated according to:

L = k · L ′, (4.11)

with L ′ as the reference grease life, that is, the grease life at low loads. The grease life reductionfactors k are listed in Table 4.2, which are called here k ′,k ′, and so on to distinguish the variousmodels.

In Kawamura [317] and Ito [293], test data can also be found, supporting the choices of thevalues for the life reduction factors. Kawamura et al. [317] tested sealed 6204 deep grooveball bearings lubricated with urea greases (10 000 rpm, 150 ◦C) with different loads (67, 294

Table 4.2 Data that is used to compile the impact of load, Eq. 4.15.

GfT [222] [4] Kawamura [317] Ito [293]

P/C k′ P/C k′ P/C k′ ′ P/C k′ ′

0.15–0.1 1–0.7 0.067 1 0.0157 1 0.014 10.15–0.25 0.4–0.7 0.125 0.5 0.0441 0.46 0.08 0.5040.25–0.35 0.1–0.4 0.25 0.2 0.0804 0.28 0.1 0.338


and 670 N). The test data is given in Table 4.2 as life reduction factors according to Eq. 4.11.Kawamura et al. fitted the test data, from which they derived a linear relation between thelogarithm of grease life and load:

log10 L50 = −8.36

(P

C

)+ 3.34. (4.12)

It should be noted here that only three tests have been done up to a relatively low load level ofF = 0.08 C (C/P = 12.5). The test data are shown in Figure 4.10a.

Ito et al. [293] conducted a very large number of tests to a somewhat higher load level(P = 0.15 C , C/P = 6.7) and saw that this linear relation between log10 L50 and P

C was onlyvalid for relatively low loads. They found a relation of the type

log10 L50 = C1 + C2

(P

C

)2

. (4.13)

These equations later evolved into equations such as

log10 L50 = 6.12 − 1.4n

nmax−(

0.018 − 0.006n

nmax

)T

−(

0.21Tn

nmax+ 0.03T + 20.5

)(P

C

)2

, (4.14)

which is valid in a temperature range of 70 ≤ T ≤ 130 ◦C and for wide temperature rangegrease, where

• n: speed (rev/min)• rev mm/min nmax : limiting speed with grease lubrication (rev/min)• T: operating temperature (◦C).

(See [441]).Eq. 4.14 shows that the impact of load on grease life increases with increasing speed (and

that it is a function of temperature as well). However, the tests reported by Gafitanu et al.[213], also up to levels of P/C = 0.15, show a linear behaviour similar to Eq. 4.12 again. Dueto the complexity of Eq. 4.14, the life reduction factors k ′′ in Table 4.2 are based on the testsfrom Ito only.

The data in Table 4.2 can now be used to make a compilation of the data given by some ofthe major bearing companies. The table shows that the data from GfT [222] and [4] is in therange 0.07<P/C < 0.35. For the lower end of the load spectrum, where loads are really low,it is good practise not to take any risk and assume that grease life will not grow with decreasing


Load ratio F × 0.05 P/C

L g

reas

e li

fe [

h]

10 000

1000

1000 2 4 6 8 10

log L = – 8.36F + 3.34

10 000

1000

100

Grease : Lithium-synthetic oil

Gre

ase

life

[h]

Load ratio P/C0 0.05 0.1

:120 ˚C:140 ˚C:160 ˚C:120 ˚C:140 ˚C:160 ˚C

}}

3000 r/min

10 000 r/min

Urea-synthetical

Urea-mineral oil

Lithium-silicone oil

Lithium-mineral oil

Lithium-synthetic oil

Temperature : 140 ˚CSpeed : 10 000 rpm

Gre

ase

life

[h]

Load ratio P/C

10 000

1000

100

100 0.05 0.1

(a) Urea greases. 10 000 rpm, 150 °C . (b) Lithium-synthetic oil.

(c) Other greases than lithium-synthetic oil.

Figure 4.10 Some examples showing L50 grease life versus load. (a) Reproduced with permission fromKawamura, Minami and Hirata, 2001 C© Taylor and Francis Group. (b) and (c) Reproduced from Ito,Koizumi and Naka, 1995 C© International Tribology Conference.

load [4]. By neglecting this safety margin (which is obviously not advised) the data from Itoand Kawamura can be used. Scaling of the data results in Figure 4.11, where the individualpoints are plotted and are fitted with an exponential equation:

L = L P/C=0.1 × 0.12

(P

C

)−0.9

. (4.15)


7

6

5

4

3

Life

red

uctio

n fa

ctor

2

1

00 0.05 0.1 0.15 0.2

P/C

0.25 0.3 0.35

Figure 4.11 Effect of load on grease life. The data for this plot is given in Table 4.2. The load impactfactor k is normalized on P/C = 0.1. The drawn line is a best fit according to Eq. 4.15.

Note that the reference load in this equation, that is the load where k = 1, is at P/C = 0.1.For lower loads, a longer grease life is obtained and for higher loads, the grease life is reduced.

At loads higher than P/C = 0.3, bearing life is likely to be shorter than grease life, so thereis no need to extrapolate the curve. Grease life at very low load may again be irrelevant sincehere skidding may occur. Again, for application engineers it is advised not to use this equationbut follow the rules that are given by the bearing manufacturer.

Figure 4.11 suggests infinite grease life for very low loads. This is obviously not the case.Bearings running at loads lower than the minimum load will fail due to skidding, which willcause excessive heat development.

4.9.2 Direction of Load

Kleinlein [333] analysed FE9 tests and found that grease life of radially loaded bearingswas about a factor of 2 longer than that of axially loaded bearings. In [13] a factor of 1.5 issuggested for this. In [455], penalty factors are given in the case that the axial-radial load ratioexceeds a value of 0.3, so Fa > 0.3Fr . According to [455], this effect is most pronouncedfor tapered and self-aligning roller bearings, somewhat less for deep groove ball bearings andonly small for angular contact ball bearings.

4.9.3 Very Heavy Loads

The relubrication intervals according to Figure 4.5 should be reduced for bearings operatingat a speed factor A > 20, 000 and subjected to a load ratio C/P < 4. Under such conditions,continuous relubrication is recommended [4].


4.10 Effect of Outer-Ring Rotation

Outer-ring rotation causes very severe conditions for the grease in the bearing. The greaseon the shields or covers is subjected to centrifugal forces exceeding the yield stress, resultingin the grease flowing continuously into the bearing; causing churning, heat development andhigh temperatures. Moreover, grease on the bearing outer-ring shoulders or seals will showaccelerated oil bleeding. In the case of outer-ring rotation, the base oil/grease is easily lost andgood sealing is therefore a prerequisite.

Scarlett [518] advises reducing the maximum speed by 50% for outer-ring rotation.Generally, a lower filling rate (only 20% in case of outer-ring rotation [13]) and a stiff grease

is recommended to prevent bulk flow. The grease should also show excellent shear stability toprevent too much softening under shear. The bulk flow/churning will cause heat developmentand in order to reduce this, a low ’grease viscosity’ is recommended, which generally means alow base oil viscosity. These requirements on the grease are quite similar to those for extremelyhigh speed inner-ring rotation.

Gafitanu et al. [213] measured the impact of outer-ring rotation and found that grease lifeis determined by the rotational speed of the cage. At the same rotational speed, outer-ringrotation causes a higher cage speed than in the case of inner-ring rotation. This was proved bytests with inner and outer-ring rotation with identical cage speeds where they measured equalgrease life.

This was also found by Kawamura et al. [317] who corrected n × dm with a factor K ,defined as:

K = Corresponding inner-ring rotational speed to the same cage speed of outer-ring rotation

outer-ring rotational speed.

(4.16)

According to [4] the speed factor n × dm needs to be calculated using the bearing outsidediameter rather than the mean diameter. This is an engineering approach to Eq. 4.16. Forhigher outer-ring speeds (i.e. higher than 40% of the reference speed), a grease with a reducedbleeding tendency is recommended.

4.11 Cage Material

The cage design and cage material will have an impact on grease life. Ito et al. [293] showedthat grease life is extended with a factor of 2 to 3 if a pressed steel cage is replaced by apolymer ‘crown’ type of cage. They ascribed this to wear particles which will cause acceleratedoxidation of the grease. The impact of brass material on grease life is quite complex. Brassparticles may act as catalysts for oxidation and therefore reduce grease life. So, for (very) hightemperature operation brass cages should be avoided. On the other hand, copper may act as asolid lubricant reducing the heat in the contacts, leading to a lower bearing temperature andtherefore extending life again. This was demonstrated by Komatsuzaki [336] in high speedtests, showing an increase in grease life if no more than 0.5 mass % copper particles is addedto grease (see Figure 4.12).


Content of foreign body, mass [%]

Ave

rage

gre

ase

life

[h]

Copper

Iron

Dust

Masuda type :

ASTM :

00

200

400

600

800

1 2 3 4 5

Figure 4.12 Impact of foreign bodies on grease life. Reproduced with permission from Komatsuzaki,2002 C© Allerton Press, Inc.

4.12 Bearing Type

4.12.1 Roller Bearings

Roller bearings require a softer grease than ball bearings (on a horizontal shaft), [410]. Angularcontact ball bearings pump grease through the bearing from the small inner ring diameter side(‘low side’) to the larger inner ring diameter side (‘high side’). In order to prevent this, ideallya stiff grease is preferred on the ‘low side’ and a softer grease on the ‘high side’. Vertical shaftapplications require a stiffer grease to prevent grease falling into the bearing.

Naka et al. [443] tested medium size (inner-ring bore 25 mm) deep groove ball bearings,cylindrical roller bearings and tapered roller bearings with polyurea greases at 10 000 and6800 rev/min at 150 ◦C and found large differences in life. Figure 4.13 shows the results. Thedifference between cylindrical roller bearings and deep groove ball bearings is more than afactor 4! The difference between tapered and cylindrical roller bearings is less pronounced. Thetests from [377, 378] confirm the bearing factor b f = 1.5 − 2 for cylindrical roller bearingsas used in [4].

Like Kuhl [347], Naka recommends for cylindrical and tapered roller bearings, greases withhigher bleeding properties and high base oil viscosity in contrast to deep groove ball bearings.In their cylindrical roller bearing tests, lithium-complex grease had a much longer life thanurea based greases. Tapered roller bearings were failing in the flange contacts, but adding anabrasion preventing agent and EP additives to the lithium soap helped increase grease life. Asa guideline, the impact of bearing type on grease life is reflected in the ‘bearing factors’, givenin Table 4.1. These factors are used to increase n × dm , which decreases grease life and canbe used to compare the expected grease life to that of deep groove ball bearings.

4.12.2 Hybrid Bearings

Due to the lower adhesion between steel and ceramic materials (leading to lower wear ratesand friction levels), the lower specific weight and the lower ‘welding loads’, grease is able to


1 2 3Grease type

(a) Deep groove ball bearings and cylindrical roller bearings, 10 000 rev/min, 150 °C.

1 2 3 4 5Grease type

Cylindrical roller bearings

Tapered roller bearings

Cylindrical roller bearings

Deep groove ball bearings

0

100

200

300

400

Gre

ase

life

(hou

rs)

500

600

700

0

50

100

150

Gre

ase

life

(hou

rs)

200

250

(b) Cylindrical and tapered roller bearings, 6800 rev/min, 150 °C.

Figure 4.13 Grease life test results of various bearing types (grease types in both figures are different).Redrawn from Naka et al., 2000, Proceedings of the International Tribology Conference.

maintain sufficiently protecting for longer times compared to steel bearings. This is schemat-ically depicted in Figure 4.14.

4.13 Temperature and Bearing Material

The maximum temperature is usually determined from the dropping point of the grease (seeSection 4.3, p. 72).


Figure 4.14 Grease life for hybrid bearings, compared to standard bearings, courtesy of SKF [14].

It should be noted though that the bearing itself also has a maximum operating temperaturefor dimensional stability. Dimensional change effects are due to [544]:

• Thermally activated microstructural reactions in the microstructure, resulting in a volumechange (for example, retained austenite transformation (volume increase), different car-bide transformation reactions (volume decrease), annihilation of crystal defects (volumedecrease).

• In the presence of a static (hoop) stress, these solid state reactions give rise to ‘transformationinduced plasticity’ (TRIP) effects, which lead to a stress driven dimensional change duringthe progress of the reaction in question.

Stabilization treatment:

Dim

ensi

onal

cha

nge

[μm

/100

mm

]

Time (hours)

100 00010 0001000100 10 1

100

80

60

40

20

0

-20

S0

SN

S1

Figure 4.15 Influence of selected stability class on the development of dimensional change for bearingrings, exposed to normal interference fit at a high operating temperature. Experimental data points forbearing rings heat treated to two stability classes, SN and S0, where the testing temperature well exceedsthe recommended operating temperature range for the standard stability class, compared to calculatedcurves from the dimensional stability model for SN, S0 and S1 stability classes. Reproduced fromSlycke and Fajers, 2002 C© ASM International. Reprinted with permission of ASM International. Allrights reserved. www.asminternational.org.


• In the presence of a static (hoop) stress, a low-temperature creep effect is also operational(this effect often dominates in cases where the operating temperature is too low to triggersolid state reactions) – dimensional change (e.g. inner-ring growth) is an important problem,which limits bearing life. When an inner-ring comes loose from its shaft (relaxation ofthe interference fit), fretting between bore and shaft may trigger cracks (corrosion fatigueassisted) that lead to ring through-cracking, and so on. Therefore, the ground rule is to alwayschoose a high enough stability class to ensure that the interference remains throughout therolling contact fatigue life. The reduced fatigue resistance due to the extra stabilization is inmost cases not a big problem.

4.14 Grease Fill

Before filling the bearing it is preferable to remove the preservative from the outside diametersurface and the bore of the bearing. The entire bearing should be cleaned in case the greaseis incompatible with the preservative or if a very thick preservative is used (sometimes forlarge bearings). It is also recommended to fully clean the bearing before greasing, in casethe bearing is used at extreme high or low temperatures. In these cases the preservative maybecome too viscous or may oxidize.

In the case that a bearing housing is used, it is advised to start with a bearing that is fullypacked with grease, while the free space in the housing should be partly filled with grease,that is 40% when the replenishment is made from the side of the bearing and only 20% whenreplenishment is made through the annular groove and lubrication holes (such as in sphericalroller bearings [4]). SKF recommends replenishment quantities of:

G p = 0.005D × B, (4.17)

if replenishment is made from the side of the bearing and

G p = 0.002D × B, (4.18)

if replenishment is made through the centre of the bearing. Here, G p is the grease quantity ingrammes, D is the bearing outside diameter in mm and B is the total bearing width in mm(height for thrust bearings).

The German Tribology Society, GfT [222], recommends choosing the quantity of grease forrelubrication, depending on the relubrication frequency: G p = 0.002D × B, G p = 0.003D ×B or G p = 0.004D × B for weekly, monthly or yearly frequencies respectively and Ga =0.01D × B in case the bearing has been standing still for several years.

For sealed/shielded bearings, as a rule of thumb the free space in the bearing should bepacked with 30–50% of the free volume.

In the case of low speeds [410, 518] the bearings may be fully packed with grease. Duringrelubrication, ideally, all grease should be replaced. In the case of bearing housings, it is goodpractice to open the housings after a few relubrications and remove the old grease and packthe bearing and housing with new grease. Excess grease should be able to be expelled fromthe bearing, otherwise excessive churning will take place, causing excess heat and eventualbreakdown of the grease. An oversupply of grease can be just as detrimental as an inadequate


amount [410]. Scarlett also recommends lightly pre-lubricating bearings (especially those withan inner-ring driven cage) with oil when high speeds are expected. In [13], a filling of 30%of the free space is recommended but only 20% for high speed bearings to facilitate greasedistribution during start-up and a full filling for low velocity bearings (n × dm < 50 000).

Calculation of the free space is not straightforward. However GfT worksheet 3 [222], givesa simple approximation for this:

V ≈[

1

4π B

(D2 − d2

)× 10−9 − G

7800

], (4.19)

the unit of V being m3 and

• d = bearing bore diameter [mm]• D = outside bearing diameter [mm]• B = bearing width [mm]• G = bearing mass [kg]

According to [454], for ordinary bearings, sufficient grease must be packed inside thebearing. Inside the housing, 1/2 to 2/3 of the space must be filled in the case that the speed isless than 50% of the limiting speed and 1/3 to 1/2 of the space in the case that the speed ismore than 50 % of the limiting speed.

Gafitanu et al. [213] published test data on sealed ball bearings showing the impact of initialfill on grease life. Their data is reproduced in Figure 4.16. Their test results show that greaselife increases with the increasing volume fraction of grease up to a level of approximately30%. A reasonably good fit to the data reads:

L = c · V 1.7p . (4.20)

At higher volume fractions grease life no longer increases. Data on relatively large sizecylindrical roller bearings (NU320) was published by Komatsuzaki and Uematsu [337] andshowed slightly different behaviour, which was consistent for four different greases:

L = c · V 0.91p . (4.21)

Sahwki and Moktar [526] investigated the impact of grease filling on operating temperatureand friction and concluded that an optimum filling exists but that this optimum is a functionof speed and load. At low loads the optimum grease quantity is less than at high loads.

4.15 Vertical Shaft

For bearings on a vertical shaft, the grease life/relubrication intervals should be halved and goodsealing is required to prevent grease leakage [4]. According to Scarlett [518], the maximumspeed should be reduced by 25% in the case of vertical shaft. In [13], it is recommended tothe use of grease with good adhesive properties of consistency class NLGI 3 to 4.


100

101

102

100

101

102

103

104

Volume fraction (%)

L (M

Rev

s)T = 60−70 °C (Gafitanu et al.)T = 120 (Kleinlein)

Figure 4.16 Impact of filling (%) on grease life. Reproduced from Gafitanu et al. [213]. Data fromKleinlein can be found in [332].

4.16 Vibrations and Shock Loads

It is difficult to quantify the impact of vibration and shock levels on grease life/relubricationintervals, since vibration levels and shock loads are not easy to quantify in daily practice. Highvibrations and shock levels will cause the grease to churn, which has a negative impact ongrease life [4]. According to GfT [222], relubrication intervals should be reduced by factorsgiven in Table 4.3. Buehler [108] mentions a factor of 10 or more for severe vibrations in thecase of high temperature and low loads.

Some level of vibration may also have a beneficial effect. Miettinen [419] has shownthat an external excitation of the bearing will decrease the level of starvation, illustrated inFigure 4.17. He used Acoustic Emission (AE) condition monitoring techniques on greaselubricated ball bearings. Figure 4.17 shows the ‘AE pulse count rate’ versus time. At thebeginning, the vibration level was 1.4 mm/s and the AE signal was approximately 5000pulses/s, which he classifies as ‘normal’. With external excitation the velocity level was raised

Table 4.3 Reduction factors for the effect of shockloads and vibrations, according to GfT [222] .

Moderate 0.7–0.9Strong 0.4–0.7Very strong 0.1–0.4


10 000

Pulses/s

AE

pul

seco

unt r

ate

5000

0

Time 00:00 4 min 00:48

1.4 mm/s 10 mm/s 1.8 mm/s

Figure 4.17 Influence of vibration on the bearing lubrication situation of a deep groove ball bearing.Reproduced from Miettinen, 2000.

to 10 mm/s and a significantly higher AE signal was measured. Surprisingly, the AE leveldecreases after this but came back to the original ‘normal’ level after a couple of minutes.These measurements suggest that the bearing is running in ‘mixed lubrication’ normallyand that some grease is released due to the excitation. This replenishes the running trackand decreases the level of starvation, making the bearing run in full film lubrication fora while.

In the case of shocks, greases with NLGI 1-2 of high base oil viscosity (460–1500 cSt at40 ◦C) could be used [13]. Shocks are said to be absorbed by the thick EHL film which willprevent wear. However, this high viscosity causes a low bleeding rate, so sufficient greasemust be available to wet the surfaces.

Alternatively, EP-greases could be used since they usually show high oil-bleeding Kuhl[347] and EP greases provide longer service life under high load [410].

4.17 Grease Shelf Life/Storage Life

A lubricating grease ages not only when it is mechanically worked or is exposed to hightemperatures. It also ages when it is stored in a drum or in a bearing. Obviously, the life of thegrease is very long in such a case. Nevertheless, it is very often considered a serious problem.No fundamental research has been done in this area and recommendations are usually basedon cosmetic changes. An example of this is observed oil separation on top of the grease in agrease drum. However, in general, these amounts are so small compared to the total volume,that this is insignificant. This effect can be minimized by keeping the surface of the greasesmooth and by avoiding temperature fluctuations.

Very often storage guidelines are given, for example by Sumerlin [562], stating that themaximum storage time for Li-greases is 12 months and for calcium complex greases 6 months.

More often, a shelf life of 1 to 2 years is guaranteed, provided that the grease is stored inits original, unopened containers. Sometimes even 5 years is guaranteed (when the grease isstored in a cool and indoor area between 0 and 30 ◦C, not exposed to direct sunlight and keptin its original packing).


Due to the thixotropic behaviour of grease (Section 5.9, p. 128) grease may harden. Veryoften greases are subsequently rejected, which is unfortunate since churning in a bearing, orpumping in a lubrication system, would soften it again to its original state.

A problem that sometimes occurs is a change in the grease due to low humidity in desertclimates. Some greases require some water and this water may evaporate from the grease,which softens it, NLGI [450].

5Lubricating Grease Rheology

The flow properties of lubricating greases are probably the dominant properties for qualifyingthe performance of grease lubricated bearings. The lubricating grease should be attached to theseals, bearing shoulders or cage, forming a lubricant reservoir and providing a sealing action.Therefore, the grease should not flow. However, in the case that lubrication is required, thegrease should easily flow, and therefore be converted into a fluid. Lubricating greases havethese properties: at low shear, they behave like (linear) visco-elastic materials, where the‘storage modulus’ is larger than the ‘loss modulus’ and apparent yield behaviour is visible. Atlarge shear rates, shear thinning occurs and the grease viscosity decreases, ultimately reachingthe base oil viscosity, giving it excellent flow and lubrication properties.

In addition to (bearing) lubrication, the flow properties are also important in lubricationsystems (pipe flow, clogging). The sealing action of grease is obviously determined by thestiffness of the grease, and therefore grease rheology. Common problems such as greaseleakage are related to rheology. Finally, the rheological properties of the grease determines thesuitability of using the grease in vertical shaft applications or environments where vibrationsare likely to occur.

5.1 Visco-Elastic Behaviour

Rheology is the study of the deformation and flow of matter.1 In general, flow is an irre-versible deformation of fluids, as opposed to the reversible, elastic deformation of solids. Thedeformation of fluids is measured by a shear rate with the unit being reciprocal seconds. Theshear rate for a flow in one direction is defined as:

γ = ∂u

∂z, (5.1)

with z the coordinate orthogonal to the velocity u.

1 The term was coined by Prof. E.C. Bingham, Lafayette College, USA, 1920.



Table 5.1 Typical shear rates [63].

Typical rangeSituation of shear rates (s−1) Application

Chewing and swallowing 101 − 102 FoodsMixing and stirring 101 − 103 ManufacturingPipe flow 100 − 103 Pumping blood flowRubbing 104 − 105 Creams to the skinLubrication 103 − 107 Machine elements

In a gap with height h, where the surfaces are moving with a difference in speed �u, andwhere the velocity profile is assumed to be linear, the shear rate can easily be calculated from

γ = �u

h. (5.2)

Table 5.1 gives some examples of typical shear rates and shows that the shear rates involvedin lubrication are extremely high. Giving typical shear rates for grease is not straightforwardthough. Grease travelling through the EHL contact will experience typical shear rates ofγ ≈ 106 s−1 whereas grease located on the bearing shoulders or on the seals will only creep,with shear rates in the order of γ ≈ 10−6 s−1.

To impose a shear rate on a liquid a shear stress is needed. This resistance to shear is theconcept of viscosity, which Newton called ‘lack of slipperiness’ in 1687, and is defined as:

τ = ηγ , (5.3)

with τ the shear stress and η the (dynamic) viscosity with unit Pa · s.Elastic behaviour is described by Hooke’s law (Hooke, 1678):

τ = γ G, (5.4)

with γ the shear and G the shear modulus. A popular method to describe visco-elasticbehaviour is through one-dimensional mechanical models consisting of springs and dashpots.The dashpot models viscous behaviour and the spring models elastic behaviour. As describedin Chapter 2, lubricating grease (but also pressurized oil) shows visco-elastic behaviour.This can be described using combinations of springs and dashpots such as the Maxwelland the Kelvin model as shown in Figure 5.1. To illustrate the difference between the twomodels, the figure also shows the clearly different response in shear to a sudden increasein stress.

The Maxwell model (Figure 5.1a) is constituted by the sum of the displacements of thespring and the dashpot giving

γ = τ

G+ 1

η

∫τdt or γ = τ

G+ τ

η. (5.5)

Lubricating Grease Rheology 101

t (s)

τ (P

a)

t (s)

γ (–

)

t (s)

γ (–

)

(a) Maxwell model. (b) Kelvin model. The vertical connectorsstay parallel at all times.

(c) Ramp in stress.

(d) Response to ramp in stress for theMaxwell model.

(e) Response to ramp in stress for theKelvin model.

Figure 5.1 The two most widely used rheology models to describe visco-elastic behaviour. The springhas a shear modulus G and the dashpot has a viscosity η.

The Kelvin model (Figure 5.1b) is constituted by the sum of the shear stresses from the springand the dashpot giving:

τ = γ G + ηγ . (5.6)

The Maxwell model describes a fluid with elastic properties (imposing a stress results in acontinuous displacement), whereas the Kelvin model describes a solid with viscous properties(imposing a stress results in a limited displacement).

By defining a characteristic time as:

tc = η

G(5.7)

the Maxwell model reads,

τ + tcτ = tcGγ . (5.8)


If a shear rate which had a constant value γc for t < 0 is suddenly removed at t = 0, it can beshown that for t ≥ 0.

τ = ηγc exp

[−(

t

tc

)]. (5.9)

So the stress relaxes exponentially from its equilibrium to zero. The characteristic time tc istherefore also called ‘relaxation time’.

The transition between elastic and viscous behaviour can be described using the Deborahnumber:

D = tct

(5.10)

where tc is again the relaxation time and t is the time of observation.

D −→ 0 : Ideal fluid

D −→ ∞ : Ideal solid.

This can be illustrated using the Maxwell model. At very high frequency displacements (fastdisplacements, short process times) the dashpot is very stiff whereas at low frequencies (slowdisplacement, long process times) the dashpot is very soft.

In the case of lubricants passing through EHL contacts, the time t is the residence time forthe lubricant in the contact, t = 2 × u × ax ≈ 10−5s. Typically for lubricating oil, G = 2 GPa[52]) and in the highly loaded EHL contacts, η = 107 Pa · s. Using these values for G and η

gives tc and D values of 5 × 10−3 s and 500 respectively. In this example, the oil will behaveas a solid. Outside the EHL contacts the pressure and therefore the viscosity is low, leading tolow Deborah numbers and the lubricating oil will show viscous behaviour.

5.2 Viscometers

There are different types of viscometers available. They can roughly be divided into instrumentswhere a flow is induced ‘through constriction’ and rotational viscometers. The first categoryis typically used for Newtonian liquids. Examples include capillary tube viscometers, wherethe viscosity is determined from the pressure drop and volume flow over a capillary tube of acertain length, and falling ball viscometers, where the viscosity is determined from the timeit takes for a ball in a tube of given length, filled with liquid, to travel when the tube hasan inclination angle. For details on these rheometers the reader is referred to, for example,Jacobson [296]. Since grease consists mainly of oil, very often high pressure oil viscometryis assumed. As an example, the pressure–viscosity coefficient that is required for calculatingthe EHL film thickness in grease lubrication (e.g. Eq. 9.60) is taken as equal to that ofthe base oil.

By far the most used method for measuring grease viscosity/rheology is through rotationalviscometers, of which two types exist: concentric cylinder viscometers and cone-plate vis-cometers, where for the latter, the cone is sometimes replaced by a plate (see Figure 5.2).Unfortunately, high pressure rheology has so far not been applied to lubricating greases. How-ever, extensive work for lubricating oil has been done by Bair [50] and Jacobson [296], and


F

h

R R

M

r

ω

α

F

M

r

ω

Figure 5.2 Parallel plate viscometer (γ = rω/h) and cone-plate viscometer (γ = ω/α, α being thecone angle.)

in the absence of grease data, similar rheology is assumed for grease. As an example, thepressure–viscosity coefficient for grease is usually assumed to be equal to that of its base oil.

5.2.1 Parallel Plate and Cone-Plate Viscometers

Figure 5.2 shows schematic representations of a parallel plate and a cone-plate rheometer. Thegrease is located between the two plates and either a torque M (controlled stress mode) orrotation ω is imposed (controlled strain mode) on one of the plates, which will shear the grease.In the case of controlled stress or controlled strain, the response in angular velocity or torqueis measured respectively. The measured or imposed angular velocity and torque are translatedinto shear stress and shear rate where the shear rate is defined by Eq. 5.2. In the cone-platerheometer the cone angle is chosen such that the shear rate is independent of the radius. Ina parallel plate rheometer the shear rate will vary from the centre of the plate to the outsidediameter of the plate, which makes it more difficult to analyse the measured signal. However,the cone-geometry in combination with high rotational speed results in high centrifugal forceswhich may cause grease leakage, which has a large impact on the measured signal, since themeasured torque will be dominated by the shear stress at the largest radius. Moreover, the gapheight is fixed. This is the reason why the parallel plate geometry is often preferred.

5.2.2 Errors in Rheometry Measurements

Edge Effects

Edge effects include rim fracture (Hutton [286], Magnin and Piau [392]) and radial migra-tion of grease. For a plate-plate configuration, these edge effects give an important con-tribution to the shear stress and normal stress because shear rates, and thus shear stressesand normal stresses, are highest at the rim. This is schematically shown in Figure 5.3. Dueto a larger flexibility in gap height, a parallel plate geometry is sometimes preferred. For


Re

(a) (b)

F

M

R

ω

Re

F

M

R

ω

Figure 5.3 Errors in rheology measurements may be caused by fracture (a) or leakage (b), reducingthe effective maximum radius of the plate.

bearing greases with consistency classes NLGI 2-3 this applies specifically at higher tem-peratures, where the grease softens and easily leaks at higher shear rates since the centrifu-gal forces drive the grease outwards. This effect could be a reason to perform measure-ments at oscillatory shear only. Oscillatory shear measurements will be described later inSection 5.3.

Heat Development

Viscous shear heating causes a temperature increase of the grease sample and therefore adecrease of viscosity. This will decrease the measured shear stress and normal stress. If thetemperature is not too high, viscous heating usually results in a reversible effect. Due to thesmall gap, the heat is easily dissipated into the plates, and therefore this effect can usually beneglected.

Shear Aging

Shear aging, which results from mechanical work on the grease, causes a breakdown of themicrostructure of the thickener in the grease. This is often irreversible and will result inpermanently lower stress values.

Hysteresis

Hysteresis may occur, characterized by a nonconsistency when several flow curves are mea-sured sequentially. This can be caused by the relaxing of the initial stress that was introduced


10

10

1010 10 10 10

τ [P

a]

[s–1]

Figure 5.4 Example of hysteresis in grease rheology measurements. The top and lower curve(s)represent nonhomogenized and homogenized grease respectively. Reproduced from Froishteter et al.,1989 C© Gordon & Breach Science Publishers Ltd.

by decreasing the gap when loading the sample and solved by pre-shearing the grease in therheometer. It is also observed in nonhomogenized grease. Thoroughly homogenized greaseshows no hysteresis, as shown in Figure 5.4. Cournonne and Vergne [138] showed that hys-teresis disappeared after heating grease to 120 ◦C for 10 days!

Crystallization

Dobson and Tompsett [170] observed crystallization of greases thickened by inorganic solidparticles. This leads to slip at low shear rates and normal behaviour at high speeds.

Shear Bands/Nonconstant Shear Rate

In the analysis of the measured torque-speed signal, the shear rate is assumed to be constantacross the gap. It has been shown, by using Nuclear Magnetic Resonance Visualizationtechniques for example that this is not always the case. Britton and Callaghan [103] showedthat shear bands may arise, where the actual shear happens in narrow bands only. This mayalso happen when fracture or leakage has taken place.

5.2.3 Errors in Thin Film Parallel Plate Rheometry Measurements

Lubricating grease in rolling bearings, seals and lubrication systems experiences a wide rangeof shear rates. Since the maximum and minimum rotational speed of a rheometer is limited,the gap height has to be reduced to obtain appropriate shear rates. However, this method willintroduce several errors in the measurements due to shear rate distribution, inertia and gapheight errors. These errors were identified by Davies and Stokes [160] as the main errors innarrow gap parallel plate rheometry. A brief summary of these errors will be given below.


Shear Stress Distribution

The shear rate distribution in parallel plate rheometry results in the highest shear rates at theedges of the plates, giving

γR = Rω

h. (5.11)

However, with a parallel plate rheometer the total torque and total normal force (which willbe discussed in Section 5.8) as a function of the rotational speed is measured. The measuredtorque and normal force represent the integrated shear stress and normal stress over theplate surface.

For the shear stress this is:

M = 2π

∫ R

0rτ (r )rdr, (5.12)

which gives [387]:

τ = M

2π R3

[3 + d ln M

d ln γR

]. (5.13)

For a Newtonian fluid, d ln M/d ln γR = 1 and the shear stress is:

τ = 2M

π R3. (5.14)

In the same way viscosity can be derived directly from the torque and speed according toDavies and Stokes [160]:

η = 3Mh

2π R4ω

(1 + ω

M

d M

3dω

). (5.15)

Inertia Effects

Inertia effects may disturb the measurement of normal stresses because the plates will bepulled together as the grease is spun outward. Davies and Stokes [160] give a correctionfor this:

�Finertia = −3πρω2 R

40, (5.16)

where ρ is the grease density, ω is the angular velocity and R is the plate radius.


Gap Height Error

To achieve high shear rates, the gap chosen may be very small (h < 100 − 200 μm). In thiscase an error may occur, arising from nonparallelism, nonconcentricity or nonflatness of theplates, and the gap-zeroing procedure.

If the gap error is caused by the height measurement, Davies and Stokes [160] give arelatively easy method to include a correction for the shear rates by using a Newtonian fluidas a reference to measure the gap error, which will be described briefly here.

In the case of an error ε in the gap height h, the real shear rate corresponding to the measuredshear rate can be calculated from

γ = γmh

h + ε, (5.17)

where γ is the actual shear rate, γm the measured shear rate, h the gap height setting and ε thegap error.

An example is given by Baart et al. [43] who illustrated the use of a gap correction for abase oil with viscosity η = 0.17 Pa · s, at 25 ◦C, in a parallel plate rheometer. Three seriesof experiments were conducted with different pre-set gaps (25, 50 and 100 μm, Figure 5.5a).The error in this setting can be determined by using the method described in Davies andStokes [160]. The viscosity ηm is determined from the slope of the shear stress–shear ratemeasurements. The gap error can be found from

h

ηm=(

1

ηr

)h +

(ε

ηr

), (5.18)

where ηr is the real viscosity. The quotient h/ηm can be plotted against the gap height setting hand fitted with a straight line. The slope of this line is the ratio 1/ηr and the intercept at h = 0gives ε/ηr , from which the error (correction to h) ε can be calculated. In this case ε = 27μm.

104

Measurement 100 μmMeasurement 50 μmMeasurement 25 μm103

102

She

ar s

tres

s σ x

y [P

a]

101

101 102 103 104 105100

Shear rate γ [1/s]

104

Measurement 100 μm

Shear stress Newtonian oil

Measurement 50 μmMeasurement 25 μm103

102

She

ar s

tres

s σ x

y [P

a]

101

101 102 103 104 105100

Shear rate γ [1/s]

(a) Uncorrected measurement. (b) Corrected for gap error of 27 μm.

Figure 5.5 Shear stress measurement with Newtonian oil at 25 ◦C [43]. Reproduced from Baart, Lugtand Prakash, 2010 C© Taylor & Francis Group.


100 102 104 106101

102

103

104

105

She

ar s

tres

s τ

[Pa]

Shear rate γ [1/s]

Measurement 500 μmMeasurement 250 μmMeasurement 100 μmMeasurement 50 μmMeasurement 25 μmModelBase oil

Figure 5.6 Shear stress–shear rate measurements, typically for grease, for different gap settings includ-ing correction for the gap error. Reproduced from Baart, Lugt and Prakash, 2010 C© Taylor & FrancisGroup.

This can be used again in Eq. 5.17 to calculate the correct shear rates. Figure 5.5b shows theresult for a Newtonian oil and Figure 5.6 for grease.

5.3 Oscillatory Shear

5.3.1 Theory

The rheology of grease can be measured by small amplitude oscillatory shear. It is a methodfor the investigation of the linear visco-elastic behaviour; it has the advantage over continuousshear that grease leakage and crack formation in the parallel plate and cone-plate viscometeris limited. Obviously, it is very important that the strains are small to ensure a linear elasticbehaviour. As an example, Yeong et al. [628] used a maximum strain of only γ = 0.001 for aLi/mineral oil grease at 25 ◦C.

Let

γ = γ0eiωt = γ0(cos ωt + i sin ωt), (5.19)

where i = √−1, ω is the frequency and γ0 is the strain amplitude which is small enough forthe assumption that the grease behaviour is linear elastic. The response to this shear will beharmonic as well but with a phase shift δ, so:

τ = τ0ei(ωt+δ) = τ0 (cos δ + i sin δ) eiωt =(

τ0

γ0cos δ + i

τ0

γ0sin δ

)γ0eiωt . (5.20)

The complex shear modulus G∗

τ = G∗γ, (5.21)


can be calculated from Eqs 5.19 and 5.20:

G∗ = τ0

γ0cos δ + i

τ0

γ0sin δ or

G∗ = G ′ + iG ′′. (5.22)

G ′ is in phase with the shear γ , and so represents the elastic part and is therefore called the‘storage modulus’. By contrast G ′′ is 900 out of phase, represents the viscous part and is calledthe ‘loss modulus’. The ratio of the two moduli reads:

G ′′

G ′ = tan δ. (5.23)

The storage and loss moduli can be calculated using the Maxwell model, Eq. 5.8. By assuminga shear stress τ = τ0eiωt and a shear γ = τ

G∗ gives

τ = tcGiωτ

G∗ − tciωτ = (tcGiω − tciωG∗) γ (5.24)

or

G∗ = G ′ + iG ′′ = tcGiω − tciωG∗ (5.25)

so

G∗ = t2c ω2 + iωtc1 + t2

c ω2G (5.26)

giving:

G ′ = t2c ω2

1 + t2c ω2

G (5.27)

G ′′ = tcω

1 + t2c ω2

G (5.28)

and

tan δ = G ′′

G ′ = 1

ωtc(5.29)

where, according to Eq. 5.7,

tc = η

G. (5.30)

Clearly, from Eq. 5.29 elastic behaviour is expected for high frequencies whereas viscousbehaviour can be expected at low frequencies.


10–3102

103

104

105

G′

G″

G′ ,

G″

(Pa)

10–2 10–1

ω (rad/s)100 101 102

Log ω [rad/s]

Log G′ ~2 log ω

Log G″ ~log ω

Log G″ ~–2 log ω

G′ = constantG′

G″

Log

G′,

G″

[Pa]

(a) Diurea/mineral oil grease T = 25 °C[390].

(b) Extrapolation of the measurement from Madiedo,using the linear visco-elastic theory from Section 5.3.1(Maxwell model).

Figure 5.7 Storage and loss modula as a function of frequency below the yield point and analysis ofthe measurement (γ � 1 and not too high temperature).

5.3.2 Application to Grease

The storage and loss moduli are, up to a certain level, independent of the amplitude of strainor stress. Karis et al. [311] have demonstrated the predominantly elastic behaviour of greaseby measuring the storage and loss moduli of three types of grease. They showed that bothparameters changed over a wide range of frequencies and that G ′ � G ′′.2 According toKaris, this behaviour is typical for all of the grease types he investigated. Madiedo et al.[390] measured both moduli at very low frequencies and confirmed that the storage modulusincreases with frequency (power law behaviour) and also showed that the loss modulus has aminimum. Figure 5.7 shows the measurements of Madiedo and an analysis of the measurementsusing the linear visco-elastic Maxwell model. At low frequencies, the loss modulus-frequencyrelation 5.28 reduces to

G ′′ ≈ tcGω (5.31)

and the storage modulus relation 5.27 reduces to

G ′ ≈ t2c Gω2. (5.32)

This gives a slope of 1 for the loss modulus G ′′ and a slope of 2 for the storage modulus inFigure 5.7b for low values of ω. At high frequencies the loss modulus reduces to:

G ′′ ≈ G

t2c

ω−2 (5.33)

2 According to Yeong et al. [628] this happens for concentrations of lithium hydroxystearate greater than 5% byvolume.


Log

G′,

G” [

Pa]

τ [Pa] τco [Pa]

G′

G″

T [K]

G′

G″

Log

G′,

G′′

[Pa]

Figure 5.8 Schematic representation of the nonlinear oscillatory behaviour of a lubricating grease.

and the storage modulus relation 5.27 reduces to

G ′ ≈ G. (5.34)

This results in a slope of −2 for the loss modulus G ′′ and a constant storage modulus inFigure 5.7b for high values of ω.

The fact that there are two maxima in the plot of log G ′′ against log ω makes it likely thatthere are at least two characteristic times. Note that the storage and loss moduli will cross atlow frequency.

The high storage modulus gives the grease its stiffness. For a good performance in rollingbearings it is vital that G ′ � G ′′.

Obviously, the linear visco-elastic behaviour is only valid up to a certain level of stress,strain or temperature, as shown in Figure 5.8. Typically for lubricating greases, the storage andloss moduli curves fall off at higher stresses and cross at a stress level which is often calledthe ‘crossover stress’, τco (see e.g. Couronne et al. [137]).

At this stress level, the grease loses its solid-like behaviour, and it is therefore often usedas a measure of the yield stress.3 As will be shown later, some flow models require a yieldstress as an input, which is very difficult to measure, and the crossover stress may be a goodalternative to this.

Delgado et al. [166] measured the visco-elastic properties of a lithium thickener/naphtenicoil grease as a function of temperature, and found that the slope of the storage modulusG ′ versus temperature plot dramatically decreased at a certain temperature and that the lossmodulus G ′′ decreased at about the same temperature (Figure 5.8). They claim that thisbehaviour is related to the yielding of the grease, and could therefore be a measure of themaximum recommended temperature for bearing operation (High Temperature PerformanceLimit). The examples from Couronne and Delgado, schematically depicted in Figure 5.8, showthat structural damage may occur due to mechanical energy (hydrodynamic forces acting on

3 The 1997 Rheology Working Group of the European Lubricating Grease Institute, ELGI found the crossover stressnot to be a useful measure for the yield stress, Nolan [452].


particles) or due to thermal energy (Brownian motion). In particle suspension rheology, thePeclet number

Pe = 6πηa3γ

kT(5.35)

is commonly used to indicate the dominant type of damage [433]. If Pe � 1, mechanical agingprevails, if Pe � 1 thermal aging will dominate. Here η is the grease viscosity, a the particleradius (assuming that the thickener can be modeled by particles) and k the Bolzmann constant(k = 1.38 × 10−23 J/K).

5.3.3 Effect of Thickener Concentration

Both storage and loss moduli will generally steadily increase with increasing thickener con-centration, Couronne et al. [137], even linearly according to Nolan [452]. This will happenup to a certain concentration, called the gel point, where a very rapid increase of the storagemodulus by a few orders of magnitude can be measured [512, 628]. At this point, thickenerfibres come into intense contact with each other and the grease loses its ability to flow. Herethe grease is in the ‘glass state’ where the thickener particles are ‘caged’ and can only move bypushing other particles away. Brownian energy is not enough to overcome this barrier (unlessthe grease is heated).

5.4 Shear Thinning and Yield

5.4.1 Grease

The viscosity of lubricating greases strongly decreases with increasing shear. This effect iscalled ‘shear thinning’. Generally, the viscosity of lubricating grease can be depicted as inFigure 5.9.

Cross model

Power law model

Herschel–bulkley model

Sisko model

ηi

ηb

Shear rate γ·

Vis

cosi

ty η

Figure 5.9 Schematic representation of the viscosity–shear rate curves for lubricating greases on adouble logarithmic scale.


At very low shear rates, the viscosity is very high and creep flow will occur. At slightlyhigher shear rates, the viscosity drops by orders of magnitude and shear thinning occurs. Thismay occur for many reasons, for example alignment of thickener fibres or loss of junctionsbetween fibres. At very low shear rates, the flow is restricted to the breaking fibre contacts (seeSection 3.3.5). At higher shear rates, the fibre height will also decrease. Hence, slip inside thefibre will occur and layers of soap will slide over each other. The fibres will be arranged withtheir long axis parallel to the direction of flow. At even higher shear rates, the fibres will bereduced in width and length [197]. At very higher shear rates the grease viscosity approachesthe base oil viscosity.

There is no model that accurately describes the full regime from extremely low to extremelyhigh shear rates. A model that describes the full curve with reasonable accuracy is the Crossmodel for pseudo-plastic flow [145]:

η = ηi − ηb

1 + (K γ )m + ηb, (5.36)

where ηi is the viscosity at very low shear rates, ηb the viscosity at very high shear rates (inthis case, close to the base oil viscosity) and K and m are constants. At medium to highershear rates, 1 + (K γ )m ≈ (K γ )m . Then, by using ηi � ηb, replacing ηi K −m with a new Kand replacing m by 1 − n, the Cross model reduces to the Sisko model, Sisko [532]:

η = K γ n−1 + ηb. (5.37)

Note that n < 1, typically n ≈ 0.5 for lubricating grease. This model can be rewritten in termsof shear stress as:

τ = τy + K γ n + ηbγ , (5.38)

where a yield stress term τy has been added to accommodate for the apparent yield at low shearrates, giving a similar equation to that given by Palacios and Palacios [461]. Also, Einstein’sformula for suspensions [63] can be used here for ηb, but then more details on the volumeof thickener would be necessary and the increase in accuracy would only be very small.Figure 5.10a shows a typical shear stress versus shear rate measurement from a lubricatinggrease, including a fit for Eq. 5.38. Indeed, Figure 5.10a suggests yield behaviour, so η → ∞.However, by zooming in at very low shear rates, it can be seen that this is actually not correct.Figure 5.10b shows that this apparent yield behaviour is caused by a very high viscosity atlow shear rates. Other models that are also frequently used in grease rheology are listed inTable 5.2.

The most widely used model is the Herschel–Bulkley model [255]:

τ = τy + K γ n. (5.39)

An example showing an excellent correlation of the Herschel–Bulkley equation with lithiumsoap greases of varying thickener concentration is given in Yeong et al. [628] who performedmeasurements in the shear rate domain 10−3 < γ < 103 s−1. Extrapolation to higher shear


100

101

102

103

104

105

10610

1

102

10

She

ar s

tres

s τ

[Pa]

3

104

105

Shear rate γ [1/s]

(a) Shear stress versus shear rate for Li/mineral oil grease at higher shearrates. The drawn line represents a fit using Eq. 5.38. Redrawn from [43].

Experimental dataSoskey–Winter functionWagner functionCarreau a model

10–7 10–6 10–5 10–4 10–3 10–2 10–1 100 101 102 103

Shear rate [s ]

107

106

105

104

103

102

101

100

η [P

a·s]

–1

(b) Viscosity versus shear for a diurea/mineral oil grease [390].

Figure 5.10 Rheology for ultra-low shear rates and higher shear rates covering a large part of thedomain that is relevant to bearing lubrication. (b) Reproduced with permission from Madiedo et al.,2000 C© ASME.


Table 5.2 Various rheological models for lubricating grease.

Herschel–Bulkley τ = τy + K γ n [255]Bingham τ = τy + K γ [82]Casson

√τ = √

τy + √K γ [120]

Czarny-Moes n√

τ = n√

τy + n√

K γ [151]Power law* τ = K γ n [167]Sisko τ = K γ n + ηbγ [532]Palacios τ = τy + K γ n + ηbγ [461]

*Sometimes called Ostwald-de Waele model

rates could lead to significant errors. If the rheology model is also used to describe the lubricantat higher shear rates, it is advised to add the base oil viscosity to this, giving Eq. 5.38.

Figure 5.11 shows the behaviour of the Herschel–Bulkey ‘consistency index’ K as a functionof temperature. Like viscosity, this parameter also shows ‘Arrhenius’ behaviour.

The Sisko model may be simplified to a simple power law model, also called the ‘Oswald-deWaele relationship’:

τ = K γ n. (5.40)

Note that this model has limited applicability in rolling bearings but may well be used forlubrication systems, as shown in Figure 5.9.

Delgado et al. [167] and Yeong et al. [628] used this relation to investigate the impact ofsoap concentration and base oil viscosity (γ < 100 s−1) in Li-greases. They found that the

3.5 3.0 2.5

10²

10¹

10

K [

Pa ×

sn ]

×10³ [1/K]1T

Figure 5.11 Herschel–Bulkley grease model factor K (consistency index) as a function of temperature[207]. Arbitrary grease types. For more information on the grease types, see [207]. Reproduced fromFroishteter et al., 1989 C© Gordon & Breach Science Publishers Ltd.


consistency index K clearly increases with increasing soap concentration whereas the flowindex n decreases with increasing thickener concentration; becoming close to zero for higherconcentrations (even at 20%). They showed that the base oil viscosity does not have a largeimpact on the shear rate/viscosity at low shear rates. This justifies the use of the simple powerlaw Eq. 5.40 over the Sisko Eq. 5.37. Again, by specifically adding the base oil viscosity tothe equation, the impact of base oil viscosity at higher shear rates is incorporated, whereasit becomes very small at low shear rates. In bearing lubrication, the shear rates vary over avery wide range and the Palacios and Palacios [461] variant of the Sisko model (Eq. 5.38) istherefore preferred over the simple power law relation.

5.4.2 Lubricating Oil

Shear thinning at a shear rate not only applies to the lubricating grease. The base oil viscositymay also be reduced. This may happen under extreme conditions, such as in the case of highpressure, where the viscosity is very high again. These conditions occur in the EHL contactsof rolling bearings. Here the pressures are typically p = 1–3 GPa, leading to extremely highviscosities (see Section 3.2.2) and in combination with the very rapidly developing high shearrates, γ = 106 − 108 s−1, this leads to very high shear stresses. If the shear stress is 1–5%of the hydrodynamic pressure, the lubricant behaviour will be non-Newtonian [296]. Shearthinning will occur up to the point where the stress reaches a limiting shear stress.

The most widely accepted model for the shear thinning of lubricating oils (Grieve andSpikes [232]) is the Eyring model:

τ = τe sinh−1

(ηγ

τe

), (5.41)

with τ e is called the Erying stress.Lately, there has been quite a lot criticism about this model. For example Bair [49] verified

various shear thinning models using a high pressure rheometer and concluded that the Rheeand Eyring [497] model is more suitable. Rhee and Eyring assumed that a lubricant consistsof N individual heterogenous flow units of molecules, each occupying xi areal fraction andeach having a relaxation time, tci . The molecular motion of the lubricant can then be describedby movements of these flow units [49]. The model reads:

τ =N∑

i=1

xiτei sinh−1(tci γ)

(5.42)

where τei = η/tci . Note that this model requires multiple Eyring stresses, τei .At higher shear rates, a limiting shear stress model is appropriate. A useful generalization

of these models has been given by Elsharkawy and Hamrock [184]:

τ = τL

[1 +

(τL

ηγ

)n]−1/n

(5.43)


00

0.2

0.4

0.6

τ/τ L

0.8

1A B

C D E

FA NewtonianB visco–plasticC Gecim&winerD Gen. n = 2E Gen. n = 1.8F Gen. n = 1

G

1 2 3 4 5

ηγ /τL

Figure 5.12 Rheological models applicable to high pressure EHL contacts [300]. Curves D, E, F referto Eq. 5.43. Reproduced with permission from Jacod, Venner and Lugt, 2003 C© ASME.

for which n = 2 gives the circular model of Lee and Hamrock [358]. These are depicted inFigure 5.12. With n = 1.8 this approximates the logarithmic model of Bair and Winer [53],and with n = 1, the linear model of Iivonen and Hamrock [287]. Another often used model isfrom Gecim and Winer [217]:

τ = ηγ tanh−1

(τL

ηγ

). (5.44)

The limiting shear stress strongly depends on pressure and reads:

τL = τL0 + ζ · p, (5.45)

with τL0 the limiting shear stress at zero pressure and ζ a limiting shear stress pressureproportionality constant. τL0 has been measured by Jacobson [295] and is of the order 1–5 MPa. Measurements of ζ can be found in Bair and Winer [54] and Hoglund and Jacobson[270], where the latter found values of 0.02 < ζ < 0.15 in the temperature and pressureranges of 20–200 ◦C and 0–2.2 GPa respectively. Hoglund [269] performed a large number ofexperiments on a bouncing ball apparatus at room temperature and found that ζ was mainlydetermined by the base oil type and that additives had no significant effect. He also found anexponential behaviour between ζ and the base oil viscosity, where high base oil viscositieslead to low values of ζ .

Shear thinning has an effect on both EHL film thickness and friction. Figure 5.13 shows anexample where films are calculated as a function of slip between the lubricated contacts. Fora Newtonian fluid, slip has no impact on film thickness whereas in the case of shear thinning,the film will be reduced significantly at high slip rates (note that in rolling bearings, the slipratio is smaller than 0.1). Friction master-curves for Eyring and limiting shear stress modelshave been developed by Jacod [297, 299, 300] and Morales and Wemekamp [430].


Cen

tral

fil

m t

hick

ness

[nm

]

400

300

200

Newtonian solution

PG460 polyglycol gear oil65 °C, 1.0 GPa, 0.5 m/s

Carreau

Ree-eyring with 2 flow units

Slide/roll ratio

2 1 0

Figure 5.13 Film thickness calculations for a polyglycol using different rheology models [49]. Repro-duced with permission from Bair, 2004 C© ASME.

5.5 Yield Stress

5.5.1 The Concept

The yield stress may be defined as the stress that is required to rupture a sufficient number ofcontact junctions in the fibre network so that flow will occur. This is clearly an engineeringdefinition. According to this definition, an obvious way to increase the yield stress would beto increase the soap content in a grease, which is confirmed by the data from Yeong et al.[628] and Nolan [452] who suggest a power law relation between yield stress and thickenerconcentration.

Barnes and Walters [64] showed that if a material ‘flows at high stresses’ it will also flow,however slowly, at low stresses. The viscosity is always finite and, if measured over a wideenough shear rate range, shows an ‘apparent yield stress’ characterized by a plateau of constantviscosity, at low shear rates, as was earlier depicted in Figure 5.9. Barnes elaborated on thatlater in an extensive review article [61]. The deformation at very low shear rates may thereforebe considered as ‘creep flow’, which would justify the simplification to ‘yield’. The yieldstress concept is widely used in the grease community and can be very well used as part of alist of specifications. It can also be used in simulation models.

The nonexistence of the yield stress makes it difficult to quantify its value. It will dependon the measurement method, and reported values of yield stress should therefore always beaccompanied by a description of how they have been measured. Rheology measurements atlow shear are often disturbed by wall-slip effects (Section 5.6), which makes interpretationdifficult.

Examples of yield stress measurements can be found in Yeong et al. [628], Yousif [630],Baart et al. [41], Salomonsson et al. [512] or Gow [230]. Gow [230] uses the term CEY(Computerized Evaluation of Yield) value as a measure for the yield stress. It is the value ofthe stress where steady flow begins, which he defines at γ = 0.5 s−1 and where the grease ispre-sheared in a grease worker. Similarly, Salomonsson et al. [512] defined the yield stress asthe stress at a shear rate of γ = 1 s−1. Alternatively, the yield stress can be measured by extrap-olating the flow curve down to zero shear rate using the model for which the measurementsare needed. For the latter measurements, γ should be done well above 0.5 or 1 s−1.


5.5.2 Influence of Temperature

Gow [230] measured the yield stress of lithium greases at various temperatures and showedthat the variation with temperature is dependent on the grease type. He introduced a so-called ‘Yield Index’ (YI), which indicates the sensitivity for an increase of yield stress at lowtemperatures which may be a valuable number to indicate start-up torque and pumpability atlower temperatures.

Figure 5.14 gives some examples of the dependency of yield stress on temperature. Theyield stress clearly decreases with temperature, except for the fluorotelomer thickened per-fluoro-polyether (PFPE). Overall, Arrhenius behaviour can be observed:

τy

τy0

= exp

[T0 − T

bln 2

], (5.46)

0 20 40 60 80 100101

102

103

104

Temperature [°C]

Yie

ld s

tres

s [P

a]

[207].(a)

x

x

x

x

x

+

+

+

+

103

102

101

τ [

Pa]

3.5 3.0 2.5

×10³ [1/K]1T

γ

(c) [207]. ordinateon1/T.

6040200–20 –40

3

2

1

NLGI 2NLGI 1

NLGI 0

NLGI 00

Temp [˚C]

log

(yie

ld s

tres

s)

[230].(d)

250100

1000

Yie

ld s

tres

s [P

a]

300 350 400

Czarny Li /Karis FL/Karis Urea/Karis

Temperature [K]

(b) [148] and [311].

Figure 5.14 Yield stress measurements at different temperatures for several types of grease. (c) Repro-duced from Froishteter et al., 1989 C© Gordon & Breach Science Publishers Ltd. (d) Reproduced fromGow, 1991 C© The Engineers, Australia.


with τy0 the yield stress at temperature T = T0. For the measurements presented in Fig-ure 5.14b, τy0 is the yield stress at 100 ◦C, T0 = 100 ◦C and b = 50 ◦C. This means that, forthis case, the yield stress halves every 50 ◦C. Other greases show a more pronounced decreaseof yield stress with temperature (Figure 5.14a). Measurements from Froishteter et al. [206]show a factor between 2.5 and 6 for each 50 ◦C increase.

Obviously, this only applies in the temperature domain in which the grease has a certaincrystallization. Outside this temperature domain the grease will behave differently. In general,the domain in which this behaviour applies corresponds to the ‘green domain’ (see trafficlight concept, Figure 4.3). In the ‘red zone’, that is at temperatures close to or exceedingthe dropping point, the grease will be fluid. At low temperatures the viscous component inthe flow behaviour will be negligible. It should be noted that wall-slip effects become morepronounced at higher temperatures (see Section 5.6) and that yield stress measurements couldbe disturbed by this. This makes it (even more) difficult to measure the yield stress at hightemperatures.

5.5.3 Consistency

Yield stress measurements have not been standardized (as yet). In practice, the yield propertiesare measured through a penetration test (see Section 16.2.1), where a standardized cone isallowed to fall from a certain height into a cup filled with grease, which will then partlypenetrate into the grease at 25 ◦C during a period of 5 seconds. The penetration depth is sub-sequently measured, where a higher penetration value reflects a softer grease. Greases arecategorized into various consistency classes according to the NLGI scale, see Table 5.3, wherebearing greases can have a consistency of NLGI 1, 2 or 3, mostly with classes 2–3. A lowerconsistency is preferred for low temperature applications or for good pumpability. An NLGI 3consistency is preferred for vertical shaft applications. Also in the case of vibrations, NLGI 3is sometimes used. In such applications, the grease is heavily ‘worked’, since the grease iscontinuously thrown back into the track and overrolled.

Table 5.3 NLGI class and penetration depth (in1/10 mm) according to DIN ISO 2137, DIN 51818.

NLGI Penetration

000 445–47500 400–430

0 355–3851 310–3402 265–2953 220–2504 175–2055 130–1606 85–115


Table 5.4 Penetration (in 1/10 mm) versus yieldstrength.

Penetration Yield stress

1/10 mm N/m2

475 74445 99430 113400 147385 169355 222340 255310 344295 404265 573250 696220 1081205 1392175 2522160 3569130 6057115 764385 13 462

Spiegel has derived a table linking the yield stress to the cone penetration depth by calculatingthe normal and shear stresses on the standardized cone (DIN ISO 2137). The results can beseen in Table 5.4.

Often, the NLGI number/yield stress is measured after some pre-shearing using the so-called ‘worked penetration test’ (Section 16.2.2). Pre-shearing is done in a grease worker(Figure 8.6), which may introduce some air into the grease. This has a significant effect onconsistency measurements, with Spiegel et al. [553] reporting variation of up to 10%!

In the case that a rheometer is not available or if only a rough estimate is required, thefollowing equations, which are a fit from data points, can be used. The data from Spiegel et al.[553] gives:

τy = 3 × 1010 · Pen−3.17 (5.47)

the data from Brunstrum and Sisko [107] gives:

τy = 4 × 1016 · Pen−5.58, (5.48)

and the data from Antonescu and Lorea [30] gives:

τy = 2 × 1010 · Pen−2.95 (5.49)


01

10

100

1000

Yie

ld s

tres

s (N

/m2 ) 10 000

100 000

1 000 000

Brunstrum & Sisko

AntonescuSpiegel et al.

100 200 300Penetration (1/10 mm)

400 500

Figure 5.15 Yield stress estimated from penetration measurements.

with Pen the cone penetration depth in 1/10 mm from the standard cone penetration depthmeasurement. The various equations are plotted in Figure 5.15. Antonescu [30] gives anestimate for the yield stress as a function of temperature as well:

ln τy = 1.27 × 10−4T 2 − 0.105T + 30.19 (5.50)

− (4.6 × 107T 2 − 3.08 × 10−4T + 0.0625)

Pen.

The temperature dependence is less pronounced for greases with low consistency properties,[230], Figure 5.14d. The soap content is clearly related to the worked penetration, Couronneet al. [137], where a higher soap concentration will give higher yield stress and lower pene-tration values.

Brunstrum and Sisko [107] introduced a correlation to calculate the grease viscosity atγ = 10 s−1 from a penetration depth measurement:

log10 η10 = 16.5882 − 5.58 log10 Pen (5.51)

where η10 is the viscosity in Poise. This may be used in the absence of a rheometer.

5.6 Wall-Slip Effects

Rheology measurements on lubricating greases are almost always disturbed by ‘wall effects’.The flow properties of lubricating grease close to the wall are different from those of thebulk material. Anomalies in rheology measurements are often ascribed to these wall effects,especially at low shear rates. Froishteter [207] measured the rheology of grease in variousinstruments and found that wall-slip occurred at shear rates lower than 102 s−1. Others suchas Yonggag and Jie [632], found that it typically happens at shear rates lower than 10 s−1


or Magnin and Piau [391] who found wall-slip at shear rates smaller than 0.5-1 s−1. Formeasurements done at higher shear rates, this effect is not significant.

Clear evidence of the occurrence of wall-slip is provided by Magnin and Piau [392], whomeasured the flow of silicone greases and showed wall-slip (and fracture) through photographs.For other thickener systems, they found (indirect) rheological evidence of wall-slip. Brittonand Callaghan [102] found evidence of wall-slip by visualizing the grease flow in a rheometerusing Nuclear Magnetic Resonance techniques. Westerberg et al. [605] even measured thethickness of the wall-slip layer (using micro-particle image velocimetry).

The occurrence of wall-slip in a flow curve measurement is shown in Figure 5.16. Yeonget al. [628] fitted the shear stress–shear rate measurements using the Herschel–Bulkley equationdown to a shear rate of γ = 1 s−1. At this point, a discontinuity in the derivative of the curve

3000

2500

2000

1500

1000

500

08006004002000 1000

Shear rate

τ [P

a]

γ

Shear rate γ [s ]–1

(a) Flow curve on linear-linear scale.

Pa

τ

(b) Flow curve on log-log scale.

Figure 5.16 Flow curve for a lithium grease showing the good fit with the Herschel–Bulkley modelfrom γ > 1 s−1 and the anomalous behaviour at γ < 1 s−1, which is generally ascribed to wall-slip.Reproduced from Yeong, Luckham and Tadro, 2004 C© Elsevier.


occurs, which is generally accepted to be caused by wall-slip (see also Czarny [150], Bramhalet al. [100] and Vinogradov et al. [592]).

The wall-slip effect (sometimes called the π -effect) in grease is not due to the materialsliding against the wall but is determined by a change of material properties in a narrow areaclose to the wall. In general it is believed that a thin oil layer is formed close to the wall, [592],[207], which is ascribed to a different ordering and/or concentration of thickener fibres at thewall, the separation of thickener, additives and base oils close to the wall due to surface energyeffects (related to the polarity of the grease components) and to a change of fibre orientationclose to the wall due to high shear (thixotropy, [60]). Bramhal and Hutton [100] assumed thatthis layer is a layer of ‘softer’ grease, which depends on the roughness of the solid body surface.

Czarny [150] rejects this and claims that the concentration of thickener is very high at thewall, forming a surface layer of mainly thickener. At some distance away from the wall, thelayer is depleted of thickener and the viscosity is much lower. With increasing distance fromthe wall, the viscosity increases until it has reached the value of the bulk of the grease. Toverify this hypothesis, he has done experiments varying the material and the roughness, whichshows that these quantities have an impact on the ‘yield’ stress.

The effect of wall-slip is more severe in narrow gaps. In this case, the wall layer forms a largerportion of the total gap. In addition, the wall-slip effect grows with increasing temperature,which leads to a lower base oil viscosity and an increasing thickness of the wall-slip layer [170].

The occurrence of wall-slip may make viscosity measurements on a rheometer unreliableat low shear rates. In general, wall-slip can be reduced by increasing the roughness of theplates [59], [109], [56]. An example from Balan and Franco [56] showing the impact of thegeometry on flow behaviour of grease by using a parallel plate rheometer with different typesof surfaces is shown in Figures 5.17 and 5.18.

The ‘ultimate rough surface’ for a rheometer, eliminating wall-slip, is a ‘vane geometry’,[59], see Figure 5.19. This geometry is therefore the best choice for measuring at very

10 10 10 10 10 10

10

10

10

G′ ,

G′′

[Pa]

G′

G′′

rough surface, 1 mmrough surface, 2 mmrough surface, 3 mmsmooth surface, 1 mmsmooth surface, 2 mmsmooth surface, 3 mm

ω [s–1]

–2 –1 0 1 2 3

5

4

3

Figure 5.17 Storage and loss moduli with frequency in the linear vicoelastic range as a function of gapheight and roughness. Reproduced from Balan and Franco, 2001 C© Taylor and Francis Group.


500450400350300250200150100500

0 200 400 600 800 1000 1200

Time [s]

She

ar s

tres

s [P

a]parallel plate geometrywith a 20 mm radial grooveplate-plate separation

1000 μm 2000 μm 3000 μmrough surfaces

Figure 5.18 Evolution of the transient shear stress with a radially grooved parallel plate geometryshowing the effect of roughness and gap height (1000, 2000 and 3000 μm), γ = 10−2 s−1. Reproducedfrom Balan and Franco, 2001 C© Taylor and Francis Group.

low shear rates and the yield stress for lubricating grease, examples can be found inKeentok [318].

5.7 Translation Between Oscillatory Shear and LinearShear Measurements

Oscillatory shear measurements are sometimes preferred over continuous shear because thislimits the occurrence of fracture and leakage of grease from the gap between the plates in arheometer. However, for the flow models described in this book, the steady shear propertiesare needed rather than the dynamic properties. Fortunately, it is possible to derive the steadyshear viscosity and yield stress from an oscillating shear experiment.

5.7.1 Viscosity

Cox and Merz [142] derived a ‘rule’, stating that the shear rate dependence of the steady-stateviscosity is equal to the frequency dependence of the complex viscosity:

η∗(ω) = η(γ ) for ω = γ , (5.52)

Figure 5.19 Vane geometry, used for measuring rheological properties at very low shear.


with η∗(ω) =√

(G ′/ω)2 + (G ′′/ω)2. However, this applies only for linear visco-elasticity(low values of shear). Due to the elasto-plastic behaviour below the yield stress and viscousbehaviour above the yield stress, this law does not apply to grease. For such materials,Doraiswamy et al. [174] developed an extension of the Cox–Merz rule:

η∗ (γmω) = η (γ ) for γmω = γ , (5.53)

where γm is the amplitude of the strain at which the angular frequency ω was imposed, withthe strain sufficiently high (γm ≈ 200%).

The method was validated by Mas and Magnin [403] for a lithium grease.

5.7.2 Yield Stress

The yield stress is the stress at which the grease starts to flow. It can also be defined as themaximum stress in which the (linear) visco-elastic model is applicable. This could be indicatedby the stress at which the loss modulus and storage modulus dramatically change, which isthe ‘cross over stress’, as defined in Section 5.3, p. 128, Figure 5.8.

An alternative is to monitor the elastic component only, that is the storage modulus G ′.Hunt and Zukoski [281] found for latex type of fluids that the yield stress is proportional tothe elastic modulus:

τy = 1

cG ′ with 0.015 < c < 0.03. (5.54)

Similar values have been found by Delgado et al. [166], indicating that this is also applicableto lubricating grease. The fraction 1/c has the dimensions of shear; therefore Eq. 5.54 couldbe replaced by

τy = G ′γmax , (5.55)

where γmax is the maximum linear elastic strain [325]. A good measure of this strain would bethe strain at which the crossover stress is measured [311]. For most colloids, γmax ≈ 0.001.

5.8 Normal Stresses

For a simple shear flow, γ = ∂u∂y and v = w = 0, the stress distribution for non-Newtonian

fluids can be expressed as:

σxy = τ = γ η σxz = σyz = 0 (5.56)

σxx − σyy = N1 σyy − σzz = N2,

with x being the flow direction, y is the direction of the velocity gradient and z perpendicular tothis. N1, N2 are the normal stress differences. For Newtonian fluids, σxx = σyy = σzz = −p,with p being the isotropic pressure and therefore the normal stress differences N1 = N2 = 0,the largest of the two is N1 and is responsible for the so-called Weissenberg or rod climbing


Rotating rod

Visco-elastic fluid

F

(a) Weissenberg rod-climbing effect of a non-Newtonian fluid.

(b) Normal stresses as they appear in arheometer.

Figure 5.20 Normal stresses in visco-elastic fluids.

effect [387], where a shear rate is imposed on a non-Newtonian fluid in a direction tangentialto the direction of the rotating rod. The response to this shear is a normal force which causesthe fluid to climb up the rotating rod, see Figure 5.20a. In practice this normal stress behaviouris to be expected from models of visco-elasticity, Barnes [63]. For lubricating greases N1 ispositive. This means that in a parallel plate rheometer, the plates tend to be pushed apart, seeFigure 5.20b. N2 is negative and usually much smaller than N1 and is therefore often neglected.The explanation for the normal stresses arises from the fact that for a grease structure at rest,‘entropic forces’ determine its structure (see Chapter 3). In shear, an originally isotropic greasebecomes anisotropic (provided that the thickener structure does not yield). The restoring forces,therefore, are also anisotropic and give rise to the normal stress differences N1 and N2.

The first normal stress difference N1 can be measured on a cone and plate rheometer,according to Barnes et al. [63] and Macosko [387]:

N1 = 2

π R2F, (5.57)

with F the measured normal force.The difference in first and second normal stress difference can be measured on a parallel

plate rheometer according to Macosko [387]:

(N1 − N2) |γR = F

π R2

[2 + d ln F

d ln γR

]. (5.58)

By having both measurements N1 and N2 can be determined.


In general |N1| � |N2|. Therefore, it can be assumed that N1 − N2 ≈ N1 which means thatone measurement would be enough.

Barnes [63] showed that for a polymer solution and a polymer melt, a power law behaviouris observed:

N1 = ψ1γm . (5.59)

For classical models like the Oldroyd-B model, the constant m = 2. Measurements on multi-grade oils also showed m = 2 [615]. However, m �= 2 was observed for grease by Baart et al.[40]. It may even be that m is different for different domains of shear stress or shear rate. Thecoefficient ψ may be approximated using the White–Metzner [63] model as

ψ1 = 2η(γ )λ1, (5.60)

where η(γ ) is the shear rate dependent viscosity and λ1 is the first relaxation time constant.The Sisko relation for viscosity (Eq. 5.37) can be substituted into Eq. 5.60, which again canbe substituted into Eq. 5.59. Then the first normal stress difference can be written as:

N1(γ ) = 2λ1(K γ n−1 + ηb

)γ m . (5.61)

The constants K and n can be found by fitting the Palacios and Palacios Eq. 5.38 to a flowcurve (shear stress–shear rate measurements) at higher shear rates. The parameters λ1 and mcan then be determined from normal stress measurements.

Examples of normal stress measurements can be found in Baart et al. [40], see Figure 5.21,who measured the rheological properties of a common lithium/mineral oil NLGI 2 grease.The variables from Eq. 5.38 were determined by fitting this equation to the flow curve (shearstress versus shear rate). Here, the yield stress was determined from the interception of this fitwith the shear stress axis. The viscosity ηb was taken as equal to the base oil viscosity. Thenormal stress measurements were fitted to Eq. 5.61. Table 5.5 shows the parameters that weremeasured for four temperatures. Note that the normal stress difference parameter m �= 2 andthat the shear thinning exponent n varies only very little with temperature.

5.9 Time Dependent Viscosity and Thixotropy

A gradual decrease of the viscosity under shear stress followed by a gradual recovery ofthe structure when the stress is removed is called ‘thixotropy’ [63], a term introduced in1935 by Freundlich [205], derived from the Greek ‘thixis’ meaning ‘stirring’ and ‘trepo’meaning ‘turning or changing’. ‘Anti-thixotropy’ or ‘negative thixotropy’ is the opposite typeof behaviour, that is an increase in viscosity under stress, followed by recovery at zero stress.Indeed, in the case that a constant shear stress is imposed on a grease, the viscosity willgenerally decrease.

The driving force for microstructural change in flow is the result of the competition betweenthe breakdown of bonds due to flow stresses and re-building due to in-flow collision andBrownian motion [60]. This also describes the pseudo plastic or shear thinning behaviour[141]. The rebuilding is usually much slower than the breakdown. Anti-thixotropy takes place


(a) T = 25 °C.

(b) T = 100 °C.

Figure 5.21 Normal stress measurements for different gap heights including a correction for the gaperror and inertia [40]. The model equation is Eq. 5.61. The deviation at low shear is due to the inaccuracyof the Sisko model in this domain.

Table 5.5 Rheology model parameters for a modern lithium/mineral oil NLGI 2 grease [40].

Model parameters

Variable 20 ◦C 70 ◦C 100 ◦C 120 ◦C Unit

τy 350 60 25 10 Paη 0.17 0.030 0.0095 0.0044 Pa · sK 20 10 5.0 3.0 Pa · sn

n 0.5 0.49 0.48 0.48 –λ1 5.6 4.6 4.2 4.0 sm 0.71 0.71 0.71 0.71 –


Completely structured – givingelastic, solid-like response

Partly structured – givingviscoelastic response

Completely unstructured – givingviscous, shear-thinning response

Resting

Shaking/shearing

Figure 5.22 Breakdown and rejuvenation of a thixotropic structure. Reproduced from Barnes, 1997 C©Elsevier.

when the thickener material is brought together by collision under shearing and slowly tornapart during stand-still by the random Brownian motion. Thixotropy is more pronounced insystems with nonspherical geometries as thickener material, [60, 481]. This is obvious fromFigure 5.22. To come back to the ideal 3D situation, such particles would have to both rotateand translate.

Figure 5.23 shows schematically a grease rheology measurement where the shear rate iskept constant and where the shear stress and time are plotted on logarithmic scales. At the startof the experiment, the grease microstructural skeleton is accumulating energy and only someweak bonds are destroyed, resulting in a linear behaviour on a log-log scale. The grease willpredominantly show (almost linear) visco-elastic behaviour. Close to the maximum shear, thisbehaviour changes, characterized by a stress overshoot. According to Delgado et al. [165],

tmax

τmax

Log τ

Log time

Constant γ γ = 0

Figure 5.23 Shear stress growth curves at constant shear rates (e.g. [165, 402]).


the deformation at the overshoot does not necessarily change with different shear rates. Atthis point, enough energy is accumulated to destroy the thickener bonds. The accumulatedenergy is released relatively slowly by the breaking up of more and more bonds, so the shearstress, and therefore the viscosity, will decrease in time until a stable situation is obtainedfor the microstructure at this shear rate. This is due to thixotropy. Note that this is essentiallydifferent from linear elastic behaviour. Both effects are transient but in the case of linear elasticviscous behaviour, the properties of the grease structure do not change, whereas in the case ofthixotropy, the properties of the grease are changing in time.

Delgado et al. [165] used a generalized model, resembling the Herschel–Bulkley model, todescribe this thixotropic behavior:

τ = K γ n[1 + (bγ t − 1)

(w1e(−t/c1)) (w2e(−t/c2))] , (5.62)

with K and n the consistency and flow indices and with b, w1,2 and c1,2 fitted parameters.Kuhn and his coworkers [165, 348] believe that the accumulated energy that can be stored

in the grease structure (i.e. the energy stored before the maximum shear stress τmax is reachedin Figure 5.23) may provide some information on the tribological behaviour of grease. Theydefined a ‘yielding energy density’:

e1 = γ

∫ tmax

0τ (t)dt (5.63)

with tmax the time required to achieve the maximum shear stress as depicted in Figure 5.23.They showed that this energy increases with decreasing shear rate γ and increasing soapconcentration and/or base oil viscosity.

The start-up torque is governed by the visco-elastic properties of the grease as the greasein bearings has to be redistrubuted and is heavily churned. At high shear rates, the grease willpredominantly behave as an elastic solid, whereas at lower shear rates, visco-elastic behaviourcan be observed, see Figure 5.24a. To reduce friction/heat development in a bearing, start-up should therefore preferably be done at a low shear rate. This specifically applies to lowtemperatures where the elastic behaviour will dominate. This start-up problem may also applyto pipe flow in lubrication systems. The required pressure during start-up will be high for thecase of grease undergoing thixotropy.

After reaching the maximum stress, the grease becomes more fluid with increasing shearingtime. This effect is sometimes called work softening. As soon as the load is removed, a rapidrestoration of broken bonds between the dispersed phase particles and the recovery of theproperties of a solid body takes place, [207] (so it is reversible). In other words, for grease, itwill take a finite amount of time to attain the equilibrium ‘viscosity’.

Shear thinning may be considered a special case of thixotropy, where both structural break-down under shear and rebuilding of the structure at rest take place very rapidly [141]. However,in the case of thixotropy, the viscosity changes over time at a constant shear rate whereas shearthinning displays a decrease in viscosity with increasing shear rate. The stress overshoot isalso observed for the normal stresses [402]).

After stopping the shear flow (γ = 0 in Figure 5.23), the shear stress decays monotonicallywith time, where the relaxation is faster for higher initial shear stresses [402] and highertemperatures [147]. However, total shear stress relaxation during stand-still takes a very long


Time of shearing

She

ar s

tres

s ←Increasing shear rate

Shear rate

1

2

3

4

She

ar s

tres

s

(a) Start-up shear stress as a function of timeat constant shear rates.

(b) Hysteresis caused by visco-elasticbehaviour and thixotropy.

Figure 5.24 Examples of transient behaviour of lubricating greases.

time. This is, according to Czarny [149], the reason that little or negligible recovery of thegrease structure occurs during relatively short stops of 20 hours or less.

After the shearing of grease, its ability to regain its consistency depends on both the grease-soap type and on the long range forces that bring the fibres close enough to each other to regaincontact points [197]. New contact points may be formed by external force or by heating. If theoriginal fibres were broken down, the number of fibres have increased and more contact pointsmay be formed. The grease will be harder than before breakdown occurred. Foster claims thatthis is indeed observed: softening after low shear rates and hardening after high shear rates.

Due to thixotropy it is very difficult to measure the steady state properties of lubricatinggreases. Pre-shearing is a must, where the time for pre-shearing is usually chosen by monitoringthe signals in the rheometer and is stopped as soon as a quasi steady state situation has occurred.However, this steady state situation only applies to the specific pre-shearing process. It makesthe application of measurements obtained under semi-steady state conditions difficult to applyin a transient environment, such as in a rolling bearing. In rolling bearings, the flow is clearlytransient during the start-up phase and during such events as described in chapter 11, but alsodue to possible vibrations or noncontinuous bearing operations.

To reach a semi steady state situation for measuring a flow curve (to obtain values forthe parameters in e.g. the Sisko equation), pre-shearing combined with several measurementloops could be used, as shown in Figure 5.24b. Initially, at small strains the grease will behaveas a semi-linear elastic material and the shear stress will rise at a steep slope. At somewhatlarger strains, the viscous character will flatten out the curve. At even larger strains, the greasestructure will begin to break down and ultimately viscous behaviour will be measured, governedby the base oil viscosity. By subsequently decreasing the shear rate over time, rejuvenationoccurs, partly restoring the soap structure. Therefore, during the next loop, the flow curvewill not follow the same line as during the first loop. However, this will ultimately lead to abalance between structural breakdown and rejuvenation so the flow curves for successive loopswill overlap.


5.10 Tackiness

It is difficult to specify the tackiness of a grease, probably because it is not really a physicalproperty such as elasticity or viscosity; it is a rather poorly-defined characteristic. It is rec-ognized as being important but never really specified. In this section some background abouttackiness will be given, including measurement methods.

5.10.1 Introduction

The soap network of a grease makes the grease ‘thick’, such that the grease is held in placeinside the bearing. This is not enough though: the grease also needs to ‘stick’. This abilityto stick is called ‘tackiness’. Tackiness is often associated with chewing gum’s ability tomake long threads when it is stretched between two fingers. In the absence of standardizedtest methods or references for lubricant tackiness, this is also how the lubricating engineer inpractice judges the tackiness of grease (the ‘finger test’). There are a wide variety of definitionsfor tackiness, referring to physical or testing aspects and vary between different branches ofindustry. To the author’s knowledge, there is no definition of the tackiness of grease, but aworkable definition for lubricating grease would be from Gay and Leibler [215]:

A material appears sticky when one has to do some work in order to remove a finger from it. Thisproperty is known as tackiness.

Three forms of tack can be defined:

• Cohesion or the intermolecular attractive forces.• Adhesion or the attraction between two substances. Adhesion holds two materials together

at their surfaces.• Autohesion or the specific adhesion or adhesion of the material to itself. Here, separation

may be either adhesive (usually after short contact times) or cohesive (usually after longcontact times) [241].

The latter is more related to contact adhesives and seems to be less relevant to lubricatinggrease. For lubricating greases, tackiness is expected to be related to the tensile strength ofthe grease, to its rheology/cohesiveness and to the adhesion/wetting of grease onto a surface.Factors that influence tack are surface roughness, contact pressure, dwell-time, temperature,humidity and flow/rheology, as shown by Gay and Leibler [215] and Verdier and Piau [591].

Some of the methods designed to determine tackiness only involve rheological characteri-zation, for example the elastic component of the material’s visco-elastic properties. However,such rheological tests do not include the adhesive aspect of tackiness. Adhesive materials areroutinely investigated with regards to their tacky nature, using a compression and release test,while monitoring the normal force and the pull-off distance (’threading’, see Section 5.10.3).

Tackiness may assist in the sealing action of grease. For this reason, tackifiers are sometimesused as an additive in lubricating grease to improve water resistance (Rudnick [507]), and forrolling bearing applications tackiness is therefore historically characterized by ‘water sprayoff’ or ‘water wash out measurements’, [20].


(a) A schematic of a roller rollingover a layer of grease.

(b) ‘Fractal’structure of grease next to the track ofthe ball after rolling over a disk. The grease formsbranches that become finer the closer they are to thetrack.

Figure 5.25 Tackiness behind the contact of ball/roller on ring.

During the churning phase in the rolling bearing, grease in the contacts is continuously beingcompressed and released by the rollers, see Figure 5.25. This may result in some tackiness,especially behind the roller where the roller and raceway are separated from each other. Inaddition, some level of tackiness is required to keep the grease on metal, rubber or polymermaterial. As described in Section 4.7.2, p. 82, the adhesive part of tackiness may be relatedto the ability to lubricate at very high speeds. Grease needs to firmly stick to the surface towithstand high centrifugal forces.

However, on the other hand, too much tackiness will prevent flow and/or create too muchdrag. Actually, Boner [88] writes that adhesion is desirable in applications like open gearing orchains. However, he also states that this quality could be detrimental when the grease is usedin rolling bearings. Generally for high speed applications greases with so-called ‘channellingcharacteristics’ are used. These keep the bulk grease away from the rolling elements andprevents too quick mechanical degradation and loss in consistency.

5.10.2 Tackifiers

In lubricating oil, tackiness additives, or ‘tackifiers’ are used to reduce the onset of turbulence.They impart tackiness or stringiness to a substance and are typically used to provide adherencein fluid lubricants and stringiness in grease and are added to discourage dripping, removal,flinging of oils, or impart texture to greases, [361].

Tackifiers have been used in lubricating greases for a long time (e.g. grease tackified withnatural rubber in 1934, [326]). They are polymers with high molecular weights (4 × 105 −40 × 105) and are several micrometres in length. Note that viscosity improvers have molecularweights between 1.0 × 105 and 2.5 × 105. Polyisobutylene (PIB), with molecular weightsbetween 1 × 106, and 4 × 106, and olefin copolymers with molecular weights around 5 × 105


Approach Contact Separation

Figure 5.26 Tackiness test as described by Verdier and Piau [591]. Reproduced from Verdier and Piau,2003 C© Wiley Periodicals, Inc.

are common examples of polymeric tackifiers. Generally, grease tackiness increases withincreasing molecular weight of the polymer, [361]. Due to the long length of the molecules,tackifiers are not very shear stable. They may be broken down by mechanical shear [507].

5.10.3 Pull-Off Test

The most widely used technique to measure tackiness is by pushing two surfaces together withgrease in between, until they reach a specified separation or force and subsequently pullingthem apart while measuring the normal force (e.g. [591]). This is schematically shown inFigure 5.26. Figure 5.27 shows the typical structure of grease after a tack test similar to theone in Figure 5.26, executed on a rheometer.

According to Verdier and Piau, there are three types of pull-off curves as shown in Fig-ure 5.28. When a viscous adhesive is pulled (5.28a), the force goes up almost instantaneouslyand then decreases slowly to zero while a long filament is formed. For a visco-elastic material(5.28b), the stress increases sharply, goes through a maximum, and then decreases again; it

Figure 5.27 Typical structure of a grease after squeezing and retracting a grease between two flat plateson a rheometer.


F(t)

t

F(t)

t

(a) (b)

F(t)

t

(c)

Figure 5.28 Different types of tack curves, where two flat surfaces are pulled from each other at aconstant speed. (a) Newtonian, (b) visco-elastic, (c) elastic behaviour. Reproduced from Verdier andPiau, 2003 C© Wiley Periodicals, Inc.

then possibly shows a plateau before dropping to zero. Fibrillation initiates after the peakforce, and the deformation of the fibrils occurs in the plateau region. The plateau may some-times be followed by a slight increase in force, attributed to strain hardening within the fibrils.However, for an elastic adhesive (Figure 5.28c), the stress increases sharply until the adhesivefails rapidly.

5.10.4 Other Tests

In addition to the ‘pull-off test’ and ‘finger test’ other tests are also done to measure tackiness,which are mentioned here for completeness. Rudnick [507] mentions, in addition to the fingertest, the ‘eggbeater’ test, in which a true eggbeater is used, where a tacky fluid climbs theshaft of the eggbeater and which is really a demonstration of the ‘Weissenberg’ effect, whichsuggests that both the ‘Weissenberg effect’ and ‘tackiness’ are related.

Rudnick also mentions a test called ‘ductless siphon’, in which a siphon generates a vacuumwhich pulls filaments above the liquid surface. Tackiness is then quantified by the maximumheight of these filaments before they snap.

Achanta et al. [20] developed a method for testing grease tackiness which resembles the‘pull-off tests’. However, they perform tests in a loop, that is successive cycles of compressionand pull-off, which makes it possible to measure tack as a function of time.

6Grease and Base Oil Flow

Grease flow in bearing applications enters at various levels of complexity, that is from a full3D-multiphase flow during the churning phase in a rolling bearing, down to a simple 1D singlephase pipe flow in a lubrication system. The complexity of the rheology in combination withthat of the internal bearing geometry makes it impossible, as yet, to solve the full flow problem.However, much can be learned from simplified calculations. In this chapter the various relevantflow problems will be briefly described, starting with pipe flow.

6.1 Grease Flow in Pipes

In fluid dynamics one of the simplest problems to solve is the circular stationary pipe flow atmoderate speeds. Indeed, this is straightforward for most fluids. Unfortunately, this is not thecase for a lubricating grease. There are several factors that complicate the problem: the strongnon-Newtonian rheology, the wall-(slip) effect and the possible occurrence of air in grease.

Pipe flow is relevant for lubrication systems, which will be addressed later in Chapter 17.In this industry a wide variety of models can be used to describe the flow of grease throughpipes. In practice, very often simple engineering models are used based on Newtonian fluidapproximations. However, for research purposes, more advanced models may be used toinclude complex rheology and wall-slip. The various rheology models can be found in Table 5.2from Chapter 5 and will be applied to pipe flow in the next subsections.

6.1.1 Approximation Using the Newtonian Pipe Flow Equations

The pressure drop in a fully developed steady laminar flow of a Newtonian fluid in a circularpipe can be calculated with the Hagen–Poisseuille law:

�pN = 128ηL Q

π D4(6.1)

where η is the viscosity, Q the volume flow rate and L , D the pipe length and inside diameter.The flow is assumed to be laminar and incompressible. The velocity profile will be parabolic.



In ASTM D1092 [153] this equation is used to calculate the apparent grease viscosity η

from a measured flow rate through a pipe Q, generated by a pressure drop �p. The viscosityis explicitly called the apparent viscosity to distinguish it from the real viscosity.

The wall shear rate in the case of a Newtonian fluid is defined as:

γw,N = 8uav

D= 32

π

Q

D3, (6.2)

with uav the average velocity. Since the 1960s[488, 489], it has been common practice tocalculate the shear rate from the required flow rate using Eq. 6.2. Next, measure the greaseviscosity at this shear rate using a rotating viscometer or by means of a table/plot and finallypredict the pressure drop using Eq. 6.1.

6.1.2 Non-Newtonian Fluid

In the case of a non-Newtonian fluid, the viscosity varies with shear rate, and the viscosity (η)in Eq. 6.1 therefore varies across the pipe. In this case the Rabinowitsch–Mooney equation[428, 483] may be used and the wall shear rate can be written as [396]:

γw = 32Q

π D3

[3

4+ 1

4

d ln Q

d ln �p

]. (6.3)

The shear stress profile for a steady flow in a circular pipe is linear, as depicted in Figure 6.1.This is the result of the equilibrium of forces on an imaginary cylindric volume with radius rand length L , assuming a uniform pressure across the pipe, giving:

πr2 · �p = 2πr L · τ, (6.4)

with 0 ≤ r ≤ 12 D.

The shear stress at the wall is therefore equal to

τw = D

4

�p

L. (6.5)

Slip layer

Bulk grease shear

Plug flow (yield region)

u τ

Figure 6.1 Velocity and shear stress profile for grease flow in a circular pipe. u = 0 at the wall.

Grease and Base Oil Flow 139

When the velocity profile is parabolic the highest stresses occur at the wall, decreasing to zeroat the centre of the pipe. So the viscosity at the wall, ηw, reads:

ηw = τw

γw

= π D4�p

32L Q

[3 + d ln Q

d ln �p

]−1

, (6.6)

an equation that can be used to measure the viscosity for lubricating greases in pipe or tubeviscometers. It can also be used to calculate the pressure drop or flow rate for non-Newtonianfluids in pipes by rewriting this equation, for example:

�pNN = 32ηw L Q

π D4

[3 + d ln Q

d ln �p

]. (6.7)

Note that for power-law fluids, d ln Q/d ln �p = 1/n (Eq. 6.15), so for Newtonian fluids(n = 1), Eq. 6.7 reduces to Eq. 6.1. Actually, for power law fluids with shear thinning parametern, the wall-slip shear rate reads:

γw = 3n + 1

4n

8uav

D. (6.8)

6.1.3 Bingham Rheology

As mentioned above, the shear stress profile across the pipe is linear, going from a high valueat the wall towards zero in the centre of the pipe (see Figure 6.1). Since most lubricatinggreases exhibit a pseudo-plastic character, meaning that the shear rate will be zero below acertain shear stress (the yield stress, τy), a ‘plug flow’ will occur, where the main shear willtake place in the vicinity of the wall. In 1955 Mahncke and Tabor [394] measured the radialvariation of the flow velocity in a glass tube and confirmed the occurrence of such a plugflow and the applicability of the Bingham equation (τ = τy + K γ ) to grease flow, which wassuggested by Singleterry and Stone [531]:

�p = 128K L Q

π D4

[1 − 4τy

3τw

+ 1

3

(τy

τw

)4]

. (6.9)

Here τw is the wall shear stress, according to Eq. 6.5. It is inconvenient that this equationcontains the wall shear stress on the right hand side, which implies that an iterative schemeis required to predict the required pressure for pumping at a flow rate Q. However, often (i.e.when τy/τw � 1) the last term may be ignored [62], which reduces Eq. 6.9 to a quadraticequation in �p with the approximate solution:

�p = 128K L Q

π D4+ 16

3

Lτy

D, (6.10)

with K replacing the Newtonian viscous coefficient, Eq. 6.10 may be seen as Eq. 6.1 with acorrection term arising from the yield stress τy .


6.1.4 Sisko Rheology

As mentioned in Chapter 5, the Bingham model only applies to grease flow at very low shearrates. For higher flow rates (or ‘thinner’ greases, which are usually applied in lubricationsystems), the grease follows the Sisko equation

τ = K γ n + ηbγ . (6.11)

Turian et al. [579] derived an analytical expression for the pressure drop using this rheologymodel, compiled by Delgado et al. [164]:

�p = 3

√8η3

bγ4w L3

uav D2G(n, X ) (6.12)

with

G(n, X ) = 1 + 4

[(n + 2

n + 3

)X +

(2n + 1

2n + n

)X2 +

(n

3n + 1

)X3

](6.13)

and

X = K

ηbγ n−1 = τ

ηbγ− 1. (6.14)

6.1.5 Power Law Rheology

In the case that a power law model is applicable (τ = K γ n), the pressure drop can be calculatedfrom [127]:

�p = 4L

DK

[3n + 1

4n

32Q

π D3

]n

. (6.15)

By using the second part of Eq. 6.2 and 6.8 this can be rewritten as

�p = 4L

DK γ n

w, (6.16)

which is again Eq. 6.5.

6.1.6 Herschel–Bulkley Rheology

In the case that a Herschel–Bulkley model applies

τ = τy + K γ n, (6.17)

the formulae given by Froishteter et al. [206,208] lead to a surprisingly simple expression forthe pressure drop:

�p = 4Lτy

αD, (6.18)


where α = τy

τwis the relative radius of the plug in the plug flow, with τw the shear stress at the

wall. Unfortunately there is no analytical expression for α. However, Froishteter et al. givea simple to use nomogram, shown in Figure 6.2, where α is given as a function of the shearthinning parameter m (m = 1/n) and what they call a ‘Bingham number’:

Bin∗ = τy

K

(D

2uav

)n

. (6.19)

For completeness the equations that were used to derive Figure 6.2 are summarized below.

Bin*

10

10

10

10

1 2 3 4 5 6 7 8 9 10

0.975

0.950

0.925

0.900

0.850

0.800

0.750

0.700

0.650

0.600

0.5500.500

0.4500.4000.350

0.300

0.250

0.200

0.150

0.100

0.075

0.050

0.025

m

2

1

0

–1

Figure 6.2 Nomogram for determining the radius of the plug flow α in a Herschel–Bulkley pipe flow.m = 1/n and Bin∗ according to Eq. 6.19. Reproduced with permission Froishteter and Vinogradov,1980 C© Springer.


The plug flow parameter α was solved from:

[m + 1

ω (1 − α)

]n

=(

D

2uav

)nτy (1 − α)

Kα, (6.20)

where ω is the ratio of the average and maximum velocity:

uav = ωumax (6.21)

and

ω = α2 + 2α (1 − α)m + 1

m + 2+ (1 − α)2 m + 1

m + 3. (6.22)

6.1.7 The Darcy Friction Factor

At low average grease flow speeds, uav, through a circular pipe – Reynolds number Re < 2000– when flow is laminar, the shear stress τw on the pipe wall is proportional to uav. To producesteady flow the pressure drop �p between the two ends of the pipe must balance the total shearforce provided by a pipe of length L and diameter D. Thus π (D/2)2 �p = π DLτw giving�p = 4 (L/D) τw which is Eq. 6.5. From Eq. 6.2 for laminar flow with parabolic velocityprofile τw = 8ηuav/D yielding:

�p = 32

(L

D

)(ηuav

D

). (6.23)

Introducing the fluid density ρ this equation may be rewritten in the form:

�p =(

64η

ρuav D

)(L

D

)1

2ρu2

av =(

64

Re

)(L

D

)1

2ρu2

av. (6.24)

Defining the ‘Darcy friction factor f ’ as:

f = 64

Re, (6.25)

the pressure drop becomes:

�p = fL

D

1

2ρu2

av. (6.26)

Here both �p and 12ρu2

av are quantities connoting energy per unit volume. For a historicalperspective of this factor the reader is referred to Brown [106].

In the regime of fully turbulent flow, Re > 2000, f can no longer be given by (64/Re) butactually becomes a constant. With constant f , Eq. 6.24 is much used in fully turbulent flows,which clearly does not apply in lubrication systems where the flow problems lie within the


laminar regime. Particularly in this laminar region, the name ‘friction factor’ for f may berather misleading, since for dry friction the coefficient of friction, often also called f , tendsto be more-or-less constant independent of the sliding speed but with a value monotonicallyincreasing with the relative roughness ε/D of the pipe wall. This, perhaps, gives sufficientreason for naming f a friction factor rather than a friction function f (uav), which might seemmore appropriate. However, as mentioned above, the grease flow problems discussed in thepresent chapter all lie safely within the laminar regime where Eq. 6.25 represents a goodapproximation, albeit with a smaller constant in the numerator arising from effects such asstrong nonlinear rheology and variation of thickener concentrations close to the wall and/orwall-slip.

This was demonstrated by Cho et al. [127] who measured the pressure drop for grease infour pipes with different diameters and found for all pipes:

f = 18.8

Rea, (6.27)

with Rea being the Reynolds number based on a viscosity measured at a shear rate givenby the wall shear rate, Eq. 6.8. Figure 6.3 shows the comparison between a fully developedlaminar flow of a Newtonian fluid and that for a lubricating grease. The figure clearly showsthat the wall effect significantly reduces τw compared to the Newtonian fluid.

Note that for a Sisko model the Reynolds number can be calculated using

Re = ρuavD

ηbGa (6.28)

Dar

cy f

rict

ion

coef

fici

ent

Reynolds number

10

10

10

10

5

4

3

2

0.0001 0.001 0.01 0.1

D = 1.554 cm

D = 0.963 cm

D = 0.904 cm

D = 0.704 cm

F = 64/Re

Figure 6.3 Darcy friction coefficient vs Reynolds number for 4 different diameter pipes at roomtemperature. Reproduced from Cho, Choi and Kirkland, 1993 C© Taylor and Francis Group.


where

Ga = G

(1 + X )4 (6.29)

with G and X according to Eqns 6.13 and 6.14 respectively.

6.1.8 Transient Effects

As described in Section 5.9, grease is thixotropic and its rheology is therefore time (his-tory) dependent. Grease that is at rest for long periods will have a higher apparent viscos-ity/consistency/yield stress/storage modulus than grease that has been flowing for some time.This will also have an impact on the start-up pressure, or more generally on transients, ina pipe. After starting up the flow, the shear rate will be highest close to the wall where theapparent viscosity will be smaller. This will lead to more breakdown of the soap structure nearthe wall giving a low viscosity layer here. This layer will progress in time through long pipes.This phenomenon has been modeled by Petera and coworkers [181,320] for thixotropic fluidsin general. The effect is obviously a function of the Deborah number (retention time in thepipe compared to the visco-elasticity) and the thixotropic behaviour of the grease. No specificmeasurements or models for lubricating grease have been reported in the literature. It goesbeyond the scope of this book to describe the fundamental rheology for this and the reader isreferred to [181, 320].

6.1.9 Air in Grease

The presence of air bubbles in grease is relevant in lubrication systems where the pressure dropmay be reduced by its high compressibility. Figure 6.4 shows a visualization of an air bubblein lubricating grease. Air decreases the cross-sectional area in pipes, which would increasethe grease velocity. In the case that the air bubbles are close to the wall, the interfacial shearstress may be reduced. The latter reduces the pressure drop in pipes significantly [508].

Cho et al. [127] show that, due to the presence of air, grease may be compressed in therange 5–15% under pressures up to about 200 kPa. Since the expected volume fraction of air

Figure 6.4 Visualization of air bubbles during the flow of grease. Reproduced from Delgado et al.,2005 C© Elsevier.


in grease is not known a priori, it is of less relevance to have predictive models and not muchattention is payed to this subject in the literature. Other than for compressibility, air in greasedoes not have a significant effect on consistency measurements [553].

6.1.10 Entrance Length

For the development of a laminar flow, a certain length is required, called the ‘entrance length’.This can be calculated with

Lentr = DRe

15.4. (6.30)

Spiegel et al. [551] give an example for grease with viscosity η = 0.5 Pa·s flowing througha 16 mm diameter pipe with a flow rate of 400 g/min, giving an entrance length ofLentr = 1.1 mm. In lubrication systems, where long pipes are used, this effect can be neglected.

6.1.11 Solid Particles in Grease Flow

In the case of particles in grease, either solid additives or conglomerates of thickener material,a nonuniform distribution may be expected due to the so-called Magnus effect. This has beenmodelled by Tudor and Nassui [578]. They show that the concentration is uniform in the centreof the pipe and that a maximum concentration will occur near the pipe wall, which dependson the yield stress of the grease and the size of the particles. This redistribution of particlesrequires a transverse motion, which will be very small. Therefore, this effect only occurs whenenough time is available, that is, in very long pipes.

6.1.12 Wall-Slip/Slip Layer

As described in Sections 5.6, 6.1.7 and in the review article by Barnes [59], a slip layer mayoccur between grease and the wall, as shown in Figure 6.1. The speed of the grease next to thewall is us , the slip velocity.

Grease velocity measurements, proving the occurrence of a slip layer, have been made ina rectangular channel (so quite similar to a pipe) by Westerberg et al. [605] using ‘microParticle Image Velocimetry’ techniques. Velocity profiles for 3 types of greases are depicted inFigure 6.5. The figure shows that the very soft grease (NLGI 00 class) behaves as a Newtonianfluid with a characteristic parabolic velocity profile. The stiffer greases (NLGI 2 and 3) clearlyshow a plug flow in the centre region of the channel. At the wall, the velocity does not go tozero and apparent wall-slip takes place. They described a model for this velocity profile using

a Herschel–Bulkley fluid model, τ = τy + K(

dudy

)n, see Section 6.1.6.

In the centre region, the shear rate dudy = 0 with low shear stress. As soon as the shear stress

exceeds the yield stress, the grease will shear and | dudy | > 0. The velocity profile close to the

wall was measured in more detail. To reach a high resolution, very small particles are needed.Unfortunately, such particles agglomerate and the smallest particles that could be used havea diameter of 7.7 μm. With these particles, the measurements close to the wall showed that


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5x 10

−3

y(m

m)

u

Figure 6.5 Dimensionless velocity profiles across the channel for three types of grease. •: NLGI 00,+: NLGI 1, and �: NLGI 2, measured using μPIV technique. On the abscissa is the normalized velocitywhile the distance across the channel is on the ordinate. The wall surface is bearing steel with roughnessRa = 130 nm. Reproduced from Westerberg, 2010 C© Taylor and Francis Group.

the wall-slip layer (see Figure 6.1) must be smaller than 16 μm. Some ‘easy to use equations’were derived in [605] to predict the velocity profile and flow rate in a wide rectangular channelwith height h. The domain is split up into three parts: a slip slayer of thickness ys , a layerin which grease ‘flows’: ys < y < yl and a thickness in which plug flow occurs: y > yl , seeFigure 6.1. This boundary can be calculated for the upper region through:

yl = h

2+ τy

dpdx

, (6.31)

and for the lower through

yl = h

2− τy

dpdx

, (6.32)

where τy is the yield stress and dpdx the pressure gradient. Note that, for a pure fluid, τy = 0,

which gives yl = h/2. So in that case, the maximum velocity occurs in the centre line and noplug flow will occur.

The maximum velocity umax., in the plug flow zone, reads:

umax. = u(y = yl) = − n

n + 1

(1

K

dp

dx

)1/n

(yl − ys)n+1

n + us, (6.33)

where τy , n and K are the yield stress, shear thinning and consistency parameters from theHerschel–Bulkley rheology.


In the zone where the grease ‘flows’, ys ≤ y ≤ yl , the velocity reads:

u(y) = n

n + 1

(1

K

dp

dx

)1/n [(yl − y)

n+1n − (yl − ys)

n+1n

]+ us . (6.34)

The problem is symmetrical in y = h2 . Therefore the velocity in the corresponding upper

region, (h − yl ) ≤ y ≤ h − ys , is

u(y) = n

n + 1

(1

K

dp

dx

)1/n [(y − yl)

n+1n − (ys − yl )

n+1n

]+ us . (6.35)

To use these equations, the grease parameters τy , K and n from the Herschel–Bulkleyequation must be known. As has been shown in Chapter 5, in the traditional parallel-plate orcone-plate rheometers these parameters are measured by assuming a linear velocity profilebetween the plates. It is unlikely that this occurs when shearing a lubricating grease of NLGIclass 1 or higher. Moreover, in the experiments from Westerberg et al. [605] the pressure dropwas not measured accurately. Figure 6.6 shows the experimental/measured velocity profilefor three greases (dotted curve) together with: (a) The analytical profile where the pressuregradient is equal to the measured value, and τy and K have been varied in order to fit theanalytical curve to the experimental (solid line). (b) The analytical profile calculated by usingthe values for τy and K from a parallel-plate rheometer measurement, and the pressure gradientis as measured. (c) Corresponding profile to (b), but where the value of the pressure gradienthas been adapted to fit the maximum velocity to the measured value (dash-dotted curve).Table 6.1 shows the measured and adapted values. There is a clear difference between theparameters obtained from the direct flow measurement and from the rheometer where thewall-slip effect is not taken into account.

6.1.13 Impact of Roughness

In the case of rough pipe surfaces, wall-slip is reduced, similar to what was found in rheometers(see Chapter 5). Delgado et al. [164] performed measurements with rough and smooth pipeswhere the smooth pipes reduce the pressure drop significantly (see Eq. 6.5). They consideredpipes with a surface roughness lower than 3 μm to be smooth and surfaces with a roughnessof approximately 40 μm to be rough. The results are shown in Figure 6.7. Using an NLGI 2Li-complex grease they measured a slip velocity of

us = 3.8 × 10−26τ 7.32w

ε/D(6.36)

where ε/D is the relative roughness of the pipe inner wall. To predict the pressure drop in apipe they derived a correction to the average velocity uav = uav,rough − us in Eq. 6.3 for theshear rate (note that the average speed is defined by Q = uav

π4 D2).


0 0.5 1 1.50

0.05

0.1

0 0.5 1 1.50

0.1

0.2

0 0.5 1 1.50

0.005

0.01

0.015

0.02

0 0.5 1 1.50

0.25

0.5

0 0.5 1 1.50

0.005

0.01

0 0.5 1 1.50

0.2

0.4

(a) NLGI 00 grease (b) NLGI 1 grease

(c) NLGI 2 grease

Figure 6.6 Analytical and experimental velocity profiles. All curves except the dash-labelled one havetheir scale on the left ordinate. Dotted: velocity profile obtained from the μPIV measurements. Solid:analytical velocity profile with adapted τy and K values, and measured pressure gradient. Dash-dotted:analytical velocity profile using the measured values of the rheological parameters and an adapted valueof the pressure gradient. Dashed: analytical velocity profile using the measured values of the rheologicalparameters and the pressure gradient. Reproduced from Westerberg, 2010 C© Taylor and Francis Group.

Table 6.1 Rheology parameters (Herschel–Bulkley, Eq. 5.39) for the greases used by Westerberget al. [605], measured on a plate-plate rheometer. The variables marked by an asterisk ∗ representvalues obtained by fitting the measured and predicted velocity profile in a rectangular channel,Figure 6.6. Reproduced from Westerberg, 2010 C© Taylor and Francis Group.

τy [Pa] K [Pa·s]1n n [-] τ ∗

y [Pa] K ∗ [Pa·s]1n n∗ [-]

NLGI 00 0 1.85 1 0 4.9 1NLGI 1 189 4.1 0.797 700 42 0.797NLGI 2 650 20.6 0.605 1200 165 0.605


Smooth Roughsurfaces surfaces

1/2”3/4”1”1 1/4”

Corrected (non-slip) flow curve

τ w[P

a]

103

102101

8u/D [s-1]

Figure 6.7 Log-log plot of (−�pD/4L) versus 8uav/D from pipe lines, varying the pipe diameterand roughness. The solid line has been calculated with a wall-slip correction according to Eq. 6.36.Reproduced from Delgado et al., 2005 C© Elsevier.

6.1.14 Grease Aging in Pipes

The method from Spiegel, described in Section 8.1, can be used to predict the mechanicalaging in pipes caused by shear. For pipe flow, Spiegels ‘Load Cycle Number’ Z reads:

Z = 8L

π D. (6.37)

As an example, take a 5 mm bore pipe with length of 50 metres, Z = 2.5 × 104. As shown onpage 178, aging a grease in a grease worker1 for a double stroke gives Z = 70. Hence, in thispipe the grease will be aging at the same rate as 2.5 × 104/70 ≈ 350 strokes in a grease worker.This number may be compared to the 60 strokes that are usually done just before measuringthe consistency of grease (ISO 2137) and the 10 000 strokes for a prolonged penetration test.Hence, in this pipe the grease will not age significantly.

6.2 Grease Flow in Rolling Bearings

6.2.1 Churning

Before start-up, the bearing and/or housing is (partially) filled with grease. As soon as thebearing starts running, this grease will move to where part of the grease quickly flows from theswept area onto the bearing shoulders and/or seals/shields, and/or into the housing. A smallvolume will also be attached to the cage. Another fraction of the initial volume will flow forlonger while it is trapped inbetween the rolling elements. Pictures illustrating the grease flow ina cylindrical roller bearing are shown in Figure 11.2 in Chapter 11. A schematic representation

1 For a description of a grease worker, see Figure 16.1.


Figure 6.8 Schematic picture of grease flow in a bearing.

is shown in Figure 6.8, where the arrows indicate the direction of flow. Obviously, it isassumed here that the initial filling is done such that all surfaces will be quickly covered bygrease. According to Cobb [129] there is no difference in grease performance (start-up torque,temperature and leakage through seals) if ball bearings are filled from one side only, providedthe same total amount of grease that is placed in the bearing is equal under either placementcondition. This implies that the initial distribution is less critical for ball bearings. For obviousreasons this will not apply to roller bearings.

Figure 6.10 visualizes the position of grease after only one minute of rotation in a deepgroove ball bearing [451]. In this figure the subsequent pictures show sections from scanningthrough the bearing. Clearly the grease is quickly sheared/removed from the raceways whilestaying attached to the cage. This is due to the high shear rates close to the raceways androlling elements, which results in a local low viscosity due to grease shear thinning, leadingto a much higher flow rate here than close to the cage where the shear rates are low.

Another illustration for this can be found in Gerstenberger and Poll [219, 220] who measuredthe positioning of grease in the vicinity of the inner-ring flange in a tapered roller bearing.Figure 6.11 shows the position of grease in time intervals of six revolutions of the inner-ring.Clearly, no macroscopic flow takes place here, which confirms that (macroscopic) grease flowonly happens in the initial phase of rotation, referred to as churning flow.

Grease may flow through the gap (clearance) between the cage and a rolling element. Thegap width varies over time due to the dynamics of the cage motion, especially in a pure

Shield

Grease Cage

Ball

Figure 6.9 Schematic distribution of grease in a deep groove ball bearing.


Figure 6.10 X-Ray CT images showing the distribution of grease in a deep groove ball bearing initiallypacked for 55% with grease after one minute of rotation. The pictures from left to right represent slicesat successive depths while scanning through the bearing. Reproduced from Noda et al., 2011 C© STLE.

radially loaded bearing. The gap also depends on the way the cage is guided, that is inner-ring, outer-ring or roller. Moreover, as will be shown in Section 10.3, it is very likely that acontinuous redistribution of grease will take place under the cage bar close to the gap dueto ‘cage scraping’. Grease that has flowed through the cage–rolling element gap will end upon the outer-ring after which it will again be picked up by the next roller. Depending on thegap width between rolling element and cage, it will be scraped off or further transported tothe inner-ring again. In addition to the macroscopic flow, a fraction of the grease will travelthrough the contacts.

The flow or churning process typically takes place in a few, up to 24, hours and is generallyassociated with an increase in temperature. After this, the grease that is not attached to anyof the surfaces in the ‘swept’ volume will have ended up next to the raceway, that is on thebearing shoulders, in the housing or on the shields/seals. The latter is schematically drawn inFigure 6.9. During this flow process the grease will be heavily worked leading to a significantweakening of its structure. The churning process should therefore not be too long. Actually,the flow process should be only long enough to provide a good grease reservoir, which meansthat all relevant surfaces should be well covered by grease. A longer churning period will leadto loss of grease life.

The above mentioned flow applies to a well performing grease. If the grease only flows in alimited churning phase the temperature behaviour will be like ‘Grease A’ in Figure 6.12. If thechurning phase does not stop, the temperature will show a temperature behaviour as ‘GreaseB’ in Figure 6.12. This is described in Horth et al. [273], who call Grease A a ‘channelling’ or

Figure 6.11 Sequence of pictures of grease on a tapered roller bearing with time intervals of sixrevolutions of the inner-ring. The figures show the inner ring with flange and two rollers. The cage iscovered by grease and is not clearly visible. Reproduced from Gerstenberger, 2000.


Grease B

Grease A

Time

Tem

pera

ture

Figure 6.12 Temperature characteristics of two types of greases. Initial churning causes higher frictionand temperature. Grease A, a channelling grease, will not re-enter the swept zone. Grease B willcontinuously flow inbetween the rolling elements, causing a continuous high friction and thereforehigher temperature.

‘clearing’ product and Grease B a ‘nonchannelling’ or ‘non-clearing’ product. They showed,by using dyed greases, that for Grease A no mixing took place, whereas for Grease B completemixing took place during running. When grease was removed from the shields, the temperaturewas low again. Surprisingly, grease A was hardening in the bearing whereas Grease type Bmaintained its consistency. It is likely that this hardening caused the grease flow/channellingto stop early, resulting in a low operating temperature.

It should be noted here that this does not apply to very slowly running bearings, which needa higher filled fraction of grease. Here the churning/flow usually takes place throughout thelife of the bearing.

6.2.2 Flow Through Bearing Seals

If bearings are overfilled, insufficient free volume is available next to the raceways and thechurning process will not end, leading to a continuously high temperature and very shortlife. Alternatively, the grease may be pushed through the seals/shields, which will reduce thevolume in the bearing (housing) and reduce the heat development again. Also flow/leakagemay take place after excessive mechanical/thermal work on the grease, in which case thegrease has lost its mechanical stability.

6.2.3 Relubrication

The grease flow properties are not only important for the bearing lubrication process itself. Inthe case of relubrication, the bearing needs to be ‘flushed’ where fresh grease should replace theaged grease, which requires different flow properties than that for the bearing operation, that is,for a rotating bearing. In this case fresh grease is pumped into the bearing using a lubricationsystem or manually with a grease gun. For an optimal performance of the lubrication systemthe grease should flow with well described quantities through pipes. Moreover, the old grease


should be replaced by fresh grease in the bearing by pumping it through the bearing. Inthis case the flow is not a simple pipe flow but a flow through restrictions such as throughthe roller sets, across the guide rings (for spherical roller bearings), across flanges, through(labyrinth) seals/shields and so on. These configurations have a complex geometry and themeasurement of the flow/velocity field is therefore also very difficult, if not impossible. Someuseful qualitative work on the flow close to the flange in tapered roller bearings has howeverbeen done [220]. Also the grease flow in the contact of a journal type bearing configurationhas been measured, [435–437] and modelled [221].

6.2.4 Grease Flow Around Discontinuities

In fluid dynamics, the flow over a step is a model problem that has been studied in numerouspapers. For example, Sousa et al. [550] modelled (using an elastic Boger fluid) and measuredthe flow in a square contraction. They observed a corner vortex but also a ‘lip vortex’. Theyfound characteristics for low and high contraction ratios. When increasing the mass flow, forlow contraction ratios they observed a vortex growth preceded by a decrease whereas for highcontract ratios only a monotonous vortex growth was observed.

Specific work on grease is rare though. Radulascu et al. [484] modelled the flow of grease ina pipe with discontinuities using a Bingham rheology model. In the core, where the shear ratesare very low, they found some stagnant grease. Grease flow measurements confirming this havebeen done by Li et al. [362,363]. Some of their measurements are shown in Figure 6.13. Herea pressure drop is applied over a channel with a wide restriction, that is the grease flows froma relatively wide channel into a thin channel and into a wide channel again. The transitions aresharp here. Like the work presented in Section 6.1.12, the measurements were made using the‘micro Particle Image Velocimetry’ (μPIV) method. Figure 6.13 shows the velocity contourplots and the corresponding velocity diagrams at various cross-sections.

The upper two pictures in Figure 6.13 show how grease flows from a relatively wide channelinto a thin channel. The grease is almost standing still in the corner. In the next two figuresthe channel expands again and the average speed reduces and again a stagnation of the greasein the corner occurs. These measurements shows that grease may not totally be refreshed inthe case of relubrication by means of a lubrication system. In some applications, it may benecessary to pump more grease through the bearing than the volume based on a single freespace calculation, such as given in Section 4.14.

6.2.5 Creep Flow

During the churning phase the grease is flowing inside the bearing, ultimately ending up onthe cage, the seal material or on the bearing shoulders. Here the shear will be so low thatthe grease will behave as a semi-solid again, a visco-elastic material with an apparent yieldstress or very high viscosity (see Chapter 5). Actually, the solid-like behaviour can often bedescribed by a very high viscosity and the result is a very slow flow, known as creep.

Also wall-slip may induce flow here. As mentioned in Section 5.6, wall-slip is caused by athin oil layer which is formed by the interaction of grease with wall material. It is thereforelikely that this will be different for different materials. Unfortunately, this is an unexplored areaand to the author’s knowledge only Czarny [150] has measured the impact of wall material


0 0.050

0.5Pos

itio

n [m

m]

1A B C D E

1.5

0.1

Velocity [m/s]

0.15 0.2

0 0.050

0.5Posi

tion

[m

m]

1

E D C B A

1.5

0.1

Velocity [m/s]

0.15 0.2

Figure 6.13 Contour plots and cross-sections of the velocity field for the flow of an NLGI 2 grease ina channel with relatively long restrictions. The top and lower figures show the speed for grease enteringand leaving the restriction respectively. Reproduced from Li et al., 2012 C© Elsevier.


2

1 Polyamide

3 Duralumin

4 ZnAl

5 Cast Iron6 Cu/Bronze

600

400

300

200

150

100

She

ar s

tres

s [P

a]

0.015 0.03 0.05 0.09 0.15 0.27 0.45 1

Shear rate [s ¹]

PolytetrafluoroethylenePolytetrafluoroethylene

Figure 6.14 Influence of wall material on the shear stresses in a lime-bases. Reproduced from Czarny,2004 C© John Wiley & Sons, Ltd.

on wall-slip. This is shown in Figure 6.14, where it is shown that polyamide has a higherresistance to shear than cast iron or bronze. This indicates that polymers are more suitable formaintaining a grease reservoir than bronze or steel cage material.

6.2.6 Flow Induced by Vibrations

It is well known that vibrations have an impact on grease life. It is most likely that this iscaused by creep flow in the bearing or in the bearing housing. This problem is not muchaddressed in the literature other than through the V2F qualification test as described in Section16.2.17. Lundberg and McFadden [385] measured the creep flow of 10 types of NLGI 2 greasessubjected to low frequency vibrations at ambient temperature. They filled a vibrating verticalcylinder with grease and observed that the vibrations induced a creep flow on the wall only.They show that this creep rate is directly related to the yield stress where a high creep ratecorresponded to a high yield stress. From these observations they conclude that a very ‘stiff’grease concentrates the acceleration forces at the interface of grease and wall material. Onemay expect a correlation with creep rate and base oil bleed rate. However, this was not found,probably due to the low frequency. They performed one experiment varying the frequencyand showed that the creep rate approaches zero at high frequency (100 Hz). A test where theacceleration amplitude was increased shows that a critical acceleration is required to causeany creep flow, which suggests that a certain critical energy is required to induce creep byvibrations.

7Grease Bleeding

P.M. Lugt and P. Baart

7.1 Introduction

Oil bleeding from grease is one of the most important lubricant feed mechanisms to therunning tracks in a grease lubricated bearing. The separation of oil from grease may beachieved by surface energy forces, by a concentration gradient (diffusion-like) or by pressure.The first mechanisms apply to stationary grease and the latter to grease under the cage wherepressure is induced by centrifugal forces, or in lubrication systems where a pump pressurizesthe grease.

The bleeding properties will depend on the grease thickener structure, the interaction forcesbetween thickener material, additives and base oil, and on the base oil viscosity. In the case oflow temperature operation, bleeding will be very low. According to SKF’s general catalogue[4], the bleeding rate of grease depends on the base oil viscosity. If the viscosity is very high(say 500 mm2/s at 40 ◦C), the bleeding will be so slow that it practically stops.

Bleeding may also be related to the stiffness of the grease. Generally, very stiff greases havepoor bleeding characteristics.

The bleeding rate, that is the bleeding per unit of time, should ideally somehow match thestarvation rate. In the beginning of bearing operation, the lubricant film will be relatively thickand no additional feed of base oil is required. A too high bleeding rate will exhaust the greaseat an early stage, leading to short grease life. If the bleeding rate is too low, the contacts willstarve rapidly, leading to early damage. Fortunately, a change in temperature has a similareffect on both bleeding rate and starvation rate, which means that oil bleeding extends thegrease life throughout the ‘green temperature’ window, that is the temperature in which thegrease can maintain its consistency and no severe oxidation takes place. The importance ofbleeding rate was confirmed by Azuma et al. [39] who tested two types of urea greases onFE9 machines.

Others consider the time period in which grease is able to bleed more important than thebleeding rate itself. For example Bartz [66] reports that tests in electric motors (T = 125 ◦C)



have shown that the lubrication of grease fails as soon as an oil loss of 50% has been reached.Alternatively, others consider the ability to bleed large volumes of oil more important [510].

The confusing interpretation of test results may be the result of a possible similarity betweenbleeding rate and bleeding volume. The bleeding rate is often a function of the concentrationof base oil left in the grease. By the time that the grease contains only 50% base oil, thebleeding rate is likely to have become much smaller. However, it is the rate which determinesthe effectiveness of replenishment.

7.2 Ball Versus Roller Bearings

Roller bearings are more difficult to lubricate with grease than ball bearings. An extremecase is reported by Armstrong [32] who reported a life reduction with a factor of 200 for acertain grease! The difference in grease life is reflected in all grease life models that can befound in the bearing manufacturers catalogues. The reason for this is not obvious and has notbeen investigated other than through testing. It is likely that roller bearings generally require ahigher bleeding rate than ball bearings. Nada et al. [443] recommend using greases with goodbleeding properties for cylindrical and tapered roller bearings. Kuhl [347], states that the idealoperating temperature for ball and roller bearings is when the oil-bleeding rate according toDIN 51 817(N) is 1% and 3% respectively, which supports this statement.

7.3 Grease Bleeding Measurement Techniques

The standard test for measuring oil separation is described in DIN 51817 [168], and in thisbook, Section 16.2.6. Here, a dead weight is put on top of a cup filled with grease, placedin an oven at 40 ◦C, where the oil is slowly pressed out through a sieve at the bottom side.After one week the mass of the oil separated from the grease is measured. A modified test issometimes performed at elevated temperature or higher internal pressure. The conditions in theDIN 51817 test are not representative for grease experiencing high centrifugal forces resultingfrom high rotational speeds. A more representative test rig for this is shown in Figures 7.1and 7.2, with typical dimensions shown in Table 7.1. This rig was designed to measure oilseparation from grease under centrifugal motion at different temperatures and rotating speeds.The cylindrical cup is filled with grease, and four of these cups are mounted on a central

Figure 7.1 Rotating grease bleeding test rig. Courtesy of SKF.

Grease Bleeding 159

Rotating cup

Grease filling

Oil flow

Sieve

Ah

Ro

ω

Figure 7.2 Sketch of the test rig set-up to measure oil separation from grease under centrifugal motion.Reproduced from Baart et al., 2010 C© Taylor and Francis Group.

Table 7.1 Test rig dimensions.

R0 67.0 × 10−3 m outer radiusA 3.14 × 10−4 m2 outflow areahcup 31.0 × 10−3 m cup length

rotating shaft. The oil bleeding out of the cup is collected in a small retrieval container that isscrewed onto the cup. This container is not shown in Figure 7.2. The mass of the oil in thesecontainers determines the oil bleed, which is measured during a test period of 24 h at a definedtest temperature and rotational speed. In the test rig, the oil flow is parallel to the centrifugalbody load resulting in a relatively simple one-dimensional flow.

7.4 Bleeding from the Covers and Under the Cage

Grease bleeding may occur from the grease located next to the running track, that is greasestored on the bearing shoulders, onto the shields/seals or in cavities that are sometimes designedfor this purpose. Hibino et al. [260, 262, 263] have investigated the effect of grease pocketsnext to the bearing that could act as grease reservoirs and showed that grease life could beextended significantly by such a design. They measured the base oil concentration by meansof putting an oil-soluble tracer in the base oil of the grease and showed that base oil wasmigrating towards the bearing. This is shown in Figure 7.3. They specifically mention that thethickener from the reservoirs barely moves and that it is therefore the oil that is the lubricatingmedium [261].

A similar design was made by Komatsuzaki and Uematsu [338] who tested three greasesin cylindrical roller bearings1 and also report that the well performing grease showed oil loss(bleeding) in the grease reservoir next to the bearing. In addition, they write that grease losesits lubricating ability when the oil content of the grease mass inside the bearings (so noton) dropped to about 50–60%, see Figure 7.4. Moreover, acid number measurements of theextracted base oil showed that the acid number (related to the degree of oxidation) increases

1 Only one single test on two bearings for each grease.


12 mm Grease(red oil tracer)

Grease(blue oil tracer)

Original depth

6 mm 6 mm

(a) Initial distribution of grease. (b) Concentration of tracer, before and after running thebearing for 100 hours.

Figure 7.3 Oil bleeding from grease located in reservoirs next to the bearing. Reproduced from Hibinoet al., 2008 C© Japanese Society of Tribologists.

∗

∗

0 1000

50

60

Res

idua

l bas

e oi

l con

tent

, wt%

70

80

90

NU 320Grease A

Bearinginside

Bearingcover

Grease BGrease C

∗ : Lubricatinglifetime

NU 324

2000Rotation time, h

3000

0 1000

50

60

Res

idua

l bas

e oi

l con

tent

, wt%

70

80

90

2000Rotation time, h

3000 4000 5000

∗

∗

Figure 7.4 Grease bleeding measurements in cylindrical roller bearings (NU 320/NU 324) with greasereservoirs in bearing covers, T = 100 ◦C, n × dm = 470 000/570 000. Grease analysis of the failed bearingsshowed that failures occur if the base oil content is between 50% and 60% (grey area). Reproduced withpermission from Komatsuzaki and Uematsu, 2000 C© NLGI.

Grease Bleeding 161

0 50 100 150 200 250

Testing time [h]

Oil

sep

arat

ion

[mas

s%]

8

7

6

5

4

3

2

1

0

Grease AGrease BCurrently-used grease

0 50 100 150 200 250

Testing time [h]

Oil

sep

arat

ion

[mas

s%]

Grease AGrease BCurrently-used grease

80

70

60

50

40

30

20

10

0

(a) Oil bleeding measurement stationary. (b) Centrifugal force (208×g) induced oilbleeding measurement.

Figure 7.5 Oil bleeding measurements. Reproduced with permission from Saita, 2009 C© NLGI.

more inside than outside the bearing (and is effected by bearing load) and that the long lifegreases show a low oxidation rate, from which they conclude that oil loss and oxidation rateare related. This indicates that oxidation may prohibit further bleeding! This will be addressedin more detail in Section 8.2.

Saita [510] developed a new grease for deep groove ball bearings and cylindrical rollerbearings in a traction motor for a high speed train in Japan, where additional grease reservoirswere made next to the bearing, similar to those of Hibino, which were shown earlier inFigure 7.3. He claims that grease life is prolonged by improved oil bleeding from these greasepockets. In addition to this, he improved the grease further by formulating it such that itsbleeding properties are even better when the grease is put under a centrifugal pressure, wherehe refers to grease located under the cage. This is shown in Figure 7.5, where the oil separationfor the standard grease and the new greases A and B are plotted. This figure shows that thenew greases A and B will bleed more oil from the stationary reservoir next to the bearing.Figure 7.5b shows that, in addition to the supply from the reservoir next to the bearing, evenmore oil will be supplied from the grease under the cage bars if grease B is chosen.

Actually, the idea of providing the bearing with a larger reservoir is quite old. In 1963McCarthy [405] modified an ‘end-cap’ on his high temperature test rig such that more greasecould be stored next to the bearing. He managed to get seven times longer grease life bydoing this.

These examples illustrate the importance of predicting the bleeding properties both underambient pressure and in the case of a centrifugal force induced pressurization.

7.5 A Grease Bleeding Model for Pressurized Grease byCentrifugal Forces

At the moment there are no models published for oil bleeding under ambient pressure. Forpressurized grease, a model has been developed by Baart et al. [45], assuming that greaseis a porous media and that the base oil flow is a pressure driven flow through the porousmicrostructure of solid soap fibres. This model will be outlined below.


(a) (b) (c)

Figure 7.6 Thickener structure: (a) picture made with AFM, (b) 1st simplification to rigid fibres, and(c) 2nd simplification to orthogonally arranged rigid fibres where the structure consists of stacked cubicunit cells of volume V0 = L3

0 at t = 0.

7.5.1 Oil Bleeding Model

Grease Microstructure Model

As mentioned earlier, grease consists of base oil, thickener material and additives. The thick-ener often forms a cross-linked network that gives the grease its consistency. Figure 7.6a showsan AFM measurement of a grease sample. The figure clearly shows soap fibres dispersed in oil.This structure is simplified to circular and randomly ordered fibres suspended in oil as shownin Figure 7.6b. To simplify the model further, the fibre distribution is assumed to be uniformwith the fibres ordered in an orthogonal arrangement, as shown in Figure 7.6c, with one axisparallel to the pressure gradient. This results in 1/3 of the fibres being parallel and 2/3 of thefibres being perpendicular to the oil flow. The orthogonal fibre arrangement has the advantagethat anisotropy, that is, fibre orientation, is relatively easy to model. In this model, base oil willflow out of the grease during oil bleed, which results in an increase in soap volume fraction.This means that the soap structure will become denser and that the permeability will decrease,that is, the resistance of the oil to flow through the soap microstructure increases. The resultwill be a decreasing oil bleed rate in time. For the model, a homogeneous soap volume fractionover the whole grease volume is assumed. This is approximately true for sufficiently smallgrease volumes.

Darcy’s Law

Fluid flow through porous media was first studied and published by Darcy in 1856 [71]. Hederived an equation for the flow as a function of pressure drop, fluid viscosity and what iscalled permeability. Darcy’s law reads in its general form as

�q = 1

η

��k · �∇ p (7.1)

where �q is the fluid velocity vector, ��k the permeability tensor, and �∇ p the pressure gradient.

Grease Bleeding 163

Darcy’s law only applies when viscous shear forces dominate the friction such that inertiaeffects can be neglected. This means that the Reynolds number must be small, that is, Re � 1as defined by Bear [71]. The force balance reads:

�∇ pbody + �∇ pfriction = 0, (7.2)

where �∇ pbody is the total of external body forces per unit volume, such as gravity and centrifugalforces, �∇ pfriction is the friction force per unit volume on the oil due to flow through the poroussoap microstructure. This equals zero, because the inertia force can be neglected, due to thelow Reynolds number.

This equation is used to describe the oil bleeding of grease. The yield stress and elasticbehaviour of the grease are not considered here. To make a complete visco-elastic model,the geometry and deformation of the soap microstructure would need to be considered in toomuch detail to be included in the force balance. This would increase the complexity of themodel enormously and is therefore not included.

Friction Force

Darcy’s law, Eq. 7.1, can be used to deduce the friction force per unit volume as:

��pfriction = η��k−1 · �q. (7.3)

This is the basic equation used in the force balance in Eq. 7.2 to calculate the oil flow velocity q.Eq. 7.3 requires values for the base oil viscosity η and the permeability k. The base oil viscosityfollows Newtonian behaviour for the low oil flow velocities in the grease and is assumed todepend on temperature only. Walther’s Eq. 3.12 is used to describe the temperature–viscositybehaviour. The permeability k strongly depends on the porosity of the soap microstructure.Gebart [216] derived analytical expressions for the permeability of flow that is parallel orperpendicular to a grid of uniaxial aligned fibres. In the orthogonal arrangement of fibresas assumed in Figure 7.6c, the combined permeability is taken as a summation of thesecontributions as

k = 2

3k⊥ + 1

3k‖, (7.4)

where k⊥ is the permeability perpendicular, and k‖ is the permeability parallel to a grid ofuniaxial aligned fibres. The expressions for permeabilities that are parallel and perpendicularas derived by Gebart [216] are respectively

k⊥ = 16

9π√

2

(√fmax

f− 1

)5/2

r2 (7.5)

k‖ = 8

57

(1 − f )3

f 2r2, (7.6)


where fmax is the maximum fibre-volume fraction, and r is the radius of the soap fibres. Eq. 7.5was originally derived for relatively high volume fractions where the pressure gradient overthe complete volume is dominated by the pressure drop over the small gap region betweentwo fibres. Gebart [216] showed that the error between his analytical equation, Eq. 7.5, andnumerical simulations is smaller than 10% for fibre-volume fractions f > 0.35. For freshgrease with an initial soap volume fraction of, for example, 0.10 and 0.20, the error is 30%and 20% respectively. The model simulation results, described later in this section, will showthat this error at low fibre-volume fractions is acceptable for modelling oil bleeding of grease.From Eqns 7.5 and 7.6, it is clear that as the volume fraction increases during oil bleed, thepermeability decreases, which is the main reason why the oil-bleed rate tends to decreaseover time. Change of the grease microstructure might cause additional reduction of the oil-bleed rate. The change in grease microstructure can be modelled in several ways. First theeffect of fibre-volume fraction increase is studied assuming that the orthogonal arrangement ismaintained during oil bleed. In this case the fibre-volume fraction increase can be achieved byincreasing the fibre radius r or by decreasing the size L of the cubic unit cell. Only the decreaseof the cubic cell is taken into account since gradual growth of the fibre radius due to oil bleedis most unlikely to happen in reality. This means that the fibre radius r in Eq. 7.5 and Eq.7.6 remains constant while f increases in time. The maximum fibre-volume fraction possiblefor the orthogonal arrangement is reached when the fibres are touching (see Figure 7.7a), andfmax = 3π/16. Secondly, a model is proposed that assumes that fibres initially parallel to thepressure gradient gradually tilt and finally become perpendicular to the pressure gradient andoil flow. Consequently, the microstructure becomes anisotropic during oil bleed, and a highermaximum volume fraction can be reached. Figure 7.7b shows the situation where all fibreshave tilted so as to be perpendicular at the maximum fibre-volume fraction fmax = π/4, whichis much higher than the case of the isotropic fibre arrangement in Figure 7.7a. Note that theconfiguration from Figure 7.7a will always leave a free path to flow whereas the configurationfrom Figure 7.7b will not. The anisotropic fibre arrangement means that Eq. 7.4 has to bemodified to include the tilting of fibres. Figure 7.8 shows one individual fibre of the group ofuniaxial aligned fibres that were initially parallel to the flow but have now tilted to an angle

(a) (b)

Figure 7.7 Two fibre arrangements for their maximum fibre-volume fraction: (a) the orthogonalarrangement and (b) the arrangement where the fibres that were initially parallel have tilted so as tobe perpendicular.

Grease Bleeding 165

dp

dzz

xy

qll = qz cos θ

qz

q⊥= qz sin θ

θ

Figure 7.8 Fibre tilted with angle θ and flow q components perpendicular and parallel to the fibre.

θ . The oil flow around this group of fibres can be decomposed into two contributions: one forflow parallel to the fibres q‖ and one for flow perpendicular to the fibres q⊥. The pressure dropdp/dz can subsequently be written as the summation of the parallel and perpendicular flowcontributions:

dp

dz= η

k⊥q⊥ sin2 θ + η

k‖q‖ cos2 θ. (7.7)

This can be written as Darcy’s equation:

qz = k(θ )

η

dp

dz, (7.8)

with the permeability of the tilted fibres written as

k(θ ) = k⊥k‖k‖ sin2 θ + k⊥ cos2 θ

. (7.9)

Assuming that in fresh grease, 1/3 of the fibres are orientated parallel, and 2/3 are orientedperpendicular to the oil flow, as in Figure 7.6c, one can calculate the total permeabilityincluding anisotropy as

k = 2

3k⊥ + 1

3k(θ ). (7.10)

To evaluate the angle θ in Eq. 7.9, it is assumed that the volume reduction of the cubic unit cellcomes only from a reduction in height L(t) such that the base surface is constant and equalsL0

2. Consequently, L0 − Lmin is the height over which the fibres tilt during oil bleed, definedas the difference between the initial volume height L0 and the minimum volume height Lmin of


the cubic cell when the maximum volume fraction is reached. The height of the fibres parallelto the oil flow at time t equals L(t) − Lmin, such that the angle θ can be written as

cos θ (t) = L(t) − Lmin

L0 − Lmin. (7.11)

By expressing the unit cell volume V (t) as L20L(t) and using the relation V (t) f (t) = V0 f0,

Eq. 7.11 can be written as a function of the soap volume fraction as

cos θ = f −1 − f −1max

f −10 − f −1

max. (7.12)

Initially, when f = f0, θ equals 0◦ and k(θ ) becomes k‖, meaning that one third of the fibresare parallel to the oil flow and that Eq. 7.10 becomes equivalent to the isotropic case as inEq. 7.4. During oil bleed, the angle θ will increase and will finally become 90◦ when fequals the maximum fibre-volume fraction fmax. Now all fibres have tilted perpendicular tothe pressure gradient, and the oil bleed stops.

Body Force

The body force acting on grease rotating with angular velocity ω at distance R around a centralpoint is mainly the centrifugal force due to rotation:

�Fbody = m �g + mω2 �R. (7.13)

This force will build-up the pressure that drives the oil out of the grease. The pressure gradientas derived by considering the body forces on an infinitesimally small volume element locatedat distance R from the centre of rotation, can be written as

∇ pbody = ρω2 R, (7.14)

where ρ is the oil density. This expression is used as the body force that drives the oil flowin Eq. 7.2. For the algorithm to calculate the bleeding rate, the reader is referred to Baartet al. [45].

7.5.2 Quality of the Model

The grease selected for this study is a lithium complex grease and has a NLGI 3 consistency.This grease has a simpler microstructure than a lithium hydroxystearate grease [284] and isexpected to be described better by the microstructure model. The fresh grease has a highpercentage of thickener content, which minimizes the error for low fibre-volume fractions inthe analytical permeability model, Eq. 7.5.

Some of the model input parameters, such as base oil viscosity and density, are easy toretrieve. The fibre diameter is determined from the AFM image. The fibre mass fraction andbase oil density can be measured using standard measuring methods where the oil is separated

Grease Bleeding 167

Table 7.2 Grease properties.

ρgrease 930 kg · m−3 grease densityρoil 870 kg · m−3 base oil densityη40 0.0983 Pa · s base oil viscosity at 40 ◦Cη100 0.0105 Pa · s base oil viscosity at 100 ◦Cb 200 nm fibre diameterfmo 0.26 – fibre mass fraction

from the soap. Values for the lithium complex grease that is used here are shown in Table 7.2.For the experimental tests, four different ambient temperatures and two different rotationalspeeds are used.

The oil-bleed model contains several equations for permeability and the grease microstruc-ture. The flow of the base oil through this microstructure is very sensitive to the permeability,which decreases with increasing fibre-volume fraction. Figure 7.9 shows the different modelsproposed for the permeability. The boundaries of the models are given by the two cases whereall fibres are uniaxially aligned and either perpendicular or parallel to the pressure gradient,that is, with permeability equal to k⊥ or k‖ respectively. It can be seen here that for the per-pendicular arrangement, the permeability is smallest and goes to zero at f = π/4, which wasdefined as the maximum fibre-volume fraction. For the parallel case, no such limit appears inthe equation. This means that even at the maximum fibre-volume fraction, a flow of oil is stillpossible. Consider the first case, as described in Eq. 7.4, where the fibres stay in the orthogonalarrangement. Figure 7.9 shows that the permeability is lower than for the uniaxial parallel fibrearrangement but follows the same trend. The second case is interesting, where the fibres thatwere initially parallel, tilt during oil bleed and finally become perpendicular according toEq. 7.10. Then the permeability decreases to values similar to the uniaxial perpendicular

0.210–20

10–18

10–16

Per

mea

bilit

y k

[m]

10–14

10–12

0.3 0.4

k = k⊥

k = k ll

k = (2/3)k⊥+ (1/3)k ll

k = (2/3)k⊥+ (1/3)k(θ)

0.5

Fibre volume fraction f [–]

0.6 0.7 0.8

Figure 7.9 Permeability models for fluid flow through the fibrous soap microstructure.


+

+

+

+

+

+3000 rev/min3000 rev/min1000 rev/min1000 rev/min

00

10

20

30

Oil

loss

[%]

40

50

60

70

5 10 15

Time [h]

20 25

++ + + + + + +

0 5 10 15 20 250

10

20

30

40

50

60

70

Time [h]

(b)(a)

Oil

loss

[%]

120 °C120 °C100 °C100 °C 60 °C 60 °C 40 °C 40 °C

Figure 7.10 Oil loss due to oil bleed for an isotropic grease microstructure. The symbols represent theexperiments, and the lines represent the model.

case. The permeability finally goes to zero, which means that the oil bleeding stops while themicrostructure still contains oil. The permeability derived for fibres perpendicular to the oilflow, Eq. 7.10, has to be used with care because this equation was originally derived for fibre-volume fractions f > 0.35. The grease used in the current study has an initial fibre-volumefraction of 0.24, but this can be lower for other greases. However, in the initial orthogonalstructure too, parallel fibres are present such that the model does not only depend on Eq. 7.10.In addition, during oil bleed, higher fibre-volume fractions are reached where Eq. 7.10 canbe used without problems. The simplest model is considered where the grease microstructureis assumed to be isotropic such that Eq. 7.4 applies and the oil bleed will decrease in timedue to the decrease in permeability. Here this decrease only comes from the increasing fibre-volume fraction. Figures 7.10a and 7.10b show the percentages of oil loss respectively atdifferent temperatures and at different speeds. The symbols represent the experiments (donewith the equipment shown in Figures 7.1 and 7.2), and the lines represent the numerical model.The model shows trends similar to those of the experiment but predicts higher values for theoil loss and oil-bleeding rate. The isotropic model, using Eq. 7.4 for the total permeability,overestimates the experimental results. This means that the predicted permeability is too highand has to decrease faster with oil loss. Finally, when the maximum fibre-volume fraction isreached, the oil bleed has to stop. This, however, does not happen here since the permeabilitydoes not become zero at high fibre-volume fractions as was shown in Figure 7.9. The stoppingof oil bleeding is fulfilled in the anisotropic model where the fibres that were initially parallelwith the pressure gradient slowly tilt perpendicular during oil bleed. Here the oil-bleed ratewill reduce faster, and there is a limit for the maximum percentage of oil loss when themaximum fibre-volume fraction is reached. Figure 7.11a shows that the results obtained withthe anisotropic model using Eq. 7.10 predict the oil loss with better accuracy. Here the oil lossat 120 ◦C is still overestimated in the beginning but finally approaches the measured values.At lower temperatures, 40 ◦C and 60 ◦C, the first hours are described very well but the modelsomewhat overestimates the oil loss at later times. Also at lower speeds of 1000 rev/min,as shown in Figure 7.11b, the anisotropic model describes experimental results reasonably

Grease Bleeding 169

+

+

+

++

++ + + + + + +

00

10

20

30

Oil

loss

[%]

40

50

60

70

5 10 15Time [h]

20 25

120 °C120 °C100 °C100 °C60 °C60 °C40 °C40 °C

+

(b)(a)

Figure 7.11 Oil loss due to oil bleed of an anisotropic grease microstructure where fibres that wereinitially parallel then tilt to become perpendicular to the pressure gradient or oil flow. The symbolsrepresent the experiments, and the lines represent the model.

well. Overall, the model seems to capture the main effect of speed and temperature on theoil-bleeding rate.

Figure 7.12 shows an extrapolation of the anisotropic model up to 1000 h and includes moretemperatures and rotational speeds. All curves finally reach the same maximum percentage ofoil loss and give a good indication of the time it takes to reach this maximum. At increasedtemperatures or rotational speeds, the maximum percentage of oil loss is reached earlier. Thiscould be correlated to relubrication intervals of bearings, which also become shorter whentemperatures or speeds are high. It is anticipated that the oil-bleed model can be used for allgreases that have microstructures similar to that of the lithium complex grease studied here.This means that lithium hydroxystearate greases and calcium greases can also be modelled in

10–10

10

20

30

40

Oil

loss

[%]

50

60

70

100 101

Time [h]

102 103

140 °C120 °C100 °C

80 °C60 °C40 °C

(b)(a)

Figure 7.12 Oil loss due to oil bleed over a long time span as an indication of relative grease life.


the same way. However, the grease properties presented in Table 7.3 will be different and haveto be measured for each individual grease. It must be recognized that the model presentedhere is not yet complete apart from conditions based on uniform fibres and the homogenousmicrostructure. Other forces might become relevant at conditions where the centrifugal force,which is the driving force in the current model, becomes small. Here one can think of thecapillary force acting at the grease−air interface. Including capillary forces into the modelresults in a reduced oil-bleed rate and in a threshold force below which there is no oil bleed.Indications for capillary effects are found in static grease-bleeding experiments where thetemperature was lowered after some time and it was observed that the oil that did bleed outof the grease was sucked back into the grease again. Also, the reduction of the oil-bleed ratefound in the current experiment at reduced filling rates of the cup, that is, grease mass, seemsto indicate the existence of capillary forces. It is expected that the dependence on filling rateof the cup will become visible in the model when additional forces like the capillary forces,fibre interactions and nonhomogeneous microstructures are included. The model also does notinclude other secondary effects such as the force needed to deform the soap network duringbleeding; oxidation of the oil, which results in growth of fibre diameter [512]; and the buoyantforce due to the difference in mass density between the thickener fibres and the oil. Includingthis last effect might lead to an explanation for the oil layer sometimes found on top of thegrease after long storage times. Nevertheless, the current model gives a good indication of theoil-bleed rate when including the anisotropic deformation of the soap microstructure.

Most of the figures and text in this chapter were reproduced with permission from Baart et al.,2010 C© Taylor and Francis Group.

8Grease Aging

P.M. Lugt and D.M. Pallister

Mechanical or physical degradation in a rolling bearing can be caused by several phenomena.The most obvious degradation is due to churning of grease in the initial phase of greaselubrication. However, grease degradation may also occur due to vibration. In these cases, thegrease is subjected to severe deformation, which may change its structure substantially. Thedegree of breakdown is a function of the grease composition and morphology. The abilityto maintain its structure is called the ‘mechanical stability’, or ‘shear stability’. The loss ofmechanical stability need not only be caused by shear. It can also be the result of oil separation.

Tests for measuring the mechanical stability of greases are the V2F test (see Section 16.2.17,Page 358) and the ‘roll stability test’ (Section 16.2.3, Page 341).

Grease can also age mechanically without any external mechanical action. This is called‘shelf life’. The latter is associated with drums where oil separation takes place due to gravityon the bulk of the grease. After a long time, oil floats on the bulk of the grease. Vibrationsmay accelerate this process. Shelf life was earlier discussed in Section 4.17 and will not becovered in this chapter. Finally, grease will lose its consistency when it operates at temperaturesexceeding the High Temperature Limit (HTL, see Section 4.2).

In addition to mechanical changes, chemical changes occur. The most pronounced chemicalchange is caused by oxidation.

In short, the grease ‘damaging’ or ‘aging’ mechanisms can be classified as:

• Mechanical: oil separation, deterioration of the grease thickener structure.• Chemical: oxidation.

Chemical deterioration is predominant at high temperature and low speed conditions whereasphysical deterioration is predominant at lower temperature and high speed conditions, [294],see Figure 8.1. These two mechanisms usually occur simultaneously and then influence eachother. An example of this is the crust formation on grease that is sometimes observed. Attemperatures higher than 120 ◦C, grease will carbonize, forming a hard crust that prevents oil



Physicaldeterioration

Physical and chemicaldeterioration

Chemical deterioration

Temperature

Spe

ed

Figure 8.1 Dominating mechanisms for grease deterioration as a function of speed and temperature.Redrawn with permission from Ito, Tomaru and Suzuki, 1988 C© STLE.

bleeding [294]. At temperatures below 70 ◦C the grease aging is considered to be governedby change in grease ‘fluidity’ (yield stress and viscosity) and oil-bleed capacity.

8.1 Mechanical Aging

The mechanism of grease lubrication of rolling bearings is established during the initial phaseof bearing operation (the churning phase). During this phase the bearing acts like a greasemill causing mechanical degradation and change in the rheological properties. The greaselubricant in operating rolling bearings shows an initial change in consistency (usually a loss)and oil-bleeding rates (usually an increase) from the mechanical action of the bearing. This willagain have its impact on the lubricating ability, reservoir formation and sealing (Chapter 14).In addition, the change in grease rheology will also have an impact on the film thickness, asshown in Chapter 9.

Mechanical aging also occurs in the EHL contacts [345, 346]. The volume of lubricantpassing the contacts is so very small (because of the very thin films) that it will only bea fraction of the bulk in the case of oil lubrication. This is different in the case of greaselubrication where the contacts are starved and very little replenishment takes place.

The grease usually softens but may also harden, depending on conditions and grease type.Both effects will be described below.

8.1.1 Softening of Grease in Rolling Bearings

Softening of grease is caused by degradation of the material by shear. The grease will experi-ence very high shear rates when travelling through the EHL contacts. Zhu and Neng [638] andMerieux et al. [417] confirmed this in ball-on-disc experiments. It is important to notice thatthe number of overrollings that can be obtained in a ball-on-disc set-up is extremely small,compared with that in a rolling bearing and that this effect is therefore much more pronouncedin rolling bearings. Lundberg et al. [382–384,386] measured the change of grease consistency

Grease Aging 173

700

600

500

400

300

200

100

00 5 10 15

Travelled distance (km)

CE

Y (

Pa)

20 25 30× 104

F

H

G

B

D

I

E

C

A

Figure 8.2 Change in apparent yield stress CEY of several greases taken from railway bearings atvarious points in time. Reproduced from Lundberg and Hoglund, 2000 C© Elsevier.

by sampling grease from railway bearings, which had been running at low temperatures. Theymeasured the change in consistency through a so-called SCEY% number (Computerized Eval-uation of Yield [CEY] value), which is the percentile of the CEY of the last field measurementand of the fresh grease. Here the CEY is the shear stress at γ = 1 s−1 determined from a flowcurve on a rheometer, so the CEY could be regarded as an apparent yield stress.1 A value of100% denotes no change in CEY. The result of the CEY measurements from samples of theserailway bearings, taken at various points in time, is shown in Figure 8.2. This figure showsthat the yield stress changes rapidly during the first 25 000 kilometres but stabilizes later on.The figure also clearly shows that there may be large differences in the change of mechanicalstability of greases in these bearings.

Lundberg and coworkers showed that the decay in apparent yield stress could not besimulated using the grease worker (Figure 8.3a) or the more severe grease aging test, the Shellroll stability test (Figure 8.3b). In Figure 8.3b, the axis labeled Roller is actually the changeof consistency in 1/10 mm. The change in consistency from the grease worker and Shellroll stability tests do not show strong correlation to the change in apparent yield stress forgrease from the bearings. Next they investigated the relation with the limiting shear strength–pressure coefficient γ 2 and found a strikingly good correlation, as shown in Figure 8.3c.According to Lundberg and Hoglund [384], high γ -values cause high shear stresses for greasein a rolling bearing, and lead to severe conditions for the thickener. High γ -values result inmore mechanical degradation than low γ greases. Lundberg and Berg [383] combined the rollstability outcome with the γ values and fitted an equation correlating mechanical stability, fordata measured in the field and values obtained from laboratory tests:

SCEY% = 223.5 − 0.0774 · Roller − 2797 · γ, (8.1)

1 A concept originally described by Gow [230], explained in more detail in Section 5.5.2 A coefficient for predicting the change of the limiting shear stress to pressure: τL = τ0 + γ p. This is relevant tohigh pressure conditions such as in EHL.


60

50

40

30

C

D

F A

E

B

Wor

k (1

/10

mm

)

20

1050 60 70

SCEY%80 90

65

60

55

45

C

D

A

E

BRol

ler

(1/1

0 m

m)

40

3050 60 70

SCEY%

80 90

35

50

0.055

0.050

0.045

C

D

F

A

E

BGam

ma

0.040

0.03550 60 70

SCEY%80 90

100

80

60

40SC

EY

% (

%)

20

0200 40 60 80 100

(a) Change in cone penetration (1/10 mmbefore and after working the grease in agrease worker versus change in CEY inthe railways bearings.

(b) Change in cone penetration (1/10mm) beforeand after working the grease in a roll stability testversus change in CEY in the railways bearings.

(c) Limiting shear strength–pressure coefficientγ versus change in CEY in the railways bearings.

(d) Measured values of CEY% versuscurve fitting (Eq. 8.1).

Figure 8.3 Comparison of the change in CEY of grease that has been run in the railway bearingsfrom Figure 8.2 with the parameters obtained from various test methods. SCEY% denotes the percentilechange of apparent yield stress from fresh grease and that taken from the railway’s bearings (after300 000 km). Reproduced from Lundberg and Hoglund, 2000 C© Elsevier.

Eq. 8.1 gives a surprisingly good fit, as shown in Figure 8.3d. Assuming that mechanicaldegradation of grease in a rolling bearing is measured by the SCEY%, it seems that greasedegradation can be simulated quite well in a laboratory with a Shell roll stability test instrument.There is not a unique relation between SCEY% and change in consistency caused by the Shellroller. The γ value of the grease has the same sign as the change in consistency in the Shell

Grease Aging 175

roller test (Roller ). So if a grease has a large value of γ , then it will give a large change in CEYwith only a small change in penetration-values in the Shell roller test, and vice versa. It shouldbe noted that they only investigated ‘Li-greases’. Moreover, this is an empirical relation andapplying it to other operating conditions should be done with great care. The most interestingaspect of this is than the change in CEY (or yield stress) could be simulated directly on theShell roller tester.

Komatsuzaki and Uematsu [337] measured the thermo-oxidative deterioration of some Li-greases in cylindrical roller bearings and also found that the grease softened with time. Theyfound that the loss of grease consistency corresponded to changes (reduction) in droppingpoint. This measured loss in consistency followed Arrhenius kinetics behaviour with respectto temperature. Komatsukaki and Uematsu also demonstrated that grease softening (lossof consistency) was not due to thermo-oxidation effects. Grease leakage measured by Ito(Figure 8.4) may have been due to loss in consistency.

Another physical aging effect of grease stems from oil bleed losses from grease. As wasmentioned earlier in this book, Booser [91] and Tomrau [574] but also Komatsuzaki andUematsu [337] observed bearing lubrication failure when grease has lost half of its oil con-tent. In Figure 8.4, Ito demonstrates an increase in grease leakage with bearing speed. Thesubsequent increase in bleed rate may be ascribed to higher levels of mechanical work andhigher levels of oil loss for increasing bearing speed. This may be ascribed to higher levelsof mechanical work on the grease. One may expect an increase in consistency caused by areduced base oil content. Apparently, at high bearing speeds with non-channeling greases,

100

50

0

100

50

010 50 100 500 1000 5000 10 000

Gre

ase

leak

age

rate

[%

]

Oil

ble

adin

g ra

te [

%]

Time [h]

3000 rpm#6200 : Seizure

125°C100°C

Figure 8.4 Physical deterioration of a Lithium grease in a ball bearing. Reproduced with permissionfrom Ito, Tomaru and Suzuki, 1988 C© STLE.


450

400

350

300

250

Yie

ld s

tres

s [P

a]

200

150

100

50

0I.E + 02 I.E + 03 I.E + 04

Z [–]I.E + 05 I.E + 06 I.E + 07

Figure 8.5 Wohler curve for grease aging, after Eq. 8.4, with τy,∞ = 10 Pa, τy,0 = 400 Pa, Z0 =1 × 105.

grease thickener deterioration and softening dominates the oil bleeding process (rather thansyneresis.3 )

Model for Grease Softening

In a rolling bearing the shear, and therefore the mechanical work, varies significantly through-out the geometry. For controlled aging experiments the bearing is therefore less suitable.The results from the previous section show that a model describing aging is convenient tocompare the aging rate for the various aging methods. Controlled mechanical aging exper-iments can be done in a grease worker. However, other methods may also be used to testfor thermo-mechanical aging of grease lubricants. Methods for testing thermo-mechanicalstability of grease lubricants also include pumping through thin section pipes and continuousshear measurements using a rheometer.

Spiegel et al. [552, 554] modelled the mechanical aging of grease. They assumed that thegrease thickener material consists of particles where shear will break down the larger thinlamellar-like particles into spherical, (micellar-like) particles. Continuous shear will lead to acontinuous reduction in particle size, which will reduce the resistance to shear (softening). Byassuming that the grease thickener may be modelled as spherical particles, by each revolution ofsuch particle its surface will be sheared twice, that is, once in the direction of rotation and oncein the opposite direction. For oscillating shear, commonly applied in plate-plate/cone-platerheometers, they write

γ = ω/2 = (π · f ). (8.2)

3 In chemistry, syneresis is the exudation of the liquid component of a gel. ‘Syneresis’ involves leakage or separationof some liquid lubricant out of the solid, soap-thickened grease structure without breakdown of the grease.

Grease Aging 177

This is very convenient since the results of oscillatory and rotational shear may be compared.The ‘number of load cycles’ can be obtained by averaging, that is

Z = 1

π

∫ te

tb

γ (t)dt. (8.3)

At constant shear, Z = γ (te − tb) /π . This reduction in particle size will continue until anasymptotic value has been obtained.

Spiegel assumes that the shear stress behaviour over time will resemble a Wohler curve:ln τy = f (ln(Z )). They therefore assume the yield stress to behave as:

τy = τy,∞ + (τy,0 − τy,∞) · e−Z/Z0 , (8.4)

where Z0 is a reference number of load cycles, τy,∞ is the yield stress for Z → ∞ and τy,0 isthe yield stress for Z → 0. The number of stress cycles, according to Eq. 8.3 is of the sameorder of magnitude as that for solid materials.

The yield stress of a grease is therefore only determined by the Z number rather than eitherthe shear stress or time alone.

To describe stress as a function of time and aging, he uses a variant of the Casson model(earlier described by the equations from Table 5.2 and/or Czarny and Moes [151]):4

(τ

τy

)n

= 1 +(

K γ

τy

)n

. (8.5)

Substitution of 8.4 in 8.5 then gives an equation for the shear stress as a function of shear rateand history:

τ n = (τy,∞ + (τy,0 − τy,∞) · e−Z/Z0

)n + (K γ )n . (8.6)

For completeness other aging models will be given here. Merieux et al. [417] use a verysimple equation:

τy = τ0

(1 + γ t)αwith τ0 = 40 Pa. (8.7)

Bauer et al. [70] use for a constant shear rate:

τ

τ∞= 1 + a

τ∞

1

tq(8.8)

with 0.39 < q < 0.51 at T = 27.8 ◦C.The standard method for measuring mechanical aging is the grease worker. The device is

described in section 16.2.2. Figure 8.6 shows a schematic representation of it.

4 Merieux et al. [417] (see Section 9.5.4) used a similar equation with the factor n = 2 here.


Figure 8.6 Grease worker.

Spiegel [552] et al. quantified the mechanical work in the grease worker in terms of shearusing their stress cycle number ‘Z’, as defined in Eq. 8.3 and found for the number of cyclesper second Z1:

Z1 = 8ϕ (Dm/d)2 H

πdi. (8.9)

For the standard grease worker (DIN ISO 2137):

• Dm = 0.075 m; diameter of the disc.• d = 0.00635 m; diameter of the holes in the disc.• H = 0.0635 m; height of the chamber.• i = 51; number of holes in the disc.• ϕ; number for the non-Newtonian behaviour, for Newtonian behaviour ϕ = 1. For grease

ϕ ≈ 1 may be taken.

Substitution of these numbers in Eq. 8.9 gives Z1 = 70 for the standard grease worker.Hence, operating the grease worker for one hour gives Z = 70 × 3600 = 25 2000 ≈ 2.5 ×105. This number in itself does not have much significance, it may be used to compare variousmethods of artificially aging grease, such as in a cone-plate rheometer (in oscillatory shearmode).

Another application is the prediction of the mechanical aging in pipes caused by shear. Forpipe flow Spiegels ‘Load Cycle Number’ Z reads:

Z = 8L

π D. (8.10)

Grease Aging 179

Example

A grease is sheared in a rheometer at a constant shear rate of γ = 10 s−1 for 3 hours. In thatcase Z = 1

π× 10 × 3 × 3600 = 11.5 × 103. The time that is required to simulate the same

mechanical work in a grease worker is then t = 11.5 × 103/70 ≈ 3 minutes. For achieving thesame aging one would need to push the grease through a 45-metre long pipe with a diameterof 10 mm.

8.1.2 Hardening of Grease in Rolling Bearings

The lubricating grease does not always soften during operation in a rolling bearing. Mas andMagnin [402] measured the grease properties of a lithium and a calcium complex grease fromtapered roller bearings (double row) and deep groove ball bearings operating for about 900hours at temperatures below 100 ◦C, which showed an increase in consistency. They ascribedthis behaviour as resulting from mixing with steel wear particles from bearing operation. Thelargest increase in ‘viscosity’ was found in grease taken from the cage bars. The grease samplestaken from the cage bars showed a marked reduction in oil content that also contributes to theincrease in apparent viscosity.

The breakdown of grease thickener fibres during mechanical work results in another mech-anism for grease hardening. The grease apparently thickens because the broken fibres behavelike additional thickener content thereby increasing the grease consistency (increase surfacearea). More contact points are formed and the grease could appear harder, [197].

However, it is also possible that broken soap molecules, especially lithium hydroxystearate,will not act like additional thickener molecules, but will reduce oil solubility and the increasepolarity of the thickener.

Polyureas may harden during storage or during standstill operations. On the contrary, it iswidely known that polyurea greases tend to soften when subjected to low shear at ambienttemperatures, [349].

8.2 Grease Oxidation

The chemical aging of grease is mainly ascribed to oxidation. It is generally accepted thatoxidation reduces grease life. Although oxygen reduces grease life, the presence of oxygen isnot unfavourable for lubrication. The formation of metal oxides from the oxidation of bearingsurfaces is an important requirement to reduce friction for boundary lubrication conditions.The iron and metal oxides are solid lubricants for contacting metal surfaces. The metal oxidelayer also acts to strongly adsorb polar boundary lubricant additives that reduce frictionduring low kappa bearing operation [440]. Moreover in practice, oxygen is usually presentin applications and the selection of oxidation resistant grease is important to avoid prematurebearing failures due to lubricant oxidation. This especially applies for harsh conditions suchas elevated temperature, presence of ozone and/or continuous air flow through the grease.

Different phenomena occur in the chemical degradation of grease:

• Acid formation.• Reaction/consumption of additives.• Thermo-oxidative degradation of the thickener.


Ant

ioxi

dant

con

tent

[%

]

TA

N, m

g K

OH

/g

3000 rpm#6200: Seizure

100

50

0

10 50 100 500 1000 5000 10 000

Time [h]

0

50

125 °C

125 °C

100 °C

100 °C

Figure 8.7 Chemical deterioration of a lithium grease in a ball bearing. Reproduced with permissionfrom Ito, Tomaru and Suzuki, 1988 C© STLE.

• Polymerization of the base oil.• Thermo-oxidative degradation of the base oil.• Varnish and sludge formation.

Figure 8.7 shows the chemical deterioration of a Li-soap/mineral oil grease measured in a ballbearing. This figure shows the exponential reduction of the antioxidant in combination witha sharp increase in Total Acid Number (TAN) at the point where the antioxidant additivesare exhausted. The rate of antioxidant decrease is higher and depletion time is shorter forincreasing temperatures. The increase of TAN is ascribed to the formation of oxidativeproducts, which arise from both base oil and thickener materials. The tests from Figure 8.7show that the antioxidants in grease are exhausted after approximately half the life time ofthe grease. Similar results were found by Van den Kommer and Ameye [340] for a mediumtemperature and an extreme pressure grease using the RULER C© method and ROF testing.This number may be taken as a rule of thumb for monitoring the condition of the grease.

Most oxidation research has been performed on lubricating oils and it is generally acceptedthat much of this can be applied to lubricating grease. Studies, particularly on grease thickeneroxidation, are rare. The thickener does play a large role in the oxidation process of grease.This can be illustrated by the fact that a simple urea grease with mineral oil and no additiveshas a better oxidation stability than a simple lithium complex and mineral oil grease [492].

The oxidation of base oil and thickener are not fully independent problems. The oxidationof grease also has an impact on the interaction between oil and thickener. As an example,oxidation may prohibit further bleeding of a grease [338].

It is important to notice that oxidation in grease lubricated bearings is more pronouncedthan that in oil lubricated bearings due to the large surface area and small thickness of thefilms (large area per volume of lubricant) that are formed in the bearing during operation.

Grease Aging 181

In the next sections, first the oxidation of the base oil will be described, followed by thethickener.

8.3 The Chemistry of Base Oil Film Oxidation

In thin film oxidation, oxidation takes place with minimal or no limitations from oxygendiffusion into the oil [440]. According to Naidu [438] this is valid up to a limit of 0.3 mm thickfilms. The oil layers for most grease lubricated rolling bearings are much less than this 300micron limitation. It should be noted that for slow rotating, large size bearings with high initialgrease fill, oxygen diffusion will be the rate determining step for the autoxidation process [334].

8.3.1 Chemical Reactions

Oxidation of lubricant hydrocarbons is assumed to progress via a free radical mechanism. Themechanism consists of various phases that largely depend on temperature [130,185,335,507,560]. Below temperatures of about 120 to 140 ◦C alkyl hydroperoxides are the primary stableproduct of the reaction of hydrocarbons with molecular oxygen [185]. The phases may besummarized as:

Hydrocarbons + Oxygen → Alkyl Hydroperoxides + Rest molecules (Low temperature)

Hydrocarbon + Oxygen → Radicals + Rest molecules (high temperature). (8.11)

Alkyl hydroperoxides + heat(−catalyst−) → Radicals + Rest molecules

Radical + Molecule → Radicals + Rest molecules. (8.12)

Radical + Radical → Terminal Product. (8.13)

The first phase is called the ‘initiation phase’. The second is quite complex and is usuallysplit up again into two phases: the ‘propagation phase’ and the ‘branching phase’. The laststep of autoxidation is called the ‘termination phase’. The underlying chemical reactions willbe briefly described in the following subsections.

Autoxidation–Initiation Phase

Autoxidation is initiated by free radical formation. Free radicals (R•, H-O• or R-O•) originatefrom the reactions of hydrocarbons (R-H) with oxygen or decomposition products of alkylhydroperoxides (ROOH), where R is an alkyl, alkyl-aryl, cycloaliphatic or lipid structure. Ini-tiation of free radicals has been found to occur upon exposure of hydrocarbon materials to heat,ultraviolet light, hydroxy radicals (OH•), transition metal ions Mn+ (especially manganese,iron and copper, but also Fe2O3 [530]) or mechanical shear stress, [507, 639].

RH + O2

Energy/Mn+−−−−−−−→ ROOH (stable hydroperoxide)

ROOHEnergy/Mn+

−−−−−−−→ RO• + HO• (low temperature mechanism)

RH + O2

Energy/Mn+−−−−−−−→ R• + HOO• (high temperature mechanism)

RH + O2 + RH −−−−−−→ R• + R• + H2O2


Alkyl hydroperoxides are the first stable product formed from the reaction of hydrocarbons withmolecular oxygen. For some hydrocarbons, hydroperoxide formation is nearly quantitativewith the amount of exposure (reaction) with oxygen. Alkyl hydroperoxides are unstableat temperatures exceeding about 100–140 ◦C, depending on the chemical structure of thehydroperoxide. Hydroperoxides thermally decompose into free radicals. Fe/Cu metal catalysiswill accelerate the hydroperoxide decomposition which accelerates the propagation phase[491]. Metal ions that originate from wear debris and/or a freshly exposed steel surfaceproduced by wear [486, 530] catalyze free radical generation.

Propagation Phase

Once a free radical has formed, it will quickly react with molecular oxygen [204] to forma hydroperoxy radical (ROO•). This free radical further reacts with the substrate to formhydroperoxides (ROOH) and more free radical species.

R• + O2 → ROO• (formation of peroxy radical)ROO• + RH → ROOH + R• (alkyl hydroperoxide and alkyl radical).

The first reaction depends on temperature and occurs very quickly. The second reaction is therate determining step for the phase. As mentioned above, at lower temperatures (100–140 ◦C),hydroperoxides are the stable product of hydrocarbon oxidation.

Chain Branching Phase

Hydroperoxide is cleaved into alkoxy and hydroxy radicals at elevated temperatures [335,486,491] or under catalysed conditions [133]:

ROOH → RO• + HO• (prod. of alkoxy and hydroxy radiacals).

These radicals can then react with hydrocarbons to form alkyl radicals (and water and alcohols),which contribute to the propagation reaction:

RO• + RH → ROH + R• (alkoxy radical produce alkyl radicals)HO• + RH → H2O + R• (hydroxyl radical produce alkyl radicals).

Termination Phase

In the last phase (termination phase), the highly reactive R• and RO• radicals, formed in thephases listed above, will disappear by recombination by the following reactions:

R• + R• → R−R (formation of long chain hydrocarbons)R• + ROO• → ROOR (formation of dialkyl peroxides)RO• + R• → ROR (formation of ethers)ROO• + ROO• → R(C=O)R′ + ROH (formation of ketones and alcohols).

Grease Aging 183

All these reactions are accelerated by temperature.In the termination step oxidation products such as acids and sludge are formed. The acids

especially are detrimental to grease since they tend to destabilize the gel structure of manytypes of grease lubricants [475, 491].

Secondary and tertiary alkoxy radicals (RR′HCO•, RR′R′′HCO•) will form aldehydes andketones (RCHO, RR′CHO). These can condensate via acid catalyzed aldol reactions, whichagain lead to sludge and varnish degradation products [486]. Aldehydes, ketones and alcoholscan be further oxidized to give carboxylic acids.

Antioxidants

Generally antioxidants or oxidation inhibitors are added to the grease. There are two types:those that react with the initiators to form inactive compounds (radical scavengers: [491]) andthose that decompose the reaction products to form less reactive compounds (hydroperoxidedecomposers: [471,491]. Additives of this type are metal deactivators and corrosion inhibitors[491]. They have an effect on the initiation phase and the propagation phase. For a moredetailed description of the type of antioxidants, the reader is referred to Section 3.4.2, p. 62.The chemical reactions can be found in Reyes-Gavilan and Odoriso [491].

8.4 Oxidation of the Thickener

Most grease thickeners, such as metal soaps or polyureas, contain hydrocarbon chains. Hence,these materials will be susceptible to oxidation, similar to the base oils. Metal soaps alreadyhave oxygen containing functional groups (e.g. hydroxyl and carboxylate groups). Greasethickeners can oxidize forming polymerized varnishes and sludge by-products that affect theperformance of the lubricant.

Salomonsson et al. [512] studied the oxidation of naphthenic greases using an open beakertest in air for 7 days at 120 ◦C, and saw aggregation of fibres. They also saw that fibres becamebroken where the average length decreased from 1 μm to 0.1 μm and where the average fibrediameter increased from ca. 30 nm to 50 nm. They suggested three reaction pathways for12-hydroxystearates:

• 12-hydroxy stearic acid to 12-keto stearic acid, and deeper oxidation leading to α, β-unsaturated systems and their cross-reaction products capable of autocatalytic oxidation(Figure 8.8)

• 12-hydroxy stearic acid to an unsaturated acid capable of autocatalytic oxidation (similar tooleic acid) and polymerization (Figure 8.9).

• Hydrolysis of the lithium soap due to increased acidity.

RCOOLiH2O−−−→ RCOOH (Li-12-hydroxystearate into 12-hydroxistaearate acid).

The first two mechanisms lead to elimination of the hydroxy group, which gives lithium12-hydroxystearate grease its mechanical stability through hydrogen bonding. Oxidation willtherefore lead to a loss of stability. The last mechanism will change the thickener morphologyand oil retention. Increased acidity increases the oil solubility in the grease. Hence, both the


–OLi+O

OH

–OLi+

O2

O2

O2

O2

O

O

–OLi+O

O

OOH

O

O

OH

HO+

O

or

O

O

Figure 8.8 Conversion of lithium 12-hydroxystaerate into lithium-12-ketostaerate and further reactionsaround the 12th position. Reproduced from Salomonsson, Stang and Zhmud, 2007 C© Taylor and FrancisGroup.

rheology (softening, drop in G’ and slight increase in G”) and the chemistry will change dueto oxidation of the thickener.

Due to the polar nature of the oxidation products, the polarity of the grease will increaseover time, which will increase the absorption of water from the air [282,512]. Water can causecorrosion which has a negative effect on bearing life.

–OLi+

O

OH

–OLi+

H+

O

OH2+

–OLi+

O

–H3O+

Figure 8.9 Conversion of lithium 12-hydroxystaerate into an unsaturated acid capable of autoxidationand polymerization. Reproduced from Salomonsson, Stang and Zhmud, 2007 C© Taylor and FrancisGroup.

Grease Aging 185

8.5 A Simple Model for Base Oil Degradation

The series of chain reactions listed above form low molecular weight products, that is productswith lower molecular weight than the original molecules. These are the ketones, aldehydes,alcohols and acids, mentioned above. These free radical oxidation by-products can polymer-ize to form higher molecular weight products, which manifest themselves as high viscosityliquids, sludge and varnish. Parallel to the polymerization reactions, evaporation of the baseoil and the formation of volatile oxidation by-products also at elevated operating tempera-tures. A first order kinetic model for this oxidation model was proposed by Padval [460]and Naidu et al. [438–440]. This model is shown in Figure 8.10. Note that the oxygenconcentrations remain constant and are therefore not included in the equations from Fig-ure 8.10. The rate determining step (at least for mineral and ester oil lubricants) is the forma-tion of the low molecular weight products [439]. A mass balance can be applied and it can beassumed that all chemical reactions are first order. So

d Moil

dt=(

Moil

dt

)reaction

+(

Moil

dt

)evaporation

(8.14)

and

(Moil

dt

)reaction

= −k1 Moil, (8.15)

where Moil is the mass of oil at any point in time t . Cho and Klaus [126] showed that theevaporation rate can also be modelled using first order kinetics:

(Moil

dt

)evaporation

= −k3 Moil (8.16)

Although, it is generally accepted that evaporation rates are proportional to the surface areaof the liquid and therefore will follow a zero order equation [599]. Similar first order kineticsapply to polymerization and sludge formation.

Evaporatedoil in vapourphase

Oil+O2 Low mol.weightoxidates

High mol.weightoxidates

Sludge andvarnishdeposits

Oillayer

Bearingsurface

k3

k1 k2 k5

k4

Evaporated low mol.weight oxidates invapour phase

Figure 8.10 Oxidation model [440, 599].


The general solution to Eqns 8.15 and 8.16 reads:

Moil = Moil0 exp (−kt) , (8.17)

with Moil 0 the mass at t = 0 and where the rate constant, k, shows Arrhenius behaviour:

k = A exp

(−Ea

RT

). (8.18)

Similar equations can be derived for all reaction steps.

8.6 Polymerization

The formation of high molecular weight molecules (polymerization) leads to an increase inviscosity. A simple, but quite accurate equation for this is given by Doi and Edwards [171]:

η ∼ M3, (8.19)

with M as the molecular weight. This strong dependence on M means that even small changesin molecular weight may have a large impact on the viscosity.

The increase in viscosity does not lead to improved lubrication conditions, although thismay be expected based on the elasto-hydrodynamic lubrication theory from Chapters 9 and10. Polymerization ultimately leads to varnish and hard lacquers which have no ‘lubricity’.

8.7 Evaporation

Evaporation is a process by which any substance is converted from a liquid state into a vapour.Evaporation is not an oxidative process. Even in the absence of oxidation, evaporation is one ofthe loss mechanisms determining the lubricant layer thickness (especially at high temperatures,[98]). Evaporation will have an impact on lubricant film viscosity. The base oil has higherevaporation rate than the thickener [88] and therefore only evaporation of the base oil isconsidered in Eq. 8.16. Evaporation of the base oil can be modelled as a zero order reaction.However, evaporation depends on the vapour pressure, which again is strongly related toviscosity, and a function of the temperature. Viscosity decreases with increasing temperatureleading to an increasing evaporation rate. Evaporation of 2% in 22 hours at 100 ◦C is a commonspecification limit for premium mineral oil greases and ranges down to 0.4% for synthetics[95]. A model for evaporation and vapour pressure–temperature measurements is given byKaris and Nagaraj [312].

The temperature in the bearing will be clearly highest on the raceways where thin films of oilexist. Synthetic esters typically have a boiling point higher than 300 ◦C. However, most containtraces of volatile components with lower boiling points. Usually, evaporation at temperatureslower than say 150 ◦C will be small [354].

In the case of space applications, or more in generally in a vacuum, evaporation may bevery pronounced. According to Buehler [108], grease can be readily used in a vacuum forpressures ranging from 10−4 − 10−5 Pa, and at temperatures ranging from 90–120 ◦C. Also,

Grease Aging 187

25

20

15

10E

vapo

ratio

n lo

ss (

%)

5

0

AlkyIb

enze

nes

Paraf

finic

solve

nt/re

fined

oils

VHVI Hyd

rocr

acke

d oil

s

Polyalp

haole

fins

Polyole

sters

Rapes

eed

oils

Figure 8.11 Dependence of evaporation loss on base oil chemistry. Redrawn from Mang and Dresel,2007 C© Wiley-VCH.

in the case of air flow through bearings, evaporation losses affect performance. Evaporationrates for some ‘spacecraft greases’ are given in Buehler et al. [108]. Figure 8.11 shows theevaporation rates of some fluids determined by the Noack test method DIN 51 581.

8.8 Simple Models for the Life of Base Oil

8.8.1 Booser’s Oil Life Model

For industrial oils, some engineering models of lubricant life are in usage. The best known isfrom Khonsari and Booser [324], which is an empirical model giving a relation between oillife and absolute temperature (in Kelvin). It reads:

ln L = k1 + k2

T, (8.20)

where 1/k1 is the characteristic rate coefficient for oxidation of a specific oil, and k2 reflectsthe kinetic energy needed in collision of two molecules to activate the oxidation reaction,typically k1 = 4750 and k2 in the range between k2 = −10.64 (uninhibited) and k2 = −8.05(heavily refined oil), [94].

Figure 8.12 from Beerbower [72] compares the life of various inhibited synthetic oils andinhibited mineral oils on steel surfaces. The figure illustrates the superiority of synthetic oils.Vegetable oil based greases undergo oxidative solidification (they are ‘dried’ by oxygen), [33].This means that the model described by Eq. 8.20 does not apply. For vegetable oil greasespolymerization processes predominate over thermo-oxidative volatilization processes.


10000

3000

1000

300

100

30

10

3

1

0 100 200 300 400

Use

ful l

ifet

ime

[h]

Temperature [°C]

Polyphenyl ethersSilicones

Polyol esters

Synthetic hydrocarbonsand diesters

Polyglycols

Alkyl silicatesAlkyl phosphates

Mineral oils

Figure 8.12 Life expected for lubricating oil in air. Reproduced from Berrbower, 1972, NASA.

8.8.2 Two Phase Model

The complex chemistry of oxidation, as described in Section 8.2 can be simplified to twophases in the useful life of most lubricating oils (Booser [94]). First an ‘initiation phase’ or‘induction period’ in which the oxidation inhibitor is slowly consumed, and a second phase inwhich the oxidation inhibitor is exhausted and oxidation reactions occur until the lubricant isno longer able to lubricate (lost its ‘lubricity’).

The ‘induction time’ can be determined by measuring the heat flow in a very small sample(2 mg) using Pressure Differential Scanning Calorimetry (PDSC). Since the oxidation reactionis exothermic, the induction time corresponds to the time at which a heat flow is measured.In such an instrument the pressure is high, which reduces volatile oxidation by-products fromthe lubricant and increases the concentration of reacting gases [495]. For a description of themethod the reader is referred to Rhee [494]. The induction time can be modelled using a firstorder equation (Arrhenius).

t = A exp

(E

RT

), (8.21)

where A is an inverse frequency factor, E the activation energy and R the universal gas constant(8.314 J/mol · K) and T is the absolute temperature (K). Rhee [494] found that the activation

Grease Aging 189

Indu

ctio

n ti

me

[min

]

Temperature [°C]

Fully formulated grease

Oxidation inhibitor only

Uninhibited grease

1000/Temperature [K]

1000800600500400300

200

1008060504030

20

1086543

2

1

150 160 170 180 190 200 210 220 230 240 250

2.35 2.3 2.25 2.2 2.15 2.1 2.05 2 1.95 1.9

Figure 8.13 Comparison of induction times for a grease consisting of a lithium complex soap, mixtureof polyalphaolefin/mineral oil and various inhibitors. Reproduced with permission from Rhee, 1991 C©NLGI.

energy E of grease is temperature independent and that it did not change during greasedegradation (measured E = 146 kJ/mol). In later work [495] he found 83 < E < 152 kJ/mol.The constant A was grease dependent and therefore would need to be measured for eachgrease type.

Rhee correlated this induction time to wheel bearing grease life test results (ASTM D 3527,Section 16.2.31, p. 372) and found a reasonably good correlation:

Grease life = 177 · t0.31, (8.22)

where the grease life and induction time t are measured in hours. Note that these wheel bearingtests are high temperature tests (160–180 ◦C). The failure mode is most likely dominated bygrease oxidation, so this life prediction method does not apply to lower temperature operation.Figure 8.13 shows a comparison of induction times for a lithium complex grease and itscomponents. It shows that the fully formulated grease gave a significant improvement ofits oxidation life, and that it is clearly different from the antioxidant life. It is this complexchemistry and interaction of all components in the grease that determine its oxidation life.

It is important to realize that the oxidative induction phase is usually shorter in practice.As an example, it may be shortened by catalytic metals and water [94]. Hurley et al. [285]


thermally aged greases with different types of ‘debris’ and found an increase in the degree ofoxidation from left to right:

Brass > Cu > Fe2O3 > Fe3O4.

Brass material in grease or oil layers is typically caused by wear of cages, Fe2O3 typicallyoriginates from corrosion (water ingress).

The text in this chapter shows that grease aging is governed by a number of processes.Physically, the grease may harden or soften depending on the grease type and conditions.Volatilization may be an important factor where this is accelerated by the formation of lightfractions caused by oxidation. Oxidation of thickener, base oil or a combination may occur.This happens by means of a free radical mechanism. Oxidation processes predominate atelevated temperatures as soon as the antioxidants are consumed which lead to oxidation by-products which reduce the lubricity of the grease. Thermo-oxidative chemical reactions areaccelerated by metal wear particles that act as reaction catalysts.

9Film Thickness Theory forSingle Contacts

P.M. Lugt, M.T. van Zoelen, and C.H. Venner

A lubricating grease will only provide a long bearing service life if a sufficiently thick filmis developed separating the rolling elements from the raceways. As mentioned earlier, inChapter 2, initially the film will be generated by hydrodynamic action with grease as thelubricating medium and fully flooded conditions prevail. Later, the contacts may get starvedand the film is determined by the lubricant supply to the contacts, which can be calculated froma mass balance where the feed rate is determined by, for example, oil bleeding, shear, spin-motion and where the oil-loss rate is determined by effects such as side-flow in the contacts andevaporation. Centrifugal forces on thin lubricant layers could either feed the contact or removelubricant from the tracks. The rate at which these effects take place is determined by the physicalproperties of the lubricant, which again may change due to oxidation or polymerization.

The theory of film thickness is crucial for understanding the lubrication mechanisms ofgrease lubrication in a bearing and it is therefore described in this book quite extensively. In thecurrent chapter the ‘single contact film thickness theory’ will be presented. In the next chapterthe application of this theory to rolling bearings will be given, extended with other phenomenathat have an impact on film thickness, including long term effects such as base oil oxidation.

In this chapter, the fundamentals of lubricant film formation in rolling bearings will begiven, starting with the derivation of the flow equation (Reynolds’ equation) and the equationfor the film geometry. Initially, the films are determined by the ‘grease viscosity’, but, as soonas starvation occurs, the film will primarily be determined by the base oil viscosity. In recentyears starvation models have been developed, which will be presented here. Starvation maybe reduced by replenishment of the tracks by reflow. This may be considered in some cases.However, as will be shown, this mechanism is usually very slow. In this chapter it is assumedthat the main source of lubricant supply to the contacts will be oil bleeding. Especially forroller bearings, it is much more important than replenishment from the side of the contacts



since oil bled from grease located on the cage bars may be supplied to the centre of the contactsdirectly, where starvation will be most pronounced. The bleeding models have been given inChapter 7. The bled oil on the raceways may be lost or supplied by pumping driven by thecentrifugal forces in the bearing. Models have been developed for this based on the so-called‘thin film’ theory. The derivation is quite similar to that of the Reynolds equations, and istherefore included here as well.

9.1 Elasto-Hydrodynamic Lubrication

By fixing the coordinate system to a rolling element–raceway contact, the surface velocityof this rolling element and the raceway is (almost) equal and the lubricant, which (at leastpartially) sticks to the surfaces, will be sheared into the gap between the two surfaces, buildingup a hydrodynamic film. However, the contact load will generate a pressure back-flow reducingthis effect again and the film thickness will be the result of the balance between the two effects.It is determined by the geometry of the contact (contact radii), speed, elasticity, contact load,lubricant rheology (viscosity) and, in the case of starvation, by the feed rate of lubricant towardsthe contact. In this section, the fundamentals of elasto-hydrodynamic lubrication (EHL) willbe described, including the flow equations, the geometry description (elastic deformation) andsome simple equations that can be used for engineering purposes.

9.1.1 History

In 1886, Reynolds published his famous article where he derived the differential equationdescribing the pressure distribution and load carrying capacity of lubricating films for jour-nal bearings (Hydrodynamic Lubrication) [493]. In 1916, Martin [401] and Gumbel [237]applied Reynolds’ equation to the lubrication of gears and found film thicknesses that weremuch smaller than the roughness on the teeth of the gears. They could not explain the suc-cessful operation of these gears. In 1941 Meldahl [416] included elastic deformations causedby the contact pressures, but the film thickness predictions were still too small. Only in1949 when Ertel [594] and Grubin [233] included elastic deformation of the contacts and apressure–viscosity effect on the film thickness, was a sufficiently thick film found. This modeof lubrication has since been called ‘elasto-hydrodynamic lubrication (EHL)’. Petrusevich[470] and Dowson and Higginson [177, 178] solved the line contact problem and based onnumerical solutions [178] developed engineering formulae for a wide variety of operatingconditions. In 1972, Kauzlarich and Greenwood [315] solved the line contact problem forgrease lubrication. Later, in 1976, when more powerful computers were available, Hamrockand Dowson [243] solved the circular problem for oil lubrication. Their curve fit to numericalsolutions is still the most widely used film thickness formula for rolling bearings (and othermachine elements operating in the EHL regime). Later, in 1987, multilevel techniques wereintroduced by Lubrecht et al. [372], which made it possible to apply very dense grids in numer-ical calculations, which increased the accuracy of the solutions significantly. In the same yearYang and Qiang [625] extended the work from Kauzlarich and Greenwood into grease lubri-cated elliptical contacts. Venner [587] further improved the numerical multigrid methodologyand introduced the possibility of making transient calculations using multilevel techniques. Acomprehensive book has been written on multigrid methods in EHL by Venner and Lubrecht[589]. In 1994, Nijenbanning et al. [447] introduced a new film thickness equation, based on

Film Thickness Theory for Single Contacts 193

a curve fit of these very accurate multigrid solutions. After 1994, there was no further needto improve the accuracy of the fully flooded film thickness formulae and research in this areawas directed towards ‘starved EHL’, where initially the same multigrid techniques were used(Chevalier et al. [124] 1996, refined by Damiens et al. [158]). Later, Van Zoelen et al. [584],in 2008, used a new approach based on thin film flow to solve this problem, making it possibleto apply the formula to longer operating times and multiple contacts.

For a more extensive description on the history and review of EHL, the reader is referredto reviews by Spikes [558], Dowson and Ehret [176], Dowson [175] or Lugt and Morales-Espejel [376].

9.1.2 The Navier–Stokes Equations

The general equations describing the motion of a Newtonian fluid in space and time are theNavier–Stokes and continuity equations. The first are derived using conservation of momentumand the second using conservation of mass.

In lubrication theory, these equations are only used for calculating the full velocity profile inEHL films, sometimes in combination with the temperature distribution or with non-Newtonianrheology. Usually, the inertia forces are assumed to be negligible which simplifies the equationsto the Stokes equations. Examples can be found in Odyck and Venner [581], Almqvist andLarsson [24] or Hartinger et al. [250]. However, in most cases, it is not necessary to solve thefull equations. The ‘narrow gap or thin film assumption’1 in EHL can be used to simplify theequations leading to the Reynolds equation, which gives solutions for the film thickness withalmost equal accuracy. Nevertheless, in order to facilitate the derivation of these simplifiedequations, the Navier–Stokes equations are listed here.

With body forces fx , fy, fz , the Navier–Stokes equations, for example White [606], read:

ρDu

Dt= fx − ∂p

∂x+ ∂

∂x

[η

(2∂u

∂x− 2

3

(∂u

∂x+ ∂v

∂y+ ∂w

∂z

))]

+ ∂

∂y

[η

(∂u

∂y+ ∂v

∂x

)]+ ∂

∂z

[η

(∂w

∂x+ ∂u

∂z

)](9.1)

ρDv

Dt= fy − ∂p

∂y+ ∂

∂y

[η

(2∂v

∂y− 2

3

(∂u

∂x+ ∂v

∂y+ ∂w

∂z

))]

+ ∂

∂z

[η

(∂v

∂z+ ∂w

∂y

)]+ ∂

∂x

[η

(∂u

∂y+ ∂v

∂x

)](9.2)

ρDw

Dt= fz − ∂p

∂z+ ∂

∂z

[η

(2∂w

∂z− 2

3

(∂u

∂x+ ∂v

∂y+ ∂w

∂z

))]

+ ∂

∂x

[η

(∂w

∂x+ ∂u

∂z

)]+ ∂

∂y

[η

(∂v

∂z+ ∂w

∂y

)]. (9.3)

1 In physics this is called the ‘lubrication assumption’.


Layer thickness Film thicknessu2

u1

z y

x

h h~

Figure 9.1 Schematic representation of a roller–raceway contact separated by a lubricant film, fed bya lubricant layer.

9.1.3 The Reynolds and Thin Film Equation

In the case of (bearing) lubrication, the Navier–Stokes equations can be simplified, leadingto the so-called ‘thin film equation’, describing the thickness of a lubricant layer on a solidsurface with an air interface and the ‘Reynolds equation’ describing the thickness of a lubricantbetween two solid surfaces, which is called a film here. The layer thickness is denoted by hand the film thickness by h. Films are found wherever there is contact, such as in the rollingelement–raceway contacts. Layers are found on the raceways between the contacts or next tothe running track. This is depicted in Figure 9.1. Both films and layers will be so thin thatthe inertia forces (except for centrifugal forces) can be neglected and the fluid flow will belaminar. For the lubricant films, the contact forces on the films are so large that body forces(such as gravity) may be neglected.

At the boundary surfaces no slip is assumed, so the fluid velocity will equal the surfacevelocity here. In the case of a layer, this applies to one side of the layer. On the other side, theair side, the friction due to air flow may be neglected, so the shear stresses will be zero on thissurface. The viscosity may be assumed constant across the film thickness. Due to shear in thecontacts, heat will develop in the films and the temperature will rise. However, the slip ratesin rolling bearings are relatively low and this can therefore be neglected as well. For films,the effective wedge angle between the surfaces in the contact region will be so small (thoughvery important) that the boundary surfaces are almost parallel. For layers, large changes in thelayer thickness, may occur and in the absence of large shear stresses on the surfaces, surfacetension forces may be relevant.

It is assumed that the flow is laminar and that inertia forces are negligible compared to viscousshear (small Reynolds number, Dv

Dt = 0). The layer/film is thin compared to the characteristiclength L (( h

L )2 � 1). This means that shear stress and velocity gradients are only significantacross the lubricant film, so all velocity gradients compared with ∂u

∂z , ∂v∂z are negligible and all

derivatives with respect to x and y will be much smaller than their equivalents with respect to


z. This also means that the viscosity can be assumed to be constant across the film (all termswith derivatives of η can be neglected). Using these assumptions, the Navier–Stokes equationsfor Newtonian fluids can be reduced to:

∂p

∂x= fx + ∂

∂zτx with τx = η

∂u

∂z(9.4)

∂p

∂y= fy + ∂

∂zτy with τy = η

∂v

∂z(9.5)

∂p

∂z= fz . (9.6)

These equations, in combination with the continuity equation:

∂ρ

∂t+ ∂

∂x(ρu) + ∂

∂y(ρv) + ∂

∂z(ρw) = 0 (9.7)

can be solved using different boundary conditions. A free surface and incompressible flow isassumed for the thin layer equation and compressible flow and no-slip boundary conditionsfor the velocity on both surfaces leads to the Reynolds equation. Integrated over the film andby applying Leibniz’s rule, the continuity equation can be written as

∂

∂x

∫ h

0ρudz + ∂

∂y

∫ h

0ρvdz + ∂(ρh)

∂t= 0. (9.8)

This equation is used to introduce the film thickness in the continuity equation.

Thin Layer Equations

In most lubrication problems the flow of thin layers can be regarded as two dimensional. Thismeans that w = 0 and all derivatives to z can be neglected.

The body forces fx , fy, fz are assumed to be constant across the layer. Eq. 9.6 is integratedover the height z with 0 < z < h. The pressure is determined by the normal force on the layerwith thickness h and surface tension forces:

p = fz(z − h) − σ (1/κ), (9.9)

where κ and σ are the radius of curvature and surface tension respectively. For small curvaturesa simple approximation can be used [561, 629]:

1

κ≈ ∂2h

∂x2. (9.10)

In that case the pressure 9.9 can be written as:

p = fz(z − h) − σ∂2h

∂x2. (9.11)


The velocity can be calculated by integrating Eq. 9.4, with the following boundary conditions:

• No-slip on the oil–steel interface, that is u = 0 at z = 0.• Negligible stress at the air–oil interface: ∂u

∂z = 0 at z = h.

This gives:

u = 1

2η

(∂p

∂x− fx

) (z2 − 2zh

). (9.12)

For a 2D flow, and assuming that the density is constant across the film, the continuity Eq. 9.8becomes:

∂ h

∂t= − ∂

∂x

∫ h

0udz. (9.13)

The velocity 9.12 can be substituted into the mass balance 9.13 and after working out theintegral reads:

∂ h

∂t= 1

3η

∂

∂x

(h3

(∂p

∂x− fx

)). (9.14)

In the case that fz is not a function of x, the derivative of the pressure is obtained from 9.11and reads:

∂p

∂x= − fz

∂ h

∂x− σ

∂3h

∂x3. (9.15)

By combining Eq. 9.15 and 9.14, the one-dimensional thin film equation is obtained:

∂ h

∂t+ 1

3η

∂

∂x

[h3

(fz

∂ h

∂x+ σ

∂3h

∂x3+ fx

)]= 0, (9.16)

where σ is the surface tension, typically 0.02 < σ < 0.04 Jm−2 for lubricating oils. Theparameters fx and fz are the body forces due to normal and tangential forces (caused by e.g.gravity and centrifugal forces).

This equation will be used later in this book to calculate the thin film flow on flat surfaceswhere the flow is driven by surface tension or centrifugal forces, that is those cases where 1

κ

is large or where fz∂ h∂x is large.

In the case of relatively smooth layers and a (small) inclination of the surface a further sim-

plification can be made, as done by Van Zoelen [582], that is∣∣∣ fz

∂ h∂x

∣∣∣� | fx | and∣∣∣σ ∂3 h

∂x3

∣∣∣� | fx |,resulting in:

∂ h

∂t+ 1

3η

∂

∂x

(h3 fx

) = 0. (9.17)


u2

u1

z

yx

z = z2

z = z1

h

Figure 9.2 Coordinates in the lubricant film.

Thin Film Equations (Reynolds Equation)

To obtain the equation describing the lubricant film between rolling elements and raceways(Reynolds equation), the same thin film approximation is used. However, due to the very highpressures in the film, the lubricant density can no longer be assumed to be constant. Due to thehigh pressure gradients the body forces can be neglected ( fx , fy, fz) = 0 now. The lubricantflows in a gap with height h between two solid surfaces at height z = z1 and z = z2, movingwith speeds u1 and u2, as shown in Figure 9.2. Again no slip at the boundary surfaces isassumed. This gives:

u = u1 at z = z1 (9.18)

u = u2 at z = z2. (9.19)

Integrating (9.4, 9.5) twice with respect to z, using a new coordinate z′, where z′ = z − z1 soh = z2 − z1 (film thickness), that is 0 ≤ z′ ≤ h, yields:

u = 1

2η

∂p

∂xz′ (z′ − h

)+(

h − z′

h

)u1 + z′

hu2 (9.20)

v = 1

2η

∂p

∂yz′ (z′ − h

)+(

h − z′

h

)v1 + z′

hv2. (9.21)

The lubricant volume flow per unit length q is found by integration over the film thickness:

qx =∫ h

0u(z′)dz′ = − h3

12η

∂p

∂x+ h

2(u1 + u2) (9.22)

qy =∫ h

0v(z′)dz′ = − h3

12η

∂p

∂y+ h

2(v1 + v2) . (9.23)

Note: the first term is the pressure flow (Poisseuille flow) and the second term is the shearflow (Couette flow). In rolling bearings, transverse motion is usually absent (or negligible), so(v1 = v2 = 0) and transverse flow (or leakage out of the contact) is only induced by pressure.


By substitution of the velocity field (9.20, 9.21) into the mass balance 9.8 the well knownReynolds equation [493] is obtained, relating the pressure to the gap height and the surfacevelocities:

∂

∂x

[ρh3

η

∂p

∂y

]+ ∂

∂y

[ρh3

η

∂p

∂y

]= 6 (u1 + u2)

∂(ρh)

∂y+ 6 (v1 + v2)

∂(ρh)

∂y︸︷︷︸wedge

+ 6ρh∂

∂x(u1 + u2) + 6ρh

∂

∂y(v1 + v2)︸︷︷︸

stretch

+ 12∂(ρh)

∂t︸︷︷︸squeeze

. (9.24)

Three effects cause pressure build-up (and therefore load carrying capacity) in the lubricantfilm:

• The ‘wedge effect’: due to a wedge-shape of the inlet of the contact.• The ‘stretch effect’: pressure generation induced by variation of tangential velocities in the

gap. This phenomenon occurs when the surfaces deform in a tangential direction such as incold rolling [373]. In rolling bearings this effect can be neglected.

• The ‘squeeze effect’: this term plays an important role when surface roughness effects areincluded, in the case of vibrations in bearings or for studying grease noise. In those casesthe problem can no longer be considered stationary.

9.1.4 Cavitation

The Reynolds equation may predict pressures below the vapour pressure of the lubricant.Since, for fluid lubrication, the pressure cannot drop below this value an additional equationmust be added to the lubrication problem: the cavitation condition. The vapour pressure of thelubricant, pv , is small compared to the mean pressure in the film p (pv � p). Therefore it isjustified to approximate the vapour pressure to the atmospheric pressure, p∞ (pv ≈ p∞) andtherefore pv = p∞ = 0. The cavitation condition can then be written as :

p ≥ 0. (9.25)

9.2 Contact Geometry and Deformation

As mentioned in section 9.1.1, elastic deformation will play a major role in the formation ofa favourable inlet geometry, which will provide a much thicker film than in the case of rigidbodies. In this section, the equation for the shape of the film will be derived based on the rigidcontact geometry corrected for elastic deformation. In addition, some useful equations will begiven for pressure and deformation, based on Hertz’ theory.


9.2.1 Rigid Bodies

The contacts between inner-ring/outer-ring raceways and the rolling element are conformaland nonconformal contacts. Close to the contact, the geometry can be simplified by assumingthat the cylindrical shape of a raceway/rolling element can be approximated by a parabola.The gap between raceway and rolling element in the x-direction, hx , then reads,

hx ≈ h0 + x2

2Rx1

+ x2

2Rx2

. (9.26)

This can be rewritten into

hx ≈ h0 + x2

2Rx(9.27)

with

1

Rx= 1

Rx1

+ 1

Rx2

, (9.28)

which actually reduces the problem to a rolling element on a flat surface, see Figure 9.3.A similar exercise can be done for the gap across the rolling direction, that is, the y-direction.

In the case of a deep groove ball bearing or spherical roller bearing inner-ring contact, thesurfaces are concave and

hy = h0 + y2

2Ry1

− y2

2Ry2

, (9.29)

which can also be reduced to the gap between a spherical element and a flat surface:

hy = h0 + y2

2Ry. (9.30)

Rx1

Rx2

Rx

u2 u2

u1 u1

hxhx

h0 h0

Figure 9.3 Gap between inner-ring raceway and rolling element in running direction.


axay

Figure 9.4 Contact ellipse.

However, now a minus sign needs to be introduced here to calculate the reduced radius:

1

Ry= 1

Ry1

− 1

Ry2

. (9.31)

Note that for most outer-ring contacts, the contact is concave in both directions.

9.2.2 Elastic Deformation

If the bodies are assumed to be rigid, then the minimum lubricant film thickness is equal tothe gap in the centre of the contact h0 (see Figure 9.3). However, the contact load will flattenthe surfaces and lead to an elliptical contact (note that this does not apply to cylindrical andtapered roller bearings or in the case of contact truncation), as shown in Figure 9.4. The sizeof this ellipse and the maximum deformation can easily be calculated using Hertz’ theory(summary by Moes and Vroegop [426, 427] from the original work of Hertz [256–259]).

Hertzian Theory

A ratio of reduced radii is defined such that x and y are the directions where the contact size issmallest in the running direction and therefore Rx < Ry . This is always the case for the rollingelement–raceway contacts in a rolling bearing. The ratio of the reduced radii of curvature isdenoted by λ:

λ = Rx

Ry≤ 1 (9.32)

and

1

R= 1

Rx± 1

Ry. (9.33)

The ± refers to a contrafrom (+ sign) and conform (− sign) contact. The contact is drawn inFigure 9.4. Note that ax < ay .

The contact size and maximum Hertzian pressure can be calculated using the formulae from[427, 447], as will be shown below.

The reduced modulus of elasticity E ′ is defined as:

2

E ′ = 1 − ν21

E1+ 1 − ν2

2

E2. (9.34)


The half-width of the contact in the x-direction can then be calculated using:

ax =(

6Rx Fκ Ec

E ′π (1 + λ)

) 13

. (9.35)

Here λ and κ are defined as the ratio of the radii of contact curvatures and contact radiirespectively:

λ = Rx

Ryand κ = ax

ay. (9.36)

Ec is the Legendre normal integral (complete elliptic integral) of the second kind [256]:

Ec =∫ π/2

0

dψ√cos2 ψ + κ2 sin2 ψ

, (9.37)

which is approximated by [447, 490]:

Ec ≈ 0.5πκ2

(1 + 1 − κ2

0.5πκ2− 0.25 ln κ

). (9.38)

The ellipticity of the elliptical contact reads [256]:

κ = ax

ay≈(

1 +√

ln (16/λ)

2λ−

√ln 4 + 0.16 ln λ

)−1

. (9.39)

Knowing the size of the contact ellipse, the maximum Hertzian pressure can be calculatedaccording to:

pmax = 3F

2πax ay(9.40)

and the mutual approach:

c = γ

(9F2

8RE ′2

) 13

, (9.41)

with

γ = κ Fc

0.5πα(9.42)

α =(

κ Ec

0.5π

) 13

, (9.43)


which requires another elliptical integral Fc, which can be approximated by:

Fc ≈ 0.5πκ2

(1 +

(1 − κ2

)ln (4/κ)

0.5πκ2− 0.75 ln κ

). (9.44)

Point-Wise Elastic Deformation

In the lubricated case, the pressure distribution no longer follows the Hertzian theory. In thiscase, the contact pressure is determined by the balance between shear flow and pressure flow,which are both a function of the gap geometry h (see the Reynolds Eq. 9.24). However, dueto the very high contact stresses in rolling bearings, the film thickness h itself is now also afunction of the pressure and can be calculated using the earlier derived Eq. 9.27, 9.30 through:

h(x, y) = h0 + x2

2Rx+ y2

2Ry+ de(x, y), (9.45)

where de(x, y) is the (local) elastic deformation. Generally, it is assumed that the size of therolling elements and rings is much larger than the size of the Hertzian contacts and that thedeformations are relatively small so that the contacting rings and rolling elements can beconsidered as semi-infinite elastic bodies and linear elastic theory applies. Moreover, plainstress prevails. The equation for the film thickness then reads:

h(x, y) = h0 + x2

2Rx+ y2

2Ry+ 2

π E ′

∫ ∫S

p(x ′, y′)dx ′dy′√(x − x ′)2 + (y − y′)2

. (9.46)

For more details on the elastic deformation the reader is referred to Johnson [331].The constant h0 in Eq. 9.46 is the mutual distance of approach of two remote points in the

bodies and may be solved from a force balance equation (Wijnant [610]):

m∂2h0

∂t2+

∫S

p(x, y)dxdy = F(t). (9.47)

9.3 EHL Film Thickness, Oil

The film thickness in EHL can be calculated by solving the Reynolds Eq. 9.24 or the Navier–Stokes Eqns 9.1, in combination with the film thickness Eq. 9.46. The boundary conditionsare given by the cavitation condition, 9.25, and the force balance between applied load andpredicted load given by the pressure distribution. Except for some asymptotic cases, it isnot possible to solve these equations analytically. Numerical solvers are required to calculatethe detailed point-wise film thickness distribution. Figure 9.5 shows examples of pressuredistributions in the running direction (X ) and across the running direction (Y ) where theload is varied from extremely low to very high. The figure shows that the pressure distributionapproaches the Hertzian elliptical distribution at very high load. Inside the contact, the pressureis high and the viscosity will be extremely high. So in this area the pressure flow can be


0.8

0.6

0.4

H (

Y =

0)

0.2

0–2 –1 0

1000

10

1

0.8

0.6

0.4

H (

X =

0)

0.2

0–2 –1 0

YX

YX

1000

10

1 2

0.8

0.6

0.4P (

Y =

0)

0.2

0–2 –1 0

10

1

1

1.2

0.8

0.6

0.4P (

X =

0)

0.2

0–2 –1 0

10 1000

1000

1 2

1

1.2

Figure 9.5 Some characteristic solutions for pressure and film thickness (from Wijnant [610]) forvarious load conditions, M = 10, 20, 50, 100, 200, 500 and 1000. The lubricant number is L = 5. Thepressure and coordinates are normalized according to P = p/pmax , H = h/c, X = x/ax , Y = y/ay .The film thickness is scaled with the mutual approach c, which may give the impression that the filmthickness strongly depends on load, which is not the case (see Eq. 9.48). The definition of M and L willbe given by Eq. 9.50.

neglected. At the area where the pressure is lower, ‘leakage’ due to pressure flow will lead tothe characteristic restriction at the side and outlet of the contact.

Usually, only the central (hc) or minimum film thickness (hm) information is consideredas characteristic. For this, curve fits have been made of numerical solutions resulting in filmthickness formula. It is important to stress that these formulas are approximations. The mostwidely used formula is the Hamrock and Dowson [245] film thickness formula from 1978:

hm

Rx= 3.63

U 0.68G0.49

W 0.073

(1 − e−0.68κd

)hc

Rx= 2.69

U 0.67G0.53

W 0.067

(1 − e−0.73κd

) (9.48)

where:

κd = 1.03

(Ry

Rx

)0.63

G = αE ′

U = η0us

2E ′ RW = F

E ′ R2.

(9.49)

This formula illustrates quite clearly the impact of the various physical parameters on filmthickness. For instance, it shows that the film thickness is mainly a function of the product of


speed and viscosity. This explains why water will only build up very thin films due the factthat the viscosity of water is pressure independent (α ≈ 0). As mentioned in Section 3.2.2, thepressure–viscosity coefficient for lubricating oils varies between 1 × 10−8 < α < 3 × 10−8

Pa−1, which is much smaller than the possible variation in viscosity itself. So, for lubricatingoils the film thickness is mainly determined by the viscosity and not by the pressure–viscositycoefficient. It is important to notice that these equations only apply to the fully flooded situation,that is when the inlet of the contact is submerged in oil/grease. It will be shown later that themechanisms in the case of starvation are quite different.

Lately, more accurate solutions for the EHL film thickness have been developed. Unfortu-nately, this could not be done without losing the transparency in the dimensionless numbersand film thickness equations. Nevertheless, these equations are preferred when high accuracyis required. If the lubricant is incompressible and follows the Barus viscosity–pressure relation(3.16), the minimum number of dimensionless groups needed to characterize the problem is,according to Moes [424, 425], only three, instead of the four from Hamrock and Dowson(listed in 9.49). These dimensionless groups are:

M = F

E ′ R2x

(E ′ Rx

η0us

) 34

L = αE ′(

E ′ Rx

η0us

)− 14

λ = Rx

Ry. (9.50)

The M-number is called the ‘load number’ and L is called the ‘lubricant number’. Theadvantage of these groups over the groups from Eq. 9.49 is that there are only three insteadof four. However, from an engineering point of view, it is confusing that the load numberM contains the viscosity, which is a lubricant parameter. This is the reason why both sets ofdimensionless groups are still used.

The Dowson and Higginson formula is only accurate in the piezo-viscous elastic regime forsmall values of α. A film thickness formula valid for the entire parameter domain has beendeveloped by Nijenbanning et al. [447] and is a function fit of asymptotic solutions, reflectedin the various dimensionless groups 9.53:

hc

Rx

√E ′ Rx

η0us=[(

H32

RI + (H−4EI + h−4

00

)− 38

) 23 s

+ (H−8RP + H−8

EP

)− 18 s

] 1s

(9.51)

with

s = 3

2

(1 + e−1.2 HEI

HRI

)and h00 = 1.8λ−1 (9.52)

and

HRI ≈ 145(

1 + 0.796λ1415

)− 157

λ−1 M−2

HRP = 1.29 (1 + 0.691λ)−23 L

23

HEI = 3.18(

1 + 0.006 ln λ + 0.63λ47

)− 1425

λ− 115 M− 2

15

HEP = 1.48(

1 + 0.006 ln λ + 0.63λ47

)− 720

λ− 124 M− 1

12 L34 .

(9.53)


This equation only applies to contacts with the entrainment direction perpendicular to themajor principal axis of the contact ellipse, that is λ = Rx/Ry ≤ 1, which is generally the casein rolling bearings (except for flange contacts). This equation may seem complicated, howeverthe film thickness is still explicitly given and can be calculated on any hand calculator orcomputer. For a more detailed description the reader is referred to [447].

9.3.1 Example: 6204 Bearing

As an example, a 6204 bearing is running at 100 ◦C, with a speed of 10000 r/min and apure radial load of 208 N (C/P = 65). The bearing is lubricated with the base oil of GWZgrease, which has a viscosity of ν = 30 cSt at 100 ◦C, density ρ = 890 kg/m3 and dynamicviscosity is η0 = 0.030 Pa · s). A viscosity–pressure coefficient of α = 1.6 × 10−8 Pa−1 isassumed for this oil. The ball radius is Rx1 = Ry1 = 3.97 × 10−3 m. The inner-ring radiiare Rx2 = 12.8 × 10−3 m and Ry2 = −4.06 × 10−3 m. By using Eq. 9.33, this gives forthe reduced radii of the inner-ring–ball contacts: Rx = 3.03 × 10−3 m, Ry = 179 × 10−3 m.The maximum load in the loaded zone of a single ball–inner-ring contact is F = 185 N, themaximum Hertzian pressure is 1.33 GPa and the contact size is ax = 70 μm and ay = 940 μm.The contacts are running in a rotating frame of reference and the surface velocities can bededuced from the kinetic behaviour of the bearing assuming pure rolling. A derivation of theequations can be found in [249]. The inner-ring–ball sum velocity is:

us = dm

2[(1 − γ ) (ωi − ωm) + γωR] (9.54)

where ωi , ωm , ωR are the angular speeds of the inner raceway, cage and balls respectively(rad/s). The parameter γ is defined by γ = D cos α

dm, where D is the ball diameter, dm is the

pitch diameter and α is the contact angle (in this example α = 0). Substitution leads to a sumspeed of us = 16.5 m/s. The Moes dimensionless numbers are then: M = 696 and L = 18.3.The film thickness according to Eq. 9.51 is hc = 0.665 μm. The film thickness according toDowson and Higginson is hmin = 0.51 μm.

9.4 EHD Film Thickness, Grease

In the case where thickener material enters the contact, the film thickness will not be determinedby the base oil only and the equations listed above do not apply. This typically occurs in thecase of a large volume of grease in the bearing, in the early (churning) phase. It could alsohappen after transient events such as during a temperature increase or in the case of vibrationswhere grease is detached from the surface. In this section both measurements and models forfully flooded grease lubricated contacts will be described.

9.4.1 Measurements

By 1972 Poon [476] measured film thickness of grease in EHL contacts. He used a two-discmachine and measured the films using magnetic reluctance techniques.


Base oil

Grease

2.0

1

00 10 20 30 40 50 120

t[min]

h /

h0

0

b

Figure 9.6 Film thickness measurement on a two-disc rig. Reproduced from Poon, 1972 C© ASME.

Poon found films which were initially thicker than those expected based on the base oilviscosity only (see Figure 9.6), followed by a decrease in time. He also measured the films ofmechanically aged grease and found significantly lower values, very close to those expectedbased on the base oil viscosity (see Figure 9.7).

Zhu and Neng [638] measured the grease film thickness in point and line contacts. Theyalso showed severe starvation leading to a continuously decreasing film thickness for pointcontacts. However, in line contacts, starvation was limited to a short initial period of aboutonly one minute, after which the film thickness remained constant. Unfortunately, they onlymeasured for 10 minutes. Like Poon, Zhu and Neng also concluded that grease ages such

2.0

1.0

0 10 20 30 40 50 90

GL 2Sample after one weekin Klein mill

Virgin sample

Time [minutes]

Gre

ase

film

/bas

e oi

l fil

m th

ickn

ess

Figure 9.7 Film thickness measurement with fresh grease and grease aged in a mill. Reproduced fromPoon, 1972 C© ASME.


Grease A1 Grease A3 Grease A2 Grease A3Grease A2A (a) Aromatic (21 °C) B (a) Aromatic (77 °C)

Grease B1 Grease B3 Grease B2 Grease B3Grease B2A (b) Alicyclic (20 °C) B (b) Alicyclic (78 °C)

Grease C1 Grease C3 Grease C2 Grease C3Grease C2A (c) Aliphatic (20 °C) B (c) Aliphatic (78 °C)

Figure 9.8 Interferometry image for low speed operation, where thickener lumps are clearly travellingthough the contact. Reproduced from Kaneta et al., 2000 C© Sage Pulications.

that the grease viscosity approaches the base oil viscosity and that the film thickness shouldtherefore be calculated using the base oil viscosity. If this were to always apply, then the oilfilm thickness equation could directly be applied to grease lubricated contacts.

Later, when very accurate optical interferometry measurements on a ball-on-disc config-uration became available, fully flooded measurements were done using a scoop to ensurefully flooded conditions. In this case grease is continuously ‘pushed back’ into the inlet ofthe contact and only a mild form of aging occurs. This makes it possible to measure overlonger times with fresh grease. Such measurements have been made by Astrom et al. [35],Williamson et al. [614], Kaneta et al. [309] and others, who showed that the film thickness isindeed higher than the fully flooded oil film thickness. The optical set-up also made it possibleto show that grease thickener lumps were entering the contact. They did not age the grease(or run for long times) and their measurements are therefore representative of the initial phaseof bearing operation (or for longer times if the bearing is running at ultra-low speed). Figure9.8 shows some images from Kanata’s measurements clearly showing the nonuniform filmscaused by grease particles travelling through the contact.

9.4.2 Film Thickness Models for Grease Rheology

When the contact is fully flooded with relatively fresh grease, as in the ball-on-disc mea-surements described above, the traditional Newtonian viscosity has to be replaced by


non-Newtonian grease rheology. In 1972 Greenwood and Kauzlarich [315] derived an analyt-ical expression for the 2D grease film using a Herschel–Bulkley model,

τ = τy + K γ n. (9.55)

Later, in 1979, Jonkisz and Krzeminski-Fredihave [306] numerically solved the line contactEHL problem with the same Herschel–Bulkley model obtaining a slightly more accuratesolution compared to the Kauzlarich and Greenwood model.

In both papers, but also later in Bordenet et al. [99] it is shown that in the inlet two layersexist. One layer where the shear stress exceeds the yield stress and where grease flows as aviscous liquid with a viscosity depending on the shear rate, and a layer where the shear stressis smaller than the yield stress and where a plug flow occurs. The thickness of this plug flowlayer depends on the yield stress of the grease and can be calculated rather easily using theresult of the Navier–Stokes equations to which the lubrication assumptions were applied (Eq.9.4). The force balance reads:

∂τ

∂z= ∂p

∂x. (9.56)

The pressure is assumed not to vary across the gap, so

τ = zdp

dx. (9.57)

Here − 12 h < z < 1

2 h, so z = 0 refers to the centre of the film. A plug flow will occur forτ < τy , so half the thickness of the central layer where a plug flow occurs is given by:

z p = τydpdx

. (9.58)

This is illustrated in Figure 9.9 for pure rolling. In the Hertzian contact, the pressures are veryhigh and due to the exponential relation of the viscosity with pressure the occurrence of a plugflow here is obvious. Upstream, viscous behaviour is observed close to the wall and a plug

h

Figure 9.9 Film profile and plug flow in a grease lubricated pure rolling EHL contact. Reproducedfrom Dong and Qiang, 1988 C© Elsevier.


flow will only occur in the centre of the film. Further upstream, which is not shown in thisfigure, the pressure gradient is small and the velocity will again be constant across the gap.Kauzlarich and Greenwood [315] give an equation for the shear rate in the nonplug flow inthe inlet of the contact.

γ =(

z − z p

z p

) 1n (τy

K

) 1n

z > z p. (9.59)

Eq. 9.59 is strictly only valid in the case that the yield stress τy and consistency indexK are pressure independent, which is a valid assumption in the inlet, that is, at the onsetof pressure build-up, where the pressures are relatively low. For the prediction of the filmthickness, Kauzlarich and Greenwood use the Grubin theory in EHL where the film thicknessis assumed to be determined by the inlet only and where the contact shape is given bythe dry contact Hertzian pressure distribution. They assume (the same) exponential pressuredependence of both yield stress τy and consistency index K . Unfortunately, no high pressurerheology measurements with lubricating grease are available and a guess has to be madeabout the pressure dependency of yield stress and consistency in this regime. Assuming anexponential relation, similar to what was done for base oil viscosity, makes it possible to derivea film thickness equation for line contacts [315]:

hn+ 1

3c = 2

32 π

16

313

(E ′

w

) 16

R12 αK0un

m

[(4 + 2

n

)n

I (n) + π√3

λnτy0 hnc

K0unm

](9.60)

with

K = K0 exp(αp)

τy = τy0 exp(αp)

I (n) =

(n − 1

3

)!

(n − 2

3

)!

2 (n!)

λ1 = 1 − 1

3

(2z p

h

)2 2n + 1

n + 1< λn < 1.

(9.61)

Here w is the load per unit width. The noninteger factorials in 9.61 can be calculated using

n! = �(n + 1) =∫ ∞

0e−t t ndt. (9.62)

This means that 23 < λ1 < 1. For bearing greases, n ≈ 0.3, so 1 < λ < 1.25 and I (n) ≈ 0.

Under practical conditions the last term in Eq. 9.60 is negligible. So the film formation isdetermined mainly by the ‘consistency index’ K0 and speed.

Kauzlarich and Greenwood theoretically evaluated the film thickness for a large number ofgreases and showed a significant difference between the grease film thickness and base oilfilm thickness (up to a factor of 14!). Such large differences are not found in experiments.


Rolling speed [m/s]

Cen

tral

fil

m t

hick

ness

[nm

]

1000

100

10

11.00 0.10 0.01 0.00

25 °C60 °C

80 °C

Figure 9.10 Film thickness versus rolling speed. Reproduced with permission from Hurley and Cann,1999 C© NLGI.

The difference is ascribed to heat development in the inlet of the contact (inlet shear heating),which is higher in the case of grease than in the case of oil lubrication. They also derived anequation for the difference in temperature between the centre line of the film and the rollersbased on the same Herschel–Bulkley model:

Tc − Ts = 2n−1(2 + 1

n

)n3 + 1

n

K (um)n+1

Kc

(h − hc)n+1

h2n, (9.63)

where Kc is the thermal conductivity of the grease and hc the film thickness at the locationwhere the pressure gradient is zero, which is approximately equal to the central film thickness.The film thickness Eq. 9.60 shows again a power law behaviour (plotting film thickness versusspeed on logarithmic scales will give a straight line) between speed and film thickness.

Film thickness measurements have confirmed this power law behaviour. However, mea-surements also show that this power law behaviour stops at very low speeds [172, 283], asillustrated in Figure 9.10.

For very low speeds, it is convenient to rewrite the film thickness Eq. 9.60 into:

hn+ 1

3c = 2

32 π

16

313

(E ′

w

) 16

R12 αK0

[(4 + 2

n

)n

I (n)unm + π√

3

λnτy0 hnc

K0

], (9.64)

to explicitly show that the film thickness goes to a nonzero value at zero speed. Accordingto Eq. 9.63, in the case of ultra-low speeds, the inlet shear heating �T → 0 for u → 0.Effectively, combining both effects, may explain the increase in film thickness at decreasing,ultra-low, speeds as depicted in Figure 9.10.


In 1988 Dong and Qiang [173] developed a line contact model using a more appropriaterheology model based on the work of Bauer [70]:

τ = τy + ηoil γ + k2 (γ )n . (9.65)

Here ηoil is the base oil viscosity. They proposed the following film thickness formula:

h

hoil=(

1 + ϒ1.1

(hoil

Rx

)1−n)0.69

(9.66)

where

ϒ = ηoil

k2

(um

Rx

)n−1

. (9.67)

Also here, the correction for the film thickness does not contain the yield stress. Dong andQiang carried out computations for a yield stress up to 3000 Pa and even at this unrealisticallyhigh value, they observed a film increase of 3% only, indicating that the yield stress correctionis negligible.

Bordenet et al. [99] used the same rheology model but now for point contacts. Unfortunatelythey do not give a film thickness formula. However, they do confirm the main conclusion fromDong and Quang, that is that the base oil viscosity is the most important parameter here,that the yield stress does not have an impact on the film thickness, and that the films can becorrected using the ‘plastic viscosity’ k2.

Yang and Qian [625] have derived a 2D solution for elliptical contacts using the Binghamplastic rheology model:

τ = τy + K γ . (9.68)

The argument that they use for neglecting the shear thinning effect is that EHL contactstypically operate under higher shear rates, where linear models apply. They derived an equationfor the width of the plug flow in the inlet:

z p = τy

[3ηum

h − hc

h3+ 3τy

2h

(1 − 1

3

(z p

h

)2)]−1

≈ τy

[3ηum

h − hc

h3+ 3τy

2h

]−1

(9.69)

and a central film thickness equation:

hc

Rx= 2.44 (GU )0.74 W −0.0733

(1 − 0.43e−0.52k

)(1 + 3.71τ )0.74 (9.70)

where U , G, W and k are the Hamrock and Dowson dimensionless parameters, given byEqns 9.49, in which the viscosity is the grease viscosity K . Note that this formula is a


modification of the Hamrock and Dowson Eq. 9.48 film thickness formula. However, itsapplication is more complex because the correction term includes the dimensionless yieldstress parameter:

τ = τyhc

2η0um, (9.71)

which depends on the central film thickness again. Assuming fully-flooded and isothermalconditions, Yang and Qian also show that the yield stress has little effect on the film thickness.In that case, the main difference between film formation from grease and its base oil is causedby the difference in viscosity. They show that the fully-flooded isothermal film thickness in agrease lubricated contact can be estimated using the following equation:

h

hoil=(

K

ηoil

)0.74

, (9.72)

with K the Bingham ‘grease viscosity’ (Eq. 9.68). It should be stressed here that the Binghammodel only applies for fresh grease. Grease present on the raceways of bearings will beoverrolled by the highly stressed EHL contacts with very large shear rates and will thereforeage rapidly. The soap structure will degrade into small particles, which causes the grease tolose its solid character and shear thinning behaviour.

Therefore, in many applications it is assumed that the fully flooded film thickness can simplybe calculated from the oil film thickness equations assuming that the viscosity is equal to thebase oil viscosity.

9.5 Starvation

9.5.1 Starved Oil Lubricated Contacts

So far the contacts have been assumed to be fully flooded, that is the film build-up is notrestricted by the quantity of lubricant supplied to the contact and the pressure build-up startsrelatively far upstream and with a near-zero pressure gradient, as shown in the left picturefrom Figure 9.11. If the inlet is not fully filled, the two layers on rolling element and racewaymerge, forming a meniscus in the inlet of the contact and the pressure build-up can only startat this point, that is closer to the Hertzian contact with a nonzero pressure gradient. This willreduce the film thickness and the shape of the characteristic pressure distribution in the contact(see right side of Figure 9.11). By reducing the lubricant supply further, the film thickness willcontinually decrease where the film will ultimately be equal to the oil layers supplied to thecontact, compressed to about 30% by the high pressures. The pressure spike close to the outletwill become smaller and ultimately vanish. This lubrication regime, in which the supply oflubricant in the inlet determines the EHL film thickness, is denoted by ‘starved lubrication’,or sometimes by ‘parched lubrication’ (Kingsbury [329]).2

The onset of starvation can be shown experimentally, using optical interferometry mea-surements of a ball running on a glass disc lubricated by a thin layer of oil only. Pioneers in

2 Kingsbury earlier defines starvation as ‘any operating condition such that an increase in oil available to the contactwill result in an increase in film thickness’, [328].


Fully flooded EHL Starved EHL

H

X

P

H

X

P

Figure 9.11 Schematic representation of film thickness and pressure in a fully flooded and starvedEHL contact [582].

identifying and defining starved lubrication using these techniques were Wedeven et al. [601],Chiu [125] and Pemberton and Cameron [469].

Images of starved contacts,which were recently published by Popovici [478], are used hereto illustrate the starvation process. Figure 9.12 shows five interferometry images of ball-on-disc experiments. The shading indicates the film thickness and the lubricant flow direction isbottom to top. The combined oil layer on ball and disc feeds the contact with lubricant, whichpartly flows through the contact and partly around the contact, reducing the lubricant layerthickness on ball and disc behind the contact. With increasing speed, the time for replenishmentof the running track of the contact between successive overrollings becomes shorter and theresult is that the supply of lubricant from the sides to the inlet of the contact will decreasewith increasing speed. This can clearly be seen in Figures 9.12a up to 9.12e, where the speedis increased step-wise. In the low speed case, Figure 9.12a, the contact is almost fully flooded.Here, the inlet meniscus at the bottom of the picture is relatively far away from the edge ofthe Hertzian contact. The inlet is relatively well filled with oil and the interferometry pictureof the Hertzian contact shows the characteristic horse-shoe shape with its uniform thicknessin the centre and its film restriction at the edges of the contact. At higher speeds, the inletmeniscus approaches the edge of the Hertzian contact region and the film is slightly reducedas can be seen from the slight change in shade in the centre of the contact. Increasing thespeed even further to 0.53 and 0.77 m/s, the film thickness is significantly reduced, first in thecentre of the contact and then towards the right where the layer thickness seems to be thinner.Ultimately, at u = 1.1 m/s, the contact is severely starved, as can be seen by the clearly visiblelarge change in shade, which is now uniform throughout the contact.

9.5.2 Starved Lubrication EHL Models

In the starved lubrication ‘regime’, the film thickness is no longer accurately predicted by theDowson and Higginson 9.48 or Nijenbanning 9.51 equations. By 1971 Wolveridge et al. [619]had established a film thickness equation for starved contacts through a relation between inletmeniscus position and film thickness reduction for line contacts, followed by Hamrock and


x [μm]

y [μ

m]

−300 −200 −100 0 100 200 300

−200

−100

0

100

200

x [μm]

y [μ

m]

−300 −200 −100 0 100 200 300

−200

−100

0

100

200

x [μm]

y [μ

m]

−300 −200 −100 0 100 200 300

−200

−100

0

100

200

x [μm]

y [μ

m]

−300 −200 −100 0 100 200 300

−200

−100

0

100

200

x [μm]

y [μ

m]

−300 −200 −100 0 100 200 300

−200

−100

0

100

200

(e) 1.10 m/s.

(c) 0.53 m/s. (d) 0.77 m/s.

(b) 0.44 m/s.(a) 0.31 m/s.

Figure 9.12 Sequence of pictures taken from an interferometry film thickness measurement deviceshowing the approach of the inlet meniscus of a starved EHL contact towards the Hertzian contact withincreasing speed [478].


Dowson [244] in 1977 for point contacts. For engineering purposes, this is an inconvenientapproach, since the inlet meniscus position is not a practical input parameter.

An alternative approach was followed by Chevalier [123] and Wijnant [610] who numeri-cally solved the starved EHL problem by assuming a layer of oil on the rolling element and ringwith specified thickness h. The location of the inlet meniscus is then determined automaticallyby the continuity condition. In grease-lubricated bearings the functional life is usually at leasta thousand hours, which is impossible to solve using these numerical techniques directly. For-tunately, these programs have been used to develop relatively easy to use curve fit equations.For severely starved contacts, semi-analytical expressions have been developed, which canbe implemented in simple computer programs relatively easily. Therefore, even more simplemodels are needed. These simple models for mild and severe starvation will be describedbelow and will be connected to cover the full range in starvation in section 10.2.1 of this book.

Mild Starvation

Chevalier et al. [124] and Damiens et al. [158] performed many calculations on starved EHLand derived simple expressions for the film thickness in circular and elliptical contacts as afunction of the inlet oil layer thickness through curve fitting:

hc

hcff= r

γ√

1 + rγ, (9.73)

with

r = 2h∞hcff ρc

, (9.74)

where

• hc = central film thickness;• hcff = central film thickness in the case of fully flooded conditions (e.g. Eq. 9.51);• h∞ = thickness of one of the oil layers in the inlet of the contact;• ρc = ratio of density at maximum Hertzian pressure and density under atmospheric pressure;

Here it is assumed that the layers on both surfaces have equal thickness. The parameter γ ,representing the resistance to side flow, was found to be determined by a single nondimensionalparameter representing the inlet length, see Figure 9.13.

In order to predict the film thickness after repeated overrolling, like in a rolling bearing,the outlet film thickness h, can be used as twice the inlet layer thickness h for the nextoverrolling (corrected for compressibility). Damiens et al. [158] have done this numericallyfor 50 overrollings and found a relation for continuous overrolling:

limn→∞

hc

hcff= lim

n→∞1

γ

√1/rγ

0 + n∝ n− 1

γ . (9.75)


1614 10 12 8 4 6 2 0

16

14

12

10

8γ

6

4

2

0

M / L

0.14

0.22

0.35

0.631.00

Figure 9.13 Starvation parameter γ as a function of the Moes dimensionless numbers (M, L) andcontact ellipticity (κ). This is valid for r = [0.5 : 1.5]. Reproduced from Damiens et al., 2004 C© ASME.

Obviously, for bearing applications, the time for 50 overrollings is usually very short. Forexample, in a bearing with 10 rolling elements, running at 10 000 rpm, these 50 overrollingscorrespond to approximately 0.05 seconds! However, the rate of starvation is not only givenby side flow: track replenishment and other effects will reduce the starvation rate and it isplausible that this starvation model applies for longer time periods.

According to Eq. 9.75, at constant speed, the film thickness decreases with time, accordingto:

hc(t) ∝ t−1/γ . (9.76)

Severe Starvation

In the case of severe starvation, the inlet length will be very small and difficult to captureaccurately using a numerical method. Therefore, as Damiens [156] points out, the numericallyobtained results for γ are less good for very thin films. In that case, the approach of Van Zoelenet al. [584] will give more accurate results.

Van Zoelen used a different approach to the solution of the starvation problem. Ratherthan solving Reynolds’ equation for the pressure distribution, he assumed a simple ellipticalpressure distribution (the Hertz dry contact solution). The film thickness is then calculated bycompressing the layer on the track with this pressure using the Dowson and Higginson relation(Eq. 3.26). So the film thickness will be about 10–30% of the combined thickness of the layeron the surfaces.

If replenishment is neglected, the layer thickness is reduced in time by side flow caused bythe pressure gradients in the contact.

The dry contact pressure assumption is a good approximation, except for mild starvationand very light loads [156, 478, 610]. Grease lubricated bearings are generally running under


starved lubrication conditions, and, very importantly, only in the case of severe starvation dobearing failures occur. Therefore, a high accuracy is primarily required for thin (starved) films.

The starved film thickness is determined by the thickness of the lubricant layers entering thecontact. It is assumed that the thickness of these layers is equal to the average layer thicknessin the tracks on the solids in contact. The layers with a total length of lt are averaged over thelength of the tracks, but may vary across the track (in y direction). The average layer thicknessh∞(y, t) can be calculated using mass conservation:

∂ h∞∂t

= −1

ltρ0

∂ qy

∂y(9.77)

ρ0 is the ambient pressure density of the oil and qy(y) is the mass flow to the side of thetrack. For a ball on disc setup with a single rolling element lt = 2π Rball + 2π Rdisc. Thecontribution to the side flow of contact k is obtained by muliplying the unit volume flowper unit length (Eq. 9.23) with the lubricant density and integration over the contact length.Neglecting transverse motion for contact k the side flow reads:

qy,k(y, t) = −(∫ a+

a−

(ρh3

12η

∂p

∂y

)dx

)k

. (9.78)

The density ρ and the viscosity η are determined by the contact pressure p using the Dowsonand Higginson relation (Eq. 3.26) and a viscosity–pressure relation (See Chapter 3).

For severely starved contacts, the film thickness h is approximately equal to the combinedthickness of the oil layers entering the contact, compressed by the high contact pressure:

h(x, y, t) ≈ 2ρ0h∞(y, t)

ρ(p). (9.79)

Here ρ(p) is the lubricant density determined by the local pressure p in the contact. Thepressure distribution resembles the Hertz dry-contact pressure distribution:

p(x, y) = ph

√1 −

(x

ax

)2

−(

y

ay

)2

, (9.80)

and the boundaries of an integral of Eq. 9.78 are determined by the boundary of the pressurizedregion:

a+ = −a− ≈ ax

√1 −

(y

ay

)2

. (9.81)

Using Eqns 9.77, 9.78, 9.79 and 9.80 one obtains:

qy(y, t) = 1

3h3

∞ρ0lt yF k(y), (9.82)


where Fk(y) is:

Fk(y) = 2ρ02 ph

2

lt a2y

∫ a+

a−

((η(p))−1 (ρ (p))−2 p−1

)dx . (9.83)

Using the density pressure relation Eq. 3.26 and the Roelands or Barus viscosity–pressurerelation (Eq. 3.19 or Eq. 3.16), the function Fk(y) can be approximated by:

Fk(y) ≈ 2

lt

ph

a2y

ax

η0π

⎛⎝(0.5παph

√1 − y2

a2y

)3/2

+ 1

⎞⎠−2/3

. (9.84)

A partial differential equation for the layer thickness distribution h∞(y, t) is obtained bysubstitution of Eq. 9.82 into Eq. 9.77. This equation can be solved numerically, see VanZoelen et al. [586]. When the layer thickness distribution is symmetrical with respect to thecentreline (y = 0) an analytical solution for the central layer thickness exists:

h∞(0, t) = 1√23Fk(0)t + h−2

0,∞(9.85)

h0,∞ is the initial layer thickness in the centre. Next, using Eq. 9.79 an analytical expressioncan be obtained for the time variation of the central film thickness in the contact:

hc(t) = 1√16 ρ2

cFk(0)t + h−2c,0

(9.86)

hc,0 is the initial central film thickness and ρc = ρ(ph)/ρ0.Fk decreases with increasing load. This means that the rate at which the film reduces in

time will decrease with increasing loads! This is caused by the exponential relation betweenviscosity and pressure. Physically, this means that the side flow from the contact reduces withincreasing load due to the rapid increase in viscosity by increasing pressure.

Another surprising phenomenon is the absence of velocity in the equations. The rate ofstarvation is only a function of time. At high speed, the frequency of overrolling will begreater. However, this has no effect on the side flow and therefore on the rate of starvation.Per unit of time, a partition of the oil layer on the track may be visited more often. However,the duration will be shorter. As mentioned above, this only applies for very thin films. Theeffect of speed, viscosity and pressure on film thickness for starved and fully flooded contactsis summarized in Table 9.1.

The table illustrates that the impact of pressure, viscosity and speed on the film thicknessitself is not straightforward. As an example, an increase in load will result in a slightly smallerinitial (fully flooded) film thickness, but a smaller film thickness decay. So the film thicknesswill be slightly smaller for short time intervals but larger after longer time intervals.


Table 9.1 Impact of speed, viscosity and pressure on the film thickness at a fixedpoint in time in starved and fully flooded EHL contacts for which the contactpressure is at least 0.1 GPa. Increasing pressure leads to a large decrease in Fk ,which increases the film thickness according to Eq. 9.86. Increasing the base oilviscosity η0 leads to a decrease in Fk , which leads to an increase in film thickness(Eq. 9.86). Increasing the speed has no impact on the starved film thickness decayunless the initial film thickness hc,0 is equal to the fully flooded film thickness.

Effect on film thickness

Starved,Input (at fixed time) Fully flooded

p ↑ h ↑ h ↘η0 ↑ h ↑ h ↑u ↑ h = h ↑

For an accurate prediction of the rate of starvation, the models from Damiens and VanZoelen should be combined. In essence, both models show the same film thickness decay

h(t) ∝ t−1/γ . (9.87)

At the onset of starvation, Damiens’ model is preferred and the power γ will be approximately3 for circular contacts and up to 15 for wide elliptical contacts. For very thin films, as isusually the case in grease lubrication, Van Zoelen’s model is preferred which gives γ = 2 forall contacts.

9.5.3 Base Oil Replenishment

When looking through the glass disc of the above mentioned ball-on-disc set-up, not just theinterferometry pictures of the contact can be seen. The shape of the oil layers and flow of theoil in the vicinity of the contact can also be seen. Figure 9.14, from Åstrom et al. [36], showsthe typical butterfly shape of oil reservoirs that are formed in the case of limited oil supplyand sufficiently high speed. Behind the contact, the film opens up and cavitation occurs in thetrack. The outlet layer thickness just behind the contact will be approximately equal to the filmthickness corrected for compressibility (the oil may be compressed up to 30% in the contactand will ‘relax’ back as soon as the pressure is relieved behind the contact). In front of thecontact, part of the oil is pushed to the side due to the diverging gap across the rolling direction.Next to the track, two ridges, or side bands, are formed. This can also be seen in Figure 9.15.The shading that results from interferometry in the contact also reveals the ‘butterfly shape’from Figure 9.14.

Some replenishment from the ridges may take place in the inlet of the contact where theridges are squeezed by the converging gap causing some transverse flow into the inlet of thecontact, reducing starvation. Obviously, this is only significant for circular contacts, wherethese ridges are relatively close to the centre of the running track. In the case of rolling bearings,the contacts are elliptical or even line-shaped, and their contribution to replenishment in the


Cavitation zoneInlet

Inlet distance

Oil reservoir

Contact

Side band

Figure 9.14 The flow around an oil lubricated point contact at moderate speeds with limited oil supply,showing side bands and oil reservoir. The contact is still fully flooded. Inlet on the left side of the figure.Reproduced from Åstrom, Ostensen and Hoglund, 1993 C© ASME.

centre of the contact is likely to be very small. On the other hand, they may help to preventfilm collapse at the sides of the contact close to the ‘fully flooded minimal film thickness’.

The ridges/side bands will not only be formed on the disc but also on the ball. This is clearlyvisible in Figure 9.16, showing the ball from the ball-on-disc set-up. Figure 9.17 shows theresult of CFD calculations where a uniform inlet layer is assumed to feed the contact (Put[482]). These calculations confirm the qualitative measurements of the butterfly shape of the‘oil reservoir’ and the formation of two distinct ridges behind the contact.

The ridges formed behind the contact may replenish the track due to body forces such asgravity and/or surface tension effects, but also by overrolling of the ridges, see Figure 9.15. Theball runs on a circular disc and, without replenishment, the inlet layer oil distribution would

Figure 9.15 Picture taken through the glass disc in a ball-on-disc rig with limited oil supply, showingthe distribution of oil around the contact, as drawn in Figure 9.14. Inlet on the left side of the figure.Courtesy of SKF.


Figure 9.16 Ball-on-disc configuration, running under pure rolling conditions and where two layersof oil are visible on the ball adjacent to the contact track. Reproduced with permission from WedevenAssociates, Inc.

be equal to the outlet layer distribution, which clearly is not the case. The figure shows thatthe outlet layer width is larger than the inlet layer width, indicating that some replenishmenthas occurred. This phenomenon was modelled in 1974 by Chiu [125], who assumed that thecontact was fed by a uniform layer of lubricant. He modelled the replenishment by solving theStokes equation without any external force and the replenishment driven by surface tension.Later Jacod et al. [298] included Van der Waals forces, which may be important for extremelythin films. They used the same approximation as Chiu for the initial profile of the lubricantprofile. Experimental visualization of the flow around an EHL contact was made by Pembertonand Cameron [469], using a very simple camera with a glass disc steel ball set-up and showedtwo side bands of oil flowing around the contact that form a meniscus around the rear end ofthe contact. At higher speeds, the two bands no longer merge and the meniscus is split intotwo side bands, similar to that which can be seen in Figures 9.15 and 9.17.

Guangteng and Spikes [236] also recognized the formation of ridges in their experimentalwork. With the quantities of lubricant that Chiu [125] was using, they could only get starvationat very high speeds. It should be noted that in Chiu’s model the ridges are assumed to beinfinitely wide (uniform layer thickness outside the track).

Recently, thin layer models have been developed by Gershuni et al. [218] for flat surfacesand Van Zoelen et al. [583] for axisymmetric rotating surfaces, where the Van der Waalsforces have been neglected and therefore are only applicable for not too thin films (h > 5 nm).These models have been used to simulate the experiments from Figure 9.18. There is a goodagreement between the model prediction and experiment and it is therefore seems justified toneglect Van der Waals forces.


Separation point

Fully filled

Height [m]1.000e – 05

9.000e – 06

8.000e – 06

7.000e – 06

6.000e – 06

5.000e – 06

4.000e – 06

3.000e – 06

2.000e – 06

1.000e – 06

0.000e + 00

Figure 9.17 CFD calculation of the flow around the contact of a ball-on-disc set-up (Put et al. [482]).The direction of flow is from right to left (Courtesy University of Twente and SKF).

With the model from Eq. 9.16, the replenishment experiment from Figure 9.18 can besimulated. The ball runs on a circular path where a small amount of oil (10 μl PAO, ν = 80 cSt)has been supplied to the contact using a syringe. The result is a track of oil, which consists ofa relatively flat thin film with side-bands on both sides, with a distance approximately 1.5 mmand with a height of approximately 15 μm. The experiment has been conducted with a 20 mmball at a speed of 0.2 m/s and a temperature of 20 ◦C. The ball was running on the disc underpure rolling conditions at ambient temperature. After a number of rotations of the disc itwas taken from the ball-on-disc machine and mounted on an optical profilometer to measurethe shape of the lubricant layer. After this, two more measurements were taken after 75 and135 seconds. Figure 9.19 shows the result of the simulation and the excellent agreement withthe result of the experiment. This confirms that the thin film approach can be used here andthat Van der Waals forces can be neglected in the prediction of this type of replenishment.

9.5.4 Starved Grease Lubricated Contacts

Line Contacts

The measurements from Zhu and Neng [638] show that, with grease as a lubricant and for linecontact, film thickness decay only occurs in the first minutes, after which they report a constant

(a) t = 0 s. (b) t = 75 s. (c) t = 135 s.

Figure 9.18 Height measurement of the two layers formed behind the ball-on-disc contact. The timebetween the three measurements was 75 and 135 seconds. Reproduced from Gershuni, Larson and Lugt,2008 C© Taylor and Francis Group.


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

x 10−5

x [m]

h [m

]

Initial profileSimulation result t = 75 sExperimental profile t = 75 s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

x 10−5

x [m]

h [m

]

Initial profileSimulation result t = 135 sExperimental profile t = 135 s

Figure 9.19 Layer measurement and computed profile after 75 s of replenishment (left graph) and after135 s of replenishment (right graph). The dashed line represents the initial profile from the experiment.The solid line is the result of the numerical simulation. Reproduced from Gershuni, Larson and Lugt,2008 C© Taylor and Francis Group.

film thickness. This behaviour is ascribed to the Herschel–Bulkey rheology of grease, whichwill prevent any transverse (y-direction) flow in the line contact inlet if the shear stresses arelower than the yield stress. This transverse shear stress in the inlet is induced by a transversepressure. The relation between pressure and shear stress was earlier derived from the reducedNavier–Stokes equations, using the ‘lubrication’ assumptions (Eq. 9.5) for the transverse (y)direction:

∂p

∂y= ∂τ

∂z. (9.88)

The shear stress in the centre of the film can be calculated by integrating this equation over z,assuming a constant pressure over z:

τ = ∂p

∂y× h

2. (9.89)

Using a Herschel–Bulkley model and an exponential pressure dependence of the yield stressτy and consistency index K , similar to that used by Kauzlarich and Greenwood (Eqns 9.55and 9.61), there will be no starvation caused by side flow in the inlet as long as

∂p

∂y× h

2< τy0 exp(αp). (9.90)

For line contacts (with finite widths) the pressure gradient across the contact will be very small,leading to a very small side flow mass flux (see Eq. 9.78) and the starvation rate will thereforealso be small. In the inlet some of the grease volume will travel through the contacts. Here theshear rates and pressures are very high, which leads to rapid aging and to a reduction of theeffective grease viscosity. Ultimately base oil-like rheology will be experienced. After this,


Grease aging Oil starvation

11γ

In h

In t

Figure 9.20 Schematic representation of the film thickness in a grease lubricated contact in the absenceof replenishment. Initially, starvation is slow due to the absence of side flow in the inlet and the high‘grease viscosity’ in the contacts. Later, base oil behaviour will be observed. Note the log-scales, meaningthat the first phase is very short and in practice not relevant, except for ultra-low speed operation.

starvation will occur, leading to a film reduction proportional to h−1/γ , similar to Eq. 9.75. So,for grease lubricated contacts the film thickness will stay fully flooded for some time, afterwhich starvation will occur with oil-like character, as shown in Figure 9.20.

Point Contact

Almost all measurements that can be found in the literature using optical interferometry inpoint contacts show that starvation occurs in the case of grease lubrication. As with oil,recovery is sometimes reported due to replenishment of the track. Sometimes replenishmentis ascribed to base oil replenishment as was addressed in Section 9.5.3. In many cases a morecomplex behaviour is observed.

Merieux et al. [417] classified grease film thickness (point contact) measurements into fourcategories, according to their replenishment behaviour:

(a) Fully flooded;(b) starved;(c) starved with stabilization;(d) starved with recovery.

This is schematically shown in Figure 9.21. Lubrication type (d) is caused by greasedegradation at the edge of the contact. Grease is pushed to the side by overrolling and thesmall quantity that is just close enough to the Hertzian contact is sheared during each passageof the ball. The grease thickener structure is thus continuously degrading. Merieux et al. writethat the grease here is transformed from a Bingham plastic or Herschel–Bulkley-like materialinto a more viscous material.

Actually, they use a rheology model defined by Czarny and Moes [151], which is a variantof the Casson model:

τ = [τ ny + (K γ )n

]1/n, (9.91)


a Fully flooded

dStarved with recovery

b

c Starved with stabilization

Starved

In h

In t

Figure 9.21 Characteristic starvation behaviour for grease lubrication [417].

where K has the dimension of viscosity. This is combined with a shear degradation model:

τy = τy,0

(1 + γ t)α(9.92)

with τy,0 the initial yield stress, t time and α a coefficient. By assuming a triangular velocityprofile in the deformed Hertzian geometry and using this degradation model they predict thefilm thickness decay and replenishment assuming that grease turns into oil as soon as a yieldstress of τy = 40 Pa is reached. An important conclusion is that the model shows that lubricantavailability critically depends on the shear stability of the grease. Unfortunately, they onlyvalidated their model with a very limited number of measurements.

In [417] it was also shown that replenishment in single point contacts is not only related tomechanical work, but also related to temperature.

Another effect that could play a role in grease lubricated contacts is the formation of bound-ary film layers formed by degraded thickener. This means that ‘behaviour c’ in Figure 9.21,that is starvation ultimately leading to a stabilized film, may not necessarily be caused byreplenishment. Cann [110] measured the thickness of such films and found that the grease filmwas composed of two parts; one that is formed by hydrodynamic action and the other formedby a residual layer:

hT = h R + hEHL, (9.93)

with residual films of thickness 6 nm < h R < 80 nm. Such films were earlier analyzed byCann and Spikes [116], showing that significant amounts of thickener are present on the track.It is presumed that this is deposited by grease as it is shear degraded in the contact. The factthat these layers are denoted by ‘residual layers’ indicates that they may be physically orchemically attached to the surface.

9.6 Spin

Axial load on ball bearings (deep groove and angular contact) causes a spinning motionof the balls. The effect of spin on starvation is relatively unexplored and no models exist


450

400

350

300

250

200

150

100

50

00.00 0.20 0.40 0.60

Speed [m/s]

Film

thic

knes

s [n

m]

0.80

No spin

Spin

1.00 1.20

Figure 9.22 Ball-on-disc measurements of film thickness in a starved contact showing the impact of spinon film thickness. Reproduced with permission from Cann and Lubrecht, 2007 C© IOP Publishing Ltd.

Figure 9.23 Contact on the onset of starvation. Spin-motion causes replenishment of the track.

as of yet. However, film thickness measurements on single contacts have shown that spinreduces/eliminates starvation and is therefore very relevant. Zhu and Neng [638], but alsoCann and Lubrecht [115] show a significant effect of spin on film thickness. An example isshown in Figure 9.22. In the absence of spin, the film thickness decreases with time whichis ascribed to starvation. In the case of ball spin, starvation occurs at low speed but at higherspeed the film thickness linearly increases with speed. In the case of a fully flooded film, theincrease would be proportional to approximately u0.7, so at a lower rate than shown in thisfigure. The higher exponent in the case of spin can be ascribed to an extra film growth dueto lubricant supply by transverse shear. Figure 9.23 shows a schematic representation of themotion imposed on the fluid in the case of combined rolling/spin motion. The ridges next tothe track are being ‘pulled’ into the track by the spinning motion of the ball, causing at leasta reduction of the starvation rate. So far, no models have been developed for starved contactsincluding spin.

10Film Thickness in GreaseLubricated Rolling Bearings

P.M. Lugt, M.T. van Zoelen, and C.H. Venner

During most of its operational time grease lubricated rolling bearings are running under starvedlubrication conditions. This means that the lubricant film thickness is primarily determinedby the lubricant layer thickness in the running tracks. This layer thickness is determined by aflow balance. Lubricant flows outside the track by side flow due to overrolling by the rollingelements with a high pressure, but the layer thickness is also affected by flow due to centrifugaleffects, cage scraping, evaporation, occasional oil droplets or grease lumps thrown off fromseals/cage/inner-ring, oil bleeding from grease, gravity, surface tension and/or air flow.

A complicating factor is that the physical properties of the grease and of the base oil oftenchange during bearing operation. This may be caused by chemical reactions such as oxidationor by mechanical work.

Intuitively small effects may have a large impact on the film formation, since the requiredfilms are so thin that even a small droplet may provide a relatively large contribution to thelayer and therefore film thickness.

In this chapter the various aspects of lubricant film formation in a grease lubricated bearingwill be described using the theory from Chapter 9 (film thickness for single contacts) as a basis.First the thin layer flow models from Chapter 9 will be applied to bearing surfaces, consideringthe flow due to centrifugal effects, in normal and tangential directions respectively. The normalcomponent may cause droplets to be thrown off from surfaces or may cause a smoothing effectof the layers, depending on the direction of the normal force on the surface. The tangentialcomponent will cause a flow along the surface. Next, the single contact EHL theory will beapplied to a complete bearing geometry. In a full bearing, surface layers are merging andseparate before and after multiple outer-ring– and inner-ring–rolling element contacts. Thelayers are overrolled/pressurized by multiple contacts, each with different contact conditions(except for a pure axially loaded bearing). The single contact theory can therefore not beapplied directly.



The scraping effect of a cage may have an impact on the film thickness. The differencebetween scraping oil and grease will be shown here through experiments. Following thediscussion of these mechanical aspects some chemical aspects will be described. The filmbuild-up and flow properties of an oil are mainly determined by the viscosity. Oxidation of oilleads to polymerization and therefore to a change in viscosity.

The mechanism determining the lubricant film thickness in rolling bearings is so complexthat no simple engineering formulae exist. In this chapter the various aspects of lubricant filmformation are described and models are given, where available. For a given application theymay be combined according to their specific significance.

10.1 Thin Layer Flow on Bearing Surfaces

In this section the thin layer flow models, that were derived in Chapter 9, Page 191, will beapplied to bearing surfaces. The driving forces for flow in free layers are the body force, airflow and forces caused by surface tension, whereas the resistance to flow is determined by theviscosity. The surface tension effect and the normal component of the body forces may onlybe relevant if the free surface or solid surface is significantly curved. This applies to the ridgesof oil that are formed by side flow from the contacts and which will be located next to thetrack, on nonsmooth surfaces or in areas such as the undercut in bearing flanges. For relativelysmooth layers these effects can be neglected. For an inclined surface the oil will flow due tothe presence of a tangential body force. In that case the flow of thin uniform layers can bedescribed with Eq. 9.17 whereas the replenishment effect by, for example, the ridges can bedescribed with Eq. 9.16.

10.1.1 Contact Replenishment in Bearings

As mentioned in Section 9.5, the EHL contacts in a bearing will cause side flow, driven bythe pressure gradients inside the contacts. In a rolling bearing, the forces on the ridges canbe quite different from those in the ball-on-disc experiment. On the inner-ring raceway, thecentrifugal normal forces will cause a growth of the ridges, where the oil may ultimatelybe thrown off the surface. This is illustrated in Figure 10.1, where a simulation of the flowof the ridges on a cylindrical inner-ring is shown. The ridges have the same dimensions asin the ball-on-disc experiment from Figure 9.18. The ring is rotating such that a centrifugalacceleration of 10 m/s2 is generated. The figure clearly shows that the ridge is thinning ratherthan widening over the surface. These results show that replenishment of the track, driven by

Figure 10.1 Cross-section of the lubricant layer behind the contact under conditions typical for theball-on-disc machine, with similar oil and temperature as in Figure 9.19 but with normal force fz = 10ρ,for t = 0, t = 105, t = 106 and t = 5 · 106 seconds. Note that the scale is different for the different plots.Reproduced from Gershuni, Larson and Lugt, 2008 C© Taylor and Francis Group.

Film Thickness in Grease Lubricated Rolling Bearings 229

0 0.010

0.2

0.4

h [m

]

0.6

0.8

1x 10–5

~d2

d1

~h0

~h1

~h2

0.02 0.03 0.04 0.05x [m]

0.06 0.07 0.08 0.09 0.1

Figure 10.2 General description of the initial profile before replenishment. Reproduced from Gershuni,Larson and Lugt, 2008 C© Taylor and Francis Group.

Table 10.1 Definition of three cases for a parametric study for the replenishment time for outer ringrotation in a NJ 312 bearing. d1 is half the distance between the ridges, d2 is the initial track width, h0 isthe layer thickness in the centre of the track, h1 is the initial height of the ridge and h2 is the height ofthe oil layer next to the ridges, as shown in Figure 10.2. Reproduced from Gershuni, Larson and Lugt,2008 C© Taylor and Francis Group.

Case d1 [m] d2 [m] h0 [m] h1 [m] h2 [m]

1 12 × 10−3 3 × 10−3 2 × 10−7 10−5 5 × 10−4

2 9 × 10−3 4 × 10−3 2 × 10−6 10−4 5 × 10−5

3 9 × 10−3 4 × 10−3 2 × 10−6 10−4 2.5 × 10−5

centrifugal or surface tension forces on the inner ring of a cylindrical bearing will not takeplace in practice. As an example, for a NJ 312 bearing,1 at the very low speed of 200 rpm thecentrifugal acceleration will reach a value of 17 m/s2, so this type of replenishment can indeedbe neglected at very low speeds. In the case of outer-ring rotation, this will be different. Herethe replenishment will be accelerated by the centrifugal forces as they are directed towardsthe surface. Gershuni et al. [218] investigated the replenishment of the running track of theouter-ring of a NJ 312 bearing, by oil layers on which a normal (centrifugal) force is acting.The configuration and notation is shown in Figure 10.2 and the dimensions of the layers forthe three cases are shown in Table 10.1. The time until total replenishment was calculated,that is, the time at which the centre of the track layer thickness started to be affected byreplenishment. The result is plotted in Figure 10.3. In order for replenishment to be effective,the calculated times should be compared to the time between overrollings. For the example here

1 cylindrical roller bearing with inner ring bore diameter of 60 mm.


101 102 103 10410−1

100

101

102

103

104

105

106

107

g [m/s2]

Tim

e [s

]

Simulation 1

Simulation 2

Simulation 3 1.02

0.98

0.97

Figure 10.3 Replenishment time as a function of the centrifugal acceleration for outer ring rotation fora NJ 312 bearing configuration, with oil viscosity ν = 80 cSt. The three simulations represent the datasetfrom Table 10.1. Reproduced from Gershuni, Larson and Lugt, 2008 C© Taylor and Francis Group.

(NJ 312 bearing) the time between overrolling are in the order of milliseconds (0.005 second atn = 2000 rpm), which is much smaller than the replenishment times calculated here.

All three calculations show a linear behaviour on a log-log scale with a slope of −1. Withthe centrifugal acceleration fz ∼ n2, this means that the replenishment time versus speedn will be a straight line with slope −2 on a log-log plot.

From the results shown in this section, the following conclusions can be drawn. The replen-ishment driven by centrifugal and surface tension forces on ridges of oil inbetween rollingelements of cylindrical bearings is too slow to give a significant contribution to a reduction ofthe starvation rate in rolling bearings. On the inner-rings, the centrifugal forces are generallyso high that a thinning effect of the ridges may occur, ultimately leading to oil being thrownoff. In the case of outer-ring rotation, the centrifugal forces on the ridges on the outer ring maypromote replenishment, depending on speed, size of contact and base oil viscosity. However,for the bearing investigated here (NJ 312), this effect is not significant for outer-ring rotation.

Replenishment may be significant immediately in the outlet of the rolling element–ring con-tact, where dynamic effects may occur, including droplet formation. In case of a pronouncedosculation, capillary effects may be significant along with other tangential pressures due tothe opening of the film. However, it is important to realize that the time between passages isvery small and that every passage will cause side flow opposing the replenishment. It is there-fore very unlikely that replenishment due to centrifugal forces and surface tension will playa role.

These conclusions only apply to the flow in thin oil layers. The flow in a grease lubricatedbearing may be more complex. Moreover, these conclusions do not apply when the centrifugal


z

r(s)

h~

~

L

s

z

R

r(s)

αh

L

s

Figure 10.4 Schematic representation of a thin layer of oil on a rotating inner ring of a spherical rollerbearing and tapered roller bearing (respectively). Reproduced from van Zoelen et al., 2008 C© ASME.

force has a tangential component, that is driving the lubricant along the surface. In this casethis flow will be competing with the pressure induced side flow from the EHL contacts. Herethe time between overrollings will determine the significance of this effect. This tangentialflow is the topic of the next section.

10.1.2 Thin Layer Flow Induced by Centrifugal Forces

In Section 10.1.1 it was shown that there is hardly any flow back onto the tracks due to surfacetension effects and the normal component of the centrifugal force. The loss of oil on theraceways may be even more severe when the centrifugal forces, working on the oil layers,have a tangential component. In that case oil may be lost by an inherent ‘pumping effect’,causing an increase of the starvation rate. This effect is significant for bearing types such asTRB (tapered rolling bearings), SRB (spherical rolling bearings) and ACBB (angular contactball bearings). In this section the free surface thin layer flow will be described on a singlebearing component. Later, the flows on the various components will be combined.

Figure 10.4 shows an inner ring, rotating with angular velocity ω (rad/s), covered by athin layer of oil, where the layer is assumed to be initially relatively smooth with constantthickness, h. In the case of rotation, a body force fs , which is the tangential componentof the centrifugal force, will cause a flow. Rotational symmetry applies and the thicknessof the layer can only vary as a function of the coordinate s along the surface of the ring.If the layer is relatively smooth,2 the surface tension effects may be neglected and, otherthan in Section 9.5.3, the normal component of the centrifugal force working on the oillayer can be neglected. For this configuration Van Zoelen et al. [583] rewrote the thin layerEq. 9.17 into:

1

3η

1

r

∂

∂s

(r h3 fs

)+ ∂ h

∂t= 0, (10.1)

2 Relatively smooth means∣∣∣ ∂ h∂x

∣∣∣� ∣∣∣ fsfn

∣∣∣ and∣∣∣σ ∂3 h

∂x3

∣∣∣� | fs |, with σ being the surface tension coefficient and fn the

normal component of the centrifugal force.


with the tangential component of the centrifugal force:

fs = ρω2r∂r

∂s. (10.2)

This equation can be solved using the method of characteristics [582, 583].For the tapered roller bearing inner-ring configuration (see Figure 10.4) an analytical solution

could be found when there is no feed of oil. Hence, the layer thickness is zero at the smallerdiameter side of the ring and the fluid can leave the domain freely at s = L . The solution thenreads:

h(s, t) =√√√√ 3η

4 sin2(α)ρω2t

(1 − 1(

sin αR s + 1

)4/3

)and

h

hi≤ 1, (10.3)

with hi being the initial layer thickness.This solution is illustrated in Figure 10.5, where the layer thickness on the raceway of a

tapered roller bearing inner-ring is plotted for various times. The initial layer thickness was40 μm. This figure shows that the layer thickness decreases in time and that the measurementsof the layer thickness, which were made with a WYKO interferometer, correspond very wellwith the calculations. At the start of the measurements it was impossible to obtain a smoothuniform layer. The discrepancy between calculations and measurements can be ascribed tothe fact that flow was obstructed by a dry area at s > 0.014 m. After half an hour the layerbecomes very smooth at the smaller diameter side of the ring surface and a perfect fit betweenmodel and measurements can be seen. The smooth domain of the layer grows in time and thenonsmooth part of the layer moves to the larger diameter where it will ultimately be thrown

0 0.002 0.004 0.006 0.008 0.01 0.0120

1

2

3

4

5

6

7x 10

−5

Surface coordinate s [m]

Laye

r th

ickn

ess

h [m

]

t = 0 h

t = 1 ht = 2 ht = 4 h

t = 1/2 h

Figure 10.5 Solution of Eq. 10.3 and measurements for the layer thickness on a raceway of a taperedroller bearing inner-ring (L = 13.5 mm; R = 25.4 mm; α = 10.9◦, ν = 1370 cSt (1.25 Pa · s). The drawnlines are the model calculations and the dots denote measured values. Reproduced from van Zoelen et al.,2008 C© ASME.


off; then the model from Section 10.1.1, where the normal component of the centrifugal forcewas included, should be applied.

10.1.3 Combining the Thin Layer Flow on the All Bearing Components

The centrifugal force induced thin layer flow will act on all rotating parts in a bearing and canbe solved individually with Eq. 10.1. Interaction between layers takes place in the contactsbetween rollers and rings, when they merge in the inlet and separate out again into two layerswith equal thickness in the outlet [585]. The flow on rolling elements is quite complex dueto the combination of rotation around the rolling element axis and the rotation around theinner-ring (planetary rotation). These aspects have been described in detail by Van Zoelenet al. [585] and the reader is referred to this paper for more details.

The thin layer theory was applied here to spherical roller bearings and tapered roller bearingsto predict the net flow, that is, the ‘pumping action’ that is induced by the centrifugal forces onall rotating elements. It was shown in [585] that the solution of the flow equations is bearingsize independent, provided that the bearings with different sizes are identical (same numberof rolling elements etc.). A master curve could be obtained describing the ‘pumping action’for spherical roller bearings, which is shown in Figure 10.6. Here, the relative layer decayh/hi is plotted as a function of a dimensionless time t/τc, where the characteristic time τc isdefined as:

τc = η

ρω2h2i

. (10.4)

The fact that the curves do not overlap is ascribed to the fact that different bearings withdifferent sizes have differences in geometrical aspects. This effect is illustrated in Figure 10.6for a 30310 tapered roller bearing where different curves are obtained for different contactangles α′.

100

102

104

106

108

10−3

10−2

10−1

100

t/τc

h/hi

TRB 8.9 TRB 20 TRB 30 SRB 22205 SRB 24020

Figure 10.6 Scaled layer thickness (h/hi) as a function of scaled time t/τ for the centre of the rollersfor spherical roller bearings (SRB) and tapered roller bearings (TRB) with inner-ring rotation. SRB(22205 and 24020) (thick lines) – TRB (30310 [8.9◦, 20◦, 30◦]) (thin lines).


As an indication of the significance of film reduction due to this pumping action an examplecan be given. Take a base oil η/ρ = 5 × 10−6 (≈5 cSt), 10 000 rev/min (≈1000 rad/s). Aninitial layer of hi = 1 μm (1 × 10−6 m) then gives a characteristic time of τc = 5 s. The initiallayer has lost 90% of its thickness at h/hi = 0.1, which corresponds to t/τc ≈ 103, so after1.4 hours, which is quite a short time and makes this effect significant.

10.2 Starved EHL for Rolling Bearings

In Section 9.5.1, starvation models in single concentrated contacts were described. Starvationwas the result of side flow of oil from the contact into the area next to the running track, incombination with insufficient replenishment. The result is a decreasing film thickness in time.It was shown in Section 9.3 that the fully flooded film thickness weakly depends on the contactload (h ∝ F−0.067). This means that the fully flooded film thickness will be quite similar forall rolling contacts in a bearing and that the thinnest film can be calculated simply by applyinga film thickness formula to the highest loaded contact. This does not apply in the case ofstarvation. It was explained in Section 9.5.1, that the rate of film decay significantly dependson the pressure in the film, through the exponential relation between pressure and oil viscosity.The side flow is pressure driven, so its rate is inversely proportional to the viscosity. Generallyin a rolling bearing, the contact pressure varies along the circumference with different loads onthe inner-ring and the outer-ring. Also, each contact contributes to the decrease of the availablelubricant in the track. Therefore, to calculate the film thickness in the case of starvation, allcontacts need to be taken into account.

The load distribution can be calculated using the formulae from Harris [249] or from deMul et al. [162]. As an example, Figure 10.7 shows the contact pressures on inner-ring andouter-ring contacts in a 6204 deep groove ball bearing running in a standard R0F3 test. Dueto the combined load, all balls are in contact but with different contact pressure.

10.2.1 Central Film Thickness

Lightly Starved Contacts

The onset of starvation without reflow/replenishment can be described using Damiens et al.[158]’s model, as described in Section 9.5.1, Eq. 9.73. Here the rate of starvation is expressedin the number of lubricant layer overrollings, n.

hcs = hcff

(r−γ

0 + n)−1/γ

, (10.5)

where r0 is the ratio of the layer thickness and uncompressed fully flooded film thicknessbefore the first overrolling:

r0 = 2h∞hcff ρc

(10.6)

3 For a description of the R0F test rig, see Section 16.2.29, p. 369.


0 50 100 150 200 250 300 350600

650

700

750

800

850

900

950

Angle [degrees]

Con

tact

pre

ssur

e, [M

Pa]

Inner-ringOuter-ring

Figure 10.7 Contact pressures in a 6204/C3 deep groove ball bearing running under combined loadconditions (Fr = 50N; Fa = 100N, R0F test rig configuration).

at t = 0. Damiens’ model was developed for successive overrollings of a single contact. In thecase of a rolling bearing the oil layers are overrolled by contacts with different size and contactpressures (with the exception of a pure axially loaded bearing). However, in this subsection itis assumed that all contacts in a bearing are equal and that the contact size and pressure willbe equal to the highest loaded contact. For a complete bearing the time between successiveoverrollings is 2drr/us , with drr = z/(πdm) the distance between rolling elements and us ,the entrainment (sum) velocity. So n = ust/(2drr ). The number of overrollings on the rolling

elements is n = us

2πdrt . The number of overrollings between roller and inner-ring is found by

averaging these two quantities and multiplying by two to include the outer-ring roller contacts.By assuming a fully flooded film thickness at t = 0, a good approximation for r0 would be

r0 = 1, so the film thickness is given by:

hcs = hcff

(1 + us

2π

(z

dm+ 1

dr

)t

)−1/γ

(10.7)

hcs =(

us

2πhγ

cff

(z

dm+ 1

dr

)t + h−γ

cff

)−1/γ

(10.8)

hcs = 1

γ

√CDt + h−γ

cff

(10.9)

with

CD = us

2πhγ

cff

(z

dm+ 1

dr

).


Unfortunately, the work from Damiens is limited to ellipticity ratios of κ > 0.14, meaningrelatively narrow contacts and relatively low loads (M < 1000), whereas in bearings generallyM is much larger and κ much smaller. As an example, for a spherical roller bearing 22205(dm = 0.036 m, dr = 0.0071 m, z = 15, loaded with a pure radial load of 900N (minimumload of this bearing, C/P = 50), the ellipticity ratio of the highest loaded inner-ring contactis κ = 0.04. If the bearing runs at 5600 rpm and T = 120 ◦C, the entraining velocity is us =11 m/s and for a typical grease with base oil viscosity η = 0.0052 Pa s, the Moes numbersare M = 5000, L = 13. This gives CD = 948h−γ

cff , with hcff = 0.14 μm. Using the data fromDamiens for the widest contacts they took into account, that is κ = 0.14, a fit can be made:

γ ≈ 0.4√

M/L + 8

0.8r + 4. (10.10)

Only mild starvation is considered, say 0.1 < r < 1. For the 22 205 bearing example, thiswould then give γ = 5.8 for r = 0.1. At the onset of starvation this number will be much largerand the rate of starvation will therefore be lower. While starvation proceeds, r decreases and therate of starvation will also increase through the decrease in γ . This leads to CD = 1.3 × 1043.This increasing starvation rate will ultimately lead to an asymptotic solution where CD and γ

will be constant, which will be shown in the next section.

Severely Starved Contacts

When the contacts are severely starved, the model from Section 9.5.1 on Page 212, can beused to calculate the film thickness. Each rolling element–raceway contact in the bearingcontributes to the decay of the layer thickness in the tracks on the raceways and the rollingelements. As in the single contact model the average layer thickness in the tracks is defined by:

∂ h∞∂t

= −1

ltρ0

∂ qy

∂y(10.11)

ρ0 is the ambient pressure density of the oil and qy(y) is the mass flow to the side of the track.For a bearing the total track length is:

lt = nr 2π Rrolling element + 2π Rinner raceway + 2π Router raceway. (10.12)

Here nr is the number of rolling elements. The side flow in the track is the sum of thecontributions of each contact:

qy(y, t) = 13 h3

∞ρ0lt yF(y), (10.13)

with:

F(y) =nc∑

k=1

Fk(y), (10.14)


where nc = 2nr is the number of contacts in the bearing. Fk(y) is the same as for the singlecontact case and can be approximated by:

Fk(y) ≈ 2

lt

ph

a2y

ax

η0π

⎛⎝(0.5παph

√1 − y2

a2y

)3/2

+ 1

⎞⎠−2/3

. (10.15)

The contact size parameters ax and ay and the pressure ph depend on the load. The contactload may vary over the circumference of the bearing, for example when a radial bearing load isapplied. Assuming that the average layer thickness will hardly change during one revolution ofthe bearing, it is justified to take the side flow in each contact averaged over the circumferenceof the bearing:

Fk(y) = 1

2π

∫ 2π

0Fk(y, �)d� (10.16)

Fk(y, �) is calculated using Eq. 10.15 with ax = ax (F), ay = ay(F) and ph = ph(F) and thecontact load F = F(�) depends on the position along the bearing circumference �.

Similarly to the single contact a partial differential equation for the layer thickness distri-bution h∞(y, t) is obtained by substitution of Eq. 10.13 into Eq. 10.11. This equation can besolved numerically, see Van Zoelen et al. [583]. However, when the layer thickness distribu-tion is symmetrical with respect to the centreline (y = 0) it is possible to solve this equationanalytically for the track centre. The solution reads:

h∞(0, t) = 1√23F(0)t + h−2

0,∞(10.17)

h0,∞ is the initial layer thickness in the centre. An analytical expression is obtained for thetime variation of the central film thickness in one of the contacts:

hc(t) = 1√16 ρ2

cF(0)t + h−2c,0

(10.18)

hc,0 is the initial central film thickness and ρc = ρ(ph)/ρ0, where ph is the pressure in thecontact of interest. The density ρ can again be calculated using the Dowson and Higginsonequation:

ρ(p) = ρ05.9 × 108 + 1.34p

5.9 × 108 + p. (10.19)

10.2.2 Combining Lightly Starved and Severely Starved

For convenience, the equation for lightly starved contacts (Eq. 10.9) is repeated here:

hcs = 1

γ

√CDt + h−γ

cff

(10.20)


with

CD = us

2πhγ

cff

(z

dm+ 1

dr

).

The transition from lightly starved to severely starved is assumed to occur at a fraction of thecentral fully flooded film thickness, htr = ct · hcff . Substitution in Eq. 10.20 gives the time atwhich this transition starts:

ttr = 1

CD

(c−γ

t − 1)

h−γ

cff . (10.21)

The equation for severely starved contacts then reads:

hcs = 1√16 ρ2

cF(0) (t − ttr) + (ct hcff)−2

. (10.22)

Figure 10.8 shows the film thickness, combining these two equations, where the transitionfrom Damiens to Van Zoelen has been chosen at htr = 0.1hcff and r = 0.1.

This figure clearly shows the transition in slope (on a log-log scale) from −γ for the Damiensmodel to 1/2 for the model from Van Zoelen.

10−4 10−3 10−2 10−1 100 101 102 103 104 105

10−3

10−2

10−1

100

Time (s)

Film

thic

knes

s (μ

m)

Van ZoelenDamiensVan Zoelen/DamiensFitted transition

Figure 10.8 Combination of Damiens’ model for lightly starved and Van Zoelen’s model for severelystarved contacts for the 22 205 bearing example (5600 rpm, C/P = 20).


In order to provide a smooth transition between the two models the following equation canbe used:

h = hZ + hD − hZ

1 + (t/ttr)m (10.23)

where ttr is obtained from Eq. 10.21. Here hZ and hD are the central starved film thicknessesaccording to the model from van Zoelen (Eq. 10.22) and Damiens (Eq. 10.20). The parameterm is a transition parameter where large values will lead to a sharp transition. Here m = 3 ischosen. This equation is adopted from the friction work from Bongaerts et al. [89].

The choice of the starting layer thickness in the model from Van Zoelen (ct hcff ) has noimpact on the resulting film thickness at longer times. This is an important observation. Afterall, the Van Zoelen model has been derived for severely starved contacts and should thereforenot be applied in the case of mild starvation. The work described above shows that the errorfor larger films has no impact on the accuracy of the prediction for very thin films.

In the case of relatively thick layers, the overall side flow is governed by side flow in theinlet of the contact (bow-wave), in addition to the side flow from inside the Hertzian contacts(high pressure flow). The Damiens model takes into account both phenomena and thereforeleads to a faster decay than the prediction according to Van Zoelen, who only incorporatedside flow from the Hertzian contact itself. This is not obvious from the equations. After all,both models show identical behaviour after the starting up phase (for the example here afterless than a second) that is:

h ∼ t− 1γ Van Zoelen: γ = 2 Damiens: γ > 2. (10.24)

However, there is a very large difference in the magnitude of the proportionality constants(CD � 1

6 ρ2cF(0)), which makes Eq. 10.24 not valid for relatively short times. The decay rate

is smaller for Damiens’ model at longer times where this time is in the order of seconds, as forthe example from Figure 10.8. Damiens’ model has been developed for a very small numberof overrollings and at these larger times (so after many overrollings) the model is not validanymore (when there is no replenishment).

10.3 Cage Clearance and Film Thickness

So far only the contacts between rolling elements and rings, the EHL contacts, have beenconsidered. However, the clearance between a rolling element and cage pocket may effect thelubricant film thickness as well. The load on the contact between cage and rolling element isrelatively low, making this sensitive to film breakdown due to side flow. This, in combinationwith pure sliding, makes these contacts sensitive to wear. This topic is the main research themefor these contacts and the impact on the lubricant layer distribution is relatively unexplored.

Damiens et al. [157] did experiments on an optical ball-on-disc machine where they mounteda cage segment with a ball on a glass disc and measured the film thickness. With oil lubrication,Figure 10.9, the cage element always decreases the film thickness. There is no clear relationbetween cage clearance and film thickness. In the case of grease lubrication the opposite canbe observed. Figure 10.10 shows that the film thickness with the cage is maintained for longer,that is, starvation is postponed to higher speeds. There is a clear relation between clearance


1.00E–0210

100

1000

Film

thic

knes

s [n

m]

1.00E–01

0.5 mm0.35 mm0.2 mm0.05 mm

Speed [m/s]1.00E+00

Figure 10.9 Film thickness as a function of speed for a single contact with cage element lubricatedby base oil only. The drawn line is the fully flooded film thickness. The legend denotes the clearancebetween cage and ball. The cage scraping effect reduces the film thickness. Reproduced from Damiens,Lubrecht and Cann, 2004 C© Taylor and Francis Group.

and film thickness where reducing the clearance leads to thicker films. This indicates that thecage here helps push the grease back into the track. They also discuss the fact that smallerclearances may shear the grease and produce a mobile lubricant, following the Merieux et al.[417] philosophy (Section 9.5.4). However, they warn about a scraping effect for too smallvalues of clearance.

1.00E–0210

100

Film

thic

knes

s [n

m]

1000

1.00E–01Speed [m/s]

1.00E+00

0.5 mm0.35 mm0.2 mm0.05 mm

Figure 10.10 Film thickness as a function of speed for a single contact with cage element lubricatedby grease. The drawn line is the fully flooded film thickness. The legend denotes the clearance betweencage and ball. The cage is likely to redistribute the grease onto the ball reducing the effect of starvation.Reproduced from Damiens, Lubrecht and Cann, 2004 C© Taylor and Francis Group.


10.4 Full Bearing Film Thickness

In 1979 Wilsson [616] measured the lubricant film thickness in radially loaded bearings. Moreparticularly, he measured the film thickness for the highest loaded contact in cylindrical andspherical roller bearings for four speeds (28 500 − 228 000 ndm) and at various temperatures,using the capacitance technique and Li-hydroxy-stearate grease. Today, the ‘capacity method’is still the most widely used technique to measure film thickness in bearings. Here the filmthickness is measured by measuring the capacity of the bearing system where the bearing iselectrically isolated and where the capacity is inversely proportional to the distance betweenrolling element and ring. A detailed description of various versions of this method can befound in Heemskerk et al. [253] or Barz [68].

If the bearings were fully replenished with grease the film thickness was always betweena factor of 1.1 and 1.4 larger than the film thickness calculated with the base oil viscosity.Wilson concluded that the grease film thickness can be calculated similarly to an oil lubricatedbearing by simply replacing the viscosity of the base oil with an ‘apparent viscosity’ valuethat is approximately 30–35% higher. Hence, the same temperature and speed dependency isobserved between grease and oil lubricated bearings (in the case of fully flooded contacts).He showed that starvation occurs almost instantaneously in normally filled bearings and thatthe temperature of grease lubricated bearings is lower than with oil. This is ascribed to lowerfriction in case of grease lubrication. The thickness of the film that he measured was about50% of the fully flooded film, even after 200 hours.

Muennich and Gloeckner [434] performed film thickness measurements on a 81224 cylin-drical roller thrust bearing, using a mechanical technique with five thickener types. Actually,this type of bearing is very convenient for film thickness measurements since all contacts areidentical in this bearing type, which simplifies the problem and therefore increases the relia-bility of the measurements. For the Li-thickener grease they found an ‘apparent viscosity’ thatwas 50–80% higher than the base oil viscosity. For sodium, calcium complexes and bariumgreases they found an apparent viscosity which was even 200–260% higher than the base oilviscosity.

At Hannover University (Barz [68]), a set-up has been developed where the film thickness ismeasured, using a capacitive technique, in grease lubricated axially loaded high-speed spindlebearings (angular contact ball bearings). Here also, all contacts are equally loaded. Barz [68]found values of the film thickness between 16–20% of those which could be expected basedon EHL theory for the base oil. An example of his measurements can be found in Figure 10.11.This measurement shows that the lubricant film thickness depends on speed and temperatureprimarily at low speeds where it is likely that fully flooded conditions prevail. However, thefilm thickness is rather constant at higher speeds, which is ascribed to starvation and theformation of boundary layers.

This was later confirmed by Franke and Poll [202] using the same ‘Hannover rig’. They alsofound a decrease in film thickness due to starvation to approximately 20% of the initial value.To compare single contact measurements to complete bearing results, Baly et al. [58] tookfilm thickness measurements again on the ‘Hannover rig’ and removed balls from the bearings(and reducing the load, such that the contact size/load was not changed). They showed thatthe film thickness is independent of the number of balls over quite a large part of the speedrange. Baly et al. explained this by assuming that the main relubrication mechanism is close tothe contact. This means that there is no interference between the various contacts in a grease


Rat

ioh

mea

sure

d

h m

in, t

heor

etic

al

1.0

0.8

0.6

0.4

0.2

00 5000 10 000 15 000 20 000 25 000

Speed n [rpm]

Test grease : FEP 502Bearing : B 7008Axial load : F = 160 NType of test : Increase of speedStationary time:10 min

Running time 11 h

Running time 135 h

Running time 231 h

Figure 10.11 Relative film thickness versus speed for spindle bearings. Reproduced from Barz, 1996.

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

Film

thic

knes

s [μ

m]

Speed [rpm]14 00010 000 12 00080006000400020000

With 17 balls

With 8 balls

Figure 10.12 Influence of the number of balls on the film thickness in spindle bearings (angular contactball bearings). Reproduced with permission from Baly et al., 2006 C© Springer.


lubricated rolling bearing and confirms the statements from [218] that replenishment betweenthe rolling elements is too slow to be significant. As is mentioned in [58], if replenishment isas significant as predicted by Chiu [125], then the 8-ball experiment would show a film twicethe thickness, which is not observed in this experiment.

By using the earlier described starved EHL theory, the film would decrease with an increasingnumber of balls. This is only observed in part of the speed-domain in Figure 10.12. There couldbe two explanations for this. The oil feed mechanisms may counteract side flow or the film ispredominantly formed by boundary layers (see Section 9.5.4), which are ‘worn off’ so slowlythat this effect is not observed during the measurement time in these tests. This is confirmed bynano-indentation tests and SIMS analysis from Wiendl et al. [609] who showed the occurrenceof Li-containing boundary layers in the same angular contact ball bearings. They reported thatthick, deformable layers with nonuniform hardness across the contact resulted in shorter lives.

11Grease Dynamics

P.M. Lugt, S. Velickov, and J.H. Tripp

11.1 Introduction

In the preceding chapters, a slow decay of the lubricant film thickness was described in termsof a ‘smooth’ curve where the supply of oil lubricant to the contacts was lower than the loss,which would ultimately lead to insufficient lubrication. In this chapter it will be shown thatthe grease lubrication process is more complex and that a dynamic component also exists.

In 1997 Wikstrom and Jacobson [613] performed spherical roller bearing (SRB) tests andmeasured the electrical capacitance [253] across the contacts and showed a dynamic signal,indicating that lubricant film breakdown is often followed by recovery. At about the sametime, Mas and Magnin [402] speculated on the release of fresh ‘grease’ after heat developmentcaused by film breakdown. They write that a grease-lubricated bearing will fail as soon asthis can no longer take place. This would imply a dynamic behaviour of subsequent filmbreakdown and ‘repair’ and explains the observations from Wikstrom and Jacobson [613].This was also mentioned by Cann and Lubrecht [114] in 1999 who showed in their singlecontact film thickness measurements that severe starvation can indeed be ‘repaired’ by addingadditional lubricant to the contact. They postulate that this replenishment may happen throughvibrations or thermal transients.

Tests on cylindrical roller bearings (CRBs) [379], which will be described below, showa dynamic behaviour not only in the electrical properties of the contacts but also in themeasured temperatures. It will be shown that even in the case of constant load and speed andin the absence of external vibrations, such transients may still occur. It is the nature of thesetransients and the underlying mechanisms that are the focus of this chapter.

11.2 Grease Reservoir Formation

As described in Chapter 2, the initial phase of grease lubrication where the grease is churninginside the bearing is known as the ‘churning phase’. During this phase, flow, or rather migration,



50

45

40

35

30

25

20

150 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time (hours)

Tem

pera

ture

(°C

)

1.8 2 2.2 2.4 2.6 2.8 3

Figure 11.1 Typical temperature profile during the churning phase, NU 309, 3000 rpm. The dotscorrespond to 30 minutes and 55 minutes of bearing operation after test start-up (note that the test doesnot start at time zero).

of grease takes place, giving rise to drag losses inside the bearing which lead to a temperaturerise. Figure 11.1 shows a typical example of such a temperature rise in a cylindrical rollerbearing (CRB). In the first few minutes after test start-up, grease located between rollers andouter ring is squeezed out and pressed over the edge of the outer-ring from where it doesnot return into the bearing. Grease sitting between the inner-ring and the rollers is also partlysqueezed out but partly collected by the cage where it remains, acting as a reservoir of oil forsubsequent use. The amount of grease collected in these cage reservoirs is influenced bothby the centrifugal force and by the cage design. At higher speeds a large amount of grease isinitially thrown away but afterwards the distribution remains more or less stable. Figure 11.2shows the grease distribution in the cylindrical roller bearing corresponding to Figure 11.1.Here, three pictures are shown, taken at various times from the rotating (open) bearing. Thethird of these, taken after 532 hours, clearly shows that the grease has hardly moved since thesecond picture, taken after about an hour. The churning phase has thus essentially ended afterless than one hour. While the grease is no longer moving or producing frictional heat due tochurning, this does not mean that the bearing temperature stays constant. As will be discussedin the following sections, the temperature continues to fluctuate due to metal-to-metal contactbetween the rollers and the raceways resulting from collapse of the lubricant film.

11.3 Temperature Behaviour

The concept of the relubrication interval for bearings is based on the life of the grease inthe bearing. Grease life is so strongly dependent on temperature that it must usually bespecified for a given temperature. As a result, life is measured by rotating bearings at a fixedmean temperature. Examples are tests that have been developed by the bearing industry andhave been standardized, for example R0F and FE9 (DIN 51 821), see Chapter 16. To avoidunacceptably long test times, the test temperature chosen is usually quite high, which meansthat the test bearings will need to be heated, using controllers, to the nominal temperature. In

Grease Dynamics 247

Figure 11.2 Grease position in the cylindrical roller bearing during the churning phase. Correspondingto the temperature signal from Figure 11.1.

order to measure grease life rather than bearing life, the bearings are not run to failure. Thoughcontrolled, the actual selected bearing temperature, measured, for example on the outer-ring,still fluctuates and the grease is assumed to have reached the end of its life as soon as afluctuation exceeds a certain predetermined temperature level. It is assumed that the lubricantfilm is then no longer able to separate the surfaces and that metallic contact is generatingfrictional heat with the accompanying temperature rise. Subsequently, the test is stopped inorder to prevent a bearing failure caused by this lack of lubrication.

At SKF, tests have been done where grease lubricated roller bearings were run not undercontrolled temperature conditions but under self-induced temperature for longer periods oftime (so not accelerated tests such as done on R0F, FE9 etc.). Examples of the outer-ringtemperature in two different tests under identical conditions are given in Figure 11.3. HereNU 312 bearings have been run under a load of 8.34 kN at a speed of 6000 rpm. The bearingswere lubricated with a conventional Li-soap grease with mineral base oil. The figure clearlyshows that the temperature is not constant but shows excursions of around 20 ◦C with a lowerthreshold of 60 ◦C. The first temperature peak is caused by the ‘churning’ phase as describedabove. Subsequent temperature excursions seen in the figure may give the impression thatseveral of these churning phases take place but it will be shown in the next section that these


0 100 200 300 400 500 600 700 8000

20

40

60

80

100

120

Time [hours]

Tem

pera

ture

[°C

]

0 100 200 300 400 500 600 700 8000

20

40

60

80

100

120

Time [hours]

Tem

pera

ture

[°C

]

Figure 11.3 Temperature measurements from two different grease lubricated cylindrical rolling bear-ings running under identical operating conditions with identical grease.

rises and falls, denoted here as ‘events’, are caused by metallic contact through the collapsinglubricant film. These events do not happen on a regular basis and have varying duration. Thefirst temperature peaks are relatively short and at a somewhat lower temperature than thosethat follow. During the last temperature increase shown, the temperature exceeds the pre-setlevel, thus defining the end of grease life for that particular test. Figure 11.3 shows that thetemperature signals for bearings running under identical conditions with identical grease maybe very different.

This test has been repeated six times where each test showed strong dynamic behaviour, asseen for example in the second panel of Figure 11.3. While details of the temperature profilesare clearly different, analysis of the time series and reconstruction of the dynamics using atime-delayed embedding approach, as presented later, reveals some remarkable similaritiesbetween them. This applies to all sets of repeated tests.

In general, there are two possible mechanisms for high temperatures in rolling bearings:lubricant churning (excessive lubrication) and metal-to-metal contact (insufficient lubrication,film collapse). Temporary excessive lubrication or grease churning may be caused by lumpsof grease entering the bearing contacts, by a surplus of grease under the cage bars or byvery slow flow of grease in the interior of the bearing where lumps of grease may break offfrom the bulk. Alternatively, film breakdown can also lead to heat development, softening ofgrease and release of fresh grease for lubrication. This in turn will lead to replenishment of thelubricant films and renewed separation of rings and rollers, with a corresponding reduction oftemperature.

Replenishment need not necessarily be due solely to the release of fresh grease. Increasedtemperature also implies an increase of base oil mobility which helps to limit the starvation.Moreover, it is well known that grease bleeding increases with temperature. Film breakdownand heat development may therefore also lead to an increase of oil release from the grease. Acombination of mechanisms may even be occurring. For example, at an event the release of asmall amount of grease from a lump under a cage bar and the consequent creation of a freshgrease surface enhances the bleeding rate of oil just because the oil concentration gradient islarger at the new surface than at the old.

Grease Dynamics 249

A change in oil bleeding may likewise occur due to a chemical change of the greasecomposition in the presence of oxygen. This forms what may be called a ‘grease skin’ whichcan lead to strong reduction of the oil-bleeding rate. Removal of the skin by a short, high,temperature increase would then restore the bleeding process.

11.4 Temperature and Film Breakdown

To investigate further the alternative mechanisms leading to the temperature fluctuations,a cylindrical roller bearing test was made at a lower speed (1500 rpm) again with a load of8.34 kN. This time, the electrical resistance over the bearing was also recorded, lower resistanceindicating lower film thickness, that is more metallic contact. The temperature and electricalresistance signals are plotted in Figure 11.4. To quantify the relation between temperature andfilm breakdown, the cross-correlation function, R, between the two signals as a function of timedelay was determined and also plotted in Figure 11.4. The figure shows a maximum (negative)value for R of 0.858 at a delay time of about 10 minutes, indicating strong correlation betweendrop in film thickness and temperature rise a few minutes later. The magnitude of this timedelay suggests that the temperature events are caused by metal-to-metal contact rather than bygrease churning. After this contact, the bearing lubrication is again properly replenished andthe temperature drops. The same transient behaviour will usually take place several times: fullfilm lubrication, followed by continuous starvation, oxidation and so on, until the next eventtakes place. Refilling the bearing with grease (relubrication) need not necessarily take placeafter the first grease-softening event but certainly before such events are no longer able to healthe bearing. As in traditional grease-life testing, an indication of this will be the magnitude ofsuccessive temperature excursions.

11.5 Chaotic Behaviour

To understand the transient behaviour of grease lubrication, the bearing is considered to be adynamic system, which means that one state of lubrication develops into another state over thecourse of time. The equations describing this development are generally nonlinear, allowingthe system to display deterministic, chaotic or even random behaviour. Analysis of both thetemperature and film resistance time series using methods of nonlinear dynamics reveals thequalitative characteristics of this behaviour.

11.5.1 Reconstruction of the Temperature Dynamics Using TimeDelayed Embedding

The reconstruction of the phase space (parameters varying in time) of a system from a scalartime series is the basis of almost all nonlinear methods exploring the dynamic (such aschaotic determinism) or the metric (such as the dimensionality) properties of the data. Thisis technically solved by the method of time delay embedding, which derives originally fromWhitney [608]. A somewhat more recent extension of this method was proposed and furtherelaborated by Takens [565], and is now known as Takens’ embedding theorem.


0 100 200 300 400 500 600 700 8000

50

100

150

Tem

pera

ture

[°C

]

Time [hours]0 100 200 300 400 500 600 700 800

0

0.5

1

1.5

Sur

face

sep

arat

ion

[−]

Surface separation

Temperature

−1.5 −1 −0.5 0 0.5 1 1.5

x104

−1

−0.95

−0.9

−0.85

−0.8

−0.75

−0.7

−0.65

−0.6

−0.55

−0.5

Time lag temperature vs film breakdown [s]

Cro

ss−

corr

elat

ion

tem

pera

ture

vs

film

bre

akdo

wn

Figure 11.4 (a) Temperature with contact intensity profile. (b) Cross-correlation function between thetwo signals.

The dynamics of a time series {x1, x2, . . . , xN } are fully captured or ‘embedded’ in them-dimensional phase space (m > d, where d is the dimension of the attractor,1 that is thegeometrical representation of the signal in phase space) defined by the vectors:

Yt = {xt , xt−τ , xt−2τ , . . . , xt−(m−1)τ } (11.1)

1 An attractor is a signal whose path in phase space never crosses itself at any point in time.

Grease Dynamics 251

where τ is a suitable time delay. This τ and phase space dimension m are chosen such thatan attractor can be constructed. When an attractor of a dynamic system exists, its dimensioneither integral or fractal (non-integral) is smaller than the dimension of the phase space.According to Whitney [608], any smooth manifold of dimension d can be smoothly embeddedin m = 2d + 1 dimensions. Takens’ theorem [565] shows that if the dimension of the manifoldcontaining the attractor is d, then embedding the data in a phase space with dimensionm ≥ 2d + 1 preserves the topological properties of the attractor. Sauer et al. [517] furtherdiscussed the generalization of the embedding theorem, emphasizing the importance of thefractal dimension of the attractor for estimation of the minimal dimension of the embeddingspace, that is m > 2d. Some authors (see, for example, Abrabanel et al. [18]) suggest that, inpractice, m > d would be sufficient.

It is most useful to calculate the dimension of a dynamic system such as a grease lubricatedbearing considered here. This dimension d represents the number of variables needed todescribe the behaviour of the system, a number which often will not be known a priori. Itgives the number of independent physical parameters required to predict the evolution of thesystem with time.

11.5.2 Estimation of the Time Delay τ

In terms of the nonlinear methods, the calculation of the time delay τ corresponding to the firstminimum of the time-delayed mutual information [203] allows a good reconstruction of thesystem dynamics in various practical applications. This delayed mutual information l(q, si ) isbased on Shannon’s entropy and can be computed as follows:

l(q, si ) = H (si ) + H (q) − H (q, si ) (11.2)

where H (si ) is the uncertainty of the value of q, given si , with si = x(ti ) and q = x(t + τ ) andH (si ) and H (q) are Shannon’s information entropies. In summary, if the optimal time delay τ

is chosen to coincide with the first minimum of the mutual information, then the reconstructedstate vector Yt (Eq. 11.1) will consist of delay components that possess minimal mutualinformation between them. The dynamics will then be optimally reconstructed (unfolded).

11.5.3 Calculation of the Dimensions d and m

The most widely used fractal dimension d quantifier is the correlation dimension dc, whichis based on the correlation integral or function analysis [143]. Obtaining a noninteger, finitedc for a time series demonstrates fractal scaling and indicates possible chaotic dynamics. Thealgorithm to calculate this dimension uses the phase space reconstruction and the so-calledcorrelation sum (integral):

C(r ) = 1

Nref

Nre f∑i=1

1

N

N∑j=1

�(r − ∣∣Yi − Yj

∣∣) . (11.3)

Here � is the Heaviside step function, �(y) = 1 for y > 0 and �(y) = 0 for y ≤ 0, r is theradius of the sphere centred on Yi, N is the number of points in Yt, and Nref is a calibrated


number of reference points taken from Yt that are needed to yield consistent statistics. Thenorm Yi − Yj is the standard Euclidean norm. The correlation function C(r ) is estimatedfor the range of r available from the time series and for several embedding dimensionsm. Then C(m, r ) is inspected for the signatures of self-similarity, usually by estimatingthe slope of log C(r ) versus log r plot. If the time series is characterized by an attractor,then for positive values of r , the correlation integral C(r ) is scaled to the radius r by thepower law:

C(r ) ∼= αrυ (11.4)

where υ is the correlation exponent (found from the slope of the log C(r ) versus log r plot)and α is a constant. For a random process, υ varies linearly with increasing m, withoutreaching a saturation value, whereas for a deterministic process, the value of the correlationexponent υ saturates and becomes independent of m for increasing embedded dimension. Thesaturation value dc is defined as the correlation dimension of the attractor of the time series. Ifthe calculation of the correlation dimension dc leads to a finite integer value, the underlyingdynamics of the system is considered to be dominated by some strong periodic phenomenon. Ifthe value of dc is fractional (and usually small) then the system is considered to be dominated bylow-dimensional deterministic chaotic dynamics governed by the geometrical and dynamicalproperties of the attractor. The correlation dimension of the attractor indicates the dimensionof the phase space (m = 2d + 1) required for a smooth embedding of the attractor which,as previously described, indicates the number of essential variables necessary to describe thedynamic evolution of the system.

11.5.4 Calculation of the Lyapunov Exponents

One of the most striking properties of deterministic chaotic systems is the limited predictability(or unpredictability) of the future evolution of the system, despite the determinism of thesystem. This limited predictability is a consequence of the inherent instability of the dynamicevolution, reflected by the sensitive dependence on the initial conditions. These sensitivities arereflected throughout the stability of the system and are closely related to the eigenvalues of thedynamic system whose generalization is expressed by dynamic invariants known as Lyapunovexponents. The Lyapunov exponents are related to the average rates of divergence and /orconvergence of nearby trajectories in phase space, and therefore, measure how predictableor unpredictable the dynamic system is. In other words, the Lyapunov exponents denote therate of loss of information in time and are usually expressed in units of bits per unit oftime. One can estimate as many different Lyapunov exponents for a dynamical system asthere are phase space coordinates, that is principal axes, which give the average exponentialrates of expansion and contraction of the attractor along these axes. Given a continuousdynamic system in d-dimensional phase space, one can monitor the evolution of a set ofinfinitesimal initial conditions in an attractor that are confined within a d-dimensional sphere(hypersphere).

Due to the locally deforming nature of the ‘flow’ (effects of stretching and folding),this d-sphere will become a d-ellipsoid in time. If one orders the principal axes of thissphere (ellipsoid) from the most rapidly to the least rapidly growing, one can compute the

Grease Dynamics 253

0 1 2 3 4 5 6 7 8 9x 105

−1

−0.5

0

0.5

1

1.5

2

2.5

Time [s]

Lyap

unov

exp

onen

ts

Figure 11.5 The Lyapunov exponents calculated for the temperature dynamics of the cylindrical rollerbearing.

average growth (expansion or contraction) rates λi (i = 1..d) of any given principal axis pi

as follows:

λi = limT →∞

1

T

∫0

T

dtd

dtln

(pi (t)

pi (0)

)(11.5)

= limT →∞

1

Tln

(pi (T )

pi (0)

). (11.6)

Here, pi (0) is the radius of the principal axis pi at time t = 0 (i.e. in the initial hypersphere),and pi (T ) is its radius after some time T . The set of λi is the Lyapunov spectrum. Whenat least one Lyapunov exponent is positive, then the dynamical system is characterized bydeterministic chaos, see Wolf et al. [618]. As an illustration, Figure 11.5 shows the right-handside of Eq. 11.6 as a function of T before proceeding to the limit, in the case of the temperaturedynamics for the first bearing from Figure 11.3. The five limiting values, λi , in this case are theLyapunov exponent spectrum corresponding to the embedding dimension m = 5. The dynam-ics is deterministic chaos due to the positive Lyapunov exponents. The maximum exponent isabout λ1 = 1.15 and one of the exponents is close to zero, thus indicating a strong determin-istic signature. The negative Lyapunov exponent indicates also the presence of a dissipationmechanism in the temperature dynamics, which might be the frictional heat generation.

11.6 Quantitative Analysis of Grease Tests

A set of 11 tests were done where bearings have been run under self-induced temperature. Thetests have been done on an R2F machine (for a description of the test rig, see Chapter 16).


Table 11.1 Analysis of the cylindrical roller bearing tests. Tests1–10 were run at 6000 rpm, test 11 at 1500 rpm.

Test m λmax λmin

1 5 1.15 −0.622 4(5) 1.16 −0.553 5 1.18 −0.674 5 1.12 −0.735 5 1.16 −0.666 4(5) 1.21 −0.587 4 1.14 −0.58 5 1.16 −0.959 5 1.17 −0.88

10 5 1.15 −0.6211 5 1.10 −0.5

The first 10 tests were done using NU 312 bearings lubricated using a commercial Li-soapgrease with a mineral base oil. The bearings were run at a speed of 6000 rpm and a load of8.34 kN. Typical running times were 400 hours. Two of the temperature signals have alreadybeen shown in Figure 11.3. The test shown in Figure 11.4 (NJ 312 bearing) was added to thetest series.

For each test, the dimension m and the m Lyapunov exponents were calculated using thetheory as described above. Table 11.1 shows the results.

The reconstructed temperature dynamics show consistent embedding dimensions of m ≈ 5.This means that five parameters (variables) are essential for a mathematical description of thetemperature development in the bearings in this test series. The temperature dynamics canbe clearly characterized as ‘deterministic chaos’ due to the existence of fractal correlationdimensions and positive Lyapunov exponents. Maximal Lyapunov exponents with valuesconsistently in the range (1.10 < λmax < 1.18) are found. This means that there is a self-similarity and consistency in the appearance of the temperature events of these tests, whichcan be expressed with this scale and time-invariant parameter. The Table 11.1 also showsthat, in each case, there is a negative Lyapunov coefficient, in line with the earlier postulateascribing this to an energy dissipation through frictional losses.

11.7 Discussion

Grease life is strongly determined by the operating temperature, so that grease life tests areconventionally done at a fixed temperature, with the bearings being heated externally. Theheaters are controlled by the measured temperature, which hides the intrinsic temperaturedynamics of grease lubrication in bearings. To overcome this, the tests reported in this chapterwere run under self-induced temperatures revealing, perhaps not unexpectedly, that the tem-perature does not remain constant. Further, contrary to common practice, bearing test timeshave been extended long enough to observe several of the ‘events’ within the bearing whichthese fluctuating temperatures indicate.

Grease Dynamics 255

The dynamic behaviour is ascribed here to the limited time interval, where the grease is ableto provide a sufficiently thick film and full separation of the running surfaces. This hypothesisis proven by film breakdown measurements using an electrical resistance technique. Metal-to-metal contact will cause heat development, followed by softening of the grease that isstored in the interior of the bearing. Subsequently, replenishment of lubricant in the trackfrom this grease will occur, after which full film conditions will once more prevail, followedagain by starvation and another film breakdown. Apparently there is a self-healing mechanismhere which makes it possible to replenish the bearing surfaces after film breakdown, before aseizure can take place.

Nonlinear dynamics or chaos theory has been applied to reconstruct the measured temper-ature signals. The analysis provides strong evidence that the temperature (and the film break-down) dynamical behaviour can be characterized as ‘deterministically chaotic’ due to the exis-tence of fractal correlation dimensions and positive Lyapunov exponents (1.10 < λmax < 1.18)in all tests. The embedding dimensions of m = 5 means that only five parameters (variables)are needed for a mathematical description of the temperature development in the bearing.

The positive maximal Lyapunov exponents (1.10 < λmax < 1.18) that were found in alltests reveal that there is a self-similarity and consistency in the appearance of the temperatureevents. This means that the life of the grease, dependent upon its ability to provide adequatelubricant films, should be predictable. The chaotic nature of these films implies, however,that grease life will be strongly dependent on the detailed initial conditions of the grease.Small variations here may have a large impact later on in time. Here, one may think of smallvariations in initial filling quantity, initial distribution of the grease etc.

The positive Lyapunov exponents show that the events will not follow each other on aregular basis. On average, the time interval between events increases over time. This mayseem surprising, since it actually means that (on average) the lubricant film can be maintainedover a longer period of time after each event has taken place.

There are indications that grease lubricated bearings can sometimes run for much longerthan anticipated by the temperature signal. As mentioned earlier, the end of grease life isgenerally measured by an increase in temperature signal, exceeding some pre-defined value.The results presented in this chapter show that grease life may depend strongly on the particularvalue of this maximum allowed temperature. If this is not too high, recovery takes place andthe bearing keeps on running at least until the next event occurs, leading to the possibility ofa considerably longer aggregate life. This is an important concern for the definition of a goodquality grease life test.

Most of the text and figures in this chapter were reproduced with permission from Lugt, Velickovand Tripp, 2009 C© Taylor and Francis.

12Reliability

J.H. Tripp and P.M. Lugt

In this chapter, the problem of predicting the length of time a bearing may be expected tofunction satisfactorily before failing will be considered. A bearing may fail for a number ofphysical reasons, such as wear due to (abrasive) contaminants either from external or internalsources, or from catastrophic collapse of the cage. In the bearing industry, however, attentionhas been focused largely on two principal causes. Historically, failure from fatigue of one ofthe raceways leading to spalling was the first mechanism considered. By contrast, the secondmode of failure concentrated not on the materials of the raceways and rolling elements butrather on the lubricants, grease or oil, introduced to separate their relatively moving surfaces.In this case failure will occur as lubricant is lost from the bearing surfaces or is otherwisedegraded for example by oxidation, resulting in excessive friction and overheating. In the firstcase modelling of the fatigue process involves a detailed study of the stress cycles enduredby the solid materials during overrolling and their influence on the initiation and propagationof fatigue cracks. Lubricant modelling, in addition to the usual quite well understood elasto-hydrodynamics of film formation, requires some knowledge of how the lubricant arrives on thecontacting surfaces and how its properties depend on the physical and chemical environmentit experiences there.

The feature which these very different failure modes share is that they are catastrophic ratherthan deterministic phenomena which means, in the case of bearings, that the particular cycleor time when a given bearing fails is never predictable. Individual failure is a probable event.What is predictable is only the fraction of a large population of supposedly identical bearingswhich survive at least for a given time or, equivalently, will fail in the next unit of time. Thetime at which failure actually does occur is known, respectively, as the fatigue or grease life.The first aim of bearing life modelling is thus to make a prediction of the failure probabilitydistribution based solely on statistical data from bearings tested under conditions controlledas closely as possible. A second aim is to provide an explanation of this distribution derivingfrom knowledge of the various physical and chemical conditions prevailing within the bearing.These two aspects are in fact rather different from one another but both are necessary if the



model is to provide information useful to either the manufacturer or the user of a bearing. Thischapter concentrates on the first, more statistical, of the two parts to this problem.

12.1 Failure Distribution

The basic relationship for the probability of a mechanical element to survive for time t wasdeveloped by Weibull following on his statistical theory of material failure published as earlyas 1939 [602, 604]. Similar forms of this probability distribution had appeared previously inconnection with particle size distributions [501] but it was the application to the fatigue lifeof rolling bearings by Lundberg and Palmgren in 1947 [380] which led to its widespreadapplication to problems involving various kinds of failure.

Rolling bearing life, whether fatigue or grease, in a population of identically manufacturedbearings is, for the purposes of a probability distribution, a random variable. In the case of theWeibull distribution this may be stated as follows: the probability S(t) that a bearing runningunder given environmental conditions has survived running at least time t is given by

S(t) = exp

[−(

t − τ

η

)β]

. (12.1)

The exponent β, the shape parameter, determines the shape of the distribution S, η, thescale parameter, essentially gives the unit in which t is measured, while τ , the locationparameter, shifts the whole distribution along the t-axis. Various shapes for S are illustrated inFigure 12.1a. In the form of Eq. 12.1 S is known as the 3-parameter Weibull distribution. Sinceconventionally a Weibull probability distribution begins at unity at t = 0 and falls to zero ast → ∞, all three parameters should be positive and no failure should occur before t = τ . Theform of S in Eq. 12.1 should therefore be extended by adding a condition, either that t ≥ τ orthat S(t) = 1, 0 ≤ t ≤ τ . Frequently the minimum life τ is taken to be zero, reducing Eq. 12.1to the 2-parameter Weibull.

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t/η

S β = 0.5

β = 1

β = 3.5 β = 10

(a) Probability of survival in a Weibullpopulation for four values of β.

0 0.5 1 1.5 20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

t/η

Failu

re r

ate

p [1

/tim

e]

β = 0.5

β = 1

β = 3.5β = 10

(b) Failure rate for various beta slope values.

Figure 12.1 Weibull functions (τ = 0).

Reliability 259

An illustration is given in Fig. 12.2a showing the rate of change of the probability of survivalor probability density for β = 0.5, β = 1, β = 3.5 and β = 10. The figure shows that for highvalues of β the failures concentrate at t = η.

The probability of survival in Eq. 12.1, will be taken simply to mean that for a populationof n0 bearings, the number

n(t) = n0S(t) (12.2)

will still be expected to be running after time t . The number expected to have failed is thenn0 F(t), where F(t) is the failure distribution. So

S(t) = 1 − F(t). (12.3)

No consideration will be given here as to how closely the ratio n(t)/n0 will approach S(t) in apractical test as the size of the population increases, a topic adequately discussed in classicaltexts on probability. Suffice it to say that as n0 → ∞, the ratio will approach the expected S(t).For a fixed n0 the ratio approaches S(t) only within confidence limits such that the probabilityof S(t) lying outside those limits can be set arbitrarily small by increasing n0. What is importanthere is that the confidence limits can be established in terms of the original distribution itself,together with the population size, n0. This will be shown later in this chapter.

The probability S(t) of a bearing surviving at least for time t is often alternativelyreferred to as the reliability R(t) of the bearing population. Reliability is a rapidly expandingsubdiscipline of system design and, in keeping with its common meaning, R(t) generallydecreases as t increases.

The expected number of bearings failing in time interval (t,�t) is

�n = n0 [S(t) − S(t + �t)] = −n0dS

dt�t. (12.4)

So, using Eq. 12.2, the probability of failure in (t,�t) is

�n

n= − 1

S

dS

dt�t. (12.5)

This gives the instantaneous failure probability rate defined as

p(t) ≡ (�n/n)

�t= − 1

S

dS

dt= d

dtln

(1

S(t)

). (12.6)

p(t) is sometimes also referred to as the Hazard function, h(t). The cumulative Hazard functionbecomes

H (t) =∫ t

0h(t ′)dt ′ = ln

(1

S(t)

)(12.7)

or

S(t) = e−H (t). (12.8)


Both the cumulative failure F and the Hazard H are increasing in time as opposed to S, whichis decreasing in time.

In the case of a Weibull distribution this instantaneous failure probability rate can be writtenfrom Eq. 12.6 as:

p(t) = (�n/n)

�t= β

η

(t

η

)(β−1)

. (12.9)

Figure 12.1b shows the failure rate for various values of β.If the failure rate is not a simple power of t , then the failure distribution will not be a Weibull

distribution.The nondimensional functions S, R, H or F are cumulative distribution functions, whereas

their t-derivatives such as p or h are density functions with dimension [t ime]−1. Anotherdensity function is

f (t) = −dS

dt, (12.10)

f (t) = β

η

(t − τ

η

)β−1

exp

[−(

t − τ

η

)β]

, (12.11)

usually known simply as the probability density. Noting that f (t)�t = S(t) · p(t)�t it isevident that f (t)�t actually expresses the joint probability that a bearing survives for time t andthen fails in the next interval �t . As can be seen in Figure 12.2a, the shape parameter determinesthe shape of a linear-linear plot of f (t) versus t/η. Eq. 12.9 shows that the instantaneous failurerate decreases with t if β < 1 and increases if β > 1 (see also Figure 12.1b).

In the case of grease life, β ≈ 2.3 [280] may indicate loss or some form of degradation oraging of the grease. A β-value < 1 could arise if the grease was initially unfavourably located

0 0.5 1 1.5 20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Pro

babi

lity

dens

ity [1

/tim

e]

β = 0.5

β = 1

β = 3.5

β = 10

(a) Probability density function f(t).

10 −1 100

0.01

0.02

0.05

0.10

0.25

0.50

0.75

0.900.950.99

0.999

t/ η

Num

ber

of fa

ilure

s % β = 0.5

β = 1 β = 3.5 β = 10

(b) Failure distribution (F(t)) for variousβ-slope values

t/η


Reliability 261

in the bearing but after some running acquired a more optimal distribution. For the particularcase β = 1, p(t) is constant, independent of time, which only means that the probability ofa bearing which has survived for time t failing in the next interval �t does not depend onthe already elapsed time t but only on the length of that interval. This illustrates the crucialdifference between the two failure rates, p(t) and f (t). In bearing tests typically β = 1.1 forball bearing fatigue life [249].

Example

The relubrication interval of a group of bearings is given as 1000 hours. Calculate the proba-bility that a bearing randomly selected from this group exceeds 10 000 hours.

The relubrication interval is L01 = 1000 hours or S = 0.99 at t = 1000 hours. Eq. 12.1 canbe rewritten as:

η = t ·(

ln1

S

)− 1β

. (12.12)

Assuming β = 2.3, this gives η = 7.4 × 1000 = 7390 hours. Again using Eq. 12.1, for t =10 000 this gives S = 0.135. So the probability of surviving 10 000 hours is 13.5%.

12.2 Mean Life and Time Between Failures

The use of the (failure) probability density f (t) allows calculation of the expected or mean lifeof a bearing, L , most straightforwardly carried out for the 2-parameter Weibull distribution,τ = 0, shown in Figure 12.2a. Hence,

L =∫ 1

0tdS =

∫ 0

∞t

(dS

dt

)dt

=∫ ∞

0t f (t)dt = η�(1 + 1/β) (12.13)

where � is the gamma or factorial function defined as �(β) = ∫∞0 tβ−1e−t dt . For the 3-

parameter distribution, this value of L is just increased by the minimum life, τ . For values ofβ > 1, �(1 + 1/β) lies in the narrow range 0.886 < �(1 + 1/β) < 1, with the lower limit atβ = 2, see Figure 12.3a. L is sometimes confusingly referred to as the mean time betweenfailures, denoting the mean time a single bearing might be expected to run after it replaces afailed bearing in an application.

Most commonly, bearings are tested in batches, where obviously the time between twoconsecutive failures depends on the size of the batch, n0, and on which two failures areconsidered. This raises the question of how the time between consecutive failures in a batchtest would be expected to vary throughout the test. From Eq. 12.4 the number of bearings failingin time interval (t,�t) is �n = n0 f (t)�t . So, the time between subsequent failures can be


1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Ave

rage

life

/η

β

(a) Ratio of expected life L and time scale factorη versus Weibull slope β according to Eq. 12.13.

0 0.5 1 1.5 20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Tim

e be

twee

n fa

ilure

s/η

β = 3.5

β = 10

β = 1

β = 0.5

(b) Factor expressing the time between failuresaccording to Eq. 12.14 for batch size 50.

t/η


calculated by taking �n = 1 in the latter equation, which then becomes �t = 1/ (n0 f (t)).This gives:

�t

η= 1

n0β

(t

η

)1−β

exp

[(t

η

)β]

. (12.14)

This is shown in Figure 12.3b where the time between failures for a batch size of 50 bearings isscaled with η. From the shape of the curves in Figure 12.2a it may be seen that, for β > 1, thefailure probability density f (t) passes through a maximum so that �t has a minimum there.

For β > 1, at early times bearings are new and performing well so not many bearings willfail and the time between failures will be large. After some time more and more bearingswill fail and the time between failures will be small. After this minimum, failures havedepleted the size of the surviving population (most bearings have failed by then) and the timebetween failures will be large again.

Setting the derivative in time of Eq. 12.14 to zero gives the time for this extremum as

(t/η)(�t)min =(

β − 1

β

)1/β

, (12.15)

and the minimum value of �t as

(�t)min = η

n0· 1

β·(

βe

β − 1

)(β−1)/β

. (12.16)

For β ≤ 1, �t has no has no true minimum. The failure rate decreases and �t increasesmonotonically with t . For these cases the minimum �t occurs at the earliest time when failuremay happen, either t = τ or 0.

Reliability 263

Example 1: calculating test time

For planning grease life tests it is most convenient to calculate the estimated test time. Assumethat for an acceptance test the expected L10 life is 1000 hours. The test is run with n0 = 5 orn0 = 30 bearings, where all bearings will be run to failure. For grease life typically β = 2.3.This means that η = 2.66 × L10 = 2660 hours (see Eq. 12.12). The mean life, accordingto Eq. 12.13 will be L = 2356 hours. The expected time between failures (calculated withEq. 12.14) is plotted in Figure 12.4. In this plot the same case but now with 30 test bearingsis plotted as well. It is very unlikely that bearings will start failing at the beginning of the test.Most bearings will fail when the probability density is high, so around 2000 hours. Eq. 12.15gives 2075 hours. After this, fewer and fewer bearings will fail and the time between failuresincreases again. It would be very inefficient to stop the test before this minimum is passed.

By increasing the number of test bearings the time between failures decreases. This alsohappens at an early stage of the test and the test time may therefore be decreased by using alarge population of bearings.

Example 2: expected failures in life testing

In an R0F+ test five sets of bearings are tested, so n0 = 5. After 1000 hours four sets havefailed. When is the last one expected to fail?

From the four failures a β could be estimated, alternatively β = 2.3 could be assumed again.S = n/n0, so S = 0.2. With Eq. 12.12 this gives η = 0.81t or t

η= 1.23. Using Eq. 12.14 this

gives �tη

= 0.33 or �t = 0.33η = 0.33 × 0.81t = 0.27t . This means that the last set wouldstill need to run roughly 27% longer, so is expected to fail at 1270 hours. It should be notedthat the precision of such late or low S failure time estimates is quite approximate.

0 1000 2000 3000 4000 5000 60000

100

200

300

400

500

600

700

800

900

1000

Time [h]

Tim

e be

twee

n fa

ilure

s [h

]

n0 = 30

n0 = 5

Figure 12.4 Expected time between failures for Example 1.


12.3 Percentile Life

According to the Weibull distribution there is some probability of a failure at any time afterτ , which offers two options for expressing the reliability or expected life of a given batch ofbearings. In the previous section the mean life L was introduced simply as the expected time abearing runs before failure. But more information about the spread of failures is contained inthe Weibull distribution. The failure probability F(t) gives the expected fraction of bearingswhich have failed earlier than t . If p = 100F is the percentage failed then L p = t is thepercentile life. Clearly for bearings tested in a series of batches of certain size the times L p

at which the percentage reaches p will be distributed, the spread being greater for p furtherfrom 50. This only applies in the absence of suspended bearings. In that case the smallestconfidence intervals occur at lower life percentiles. For fatigue life the bearing industry hasfrequently adopted L10 as an adequate measure of reliability, whereas for grease life, L50 themedian life, is more commonly used. From p = 100(1 − S(L p)) it follows that

p/100 = 1 − exp

[−(

L p − τ

η

)β]

. (12.17)

Rewriting gives

L p = τ + η

(ln

1

1 − p/100

) 1β

. (12.18)

For the particular value p = 100(1 − e−1) = 63.21%, L p = τ + η for any value of β. Becauseτ is often taken as zero, η is known as the characteristic life of the distribution. Eq. 12.13 showsthat the characteristic life is quite close to the mean life if β > 1. The expression ‘remaininglife’ is occasionally used to denote the difference between its L10 and the actual time a bearinghas already run. This usage fails to recognize the random nature of bearing life and leadsto a negative residual life whenever the reliability R(t) has fallen below 90%. To avoid thisanomaly it might be preferable simply to provide the current reliability figure.

Using Eq. 12.18 and τ = 0, the ratios of various commonly used L p values may easily bewritten as:

La

Lb=[

ln (1 − a/100)−1

ln (1 − b/100)−1

]1/β

. (12.19)

For the specific time of L1,L10, L50:

L1 = η

[ln

(1

1 − 0.01

)]1/β

= η (0.0101)1/β (12.20)

L10 = η

[ln

(1

1 − 0.10

)]1/β

= η (0.1054)1/β (12.21)

L50 = η

[ln

(1

1 − 0.50

)]1/β

= η (0.6931)1/β . (12.22)

Reliability 265

For grease life, typical values of β and τ are respectively 2.3 and 0. Thus for example

L50

L10=(

0.6931

0.1054

)1/β

= 2.3 (12.23)

L50

L1=(

0.6931

0.0101

)1/β

= 6.3 (12.24)

L10

L1=(

0.1054

0.0101

)1/β

= 2.8. (12.25)

Generally L50 is used as a measure of grease life. The reason for this is the small population ofbearings that is usually tested in grease life. By taking L50, rather than L10 smaller confidenceintervals are obtained [25].

12.4 Point and Interval Estimates

It has been assumed in this chapter that the failure probability distribution best suited tofatigue or grease life prediction of bearings is a Weibull distribution. The question of whetherthe observations could actually be better accounted for by some different distribution will notbe discussed. Attention will instead be focused on the problem of how to determine fromtest measurements the parameters governing this distribution, realizing that such observations,themselves random numbers, can only yield point values which in some sense are best esti-mates, together with confidence interval estimates outside which these values are expected tofall only with some suitably small probability.

12.4.1 Graphical Methods for Point Estimates

For the sake of simplicity the case τ = 0 will be considered, acknowledging that failures mayoccur right from the beginning of a test – there is no threshold or minimum life. In the simplestcase n (or n0) bearings are run to failure, the failure times in ascending order being recordedas t1 < t2 . . . < tn . Such a test is known as uncensored or complete, providing n values of tbut no values of S to insert in Eq. 12.1. Rewriting this as

ln ln1

S= β [ln t − ln η] , (12.26)

the shape parameter β could be obtained as the slope of a log-log plot of ln(1/S) versust . Figure 12.2b gives an example of such a plot. Parameter β is thus often referred to asthe Weibull slope. But first the values of S or (1 − F) must be estimated for each failure,j = 1, 2 . . . n. For each t j , the required value for F is the fraction of the whole populationwhich would be expected to have failed before this particular time, imagining that the wholepopulation could be tested. In other words, F is the probability of a bearing failure at sometime before t j . This is known as the true failure rank and denoted by Fnj , since it will dependon both n and j . Clearly, the true rank is not known precisely and a procedure must thereforebe adopted to estimate it. For the bearing failing at t j its rank is given by the joint probability


that exactly ( j − 1) bearings fail before t j and exactly (n − j) afterward while one fails in theinfinitesimal interval (t j , dt). Given, then, that the rank is a probability, it has a probabilitydensity and a cumulative distribution function, requiring a decision to be made as to how tocharacterize this distribution with a single number. The choice is usually one of two numbers,the mean or the median of the distribution. The median rank is most frequently preferred sincethen the positive and negative deviations from the true rank cancel [303].

Failures before t j occur with probability Fnj while afterwards they occur with probability(1 − Fnj ). The joint probability of a bearing surviving until t j and then failing in (t j , dt) is, asshown earlier, dFnj/dt · dt = dFnj . Thus the joint probability defining the rank Fnj becomes

n!

( j − 1)!1!(n − j)!F j−1

nj

(1 − Fnj

)n− jdFnj = g(Fnj )dFnj (12.27)

where the pre-multiplying factor is just the number of ways of selecting the three groups( j − 1), 1 and (n − j) from the group of size n. In this form, g(Fnj ) is evidently the probabilitydensity function of Fnj . The indefinite integral of g(Fnj ) then yields the cumulative distributionfunction G(Fnj ) as a polynomial of order n in Fnj , a different polynomial for each j . SettingG(Fnj ) = 1

2 and solving for Fnj gives the median rank value of F needed for the plot ofln ln (1/(1 − F)) versus ln t . There is just one solution of G = 1

2 in the range of F from 0 to1. Tables of these median rank solutions for a wide variety of n and j values may be foundin the literature. To an unexpectedly good approximation these tables may be summarized bythe simple expression [74]:

Fnj = j − 0.3

n + 0.4(12.28)

which may be multiplied by 100 if percentiles are needed. The mean value Fnj of Fnj maybe obtained by integrating Fnj · g(Fnj ) with respect to Fnj from 0 to 1, giving the exact resultFnj = j/(n + 1) for the mean rank, as opposed to the median. Note that Eq. 12.28 also givesthe exact result 1

2 for the j = 12 (n + 1)th failure in any test with an odd number of bearings,

which in this case also agrees with the mean value.Using Eqns 12.26 and 12.28 (with Snj = 1 − Fnj ) the observed failure times may now

be plotted against their median ranks with the slope of the best fit straight line giving apoint estimate for β, the Weibull shape parameter. The abscissa corresponding to the ordinateF = (1 − e−1) or 0.6321 gives the value of the scale parameter or characteristic life η ofthe Weibull distribution. Special Weibull probability paper is available to make this graphicalapproach quite straightforward to carry out.

Example

This will be illustrated using an example where grease life has been measured on a R0F+ testrig, neglecting, for now, the suspended bearings. The measured lives from five bearings are:592, 303, 674, 677 and 528 hours. First the values are ordered: t1 < t2 < t3 < t4 < t5 and nextthe median rank values are calculated using Eq. 12.28. Table 12.1 shows the results.

The numbers from Table 12.1 are the dots in Weibull plot, Figure 12.5. In this plot theWeibull distribution is also plotted (drawn line).

Reliability 267

Table 12.1 Example of an R0F + test result, excludingthe suspended bearings.

Failure order (i) Life (hours) Median value (F)

1 303 0.132 528 0.313 592 0.504 674 0.695 677 0.87

12.4.2 Suspended Tests, Censored Data

From the shape of the reliability curve it is clear that the test time needed to run all the bearingsin a sample to failure will sometimes be impractically long. To avoid this, various schemesof censored testing have been developed whereby not every bearing is failed. Censoring mayalso be done for practical reasons It could be part of the test strategy (e.g. sudden death, seeSection 12.5). However, censoring may also be a result of a malfunctioning of the test rig.Examples of the latter are unexpected electrical power problems (note that life tests could berunning for a full year), drive problems (belt drives, where a belt may break) and so on.

Information from the unfailed bearings still makes a contribution to the Weibull parameterestimates. So-called Type I right censoring involves suspending some of the bearings oncethey have run longer than some assigned time, possibly different for each bearing. In thiscase, the number of failures in a given test is not known beforehand. By contrast, in Type II

101 102 103

0.01

0.02

0.05

0.10

0.25

0.50

0.75

0.900.950.99

0.999

Time [h]

Num

ber

of fa

ilure

s [%

]

Individual failuresWeibull excluding suspended bearingsCorrected failuresWeibull including suspended bearings

Figure 12.5 Examples from Tables 12.1 and 12.2 plotted on ‘Weibull paper’ including and excluding‘suspended bearings’ from an R0F test.


censoring, testing is suspended once an assigned number of failures have occurred. If all thesuspension times exceed the longest failure time, Eq. 12.28 may still be used for the rank ofthe j th failure enabling the Weibull plot to be made. On the other hand, if the suspension timesare interspersed with the failure times, mixed censoring, then the ordinal number j of thepossible failures is not uniquely known and this plotting technique cannot be directly applied.However, a similar method known as ’Hazard plotting’ (Nelson [445, 446]) has been devisedto determine the failure rank for such mixed censored tests.

Suppose in a test of n bearings that r are run to failure and (n − r ) are suspended. Thefailure times t f and the suspension times ts are assembled in a single list in ascending order,t1 < t2 . . . < tn and a rank assigned to each in descending order, known as the reverse rank,n, (n − 1), . . . 1. The reciprocal of this reverse rank, known as the Hazard, h, is evaluated onlyfor each failure, so that like the failure times themselves, the Hazard h f is listed in ascendingorder, h f 1 < h f 2 . . . < h f r . Next the cumulative Hazard Hj is evaluated from

Hj =j∑

i=1

h f i , j = 1, 2..r. (12.29)

This quantity is identified with the cumulative Hazard function of Eq. 12.7 with argument t j .So from Eq. 12.7 the failure rank of the j th failure becomes

Fnj = F(t j ) = 1 − e−H j (12.30)

which as before may be plotted on Weibull probability paper to evaluate the parameters β

and η.It may be seen that Hazard plotting using reverse ranking is one way of assigning failure

rank when the ordinal number is unknown. Comparing Hazard ranking for an uncensored testwith Eq. 12.28 shows that, except for a few early failures, the rankings of the two methodsagree to better than 10%, with the Hazard ranking being consistently higher. This would returna somewhat lower Weibull slope for hazard plotting but the difference is small compared withthe confidence limits or sampling variability, so for most purposes the estimate is sufficientlyaccurate.

Example: Hazard plotting

The test from Table 12.1 will now be expanded with some suspended bearings, shown inTable 12.2, which are labelled S, the failed bearings are labelled F . The hazard is the reciprocalof the reverse rank but computed only for the failed bearings. The cumulative hazard for eachfailure is the sum of the hazard values for that failure and all failures that occurred at an earlierrunning time. The Weibull plot can now be made by plotting the life versus F . This is shownin Figure 12.5 where both the uncensored and censored (corrected) results are plotted. Thefigure illustrates that the calculated life is longer in the case that the suspended bearings areincluded. The suspended tests have reduced the median rank values which effectively movesthe Weibull distribution to the right on the timescale, while maintaining the Weibull slope.

Reliability 269

Table 12.2 Example of an R0F + test result, including the suspended bearings.

Reverse rank (RR) Life Hazard h (1/RR) Cumulative Hazard (H ) F (1 − e−H )

10(S) 303 – – –9(F) 303 0.111 0.111 0.10518(S) 528 – – –7(F) 528 0.143 0.254 0.22436(S) 592 – – –5(F) 592 0.200 0.454 0.36494(S) 674 – – –3(F) 674 0.333 0.787 0.54482(S) 677 – – –1(F) 677 1.000 1.787 0.8325

12.4.3 Weibull Parameters η and β: Maximum Likelihood Method

Because the test failure times are themselves a sample of random variables coming froma supposed Weibull distribution whose parameters η, β are to be estimated, it follows thatthese estimates η, β, called the maximum likelihood estimates of η, β, are themselves randomvariables each depending on the particular set of sample times as well as on its size. Theseestimates η, β therefore follow their own probability distribution, known as the samplingdistribution, which generally cannot be found analytically but which is certainly amenableto Monte Carlo methods. Once the sampling distribution of a parameter estimate is known,average values and confidence limits for that parameter are readily found.

Suppose that of n bearings in a given test, r fail and (n − r ) are suspended (r ≥ 1). Thus thereare r bearings each failing within an (infinitesimal) time interval �t at times ti , i = 1, 2, r, and(n − r ) bearings surviving for ti or longer, i = (r + 1), (r + 2), n, where index i denotes noparticular order for the ti . Each failure occurs with probability f (ti ) · �t , while each suspendedbearing survives with probability S(ti ). So the joint probability that the whole sample of ntimes actually happens is

G(r, n) = n!

(n − r )! r !(�t)r

r∏i=1

f (ti )n∏

i=(n−r )

S(ti ). (12.31)

Without the pre-multiplying factor, this probability is more commonly known as the likelihood,L, a term sometimes applied also to its logarithm. So

L(r, n) =r∏

i=1

f (ti )n∏

i=(r+1)

S(ti ). (12.32)

The method of maximum likelihood adopts the quite reasonable principle that the best esti-mates for the parameters of the Weibull distribution which produced the sample times ti are


those which maximize the joint probability of their occurrence. For the 2-parameter Weibulldistribution this leads to two equations which may be written as

∂ lnL∂β

= 0 (12.33)

∂ lnL∂η

= 0 (12.34)

whose simultaneous solution yields the maximum likelihood estimates or MLE, β and η, forthe Weibull parameters. Substituting Eq. 12.1 (with τ = 0) for S(t), −d S/dt for f (t) intoEq. 12.32, dropping the factorial factor and taking the logarithm yields

lnL = r (ln β − β ln η) + (β − 1)r∑

i=1

ln(ti ) −n∑

i=1

(tiη

)β

. (12.35)

Eq. 12.34 yields

r =n∑

i=1

(tiη

)β

(12.36)

which may be substituted into Eq. 12.33 to give

1

β+

r∑i=1

ln ti

r−

n∑i=1

tβ

i ln ti

n∑i=1

tβ

i

= 0. (12.37)

Eq. 12.36, the equation for the Weibull scale parameter, may now be rewritten into:

η =(

1

r

n∑i=1

tβ

i

)1/β

. (12.38)

The nonlinear Eq. 12.37 contains only parameter β and may be solved for example by theNewton–Raphson technique, yielding the MLE β. Substituting this in Eq. 12.38 then gives theMLE η. Eq. 12.37 shows that 1/β is just the difference of two differently weighted averagesof ln ti . η is the MLE of L p when p has the particular value (1 − e−1) and from it the MLEof any other life percentile is found using β and η in Eq. 12.18, since it may be shown thatthe maximum likelihood value of a function of MLEs is the MLE of that function, a usefulproperty (McCool [407]).

A common application for the MLEs β and η from a bearing test is to predict the reliability Sor life of other supposedly identically manufactured and identically greased bearings from thesame population. Since these MLEs follow their own sampling distribution, they themselves

Reliability 271

and any predictions of S are known only within certain confidence intervals, which may befound directly from this distribution.

To find the parameter sampling distributions for a testing procedure in which n bearingsare run, r failures occur and (n − r ) are suspended at various times, it would be necessaryto generate a large number, N – many thousands – of samples of r failure times and (n − r )suspension times, using each sample to give one pair of β and η. Clearly it would be impossibleto carry out so many actual tests. The failure times may instead be drawn from an arbitrary2-parameter Weibull distribution with β = βW , η = ηW and τ = 0, where for convenience(βW , ηW ) might be chosen as (1, 1). The failure times are most easily generated by taking arandom number uniformly distributed in the range 0 to 1 as the left-hand side, S, of Eq. 12.1and then solving it for t . This kind of approach has been named a Monte Carlo method. Foreach such sample Eqns 12.37 and 12.38 are then solved, giving N values of (β, η). In thismethod suspensions are not generated and it therefore only applies when suspended subgroupshave a suspension time equal to the last failure.

From these N values it would be possible to enumerate the quantiles (percentiles), forexample βq of the sampling distribution of β simply by arranging them in ascending orderto find the percentage q of values less than βq . These values would, however, group aroundthe arbitrary value βW of the Weibull distribution used to generate the random samples andcould not be used for the percentiles arising from a general or unknown distribution. However,forming a new function

v = β/β (12.39)

where both β and β come from the same Weibull avoids this limitation. This function andits quantiles (percentiles) vq depend on (r, n) but not on (β, η) so that vq may be computedby Monte Carlo sampling and then applied to various actual test results. Functions with thisbehaviour are known as pivotal functions [360].

Function v, a kind of normalized shape parameter, is used to evaluate point and intervalestimates of the Weibull β. To treat point and interval estimates of life percentiles, L p, a secondpivotal function u is introduced [408], defined by

u(p) = β lnL p

L p. (12.40)

With τ = 0, Eq. 12.1 may be used to rewrite u as

u(p) = β lnη

η+ (1 − v) ln ln

1

1 − p(12.41)

where p replaces the percentile value used previously. Like v this pivotal depends on (n, r )but not on (β, η). For the particular value of p = (1 − e−1) the second term vanishes and usimplifies to u(p) = u(0.6321) = β ln(η/η). By arranging the N values of u(p) in ascendingorder, the quantiles uq (p) are obtained in the same manner as for v. The quantiles vq and uq

of these two pivotals represent the cumulative sampling distributions respectively of β andL p. The form of Eq. 12.41 shows that the sampling distribution for u(p) may be obtained


from separate Monte Carlo calculations for each p-value. It is useful to remember that thesedistributions depend on n and r but not on N provided this is sufficiently large.

12.4.4 Bias of Point Estimates

The maximum likelihood method represents one way to arrive at an estimate of the parametersof the underlying Weibull distribution extracted from groups of n observations (failures orsuspensions) and, by Monte Carlo sampling, to obtain the sampling distributions of theseestimators resulting from the randomness of the n individuals in these groups.

In discussing the determination of failure rank (Section 12.4.1) which also follows a proba-bility distribution, it was mentioned that there are various ways to characterize such a distribu-tion by means of a single number. Similarly in the present case, the mean and median valuesare possible candidates. Before proceeding further it is useful first to introduce the concept ofstatistical bias, using Weibull β as an example.

An estimate of a statistical parameter is produced by some operation on the n failure times,an example being the solving of the maximum likelihood Eq. 12.37 for β. If a small (odd)number nt of tests of n bearings with r failures were carried out yielding nt values of β, thenthat value having equal numbers of smaller and larger values would be the median and the sumof the values divided by nt would be the mean. The question of bias concerns how closely suchestimates lie to the values, known as the expectation or E-values, which would be expected ifsomehow the entire bearing population were tested n bearings at a time. If the E-value equalsthe true value, then the estimate is said to be unbiased. Consider first the median value. A singletest gives one value of β while Monte Carlo calculations give an arbitrarily large number ofvalues of the ratio v = β

β. Because v is pivotal its values do not depend on β and furthermore

its quantiles do not depend on N , so that E[vq ] = vq . Thus if β is estimated as

β ′′ ≡ β

v0.50. (12.42)

then E[β ′′ − β] vanishes, signifying that β ′′ is indeed the median unbiased estimate. It is thevalue whose expectation value is as likely to be less than as greater than the true Weibull β.

A parallel argument may be made for the mean unbiased estimate. The mean value of vq isgiven by

v =∫ 1

0vqdq. (12.43)

Thus if β is estimated as

β ′ ≡ β

v(12.44)

then E[β ′ − β] = 0, showing that β ′ is the mean unbiased estimator for the Weibull shapeparameter. It is important to recall that estimates 12.42 and 12.44 are not equations – hencethe identity sign – but expressions whose values, based on multiple tests, would approach thetrue parameter.

Reliability 273

Table 12.3 Percentile values for the pivotal functions u, q and v for the calculation of 90%confidence intervals for L10, β and their precision ratios including sudden death testing (m > 1). For

R↔β

the value for↔β is taken as v0.5. In a complete sudden death test the number of samples (subgroups

of size m) is l, the same as the number of failures r . If m = 1 function q equals u. For the calculation ofu or q for other percentiles (e.g. L50 or L01), Eq. 12.41 may be used by taking v = v0.5.

SubgroupSubgroups l size m q0.05 q0.5 q0.95 v0.05 v0.5 v0.95 R R↔

β

5 1 −1.14 0.45 4.45 0.68 1.23 2.81 4.13 94.15 2 −1.02 0.30 3.25 0.68 1.23 2.81 4.13 32.25 4 −0.95 0.14 2.22 0.68 1.23 2.81 4.13 13.2For m = 1 (single bearing on a shaft): u = q

Source: row 1, q = u and v from Table 20.4 in Harris [249] for the case r = 5, n = 5; rows 2 & 3, qfrom Table 20.5 in Harris [249] for the cases l = 5, m = 2 & l = 5, m = 4 and v (independent of m)same as in first row of this Table.

12.4.5 Confidence Intervals for β

In addition to correcting for bias, the sampling distribution v may also be used to constructconfidence intervals for β. From the single value of β yielded by a test, it follows from thedefinition of v that the probability that β/β < vq is q, if all suspensions occurred at the timeof the last failure. Here β is the required or true shape parameter of the Weibull bearingdistribution. Symbolically Pr{β > β/vq} = q and Pr{β < β/vq} = 1 − q. Setting q = 0.95in the first inequality and 0.05 in the second, a 90% ML confidence interval estimate for β

may be written

β

v0.95< β <

β

v0.05. (12.45)

Tables of the quantiles vq (r, n) are available in the literature (e.g. Thoman [572] and McCool[407]). Some values for a test with five (groups of) bearings, which is the most used configu-ration in grease life testing, are given in Table 12.3.

12.4.6 Confidence Intervals and Unbiased Point Estimatesfor Life Percentiles

Using the same N samples used to assemble the sampling distribution of the pivotal functionv, Eq. 12.38 is solved to give N values of η, which are then inserted in Eq. 12.40 to give Nvalues of u. The required values for β and v have already been computed, the value for η

is ηW (the nominal value for the Monte Carlo sampling), while the value of p is that of thedesired percentile. In discussing a particular bearing test characterized by (n, r ), the explicitdependence of uq (p) on (n, r ) will be omitted for simplicity. The quantiles uq (p) give thecumulative sampling distribution for the life percentiles L p. With the (β, η) values providedby the ML estimates using the observed test data, the value of L p is found from Eq. 12.18,setting τ = 0. From Eq. 12.40 this leads to quantile values for L pq

L pq = L p exp

(−uq (p)

β

). (12.46)


By definition of the quantiles of u,

Pr{β ln(L p/L p) < uq (p)} = q

and

Pr{β ln(L p/L p) > uq (p)} = 1 − q.

Setting q = 0.95 in the first and 0.05 in the second inequality a two-sided 90% confidenceinterval for L p is constructed in the same way as for β. Hence

L p exp

(−u0.95(p)

β

)< L p < L p exp

(−u0.05(p)

β

). (12.47)

A median unbiased estimate for L p is obtained from the median value exp(

u0.50(p)β

)

L ′′p ≡ L p

exp(

u0.50(p)β

) . (12.48)

Similarly, a mean unbiased estimate for L p is found from the mean of exp(

uq (p)β

)as follows

L ′p ≡ L p∫ 1

0 exp(

uq (p)β

)dq

. (12.49)

Clearly, due to the presence of β, this expression cannot be written in terms of some universalaverage value of u(p) as was possible for v in the unbiased mean of β. The integral mayhowever be calculated approximately, for example by using for β the unbiased mean estimateof β ≡ β/v, with β taking the value obtained by ML from the experimental data.

The median and mean estimators for β given as Eqns 12.42 and 12.44 may differ significantlyfrom each other as may also the median and mean L p estimators given as Eqns 12.48 and12.49. In determining which to choose to characterize a particular bearing test it thus becomesnecessary to consider what practical use will be made of the test data. Clearly both medianand mean estimates fall within their respective 90% confidence intervals.

12.4.7 Estimate Precision

Inequalities 12.45 and 12.47 indicate the width of the range of values within which the shapeparameter or life L p should lie with 90% certainty. As a measure of the precision with whichthese quantities are known the ratio of the two ends of these confidence intervals is sometimesused. For β this becomes simply

R = v0.95(r, n)

v0.05(r, n). (12.50)

Reliability 275

The precision ratio for a percentile life depends on the value of β, but for purposes of estimating

the value of this ratio it may be sufficient to substitute the median value↔β , to yield

R↔β

(p) = exp

(u0.95(r, n, p) − u0.05(r, n, p)

↔β

)(12.51)

where↔β= v0.50β.

As might be expected, with increase of n both of these precision ratios become smaller andthe precision of the estimates improves. An exception to this occurs however in the case ofR0F+ testing, Table 12.1, where the increase of n is due to the increase in the number ofsuspensions while the number of failures stays fixed. In this case R remains fixed but woulddecrease if the number of subgroups, that is failures, increased. Some values of R and R↔

β(0.10)

are shown in Table 12.3, based on the assignment β = 1 or↔β= v0.50. Eq. 12.51 shows how

the precision of life percentile estimates improves as the Weibull slope parameter increases:

R↔β

(p) = [R1(p)]1↔β . (12.52)

12.5 Sudden Death Testing

It is very common (R0F/R0F+ , but also in many more test rigs) to test bearings in pairs or inmultiple pairs. As will be described later in Chapter 16, in the R0F/R0F+ rigs five pairs ofbearings are tested at controlled temperature where a pair is stopped as soon as the temperatureof one of the two exceeds a pre-defined value (one failure and one suspended bearing) or whenincreased friction causes motor overload (thermal switch).

The strategy is called ‘sudden death’ testing. The pair failure data will now be used tocalculate confidence intervals and life ratings for individual bearings (such as L50 or L10) asdefined above.

In the general case of sudden death testing a group (of bearings) of size n is divided into lequal subgroups of size m and the testing of each subgroup is suspended when the first failureoccurs. The survival probability of a single bearing S, which may be referred to as the parentdistribution, is given by:

S(1, t, β, η) = exp

[−(

t

η

)β]

. (12.53)

For bearings tested in subgroups of size m, with a subgroup failure regarded as the failure ofjust one of the bearings, the subgroup survival probability is just the joint probability

S(m, t, βm, ηm) = S(1, t, β, η)m = exp

[−m

(t

η

)β]

= exp

⎡⎣−

(m

1β t

η

)β⎤⎦ (12.54)


revealing immediately a Weibull distribution for the subgroup having parameters βm = β and

ηm = ηm− 1β . Consistent with this, the maximum likelihood equations yield

βm = β and ηm = η · m− 1β (12.55)

where β and η represent the ML values for l failures and a set of (m − 1) suspensions coincidentwith each failure time. Eq. 12.54 then shows that a subgroup should be treated statistically asan object different from an individual bearing, although the analysis for the two situations isquite similar.

First, it is necessary to construct the pivotal functions v(l, l) and u(l, l, p) for a completeuncensored test of the l subgroups. Eq. 12.55 shows that v = βm/β = β/β is unchanged fromthe values given by the parent distribution, whereas u must be recalculated. Clearly fromEq. 12.55 an estimate for L p, denoted by L p, may be written (McCool [409]) as

L p = m1

βm · L pm, (12.56)

which leads to

u(l, l, p) = βm ln

(L pm

L pm

)= βm ln

(m− 1

βm L p

m− 1βm L p

). (12.57)

Dropping subscript m from the shape parameter this expression may be rewritten as

u(l, l, p) = β ln

(L p

L p

)−(

1 − β

β

)ln(m) = β ln

(L p

L p

)− [1 − v(l, l)] ln(m). (12.58)

The term β ln(

L p

L p

)contains the estimate of L p from Eq. 12.56 and may be used to define a

new function

q(l, m, p) ≡ β ln

(L p

L p

)= u(l, l, p) + [1 − v(l, l)] ln(m). (12.59)

This function depending on the pivotals u and v is another pivotal and so its quantiles maybe evaluated by Monte Carlo methods. Some values for p = 0.10 are given in Table 12.3.When m = 1 the subgroup becomes the individual and, as shown by Eq. 12.59, the functionq(l, m, p) reverts to u(l, l, p) introduced earlier. In the same way as for L p when found by theMLE method based on individual bearing failures and suspensions, the quantiles of q(l, m, p)are used to construct confidence intervals for L p from sudden death tests. Thus, a symmetrictwo-sided 90% confidence interval is given by

L p exp

(−q0.95

β

)< L p < L p exp

(−q0.05

β

)(12.60)

Reliability 277

closely resembling the result shown in Eq. 12.47. Comparing the two functions u and qwill determine, for different numbers of failures, which of the sudden death or conventionaltesting strategies is the more precise. Also, making use of the median (failure) rank equation,Eq. 12.28, the S value at the termination of either type of test is determined, allowing therespective expected durations of the tests to be estimated. If only r of the l subgroups insudden death testing are run to failure and the remaining (l − r ) are suspended, that is if thesudden death test is incomplete, then the functions u(l, l, p) and v(l, l) on the right-hand side ofEq. 12.59 are replaced by u(r, l, p) and v(r, l), while the left-hand side becomes q(r, l, m, p).

In the particular case of R0F+ or R2F tests, l = 5, m = 2, so from Eq. 12.55 the per-centile lives of individual bearings are a factor 21/β greater than for a pair of bearings,reflecting the common observation that an object with two or more parts fails sooner thaneach part separately, the factor amounting to 1.35 for pairs with a characteristic Weibull β

value of 2.3. An illustration is given in Figure 12.6, showing a Weibull plot of typical testdata. It may be worth repeating that the two lines show failure data representing two dif-ferent objects, for example, a single bearing (conventional conditions) and a shaft supportedby one identical bearing at each end (sudden death conditions), with all bearings runningunder identical operating conditions. In this case, the failures plotted for both objects occurat the same times. The failure ranks for the shafts can be obtained from Eq. 12.28 withn = 5. The failure ranks for the individual bearings may be obtained by the Hazard method(see Section 12.4.2).

Table 12.3 gives some percentile values of the distributions q and v used to calculateconfidence intervals and precision values for R0F and another widely used test method wherefour bearings are running on a shaft and where the test is stopped as soon as one of the fourhas failed.

99

9590807060504030

20

10

5

2

1

F%

54325432 103

Life [hours]

Weibull Probability PlotIncluded lives: L10 L50 | Conf interval: 90%-2sided

m = 2

m = 1

Figure 12.6 Weibull distributions for subgroup sizes m = 1 and m = 2.


Example

Calculate the Weibull parameters for an R0F/R0F+ test.To illustrate the theory given above, the example from Table12.2 is taken. In this case

n = 10, l = 5, m = 2 (10 bearings running on 5 shafts with 2 bearings per shaft where a teston a shaft is stopped as soon as one of the bearings has failed). By using Eq. 12.37 and the pairlife times from Table12.2 the shape parameter estimate β2 = β can be calculated. This has tobe done numerically, giving β = 5.4. The scale parameter η2 is calculated using Eq. 12.38:

η2 =(

1

5

(3035.4 + 5285.4 + 5925.4 + 6745.4 + 6775.4

))0.185

= 605 hours.

Eq. 12.1, with τ = 0, can be written as t = η(ln 1

S

)1/β, so in the case of pair testing the L10

life of a pair may be estimated as:

L10 = 605

(ln

1

0.9

)1/5.4

= 399 hours.

Thus for a single bearing, from Eq. 12.55, the L10 estimate becomes

L10 = 20.185 × 399 = 454 hours.

The median unbiased estimate of β is, according to Eq. 12.42 and Table 12.3:

β ′′ = β

v0.50= 5.4

1.23= 4.39.

The 90% confidence interval for β can be calculated with Eq. 12.45 and the values fromTable 12.3 are:

β

v0.95< β <

β

v0.05

5.4

2.81< β <

5.4

0.68

1.42 < β < 7.94.

The median unbiased estimate for L10 can be calculated using Eq. 12.48 with qq substitutedfor uq

L ′′10 = 454 exp

(−0.30

5.4

)= 429 hours.

Reliability 279

Likewise the 90% confidence interval can be calculated using Eq. 12.60:

454 exp

(−3.25

5.4

)< L10 < 454 exp

(1.02

5.4

)hours

249 < L10 < 548 hours.

The precision R↔β

= 2.20, much improved over the value given in Table 12.3 as a result of the

larger↔β value used here.

Example

Calculate the Weibull parameters for an FE9 test.Again the data from Table 12.1 is taken. Now n = 5, l = 5, m = 1 (5 bearings running on

5 shafts with 1 bearing per shaft where a test on a shaft is stopped as soon as the bearing hasfailed). The failure data now represent the failure times of a single bearing rather than a pair.If R0F+ data were truly the same as FE9 then the single bearing life in the R0F+ test wouldbe larger. Again (using Eq. 12.38) while Eq. 12.38 yields η = η1 = 605 hours and L10=399hours. The median unbiased estimate of β is again β ′′=4.39. Also the 90% confidence intervalfor β is that from the previous example as the absence of suspended bearings has no impacton this. Thus

1.42 < β < 7.94.

The median unbiased estimate for L10 can be calculated using Eq. 12.48:

L ′′10 = 399 exp

(−0.45

5.4

)= 367 hours.

The 90% confidence interval can be calculated using Eq. 12.47:

399 exp

(−4.45

5.4

)< L10 < 399 exp

(1.14

5.4

)hours

175 < L10 < 493 hours.

Obviously, the tests from Table 12.1 and Table 12.2 do not represent the results of a R0F andFE9 test for the same grease. The data has only been chosen for convenience. FE9 tests donot give shorter L10 lives. However, since fewer bearings are tested (5 versus 10), the lifepercentile confidence interval for the FE9 test will always be wider.


12.5.1 Maximum Likelihood Method for a 3-ParameterWeibull Distribution

If the minimum life or location parameter, τ , of the Weibull distribution is set equal tozero, the 3-parameter Weibull reduces to its 2-parameter form [369]. A number of methodsfor estimating these two parameters from test data have been presented. The more generalproblem of estimating all three parameters will now be addressed. This is of particular interestbecause frequently the Weibull plot of observational data departs from the expected linearform, which is sometimes an indication of a nonzero minimum life parameter. In the fieldof reliability engineering there is evident commercial value in such a quantity. Fortunately,although considerably greater computational effort may be required, this third parameter canbe conveniently extracted by much the same technique as for the 2-parameter Weibull [462].

For the 2-parameter case it has been argued on physical grounds that both β and η shouldbe positive parameters. In solving the two equations produced by the method of maximumlikelihood it has been shown that one and only one admissible solution for these parametersexists. The location parameter τ , by contrast, must satisfy two constraints. First, like theshape and scale parameters it must be positive, since if it were negative, failures would occureven before test initiation, conventionally at t = 0. Secondly, the earliest failure cannot occurbefore t = τ , even when τ is positive, since according to the Weibull relationship this wouldin general lead to a complex failure probability. Instead of viewing this as a constraint on thefailures it will be considered a constraint on τ . Thus, τ < tmin , where tmin is the earliest failuretime observed in the particular test used in the estimation of the three parameters. As τ is theestimated minimum life of the full population it is reasonable that it should be less than anyactually observed life.

In this way the test data render directly a range within which the third parameter must lie, anadvantage allowing the 3-parameter Weibull estimation problem to be reduced essentially tothe 2-parameter problem whose solution is already known. The simplest manner of achievingthis is to divide the permitted domain for τ , 0 ≤ τ ≤ tmin , into a number of equal smallintervals, �τ , assigning the value τk , k = 0, 1, 2, . . . to each point in this interval. Employingthe method of maximum likelihood described in Section 12.4.3, the Eqns 12.37 and 12.38 to besolved for β and η remain the same, provided the failure and suspension times ti are replacedby xi = (ti − τk). The domain of τ should actually be reduced by some small number at itsupper end to avoid the argument of ln(tmin − τk), which appears in the maximum likelihoodequations, from becoming zero. The quantities xi may be regarded as another sample of randomfailure times and so the equations are assured of a solution just as for the 2-parameter problem.Naming these solutions βk and ηk , both dependent on τk , the three parameters (βk, ηk, τk) arenow such that lnL is maximized with respect to the first two. As an alternative to attemptinga solution to

∂ lnL∂τ

= 0 (12.61)

simultaneously with Eqns 12.33 and 12.34 [360] in order to find a turning point for lnL, a morerobust procedure is simply to calculate lnL directly from Eq. 12.35 as a function of τk . Foreach value of k in the allowed domain, new values of βk and ηk , are also found. A simple plot

Reliability 281

of lnL against k (or τk) immediately reveals the positions of any extrema, together with thecorresponding βk and ηk , so that the whole three-dimensional parameter space is effectivelyscanned. A maximum in lnL versus τk then locates the absolute maximum likelihood, therequired solution for the point estimates of the three Weibull parameters. A minimum in lnLversus τk on the other hand indicates a saddle point which would not be an acceptable solution.The locations of these turning points can, of course, be made more precise by subdividing theinterval �τ in their vicinity.

Clearly, the solution of the 3-parameter Weibull depends entirely on the random numbersrepresented by the empirical test sample data. While a unique absolute maximum likelihoodalways exists in the 2 parameter case, this is not assured when a third parameter is introduced.Several situations have been found to arise [462]:

• There may be no turning point in the allowable parameter space.• There may be only one turning point, in which case it is a saddle point.• If there are two turning points, the one with the larger τ is a saddle point while the one with

the smaller (minimum life) parameter is the absolute maximum.• In cases where a true local maximum exists within the permitted parameter space, the

maximum likelihood may nevertheless be greater at a corner or edge of the domain.• Cases may also occur showing more than two turning points.

If a true maximum does exist, the method outlined here will always be able to find it.

12.6 System Life Prediction

In the case that more bearings are used, or in the case that the bearings are part of a systemcontaining more critical components, the reliability S or the probability of failure F = 1 − Scan be calculated from the lives of the individual components. The reliability (or probabilityof survival) of a system Ssys is the product of the reliability of its n independent components:

Ssys = S1 × S2 × · · ·Sn. (12.62)

Using the 2-parameter Weibull distribution function, the system L10 life L10sys can be calculatedfrom the individual lives, L10i of the components, i here taken for simplicity as having acommon shape parameter, βi = β. So,

n∑i=1

[L10sys

L10i

]β

= 1. (12.63)

Despite the fact that grease may be considered a component of a bearing, the bearing servicelife should not be computed as a combination of its fatigue life and grease life. Grease lifenumbers or equations that are given by the bearing manufacturers or in this book have beenobtained from bearing tests, and grease life is therefore already a combination of the reliabilityof all components in the bearing. The bearing service life should therefore be calculated as theminimum of grease life and bearing life.


Example

A bearing system is running consisting of two bearings with calculated grease lives of 11 000hours and 2750 hours. The fatigue lives are much longer than either of the two. What is thebearing service life?

The system life can be calculated assuming β = 2.3 in Eq. 12.63 giving:

(L10sys

11 000

)2.3

+(

L10sys

2750

)2.3

= 1 (12.64)

so L10sys = 2702 hours.

13Grease Lubricationand Bearing Life

P.M. Lugt and A. Gabelli

In this chapter the various aspects of bearing life in the case of grease lubrication will beaddressed. First the impact of grease lubrication on the stresses in the bearing and its impacton life will be explained. Next, the chemical aspects related to bearing life will be described,including the effect of water. Finally, an illustration of engineering the bearing surface toextend bearing service life will be given.

13.1 Bearing Failure Modes

When a rolling element in a rolling bearing is loaded against a counter surface (ring) thesubsurface stress field is typically like that in Figure 13.1, showing the von Mises subsurfacestresses caused by a Hertzian stress distribution. The figure shows that the maximum stressesdo not occur at the surface but somewhere under the surface at a depth usually denoted by z0.This is where the traditional spalling due to subsurface fatigue will occur. A crack is initiatedat this depth z0, after which it grows towards the surface. The result is a spall leading to bearingfailure.

However, in the last decades the failure mode in bearing operation has dramatically changedfrom subsurface initiated to surface initiated failures. This is the result of a continuouslyincreasing cleanliness of bearing steels [209, 210], but also due to the trend to reduce energyconsumption through the use of thinner oils and grease lubrication which both lead to thinnerlubricating films. Surface initiated failures can be classified into two categories: surface distressand (mild, corrosive, adhesive) wear. Surface distress is again caused by fatigue. However,unlike the classical subsurface initiated fatigue, here fatigue occurs in the near surface areawhere local high stresses are generated by the loaded surface asperities (see Figure 13.2a).The asperity contacts can be regarded as small (possibly EHL) Hertzian contacts with their



–0.50

0.1

0.2

0.3

z (m

m)

y (mm)

Von Mises stress (MPa)

0.4

0.5

0.6

0.7

–0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4 0.5

200

400

600

800

1000

1200

1400

Figure 13.1 Subsurface Von Mises stress field in rolling bearings.

(a) Roughness on the bearing EHL contacts. (b) Typical example of micro distress(Scanning Electron Microscope).

Figure 13.2 Surface roughness in the bearing contacts and the resulting micro-pitting damage.

Grease Lubrication and Bearing Life 285

Figure 13.3 Adhesive wear.

specific subsurface stress distributions and their local z0’s, which are now very close to thesurface. Local fatigue will cause micro-spalling. An example of such a surface can be seen inFigure 13.2b. The second failure mode, wear, is also caused by an insufficiently thick EHL filmcreating asperity contact. Adhesive wear is the result of local ‘welding’ of asperities. It occursin the case of sliding contacts, where significant heat development takes place. Mild, corrosivewear is less dramatic and results in material removal and particle generation. Sliding in rollingbearings can be a result of the kinematics in the bearing but also a result of accelerations whereroller inertia forces cannot be balanced by frictional forces. Wear does not necessarily lead tobearing failures directly. It is in the case that the profile is disturbed, leading to high stresses,that bearing failure will occur. The latter is generally referred to as smearing. An example isshown in Figure 13.3.

In the case of contamination, which may be caused by wear particles from, for example,the cage or surrounding components such as gears, or by insufficient sealing, overrolledcontaminants create dents in the surfaces leading to stress concentrations at the edges of thedents, which again lead to (micro)spalls and failure.

There are more failure modes, such as false brinelling, fretting, corrosion pitting, and so on,but it goes beyond the scope of this book to describe them in detail. For these, the reader isreferred to Tallian [569] and ISO 15243.

13.2 Rated Fatigue Life of Grease Lubricated Rolling Bearings

13.2.1 Introduction

As in grease life, commonly used standard models for rating the fatigue life expectancy ofrolling bearings [7, 288] apply a probabilistic approach to deal with the dispersion of fatigueperformance. This approach was introduced by Lundberg and Palmgren in 1947 [380, 381].In their fundamental work Lundberg and Palmgren applied the Weibull statistics [603] torepresent the dispersion of the fatigue strength of rolling bearings. For a description of Weibullstatistics the reader is referred to Chapter 12. The Lundberg–Palmgren model for the predictionof bearing reliability was independently validated by Lieblein and Zelen [365] of the US


National Bureau of Standards using endurance test data provided from different bearingsmanufacturers. In total 213 test series were analysed, amounting to a total of 4948 endurancetested bearings. The statistical setting of bearing life dispersion was also validated by Tallian[566] by pooling together a large number of bearing life tests: a composite sample of over 2500bearings was used in this additional study. The original Lundberg–Palmgren model constitutedthe foundation, and it is still today the nucleus, of all national and international standards forfatigue life rating of rolling bearings, subsequent theories and developments. Basically theLundberg–Palmgren theory [380, 381] laid down the basis for the calculation of the dynamicload rating and equivalent dynamic load of rolling bearings as it is applied today in the ISO281 [288] basic rating life equation:

L10 =(

C

P

)p

. (13.1)

In the above equation L10 is the rated fatigue life, at 90% reliability, in millions of revolutions,C is the basic dynamic load rating of the bearing for a rated fatigue life of one millionrevolutions, P is the standardized dynamic equivalent load of the bearing and p is the lifeequation exponent. Ioannides et al. [290,291] further developed this model using an integratedsystem approach to provide a better account of the environmental operating conditions of thebearing and the fatigue limit stress of the material. This was accomplished by adopting a stresslife modification factor that is applied to the basic rated life of the bearing [65, 249, 290], asshown by the following equation:

L10 = aslf

(C

P

)p

. (13.2)

The stress-life modification factor aslf has the following form [288, 289]:

aslf = 1

10

⟨1 −

(ηb · ηc · Pu

P

)w⟩−c/β

, (13.3)

in which Pu is the fatigue load limit of the bearing in Newton, w is the exponent relating load tostress, β is the Weibull exponent and c is the stress-life exponent of the rolling contact. Here theMacauley bracket notation is used, which means that the term 〈..〉 is set to zero if the enclosedquantity is negative. The effect of unfavourable environmental conditions for the bearing, suchas thin lubricant films or the presence of contamination particles, will manifest themselvesas increased interactions of the raceway topography resulting in an increased concentrationof surface stresses. This additional stress acts in combination with the nominal stress of thecontact and is taken into account in the fatigue life calculation, using two penalty factors0 ≤ ηb · ηc ≤ 1 applied to the fatigue load limit of the bearing Pu . The two quantities ηb andηc are the lubrication and contamination penalty factors of the bearing that concurrently act inthe reduction of the fatigue load limit of the bearing. Both factors are mutually dependent onthe viscosity ratio, κ , that is the standardized lubrication quality rating used in rolling bearingapplication engineering [28, 85, 211, 252, 429].


13.2.2 The Lubrication Factor

The functional link of the lubrication factor and the lubrication quality rating of the bearinghas the following form [211, 290, 429].

ηb(κ) = bbrg

(3.387 − b1(κ)

κb2(κ)

)5/2

. (13.4)

In the above equation the constant bbrg characterizes each of the four main types of rollingbearings: radial ball, radial roller, thrust ball and thrust roller bearings, while the constantsb1 and b2 are assigned for three ranges of the lubrication quality rating κ . The numericalimplementation is given in Eq. 13.8. Basically the κ parameter provides a measure of thedegree of surface separation between contemporary, high quality, hardened steel bearingsurfaces. Strictly speaking, the viscosity ratio κ is the ratio of the actual lubricant viscosity ν

(kinematic oil viscosity at the operating temperature of the bearing) and the reference viscosityν1 rated as adequate for rolling bearings lubrication [28, 85, 211, 252, 288–290, 429]:

κ = ν

ν1. (13.5)

The calculation of κ is based on mineral oils and on bearing raceway surfaces finished inaccordance with good quality bearing manufacturing practices. Furthermore κ can also beused in the case of synthetic oils. Synthetic hydrocarbon oils have a large viscosity index(small change of viscosity with temperature) which is compensated for by the larger pressure–viscosity coefficient of mineral oils. In this way about the same oil film is built up at differentoperating temperatures if both types of oil have the same viscosity at 40 ◦C.

For good quality bearing surfaces the reference viscosity ν1, can be estimated by means ofa simple diagram, see ISO 281 [288] Fig. 2 and Harris [249], or as a function of the bearingspeed and mean bearing diameter dm , using the following equations, [288, 289]:

ν1 = 45 000 · n−0.83d−0.5m for n < 1 000 rpm

ν1 = 4 500 · n−0.5d−0.5m for n ≥ 1 000 rpm.

(13.6)

This standard rule for the estimation of the lubrication quality of the bearing was developedby Andreason and Snare [28] partly using the elasto-hydrodynamic theory of bearing surfacesand partially based on experience and endurance testing of bearings operating under full andreduced film conditions [25–28,85,252,359]. The ISO 281 diagram, Fig. 2 of [288], and Eqns13.5 and 13.6 for the estimation of the reference viscosity ν1, apply equally well to the base oilviscosity of greases [7, 28, 288]. The main mechanism by which the grease supplies lubricantto the rolling contact has been described in Chapters 2, 7 and 10.

For a well designed and sealed grease lubricated system a continuous supply of oil to therolling contacts can in principle be achieved [533–541]. In some applications this can onlypartially be attained because of a loss of the oil supply mechanism. Depending on the amountof grease available to the bearing, its type, reservoir position and the supplying characteristicsof the grease at the operating temperature and speed of the bearing, lubrication of the rollingcontacts can vary from fully flooded, to starved lubrication of the rolling contacts. However,


the films could also be thicker than those based on the base oil viscosity, for example whena bearing housing is fully packed with grease [540], during running-in or after relubrication.These effects were earlier described in Chapters 2, 9 and 10.

In Barnsby [65] a penalization of the rated lubrication quality of the bearing is proposed tocompensate for the negative effect of oil film reduction (by starvation) of the contact. Otherpractices also suggest limiting κ ≤ 1 in the fatigue life estimation of greased bearings thatcannot be easily relubricated. However, given the variety of actual conditions present in agrease lubrication system, some of which can be favourable and others unfavourable to thelubricant film formation and separation of the working surfaces of the bearing raceway, themost common and standardized approach to rate the lubrication quality of grease lubricatedbearings is by applying Eq. 13.4 to the base oil viscosity of the grease as suggested inAndreason and Snare [28], ISO [288] and SKF [7].

13.2.3 The Contamination Factor ηc

The standard method for classifying the contamination conditions of a lubricated system isdescribed in ISO 4406:1999. In this classification system the results of solid particle countingare converted into a classification code using a scale number. In the case of grease lubricationthis methodology cannot be applied due to the presence of the grease thickener that prohibitsautomatic particle counting (see also Chapter 15). Therefore in ISO 281:(2007) [288] theassessment of the contamination factor ηc for grease lubricated bearings is based on a ratingsystem of the cleanliness condition of the bearing, as described in Table 13.1.

Table 13.1 Cleanliness classification ratings of grease lubricated bearings (ISO 281:(2007) [288].)

Operating conditions and cleanliness classification c1 c2

High cleanliness: Very clean assembly with careful flushing;very good sealing in relation to operating conditions; regreasingcarried out continuously or at short intervals. Sealed bearings,greased for life with effective sealing capacity in relation tooperating conditions

0.0864 0.6796

Normal cleanliness: Clean assembly with flushing; goodsealing in relation to operating conditions; regreasing accordingto manufacturer’s specification. Sealed bearings, greased forlife with proper sealing capacity in relation to operatingconditions, e.g. shielded bearings

0.0432 1.141

Slight to typical contamination: Clean assembly; moderatesealing capacity in relation to operating conditions; regreasingaccording to manufacturer’s specifications

0.0177 1.887

c2 = 1.677 for dm > 500 mm

Severe contamination: Assembly in workshop; bearing andapplication not adequately washed after mounting; poor sealingcapacity in relation to operating conditions; regreasing intervalslonger than recommended by manufacturer

0.0115 2.662

Very severe contamination: Assembly in contaminatedenvironment; inadequate sealing; long regreasing intervals

0.00617 4.06


Table 13.2 Model constants of the stress-life modification factor of Eq. 13.8 for radial bearings (ISO281:(2007) [288].)

Type lub.quality a1 a2 a3 w1 w2 c/e

Ball bearings 0.1 ≤ κ < 0.4 2.5671 2.2649 0.054381 0.83 1/3 9.30.4 ≤ κ < 1 2.5671 1.9987 0.19087 0.83 1/3 9.3

1 ≤ κ ≤ 4 2.5671 1.9987 0.19987 0.83 1/3 9.3

Roller bearings 0.1 ≤ κ < 0.4 1.5859 1.3993 0.054381 1 0.4 9.1850.4 ≤ κ < 1 1.5859 1.2348 0.19087 1 0.4 9.185

1 ≤ κ ≤ 4 1.5859 1.2348 0.071739 1 0.4 9.185

The contamination factor ηc of a given bearing application can be derived from the clean-liness class of the application, Table 13.1, which provides the constants c1 and c2, and the κ

and dm of the bearing. The standardized engineering model of ηc is described by the followingconditional equation [211, 288]:

ηc = min[c1 · κ0.68 · d0.55

m , 1] (

1 − c2

d1/3m

). (13.7)

13.2.4 The Stress-Life Modification Factor aslf

By combining Eq. 13.3 and 13.4 the functional form of the stress-life modification factor of agrease lubricated bearing can be obtained. Following [288] this reads:

aslf = 1

10

⟨1 −

(a1 − a2

κa3

)w1 ·(

ηc · Pu

P

)w2⟩−c/e

. (13.8)

The model constants of Eq. 13.8 can be found in Table 13.2 for radial ball and roller bearings.The contamination factor ηc used in the stress-life modification factor of Eq. 13.8 can be

derived using Eq. 13.7. The value of the fatigue load limit of the bearing Pu can be foundin most bearing manufacturers’ catalogues [7]. The equivalent dynamic load of the bearingP can be determined using ISO [288] formulae or the guidelines provided in the bearingmanufacturers catalogues and handbooks.

A quick estimation of the stress-life modification factors aslf can also be obtained from theparametric κ curves function of the variable

(ηc

PuP

)index of the stress condition of the bearing.

aslf = aslf

(ηc

Pu

P, κ

). (13.9)

An example of parametric κ curves of aslf for radial ball bearings is given in Figure 13.4.

13.3 Background of the Fatigue Life Ratings of GreaseLubricated Bearings

13.3.1 Fatigue Life and Endurance Testing in the Period 1940–1960

In the early development of calculation methods of the fatigue life of rolling bearings [381,603],the effect of the lubrication conditions of the rolling contact was not accounted for. Indeed,


PP

ucη

slfa

50

20

10

5

2

1

0.5

0.2

0.1

0.050.005 0.01 0.02 0.05 0.1 0.2 0.5 1 2 5

2Κ =

4

1

0.6

0.2

0.3

0.4

0.5

0.8

0.15

0.1

Figure 13.4 Curves of aslf for various values of κ for radial ball bearings. Courtesy of SKF.

calculation methods to predict the lubricant film thickness in concentrated Hertzian contactsonly became available several years after this. In performing endurance testing of rollingbearings, practical rules were applied to ensure an adequate lubricant film development in thebearing contacts [533–541]. At the beginning of the industrial application of rolling bearings,a strong advantage of their use as replacement of the traditional sleeve bearings was thatball bearings were quite suitable for grease lubrication, while sleeve bearings require a morecomplicated oil lubrication system. The ability of ball bearings to fulfil their functions at thebest of their performance using a very small supply of lubricant that could be provided by thegrease was a key advantage in promoting their use on a wide range of applications throughoutthe industry [533, 534].

From the very beginning of the industrial use of rolling bearings, grease lubrication wasthe preferred choice in many bearings applications due to the many advantages that greaselubrication offers compared to oil lubrication [536,538,541]. Practical rules for the proper useof grease [533, 534] and design guidelines of the bearing housing were developed to supportthe use of grease in many applications [539, 540]. In practice grease lubrication was, and stillis, the dominating lubrication method in rolling bearing applications [536, 538, 541].

In 1961 Tallian [566] examined the fatigue test results of 93 endurance test series comprisingmore than 2500 bearings of different types that were endurance tested during the period


B A

C

Running test machine. A: Test housing; B: Hanger; C: Electric heating elements

B

Figure 13.5 SKF bearing life test rig for grease lubricated bearings (1948) BBJ 78/1948.

1940–1960. Tallian’s results shows that 77% of the bearing test series (72 test series), wereprovided with grease lubrication. Lithium, calcium and sodium based greases were used inthose early tests. This shows that the development of the bearing life model of Lundberg andPalmgren [381] that took place in the same period, (1940–1960), relied on fatigue test resultsthat, in most cases, were from grease lubricated bearings. An example of a test rig used at thattime is shown in Figure 13.5.

From Tallian’s work [566] we can also deduce that grease lubrication was the dominatinglubrication method of endurance testing in the period 1940–1960. This leads us to conclude thatthe statistical investigation of the Lundberg and Palmgren life model performed by Liebleinand Zelen of the US National Bureau of Standards [365] in 1956 also relied to a very largeextent on fatigue test data originated from grease lubricated ball bearings. Lieblein and Zelen[365] performed a statistical analysis of 213 endurance test series (4948 bearings) from variousmanufacturers. The conclusions from their study supported the parameter setting developedby Lundberg and Palmgren [381] that was later standardized in ISO 281.

13.3.2 Fatigue Life and Endurance Testing After 1960

The discovery of elasto-hydrodynamic l (EHL) by Alexander Mohrenstein-Ertel in 1944 [594],spurred new research efforts during the 1950s to fully understand and explain the lubricationmechanism of rolling bearings that was until that time a matter of opinion and differentconjectures [144, 177].


In the 1960s EHL became an important research topic in rolling bearings. In the beginningthis work concentrated on the validation of EHL calculation tools for the prediction of thelubricant film [357, 570]. Later the focus altered to include the effect of the roughness [288]and ways to factor the quality of the lubrication into the performance of the bearing [6, 159,288, 367, 432, 543, 567, 568].

During this development, the use of grease as a lubricant for endurance testing bearingswas drastically reduced. This was in an effort to achieve a better correlation between theexpected lubricant film operating in the bearing and the fatigue performance of the rollingcontact. Grease and its complex rheology/chemistry and other complicating effects related tothe bleeding and feeding mechanism of the lubrication of the rolling contact, could be avoidedby adopting oil lubrication during the endurance testing of the bearings [25, 86, 252, 359].

However, it was clearly understood that the results correlating the lubrication quality (ingeneral represented by the expected amount of separation of the mating surfaces) based on oillubricated testing, could simply be transferred to grease lubricated bearings. The methodologysuggested was to use the viscosity of the base oil of the grease to assess the expected lubricationquality of the bearing [27, 28].

Based on the large experience on expected performance gained in the endurance of greaselubricated bearings during the 1940s and 1950s, the use of this procedure was probablyconsidered conservative [27,28,85]. This can also be seen in the work of Snare in 1970 [547].In this paper Snare evaluated bearing life at high reliability levels (larger than 90%) using apopulation of 500 grease lubricated ball bearings. From the statistics of the bearing failuresSnare found that the minimum life of this large bearing fatigue sample could be extrapolatedand used this for the estimation of the expected minimum life of the general bearing population,see Figure 13.6. The results gained from grease lubricated bearings were then used to assessthe reliability of cylindrical roller bearings in papermaking machines, which are typicallylubricated using an oil circulation system.

Notable is the work of Andreason [26, 27], in which the lubrication factor for bearing liferatings is discussed. Andreason recognized that the complex rheological properties of greasesare difficult to handle in calculations. Endurance testing, however, may offer practical waysto assess the effect of grease lubrication in rolling bearings in a more practical approach. Thelubrication factor is therefore partially based on EHL theory and partially on experience gainedthrough endurance testing [26–28]. This is also the conclusion from the recent sophisticatedanalysis of the lubrication factor for rolling bearings by Gabelli et al. [211] and Morales-Espejel et al. [429].

13.3.3 The Reliability of Grease Lubricated Bearings

Due to the complexity of grease rheology and the related bleeding mechanism of grease lubri-cation, it is interesting to examine the literature about the failure statistics of grease lubricatedbearings that are operating in the field. Bergling in [78] discussed the general methodologyused to predict bearing failure rates using the bearing life equation. He subsequently appliedthis method to estimate the operational reliability of grease lubricated railway axlebox bearings[77]. In Bergling’s study the reliability of very large bearing populations, that is, of the orderof 50 000 up to 2.2 million bearings consisting of cylindrical and spherical roller bearings,was checked. All bearings were lubricated with sodium or calcium based greases with a base


959080

50

20

10

5

2

1

0,5

0,2

0,1

51020

50

80

90

95

98

99

99.5

99.8

99.91 2 5 10 20 50 100 200 5000.5

L Mr

S [%]F [%]

1

2

Figure 13.6 Weibull distribution of 500 grease lubricated 6309 bearings running at a speed ofn = 1000 rpm (n dm = 72 500) and relatively heavy load (catalogue life was 10 million revolutions,167 hours), Snare [547]. Weibull curve 2 is for L0 = 0.05L10, 3-parameter Weibull distribution, seeChapter 12.

oil viscosity of 20 to 25 mm2/s at 50 ◦C. Bergling found that the reported spalling percentagefor the axlebox bearings was just below that of the predicted fatigue life calculations based ona lubrication quality derived from the viscosity of the grease base oil.

A similar result on grease lubricated axlebox bearings was found by Poutanen and Bergstrom[479]. Here the failure rate was also in accordance with the calculated rate, although this studyconcerned only a few hundred axlebox bearings.

The most difficult conditions for the lubrication of a rolling bearing are found during lowspeed operations. Bergling [79] studied the lubrication performance of large size sphericalroller bearings operating at very low speeds (5 rev/min). Following the basic oil viscositydesign rule a grease with a viscosity of 760 mm2/s at 40 ◦C was adopted, basically resulting ina viscosity of 500 mm2/s at the operating temperature of the bearing. This solution was foundto perform well, ensuring up to eight years of operation as predicted by the lubrication factorof grease base oil viscosity used in the rated life equation.

In some specific cases of this application, more common types of greases with a much lowerbasic oil viscosity were adopted during maintenance. This resulted in reduced performancefor the bearings as predicted from a lower lubrication factor and the rated life. Similar resultswere reported by Nuanta et al. [155,444] at higher speeds. They tested tapered roller bearingsin hub units varying the base oil viscosity and also found an increase in life with increasingviscosity, see Figure 13.7.


260

210

160

110L 10

[hou

rs]

60

105 6 7 8 9 10

Viscosity [mPa]11 12 13 14

Figure 13.7 Life of grease lubricated double row angular contact ball bearings, as a function of thebase oil viscosity. The bearings were run with a load generating up to 3.7 GPa pressure in the bearings(data from Nuanta et al. [155, 444]).

All this illustrates that the base oil viscosity at the operating condition may be used as ameasure for the lubrication quality. However, in the work on large size bearings from Bergling[79] it was shown that the increase in bearing life with increasing base oil viscosity is limited.Tests with very high base oil viscosity were discouraging, showing the limits for which greasecan properly work and provide sufficient oil bleeding.

Generally it can be anticipated that greases based on oils with higher viscosities than 500 cStat 40 ◦C bleed oil so slowly that the bearing may not be adequately lubricated. Therefore, ifsuch a high viscosity is required because of low speeds, extreme care should be taken.

The effect of a reduced film thickness on bearing life in grease lubrication bearings wasillustrated in the tests from Ohno et al. [458]. They tested the life of thrust ball bearings withfully formulated greases but also with base oil only. Figure 13.8a shows the result of thesetests where the surface separation is measured by means of the � parameter. This parameter isdefined as the ratio of EHL film thickness, calculated using the base oil viscosity of the greaseand combined surface roughness:

� = h

Rq. (13.10)

This parameter had already been applied in 1962 by Dawson [161] to link the lubricatingproperties to micro-spalling life on rolling discs. Here Rq is the root mean square deviationof the roughness height from the mean plane of a surface (for a definition of roughnessparameters, see for example Whitehouse [607]):

Rq =√

1

L

∫ L

0z2dx, (13.11)

where L is the measurement length and z is the height deviation from the mean plane.


50

10

10 2 4

Base oil series

Grease series

L

L

50

10

L

L

L

L10

0,

50

0

Film parameter [Λ]

(a) Bearing life versus Λ-parameter, calculatedusing the base oil viscosity.

L

L

50

10

10 50 100

10

50

L

L

L

L10

0,

50

0

Average separation rate [%]

(b) Bearing life versus (measured) separation.

Figure 13.8 Test results to compare oil (open symbols) and grease (dark symbols) [458]. L10 = 11.38hours and pmax = 4 GPa. The open symbols refer to oil and the closed symbols to grease. Reproducedfrom Ohno et al., 1998 C© Allerton Press Inc.

Figure 13.8a shows that, if the viscosity of the oil is equal to the base oil viscosity, thesegrease lubricated bearings will be running shorter than in the case of oil lubrication. Ohnoet al. ascribed this to starvation. They also measured the separation by measuring the electricalresistance over the bearing and found that bearing life for oil and grease is equal if equalfilms are generated (see Figure 13.8b). This suggests that, as in the case of oil lubrication,bearing life is governed by the film thickness, which, for this configuration, is lower for greaselubrication despite the fact that the (base) oil viscosity is equal. This is most probably due tostarvation which is then more pronounced in the case of grease lubrication than in the caseof oil lubrication. As a reference, Ohno et al. mention that these results can be explained byassuming that, in the case of grease lubrication, starvation will reduce the film thickness to25–50% compared to oil lubrication. These results are in line with the theory described inChapter 10. It is important to note though that these results only apply to bearings that arenot ‘plentifully’ supplied with grease. If the bearing (so not only the housing) is fully packedwith grease, which can only be applied at extreme slow rotation, the film may even be thickerthan those calculated with the base oil. In such cases, sometimes κ is calculated assuming aviscosity of 20–25% higher than the base oil viscosity (Wilson [616]). However, this may betoo optimistic. After all, the grease thickener could easily degrade due to a milling process inthe bearing, reducing its apparent viscosity.

Generally, for ultra-low speed operation it is recommended to completely fill the bearingand housing with grease. Heat development due to grease churning will be very low and anexcess of grease will ensure a fully flooded situation. Moreover, wear particles, generated bymetal-to-metal contact will be taken away by the grease flow and thereby reduce damage torolling elements and raceways. If the loads are low, a low consistency grease is advised. Forheavy loads a high viscosity grease with good EP characteristics is required. For moderateload and poor lubrication conditions, the life of the bearing will be governed by wear. Wear


can be prevented by the use of EP/AW additives. However, care should be taken in the use ofthis since such chemistry may reduce fatigue life, as will be explained in the next section.

Pittroff [472] investigated the operational reliability of rolling bearings used in electricalmotors provided with grease lubricated bearings. For this he examined 2000 electrical motorsand found that the field reliability was well above the basic rated life of the application. Herecognized that the most critical conditions occur in the case of small electrical motors thatadopt sealed or shielded grease lubricated bearings, that is deep groove ball bearings withan internal free volume which can retain only a very small amount of grease. In this type ofapplication, especially for high operating temperatures, more grease degradation was found,requiring frequent relubrication of the bearing. Typically, this could be up to five times duringthe basic rated life of the application.

From the application cases reported here, it appears that the rule to use the grease basic oilviscosity for the estimation of the lubrication condition of a bearing works in general fairlywell. This under the conditions that a sufficient amount of base oil is provided to the rollingcontacts of the bearing. Obviously, this does not always occur. This is more likely to occurin bearings running in well-designed housings, rather than shielded/sealed bearings with arelatively small grease reservoir. Practical experience and good judgement should by appliedto recognize the applications in which grease lubrication is critical and frequent relubricationand other counter-measures become important to ensure proper operation.

13.4 Lubricant Chemistry and Bearing Life

The impact of lubricant chemistry on bearing life has mainly been studied using oil lubricatedcontacts running in full film or mixed lubrication. Very good studies have been done onthe impact of grease chemistry on ‘single contact tests’ (e.g. Fish and Ward [194]) but,to the author’s knowledge, there are no studies on the impact of the grease chemistry onbearing (fatigue) life. In this chapter it is assumed that much of the knowledge that has beenobtained with oil lubrication could also be applied to grease lubricated bearings. An importantdifference between oil and grease lubrication is that bearing greases are developed specificallyfor bearing applications. In the case of oil lubrication the oil (chemistry) is generally designedfor lubricating multiple machine elements in an application. A good example are automotiveand industrial gearboxes, in which bearings and gears are usually lubricated with the same oil.In the case of sufficiently high viscosity oils, the dominant failure mode in bearing lubricationis fatigue, whereas for gears the risk of scuffing or smearing is much higher. Generally, suchgearbox oils contain Extreme Pressure (EP) additives, which will protect the surfaces againstscuffing and will thus extend the gear life (e.g. Towsend and Zaretski [576]). In the lastdecade(s) it has become more and more clear that these additives may have a life-reducingeffect on contacts that are not subject to heavy sliding and are failing due to fatigue only, suchas rolling bearings. The term anti-wear (AW) and extreme pressure (EP) additives are veryoften mixed up. This may be because of a lack of understanding of the chemistry or becausechemical substances may have both an EP and an AW effect. It may be better to use the termLoad Carrying Capacity (LCC) enhancing additive, that is an additive that gives the grease theability to withstand heavy loading without scuffing or scoring [194]. However, since it is stillcommon to call these EP/AW, this terminology will be used in this book. For a description ofthe chemistry of various additives, the reader is referred to Chapter 3.


13.4.1 Anti-Wear Additives

Additives of the so-called AW (anti-wear) type provide surfaces with a reaction layer with astrong adhesion to the surface. This layer prevents metal-to-metal contact and has a low resis-tance to shear. Hence, the asperities are sliding over each other rather than ‘welding together’,which would cause high wear rates. Anti-wear additives typically contain phosphorous, butsolid additives (e.g. graphite or MoS2) are also usually classified as anti-wear.

13.4.2 EP Additives

In the case that the oil film between the rolling elements and rings is not thick enough tofully separate the surfaces, local asperity contact will occur leading to a local extreme hightemperatures for a very short time (flash temperature, see Blok [83]). This temperature mayactivate so-called EP (extreme pressure) additives. The result is the formation of a (chemicalreaction) layer with a low resistance to shear. In time, the asperities will wear off and the resultis a smoother surface. This process will proceed until no asperity contact takes place or untilthe initial volume of EP additives is consumed. This smoothing increases the � or κ value.This may be an oversimplified explanation though [507]. EP additives are usually used incombination with other functional additives. There may be a strong interaction between them.EP additives typically contain organic sulfur, phosphorous or chlorine compounds. Theseadditives may promote corrosion, especially if they are in contact with brass.

13.4.3 The Influence of Lubricant Additives on Bearing Life

There is a consensus that EP/AW additives are favourable in the case of very low speed and/orheavy load. However, it is becoming more and more clear that they may have a detrimentaleffect on bearing life in the case of relatively mild contact or full film conditions. In the nextsections some examples will be given showing the negative impact of EP/AW on bearing life.

Fatigue Testing

Torrance et al. [575] stated that corrosive wear occurs if the chemical reactivity is too high andthat a possible fatigue failure is probably caused by corrosion within cracks. They measuredfatigue life on a rolling contact fatigue machine, or if the test is suspended, the wear from thechange in surface profile. With HVI 160 the S-P additives weakly lowered the L10 life (factor3) and had no effect on L50. The failures in the test of Torrance et al. occurred by spalling. Thisapplies to the oils with and without additives. Before a spall occurs, small cracks start at thebearing surface and grow downwards to some 10 microns (there were many more with thanwithout additives). These cracks form micro-spalls, which lead to larger cracks and finallyfailure. With the oil with EP additives, the track was completely ‘disintegrated’, contrary tothe base oil where no multiple spalling was observed. Track inspection revealed that the oilwith EP additives showed tiny depressions of about 2 microns across as if it had sufferedchemical attack. They stated that the S-P additives increased the number of possible nuclei forspalls. Wear measurements showed that the wear rate using EP additives was smaller than withthe base oil alone and this would prevent running-in. Hence, the surfaces are not smoothed,


leading to high stress asperity contacts, which again promotes corrosion-enhanced fatigue.They state that this life reduction is only observed when the � ratio is small enough to allowasperity contact! Another interesting statement from them is: ‘S-P EP additives decrease themechanical distress of the bearing surface at an expense of an increase of chemical distress’.

Chandler and Talbot [121] have carried out the most interesting experiments on corrosionfatigue using a rotating beam that could be submerged in a lubricant. They used case hardenedsteel in automotive lubricating oils at 25 ◦C. Already at this low temperature, remarkabledifferences in life could be observed. Life was shown to increase when detergents were added(metal soaps that neutralize acidic contaminants). Life was shown to decrease when ZDDP(zinc di-alkyl di-thio phosphate) was added.

Bearing Tests

In 1983 Cantley [119] reported that tests with SAE 20 base oil with ZDDP additives (1.0and 0.50%) gave a bearing life reduction of a factor of 2 to 10 as compared to the base oilwithout the additives. He performed both tapered roller bearing life tests and ring-on-blocktests (ASTM D2782-like) using base oils (SAE 5 and 50) and the same oils with additives withvarious formulations (including ZDDP) under two different temperatures (52 ◦C and 79 ◦C).He correlated bearing life and additive activity, depicted in Figure 13.9.

Figure 13.9 confirms that there are also additives that increase bearing life. These additivesdecrease wear of sliding surfaces but do not influence the fatigue properties of the material. It

3.0

2.0

1.5

1.0

0.5

0.25

0.1

0.25 0.50 0.75 1.0 1.5 2.0 2.5 5.0 10.0

Weight loss (normalized)

Non-reactive Reactive

Bea

ring

lif

e (n

orm

aliz

ed)

Figure 13.9 Correlation between tapered roller bearing life and weight loss in block-on-ring tests.Reproduced from Cantley, 1983 C© Taylor & Francis Group.


is a surprise to see that fatigue life correlates so well with sliding wear. However, as indicatedby Rounds in the discussion of the paper, the tests from Cantley [119] have all been performedunder very light load. Moreover, there are strong indications that the hydrodynamic filmthickness was quite large. So the conditions were very mild and the wear mechanism could beoxidation wear instead of adhesive wear as one may expect under simple sliding conditions.That these additives only have a negative effect when the conditions are not too severe (mixedrather than boundary lubrication) was confirmed by Rounds [503] who reported that manyattempts to correlate fatigue life to wear by using heavily loaded test rigs with severe sliding(4-ball type) were not successful. Cantley’s work indicates that single contact tests (undersmall slip rates) may be a method that could indicate an influence of additive package on life.

Later, in 1994, Wan et al. [596,598] reported tests on ball bearings using a turbine oil with asulfur/phosphorous EP additive package, running at � = 1.2 where a life reduction of at leasta factor of 5 was seen (see Figure 13.10). They inspected the suspended inner-rings and foundthat the honing lines had completely disappeared if the oil with additive was used, whereasthe honing lines were still clearly visible after the tests with base oils only (see Figure 13.11).When using the additive, the surface roughness decreased by a factor of three. Like in thework of Cantley, the bearings were running in mixed to full film lubrication, so the conditionswere not too severe.

Wan also did experiments under somewhat thicker films (� = 2.1) [595] on the Polymet.Again the life was reduced by the use of EP additives (factor of 5). He also measured the wearof the test samples and found that the diameter of the sample which had run in the oil withadditive had been reduced by several microns, which was not the case on the samples that hadrun in base oil only.

10 0001000100

50

10

5

EP oil

Fail

ed in

ner

ring

s [%

]

Life [million revolutions]

Base oilL = > 1000 × 1010, IR

6

Figure 13.10 Weibull plot of tests with base oil and EP oil, � = 1.2. Reproduced with permissionfrom Wan, Van Amerongen and Lankamp, 1992 C© IOP Publishing Ltd.


Reduced film lubricationLambda = 1.2 6309-IR

Surface finish

Base oil +EP additiveBase oil

Outerpositionof thecontact

Outerslip band

Zeroslip band

Midslip band

Magnification × 46.5

Con

tact

elli

pse

Figure 13.11 Optical micrographs of suspended inner-ring surfaces. With base oil and EP oil, � = 1.2.Reproduced with permission from Wan, Van Amerongen and Lankamp, 1992 C© IOP Publishing Ltd.

Similar life reducing effects by EP/AW additives were observed in tapered roller bearingtests by Kepple and Johnson [322] and Nixon and Zantopulos [448,449]. The latter with baseoils, base oils with EP additives (S-P types) and gear lubricants. In all three papers it was clearlyshown that EP additive packages have a detrimental effect on life. Values of 50% reductionin L15 life were found. All tests from Nixon and Zantopulos were run under conditions wherean application engineer would recommend using EP additives (low � operating conditions)to extend bearing life! They tested a standard SAE 20 mineral oil with and without a gearlubricant additive packages on various steel qualities and found that the bearing life for thebase oil was indeed significantly different. The bearing life for the oils with additive packagewas low and equal for all bearing steel qualities! They also tested tapered roller bearings atvarious cleanliness levels and surface finish and also showed that bearing life under low kappaconditions is dominated by EP packages.

A simple way to identify ‘chemical aggressiveness’ is by performing steel ball immersiontests such as those done by Wan et al. [598]. They dipped steel balls in oils and heated thesamples for 7 hrs, 24 hrs and 1 week. EP additives caused a discolouration of the balls anda thick ‘corrosive film’, which was rich in sulfur and phosphor. The base oil test showed noindication of chemical attack, except for possible oxide films (see also the test described inSection 16.2.25).


5.0

4.0

3.0

2.0

1.0

0.0Oil A

L10

(Exp

erim

ent)

L10

(exp

erim

ent)

of o

il E

Oil B Oil C Oil D Oil E

Figure 13.12 Spherical roller bearing life test results with different gearbox oils with similar viscosity,κ = 0.4 and C/P = 1.1. For a description of the oils, see Table 13.3. Reproduced from Pasaribu andLugt, 2012 C© Taylor and Francis Group.

Figure 13.13 Optical images of typical failure mode on inner-rings of a tested bearing from Figure13.12. Reproduced from Pasaribu and Lugt, 2012 C© Taylor and Francis Group.

A Model for the Impact of EP/AW Additives on Bearing Life

Recently, Pasaribu and Lugt [464] reported spherical roller bearing tests with various gearboxoils running under severe conditions: κ = 0.4 and C/P = 1.1. All bearings were failing dueto surface initiated fatigue, see Figure 13.13. The resulting lives are shown in Figure 13.12.Here oil A is an oil with only a very small amount of additive. This oil is used as a referenceand the figure clearly shows the significant life reduction in the presence of S-P additives. Inthis study it was shown that the performance of various oils could be related to the compo-sition of the reaction layers that were formed while the bearings were running. Figure 13.14

Table 13.3 Combination of base oil and additives used in Figure 13.12.

Lubricant Base oil EP/AW Additives

A PAO Only traces of complex sulfur/phosphorus additivesB Polyglycol Complex sulfur/phosphorus additivesC Mineral oil Phosphorus additivesD PAO ZDDPE Mineral oil Complex sulfur/phosphorus additives


35

30

25

20

15

10Oxy

gen

(At %

)

5

00 10 20 30

Depth (nm)

40 50

Oil A (Oxygen)

Oil B (Oxygen)

Oil C (Oxygen)

Oil D (Oxygen)

Oil E (Oxygen)

50

40

30

20

10

Sul

fur

(At %

)

00 10 20 30

Depth (nm)

40 50

Oil A (Sulfur)

Oil B (Sulfur)

Oil C (Sulfur)

Oil D (Sulfur)

Oil E (Sulfur)

30

25

20

15

10

Pho

spho

rus

(At %

)

5

00 10 20 30

Depth (nm)

40 50

Oil A (Phosphorus)Oil B (Phosphorus)Oil C (Phosphorus)Oil D (Phosphorus)Oil E (Phosphorus)

(a) Oxygen.

(b) Sulfur.

(c) Phosphorus.

Figure 13.14 SNMS depth profiles obtained from the inner-rings of bearings that were running for 15hours only. The characters A–E refer to Table 13.3. Reproduced from Pasaribu and Lugt, 2012 C© Taylorand Francis Group.

shows normalized Secondary Neutral Mass Spectrometry (SNMS) depth profiles for oxygen,phosphorus and sulfur. The graphs clearly show the different composition of the reactionlayers formed at the raceways of bearings that were run for only 15 hours. There is a majordifference between the various concentrations at the surfaces and in the penetration depths. Asan example, Figure 13.14 shows that the reaction layer formed by oil E (the worst performingoil tested here) has a significantly higher concentration of sulfur and a lower concentration of


oxygen, while the reaction layer formed by oil A (the best performing oil tested here) has asignificantly higher concentration of oxygen and a very low (not noticeable) concentration ofphosphorus and sulfur.

Forster [199] and So and Lin [549] found that the diffusion equation can successfully beused to fit the concentration of the chemical elements (including Fe and C) as a function ofdepth in the reaction layers. The diffusion equation reads:

C(x, t) = Cs exp

[1 − erf

(x

2√

Dt

)], (13.12)

where C(x, t) is the concentration of an element as a function of depth x , Cs is the concentrationof an element at the surface (x = 0), D is the coefficient of diffusion and t is time (in thiscase 15 hours). All depth profiles presented in Figure 13.14 could be fitted reasonably wellwith this equation. Obviously, these elements will not really diffuse into the steel. There willbe a complex dynamic process of ‘mixing’ Fe , C, H, O, S and so on by means of diffusion(Fe into the reaction layer) and wear where the final result can be described by the diffusionequation. Increasing temperature and mechanical stress will accelerate this process. The resultis a weakened surface with a reduced fatigue strength. In [464] the effective thickness xcg ofthe reaction layer with respect to the various elements was calculated through

xcg =∫∞

0 xC(x, t)dx∫∞0 C(x, t)dx

. (13.13)

A clear correlation was found between bearing life and the product of the concentration ofoxygen at the surface and the thickness of the oxygen reaction layer, see Figure 13.15:

L = f(Cs × xcg

) ‖oxygen. (13.14)

A thick reaction layer with a high concentration of oxygen protects the surface well from theunfavourable ‘mixing’ of various chemical elements at and close to the surface.

6.0

5.0

4.0

3.0

2.0

1.0

0.0

6

5

4

3

2

1

00 1 2 3 4 0 1 2 3 4

L10

(Exp

erim

ent)

L10

(exp

erim

ent)

of o

il E

Wei

bull

slop

e

Wei

bull

slop

e oi

l E

(Cs × Xcg)oxygen

(Cs × Xcg)oxygen of oil E

(Xcg × Cs)Phosphor + (Xcg × Cs)Sulfur

(Xcg × Cs)Oxygen

Figure 13.15 The correlation between the oxygen depth profile parameters and L10 life and (b) Thecorrelation between the concentration of phosphorus and sulfur with the Weibull slope. Reproduced fromPasaribu and Lugt, 2012 C© Taylor and Francis Group.


13.5 Water in Grease

13.5.1 Introduction

Water is a very poor lubricant mainly due to the fact that the pressure–viscosity coefficientα ≈ 0. In addition, the viscosity is very low (typically a factor 200 smaller than oil). Thismeans that water as a lubricant will barely build up an elasto-hydrodynamic film. Rollingbearings are never lubricated with water but water is the most common contaminant and willhave an impact on the performance of the bearing. Water enters the lubricant system through,for example:

• Adsorption (oil is hygroscopic);• condensation;• oxidation reactions (creating a corrosive environment, Salomonsson et al. [512]);• water entry (though the seals);• water release by the polymer cage.

Also a fresh lubricating grease will contain some water, which is as a result of the manufacturingprocess.

The impact of water in grease on bearing life has not been investigated specifically. However,the impact of water in lubricating oil is known to some extend and could be applied to greaselubrication as well. The contribution of the thickener to this process is not known.

13.5.2 Film Thickness

Wan and Spikes [597] showed that small amounts of water reduce the viscosity–pressurecoefficient α and therefore the film thickness for polyglycols and monoglycols. However, ifwater is absorbed in all other common types of oil it has no impact on the film thickness(up to approximately 30% water), which was demonstrated by film thickness measurementswith emulsions by Hamaguchi [240], Dalmaz [154], Wan and Spikes [597]. It is likely thatdispersed water particles are rejected from the contact so that the film is essentially formed bythe oil only.

13.5.3 Water in Oil and Bearing Life

Despite the fact that the water in oil usually does not have an impact on film thickness, watercan have a large impact on bearing life. It may be detrimental, as was shown by Grunbergand Scott [234] in the 1950s. However, it can also be counteracted by additives, Grunbergand Scott [235, 520]. Hobs and Mullet [267, 268] report a bearing life reduction of 30% forwater-in-oil emulsions and over 60% for water-glycol hydraulic fluids.

Kenny [321, 626] have correlated fatigue life in a number of test rigs for different types ofwater based hydraulic fluids and found that the life reduction was not only a function of oiltype and water content but also of load. They modified the life equation to:

L10 =(

C

KP

)p

(13.15)


700

600

500

400

300

200

100

0Impact of water on bearing life

Lif

e [h

]

L50na

Polyglycol 2% water

Polyglycol with 5% free water

Polyglycol without water

Polyglycol with 5% water

M320 with 2%

Figure 13.16 Impact of water on bearing life. L50na is the measured bearing life in the absence ofwater. M320 is a mineral oil. All oils have a viscosity of 320 cSt. Reproduced from Siebert and Mann,2003 C© Antriebstechnik.

where p, K are functions of the fluid type. They measured 2.5 < p < 3.4 and 1.2 < K < 2.This is an empirical formula and only applies to their test conditions. Nevertheless, this isan interesting concept which may also be used in practice. In addition, it shows that the lifereduction at heavy loads is less pronounced than at lower loads. Since bearing life tests areusually performed at high loads, this effect is minimized in tests and will be much morepronounced in normal operating conditions (Spikes [556]).

As an illustration, some results of bearing life tests with different types of oils are givenin Figure 13.16. This figure illustrates that very small amounts of water may not signifi-cantly reduce the bearing life. Moreover, very importantly, free water is more dangerous thandissolved water. Free water can enter the bearing through contamination or by condensation.

13.5.4 Concentration of Water

The most widely equation illustrating the impact of water concentration in oil on bearing lifeis from Cantley [640], published in 1977:

L =(

100

x

)0.6

(13.16)

with L is the life reduction factor and x is the amount of water (ppm). So 100 ppm is a referencelevel. He tested tapered roller bearings (2.03 GPa) using a SAE 20 rust and oxidation inhibitedmineral oil. Cantley found that subsurface initiated fatigue spalling was the failure mechanism.

It is important to notice that the reference level of 100 ppm is so low that it cannot really beused in practice.


13.5.5 Water in Grease

The phenomenon ‘grease and water’ is more complex than the case of oil lubrication. Waterdoes not enter the bearing easily due to the sealing action of grease: there is usually a greasecollar attached to the bearing seals/shields/housing, which prevents a fast penetration of watertowards the bearing contacts. However, water will have an impact on the consistency of thegrease and the sealing action will therefore deteriorate in the presence of water. Similarly tooils, some greases perform well with large quantities of water adsorbed, others do not. Waterhas an impact on bearing life when dissolved in the grease but even more if free water ispresent. Generally, greases have a resistance to water if their components do not react withwater and are not soluble in water [66]. This does not mean that such greases are favourablein bearings. After all, free water is more detrimental than dissolved water.

Generally, in the presence of water, sodium and lithium soap greases are recommended.Sodium absorbs water (emulsifies) but may soften because of this and therefore lose its sealingaction (resistant against water pressure [410]) and may be easily washed out. Sodium greasesform a noncorrosive emulsion when mixed with some water under agitation. They should notbe used when the bearing has long times at standstill. In this case the bearing may corrodeagain.

A lithium grease does not emulsify and provides therefore a good protection against corro-sion, [13]. Li-complex and Ca sulfonate complex greases adsorb relatively large quantities ofwater (3–60%). Polyurea greases tend to pick up less water than metal soap based greases.

Water resistance is measured by the water spray-off test (ASTM D 4049) [12] and theASTM D1264 Standard Test Method for Determining the Water Washout.

13.6 Surface Finish Aspects Related to Grease Lubrication

As mentioned above, the lubricant film should preferably be thick enough to fully separate thesurfaces. In the case of perfectly smooth surfaces a very thin film will be enough. However,this requires expensive finishing techniques. Another reason for not having perfectly smoothsurfaces is the very large real area of contact during start-up and stops and so on, whichwill lead to extensive damage [265]. An alternative is to design the surface topographythrough patterning such that the film formation is enhanced. This was studied in the 1970sby, for example, Patir and Cheng [466, 467]. The main conclusion from this work is that theroughness lay should be transverse to the running direction, particularly when sliding is presentin the contact. Manufacturing transverse roughness while keeping waviness under control is,however, very difficult.

Akamatsu et al. [22,23] were the first to publish papers describing dimpled surfaces, whichimprove the life and percentage of metallic contact under low values of �, in rolling bearings.Their ‘isotropic’ surfaces outperformed superfinished specimens.

A response to this paper was given by Zhai et al. [633]. They specifically investigatedtumbled surfaces. Their calculations show that such dimpled surfaces would actually decreasethe film thickness and induce pressure spikes and therefore have an adverse effect on bearingcontact fatigue. This need not apply to starved conditions or to extremely low speeds though.

Under such conditions, the lubrication mechanisms are different and there is some evidencethat such a surface topography may help to improve life. This has been investigated in detail


by Dumont et al. [180] and Zhao and Sadeghi [635]. High quality measurements on this havebeen made by Krupka and Hartl [344].

Starved lubrication is caused by an insufficient volume of lubricant on the running tracks toprovide a fully flooded inlet of the rolling element–ring contacts. In this case, more lubricantwill cause a thicker lubricant film under the same operating conditions. Dimples on the surfacewill act as lubricant reservoirs, supplying an additional volume of lubricant to the inlet of thecontacts which will increase the film thickness.

The design of a surface using the ‘dimple concept’ is not straightforward. The film increasingeffect of a single dimple depends on the level of starvation, which is influenced by its precedingdimple (but also by the grease properties). The effect of the second dimple is therefore lesspronounced than that of the first. It can therefore be assumed that the mechanism can beattenuated when several pits are in the contact. The results of a single dimple cannot simplybe applied to the case of several dimples. This will require an optimization process.

In addition, the dimples will generate pressure perturbations over the smooth surface stressfield which may reduce the bearing life. Obviously, these need to be limited, which limits thepossible width and depth of the dimples. Tripp and Ioannides [577] showed that such affectscan be neglected as long as �q < 2◦ and Sk < 0 (see Figure 13.17). Here

�q =√

1

L

∫ L

0

(θ − θ

)2dx, (13.17)

1

0

–1

–2

Log relative L10 life

–3

–4

–5

6–1.2–0.8

–0.40.0

Skewness0.4

108

Δ q [Degrees]42

10

Figure 13.17 Life reduction as a function of slope and skewness [577].


with

θ = 1

L

∫ L

0θdx, (13.18)

where θ is the slope of the profile at any point x and θ is the surface slope deviating from themean slope.

The skewness is defined as:

Rsk = 1

nR3q

i=n∑i=1

z3i , (13.19)

with zi the surface height in point i and n the total number of measurement points. Rq isdefined by Eq. 13.11. This implies that the dimples should be very shallow. Moreover, it isimportant that the number of dimples is sufficiently large inside the Hertzian contact, say aminimum of 10 dimples across the contact.

Obviously, it is not possible to manufacture the idealized dimples described in the sectionabove. Moreover, in grease lubricated bearings, the level of starvation will not be constantduring bearing operation and definitely not uniform across the running tracks. The workdescribed above should therefore be seen as revealing the lubrication mechanisms in the caseof ‘negatively skewed’ surfaces, that is surfaces with a value of the roughness parameterRsk < 0. Honed surfaces generally have these properties, but shot-blasted surfaces, de Vrieset al. [163] and laser machined surfaces (Krupka and Hartl [344]) will also give these features.One aspect that was not considered above is the fact that the lubricant volume inside thedimples is ‘consumed’ when they enter the contact. This means that they will have lost mostof their oil when they leave the contact. If the dimples are not replenished then the beneficialeffects will definitely be lost. There are several options for this: one could use a surface energydifference between the surfaces inside the dimples and the lands between the dimples (e.g. bymeans of coating inside or outside the dimples) [375] or make sure that the cage will replenishthe nonuniform layers on the tracks.

14Grease Lubrication Mechanismsin Bearing Seals

P.M. Lugt and P. Baart

14.1 Introduction

Usually, grease lubricated bearings are sealed to prevent contaminants entering the bearingand to keep the grease and its evaporation products inside the bearing [393].

Bearing seals can be divided into contacting and noncontacting seals, the latter are oftencalled ‘shields’. In these shields, the sealing action is provided by closing off the bearingand leaving only a very thin gap between shield and shaft. The weak aspect is that there isstill a gap through which contaminants may enter the bearing and/or grease may leak out. Toincrease the sealing ability of noncontacting seals, the width of the gap is sometimes increasedand cornering introduced. Such seals are called labyrinth seals. A high sealing efficiencyis obtained by eliminating the gap leading to contacting seals but obviously at the cost ofhigher frictional losses. Figure 14.2 shows a contacting seal where close contact is ensured byapplying a normal force by means of a garter spring.

Figure 14.1 shows an example where tapered roller bearings in a truck hub unit are sealedwith with contacting seals on both sides of the unit.

14.2 Lubrication Mechanisms for Elastomer Contact Seals

A rotary shaft seal consists of a lip which is in contact with the rotating shaft surface andis supported by a metal reinforcement. A garter spring may be used to apply a constant lipforce. ‘Oil seals’ are designed with asymmetric lip angles as shown in Figure 14.2. The angleα between the shaft and lip on the air side is smaller than the angle β on the lubricant side toprevent lubricant from leaking out of the system. In ‘bearing seals’ the difference in anglesis less pronounced and often reversed to provide better sealing against contaminants from the



Figure 14.1 Truck hub bearing unit, courtesy of SKF.

environment. Grease does not easily leak out of the bearing and therefore the primary role ofthe seal is to keep contaminants away from the bearing contacts.

Generally, the seal is attached to the outer-ring of the bearing and pure sliding occurs betweenthe soft elastomer seal lip and the hard metal inner-ring. Since the wear rates and friction arerelatively low in this contact, it is generally accepted that these contacting seals operate inthe mixed or full film lubrication regime. The presence of a lubricant film (in oil seals) wasreported by Jagger [301] in 1957. He showed that the frictional torque of a seal is much lower inlubricated than in dry conditions. Even when increasing the load, the lubricant film remainedat the interface. Many hypotheses have been formulated on the lubrication mechanisms of(oil) seals. In 1965 Hirano and Ischiwata [264] suggested that the film formation is a resultof micro-hydrodynamic lubrication between the rough shaft surface and a smooth seal. Oneyear later, Jagger and Walker [302] claimed that the seal surface is rough rather than the shaftsurface. Today, it is generally accepted that both the seal and shaft roughness are important for

Housing

Garter spring

Lubricant side

β α

Contact width

Rotating shaft

Air side

Radial lip seal

Figure 14.2 Radial shaft seal. Reproduced from Baart, Lugt and Prakash, 2009 C© Sage Publications.

Grease Lubrication Mechanisms in Bearing Seals 311

the film build-up characteristics of a seal. Numerical models support this hypothesis: Gabelliand Poll [212], Shen and Salant [152] and Hajjam and Bonneau [239]. Horve [275] has shownthat a high seal roughness and a shaft roughness of 0.25–0.5 μm Ra are critical for long seallife and good sealing performance. Critical for a good sealing action is the ability to pumpacross the seal contact. Oil seals are supposed to pump lubricant to the ‘lubricant side’ andgrease seals are supposed to pump to the ‘air side’ of the seal.

Several hypotheses have been formulated to explain why oil seals do not leak. These includevarious physical aspects such as surface tension, capillary forces, Weissenberg effect, vortexflow, seal lip dynamics and tangential deformations in the seal contact. The latter was proposedby Kuzma [350] in 1969 and was further developed by Kammuller [308] in 1986. Today, thetangential deformation theory is widely accepted as the primary sealing mechanism. The other‘secondary’ mechanisms can still be very important in certain operating conditions.

Figure 14.3 shows the contact between seal lip and rotating shaft where the shear stresseson the surface of the seal cause a tangential deformation. The nonsymmetric design of the sealcauses a nonsymmetrical pressure distribution and therefore a nonsymmetrical shear stressdistribution and tangential deformation of the seal surface. The surface roughness will forma V-shape and lubricant will be pumped into the contact. Due to the asymmetric tangentialdeformation with the maximum pressure closer to the lubricant side, there will be a net pumpflow from the air side to the lubricant side of the seal.

Despite the fact that all fundamental work on rotary shaft seals was done on oil seals, greatprogress has been made in the development of bearing seals. This applies to both friction,reliability and sealing.

Oil-side Air-side

standstill undeformedroughness

Friction inducedshear stresses

deformed roughnessstructure

Rotation

Figure 14.3 Tangential deformations and the pumping effect. Reproduced from Kammuller, 1986.


Grease dam

Figure 14.4 Grease lubricated seals: left a conventional oil seal and right a grease seal with extra lips toprevent contaminants from entering the system [515]. Reproduced from Baart, Lugt and Prakash, 2009C© Sage Publications.

As an example, Figure 14.4 shows the SKF mud block seal, Sassi [515]. In addition to theconventional lip with the garter spring, the seal contains several inner lips, which form barriersagainst contamination. These inner lips are lubricated with highly water resistant grease thatfills the space inbetween the lips. The grease not only lubricates the lips but also has aninherent sealing function. This sealing function is also present in conventional seals, as shownin Figure 14.4. A stationary ridge of grease (grease dam) prevents contaminants enteringthe bearing.

14.3 Sealing Action of Grease

The sealing action of the sealing system is not only provided by the (almost) contacting seallips. The grease can also provide a sealing action. Seals, such as the one showed in Figure 14.4are equipped with additional lips creating pockets of grease which act as a barrier againstcontaminants [353]. Two other examples are shown in Figure 14.5.

The sealing action of grease is a relatively unexplored area and, to the author’s knowledge,it has only been investigated by Baart et al. [40, 44]. Baart identified three mechanisms thatwould provide a sealing function by the grease:

1. Migration of contaminant particles in the seal pocket.2. Migration of contaminant particles in the vicinity of the sealing contact.3. Pressure difference and a limited flow depth into a seal pocket.

Figure 14.5 Seals equipped with additional lips and a ‘pocket’, referred to as the seal pocket, in betweenthe lips for better contaminant exclusion (figure reproduced from Baart [40]).


In the next sections the radial and transverse flow of contaminant particles inside and in thevicinity of the seal will be described. This flow of particles, away from the bearing interior orto an area where they cannot do any damage, reflects the sealing action of grease.

14.3.1 Migration of Contaminant Particles in the Pocket

Figure 14.6 shows a schematic representation of a seal grease pocket, where the pocket hasa rectangular shape. Solid contaminant particles that have entered into the grease pocket willmove with the same circumferential velocity as the grease. Since the specific weight of theparticles is usually larger than that of the grease, these particles will migrate to a larger radiusdue to the centrifigal forces. The radial particle velocity will be determined by the balance ofthe centrifugal force and the drag force. The centrifugal force reads:

Fc,r = 4

3πa3

(ρp − ρg

) u2θ

r, (14.1)

where a is the particle radius,(ρp − ρg

)the density difference between the particle and the

grease, r the radial position and uθ is the circumferential velocity of the grease. The drag forcecan be calculated using the Stokes drag equation, assuming Re � 1 [69]:

Fd,r = −6πaηu p,r , (14.2)

where η is the viscosity (at the local shear rate) and u p,r is the particle velocity in radialdirection. By neglecting inertia forces and acceleration, the force balance results in:

u p,r = 2

9a2 1

η

(ρp − ρg

) u2θ

r. (14.3)

Figure 14.6 Schematic representation of a sealing grease pocket incorporated in a radial seal.


Here, uθ is the circumferential velocity of the grease. Batchelor [69] gives the equation of one-dimensional Newtonian flow between concentric cylinders. Baart et al. [41] use this equationfor their idealized rectangular wide pocket:

uθ (r, T ) = us

[ro/r − r/ro

ro/ri − ri/ro

](14.4)

where us is the shaft surface velocity, ri the inner-ring radius and ro the pocket housing radius.For sufficiently small gaps where the gap height is small relative to the shaft radius, that is(ro − ri )/ri ≤ 1, Eq. 14.4 approaches a linear velocity profile. Figure 14.7 shows the case inthe situation where the inner-ring radius is 20 mm and the gap is 1.5 mm. For a (nonlinear)lubricating grease Eq. 14.4 does not apply. By using a 4-parameter Herschel–Bulkley modeland the methodology from Kelessidis and Maglione [319], the velocity profile for a lubricatinggrease in a wide gap can be calculated, which is shown in Figure 14.7 for greases A and B at0.01 m/s and 0.05 m/s inner-ring speed respectively. The velocity profile of the Newtonian oilis approximately linear. The soft NLGI 1 grease A shows a small deviation from the Newtoniancase due to shear thinning. For the NLGI 2 grease B at low shaft velocity some grease, at theradius >0.021, does not flow as the shear stresses are locally too low to exceed the yield stress.However, note that when the shaft velocity or temperature is increased, this effect reduces andthe velocity profiles become more linear again.

If the grease pocket is narrow, wall effects become important and the flow can no longer beregarded as one-dimensional. The velocity in the major part of the pocket will be smaller thanin the case of a wide pocket. Complex numerical computational fluid dynamics calculationsare required to solve this.

Newtonian 1DNLGI2 1D HB-modelNLGI1 1D HB-model

0 0.010.02

0.0205

0.021

Rad

ial p

ositi

on r

[m]

0.0215

0.02 0.03Flow velocity u [m/s]

0.04 0.05

Figure 14.7 One-dimensional velocity profile in a wide pocket for a Newtonian oil and two greases attwo different inner-ring speeds. Reproduced from Baart et al., 2011 C© Taylor and Francis Group.


Table 14.1 Grease type dependent parameters todescribe the velocity profile in a narrow seal pocket.

Grease type a[(m · T )−1

]b[m−1

]A (NLGI2) 1160 −6720B (NLGI1) 790 −4540

Baart et al. [41] showed that, for an idealized rectangular narrow pocket, the velocity closeto the wall can be calculated from:

uθ (r, T ) = us

[ro/r − r/ro

ro/ri − ri/ro

]exp [(a ln(T ) − b) (r − ri )] , (14.5)

where T is the temperature and a and b are grease type dependent constants. Values for theseconstants were determined for the A and B grease and are presented in Table 14.1.

Due to the nonlinear behaviour of the viscosity η in Eq. 14.3, it is not possible to give ananalytical expression for the particle migration. This equation was therefore solved numeri-cally. The results are plotted in Figure 14.8. In the case of a narrow grease pocket, the greasetangential velocity is reduced by the stationary side walls resulting in a nonlinear velocityprofile with centrifugal forces decreasing quickly with the radius. The result is a relativelyslow migration of particles towards the outer radius of the seal pocket. The relatively lowgrease velocities in the major part of the narrow pocket provide relatively low shear rateswhich also affect the grease viscosity. Therefore, in the case of narrow pockets, the particlemigration will be more significantly a function of the stiffness of the grease. In the central

NLGI2 wideNLGI1 wideNLGI00 wideNLGI2 narrowNLGI1 narrowNLGI00 narrow

10–10.02

0.0205Rad

ial p

ositi

on [m

]

0.021

0.0215

100 101

Time [h]102

Wide

NLGI00 narrow

NLGI1 narrow

NLGI2 narrow

103

Figure 14.8 Radial particle migration as a function of time in a narrow and wide grease seal pocket.The particle has a diameter of 14 μm and the greases are labelled with their consistency number. Theinner-ring speed is us = 1 m/s and T = 25 ◦C. Reproduced from Baart et al., 2011 C© Taylor and FrancisGroup.


part of wide pockets, the influence of the side walls is very small and the velocity profile isalmost linear. Consequently, centrifugal forces decrease less quickly with the radius than inthe narrow pocket case. The almost linear velocity profile leads to a constant shear rate andthe grease viscosity does not vary throughout the central part of the pocket. As a result, forwide pockets, the particle migration is only a weak function of the stiffness of the grease. Thisis depicted in Figure 14.8.

14.3.2 Migration of Contaminant Particles in the Vicinityof the Sealing Contact

In addition to radial migration of particles, as described in Section 14.3.1, particles may alsomigrate in the transverse direction. In a shear thinning fluid the particles migrate to the highshear rate region. By contrast, in an elastic fluid, the particles migrate to the low shear ratearea. This migration behaviour is independent of the particle shape (similar results were foundfor small disc and rod shaped particles), Gauthier et al. [214].

Karnis and Mason [313] found that for an elastic fluid in a pipe flow at low Reynoldsnumbers, neutrally spherical buoyant particles migrate in the radial direction to the pipecentre. In a Couette flow the particles migrate to the outer wall. This was confirmed by Hoand Leal [266] in a numerical study who showed that normal stress differences in the fluiddrive this particle migration. In shear thinning fluids, Gauthier et al. [214] found that neutrallybuoyant particles migrate to the pipe wall in a pipe flow. For a Couette flow they showed thatthe particles migrated towards the inner cylinder wall.

Here the driving force of these particles is generated by the nonconstant shear rate in bothpipe and Couette flow. Shear thinning will cause a viscosity gradient, which enhances particlerotation, which cause the migration of contaminant particles towards the high shear rate andlow absolute viscosity zone. This rotation is slowed down by the fluid elasticity again. Snijkerset al. [548] showed that particle rotation is slowed down by the fluid elasticity when

Wi = N1 − N2

τ< 0.5, (14.6)

where Wi is the Weissenberg number, N1 − N2 is the normal stress difference and τ is theshear stress.

Such migration also takes place in bearing seals. The vicinity of the sealing contact, wherecontaminant particle migration is considered, is schematically presented in Figure 14.9. Thelower plane in the figure represents the inner-ring, which rotates with a surface velocity us ,and the top plane represents the stationary seal lip, with a lip angle α. A spherical contaminantparticle with radius a is located close to the seal lip, as drawn in the figure. The decreasinggap height across the flow direction of the grease will cause a decreasing shear rate away fromthe contact. For a (non-Newtonian) lubricating grease this will lead to a variation in viscosityand normal stress difference.

In Baart et al. [44] the theory above was applied to the seal configuration, which means that

∂η

∂xlarge ⇒ particles migrate to the sealing contact

Wi large ⇒ particles migrate away from the sealing contact


x

α

us

y

z

Figure 14.9 Particle in a fluid velocity field in the vicinity of the sealing contact. The particlemay not only flow in the direction of grease flow (x-direction), but also in the transverse direction(y-direction). Reproduced with permission from Baart, Lugt and Prakash, 2011 C© ASME.

The viscosities and normal stress differences for five different greases, one base oil and onestrong elastic fluid (0.5 weight% polyethelene oxide, Mw = 8 000 000 solution in water, PEO)are shown in Figure 14.10. The grease properties are listed in Table 14.2.

Figure 14.10a shows that the base oil and PEO have an almost constant viscosity. The valuesfor the normal stress difference for PEO are quite similar to those found for the lubricatinggreases. However, PEO has an extremely low viscosity.

Figure 14.11 shows an example of particle migration where the particles in grease, in thevicinity of the seal lip, were observed through a saphire shaft. The figure clearly shows thatthe particles migrate away from the seal lip. Similar measurements have been performed forall greases from Table 14.2. The migration towards or away from the seal lip is denoted in thelast column by ‘ + ’ and ‘−’ respectively.

Table 14.2 shows that the Weissenberg number Wi > 0.5 for the PEO fluid and the normalstress differences induce particle migration to low shear rate zones, that is, away from the

LG1LG2LG3LG4LG5PEOLG1 base oil

0 0.20

0.5

1

1.5

2

2.5

Vis

cosi

ty η

[Pa

. s]

3

3.5

4

4.5

5

0.4 0.6 0.8 1

Distance from sealing contact x [mm]

1.2 1.4 1.6 1.8 2

5000

4500

4000

3500

3000

2500

2000

Nor

mal

str

ess

diffe

renc

e N

–N [P

a]

1500

1000

500

0 0.2 0.4 0.6 0.8

Distance from sealing contact x [mm]

1 1.2 1.4 1.6 1.8 2

LG1LG2LG3LG4LG5PEOLG1 base oil

(a) Viscosity across the seal. (b) Normal stress difference across the seal.

Figure 14.10 Grease rheology in the vicinity of the seal lip with shaft speed 0.1 m/s, a 12◦ lip angleand ambient temperature (25 ◦C). A constant temperature is assumed. Reproduced with permission fromBaart, Lugt and Prakash, 2011 C© ASME.


Table 14.2 Grease type and properties for the greases used in Figure 14.10. Wi represents theWeissenberg number calculated with Eq. 14.6, using the values from Figure 14.10. The ‘-’ and ‘ + ’sign indicate migration away and towards the seal lip respectively.

ηoil

Grease type Thickener/base oil at 25 ◦C [Pa · s] Wi∂η

∂xMigration

LG1 Lithium/mineral 0.25 >0.5 1.75 −LG2 Lithium/mineral 0.45 >0.5 1.65 −LG3 Lithium/PAO 0.03 >0.5 1.6 −LG4 Lithium/mineral 0.21 <0.5 2.1 +LG5 Lithium/mineral 0.33 >0.5 1.5 −Oil Mineral 0.25 0 0 0PEO Water 0.04 >0.5 0 −

contact. For the base oil no normal stresses are present and the Weissenberg number istherefore zero. In addition, no shear thinning takes place, so there is no particle migration. Forthe LG1, LG2, LG3 and LG5 grease Wi > 0.5 and ∂η

∂x is relatively small, which explains theparticle migration away from the contact, which is also observed in the migration experiments.By contrast, for the LG4 grease, Wi < 0.5 and ∂η

∂x is relatively high. Consequently, migrationtowards the contact can be expected for LG4, which is confirmed by the experiment.

These results must be combined with the fact that high base oil viscosity greases maygenerate more heat leading to a higher temperature gradient and therefore increase the viscositygradient. LG3 grease has a very low base oil viscosity, leading to much lower temperaturegradients and therefore only a small increase of the viscosity gradient at higher speeds. Ahigher viscosity gradient would enhance the particle migration towards the sealing contact.

LG2 t = 0 min

LG2 t = 45 min

Figure 14.11 Particle images taken before and after running a seal on a transparent shaft with greaseLG2. The sealing contact is indicated by the dashed line. The shaft speed was 1.0 m/s. Reproduced withpermission from Baart, Lugt and Prakash, 2011 C© ASME.


Figure 14.12 Grease flow in a sealing system with grease pocket. The dark grey region represents thegrease that remains stationary. The light grey area denotes the grease that is flowing.

Pressure Difference and a Limited Flow Depth into a Seal Pocket

A pressure difference over the seal may cause a transverse grease flow through the sealing gap.This may be caused by temperature fluctuations, for example caused by disc brakes close tothe hub bearing unit. Contaminant particles that have entered the grease pocket may flow withthe bulk grease flow. However, this flow is partially restricted by the geometry of the seal. Thisis shown in Figure 14.12. In the case of a pressure difference across the seal, the grease willflow through the narrow restrictions into the pocket. In the case of a narrow pocket the greaseflow will not fully develop and grease at the outer radius will not flow. Similarly to Figure 14.7the result is stationary grease in the pockets at the outer radius. In the case of wide pockets thetransverse grease flow has time to develop and only close to the corners is the grease stationary.This was already indicated in Section 6.2.4 where measurements were shown of grease flowin a channel with restrictions. The grease velocity is high over the restrictions but very lowbehind the restrictions, and may even not flow in the pocket between the restrictions. In thesestationary areas, the contaminant particles will not move. Here the grease has ‘captured’ theparticles and they will not enter the bearing.

This is an important aspect for the design of the seal. Take for example Figure 14.12and assume inner-ring rotation. In the case that contaminant particles have entered the zonebetween two restrictions, due to centrifugal forces the particles will migrate to a large radius,so close to the seal surface. A subsequent pressure drop over the seal will cause a transverseflow of grease primarily close to the inner-ring surface. The grease in the pocket close tothe seal will remain stationary and the contaminant particles will remain in the pocket ratherthan entering the bearing as long as the pocket height is large compared to its width. Thisparticularly applies to stiff greases, the effect reduces with decreasing NLGI grade [362].

14.4 Softening and Leakage

A well known problem is that seals only start leaking grease after some period of operation.In this case leakage is usually caused by softening of the grease. This was addressed inSection 8.1.1, p. 172. Grease softening often manifests itself after an induction time.


14.5 Compatibility

Similarly to plastics in lubrication systems, bearing seals (and cage materials) may not becompatible with the lubricant. The stability of rubber materials is determined in accordancewith ISO and DIN standards. If grease comes into contact with seal material, then interactionsoccur between the two. An essential distinction is made between physical and the chemicalinteraction. In the case of the physical influence, an absorption of the grease by the materialand an extraction of the components to be dissolved (plasticizers in particular) takes place.The absorption of the medium by the rubber material leads to an increase in the volume(swelling), the extraction of soluble components leads to a volume reduction (shrinkage). Thedimension of the change in volume depends on the type of influencing medium (aromaticscontent with mineral oils), the structure of the sealing material (with NBR, ACN and plasticizercontent), the temperature (the aggressiveness of the oil increases as the temperature increases),the type and quantity of the additives added and the geometry and the tension status ofthe seal.

14.6 A Film Thickness Model for Bearing Seals

Today, the film thickness models for radial seals are based on oil lubrication. Recently, a modelfor the film thickness in grease lubricated seals was developed by Baart et al. [40, 46]. In thissection a brief summary of this model will be given. The model is applicable to axial lipcontacts that are suffering from starvation due to centrifugal forces. An example is shown inFigure 14.13. Here, a grease reservoir is present somewhere on the rotating part of the seal (inbox (b) in the figure). This reservoir may simply consist of grease attached to the flinger. Thecentrifugal forces will cause the grease to bleed oil (see Chapter 7) and feed the lip contact.However, these centrifugal forces will also reduce the lip film again due to a loss from thecontact. The resulting film thickness can be calculated from a mass balance:

h =∫ t

0

(Qfeed − Qloss

)dt + V0

2π Rcb, (14.7)

a

b

Figure 14.13 A grease lubricated seal with axial sealing lip contact indicated in box (a), and a greasereservoir indicated in box (b). Reproduced from Baart, van Zoelen and Lugt, 2011 C© Taylor and FrancisGroup.


Qpump

hmax

Flip

Rc

b

h

z

Qbody

(a) (b)

Figure 14.14 Dimensions of the sealing contact with (a) oil loss due to seal pumping and (b) ingestedmeniscus and oil loss due to centrifugal body load. Reproduced from Baart, van Zoelen and Lugt, 2011C© Taylor and Francis Group.

where Vo is the initial volume of oil in the contact and Q f eed and Qloss are the flow rates ofthe oil feed and oil loss respectively. Rc is the radial position of the contact and b is the contactwidth assuming a uniform oil film thickness, as defined in Figure 14.14.

14.6.1 Oil Feed

The oil feed to the contact is the result of centrifugal forces on the grease reservoir. By using thepermeability model from Darcy as described in Chapter 7, the fluid velocity can be written as:

u = − k

η∇ p, (14.8)

where k is the permeability, η the base oil viscosity and ∇ p the pressure gradient. The pressuregradient is replaced by the centrifugal force, so the oil feed rate reads:

Q f eed = −2π RoWk( f )

η(T )ρω2r, (14.9)

where Ro is the outer radius of the grease reservoir, W is the width of the grease reservoir andk the permeability, which is a function of the thickener volume fraction in the grease f .

14.6.2 Oil Loss

The oil loss from the seal lip contact reads:

Qloss = Qpump + Qbody, (14.10)


where Q pump is the oil loss caused by the pumping effect in the seal lip contact and Qbody isthe oil loss due to centrifugal forces.

The oil pumping can be predicted using the model from Horve [274], who derived anempirical equation based on oil seals:

Qpump = 1.04 × 10−8 R3c

n

60G− 1

3 , (14.11)

where Rc is the radial position of the contact (see Figure 14.14), n is the shaft speed in rpmand G is the duty parameter:

G = 2πbn

60

η

Flip. (14.12)

Here Flip is the specific lip force. The maximum film thickness, assuming fully floodedconditions, is purely given by the viscous shear in the lubricant film and according to Horve[274] reads:

hmax = 0.011RcG59 . (14.13)

Horve’s equations are only valid for fully flooded contacts. As soon as the contact is starved,the pumping action will stop [511] and the volume of oil that will subsequently be present inthe contact is:

Vmax = 2π Rcbhmax (14.14)

where b is the width of the oil volume (see Figure 14.14b) and hmax is the maximum filmthickness when fully flooded (see Figure 14.14a). In the case that the volume of oil is largerthan this maximum, Voil > Vmax , an oil buffer is created at the inside of the contact and theoil loss is dominated by pumping. Otherwise, oil will only be lost due to the centrifugal forceon the oil film. It can be assumed that the velocity profile in circumferential direction is linear.Considering a thin layer, the centrifugal force acting on the flow then reads:

ηd2ur

dz2= ρ

(ω

z

h

)2

r (14.15)

with ρ the oil density, ω the angular shaft velocity and r the radial position.Solving ur from Eq. 14.15, integrating it over the film height and multiplying it with the

circumference gives the oil loss from centrifugal forces:

Qbody = 2π Rcρω2 Rc

40ηh3. (14.16)

In the film thickness model three phases of operating conditions can now be identified. Inthe churning phase the grease reservoirs are formed. During this phase the film thickness in thecontact is equal to the maximum film thickness hmax . After this, the sealing contact is supplied


10–3 10–20

1

2

3

4

Film

thic

knes

s h

[μm

]5

6

hcrit

T = 70 °C, n = 2000 rpm

T = 25 °C, n = 500 rpm

Ar = 0.5 mm2

Ar = 0.0 mm2

10–1 100

Time t [h]101 102 103

T = 70 °C, n = 500 rpm

Figure 14.15 Oil film thickness in the sealing contact for various speeds and temperatures. Reproducedfrom Baart, van Zoelen and Lugt, 2011 C© Taylor and Francis Group.

by oil that is released by the grease in the reservoir. Simultaneously, oil is lost from the contactdue to centrifugal forces and seal pumping (as long as the contact is fully flooded). After sometime, the oil bleeding will slow down and the contact will become starved. The maximum filmthickness cannot be maintained and the seal pumping stops (Figure 14.14b). The centrifugalforces will cause a continuous oil loss leading to a continuous decrease in film thickness.

Typical model results for a lithium complex grease are presented in Figure 14.15 where thefilm thickness is plotted for various values of speed and temperature. The figure clearly showsthe impact of the grease reservoir on the film thickness. For the case that a grease reservoir ispresent (Ar = WHo = 0.5 mm2), the maximum film thickness remains constant for a certainperiod of time until the grease bleeding deteriorates such that the replenishment of the seallip contact is insufficient to provide enough oil feed. At this point the film thickness startsto decrease. At lower speeds the maximum film thickness is smaller but can be maintainedfor a much longer period of time. The lower centrifugal forces cause less oil bleeding andit will take longer for the grease to become exhausted. In the absence of a grease reservoir(Ar = WHo = 0), the predicted film thickness starts to decrease instantaneously and willquickly reach very small values.

The seal will not suffer from wear as long as the contact is operating the full film regime.Surface contact will increase friction and wear and reduce the reliability of the seal. In thisfigure it is assumed that this may start at λ = 1. With a counter surface roughness of 0.25 μmthis will result in a critical film thickness hcrit = 0.25 μm.

A simple engineering model can be made [46], based on a characteristic parameter groupin the oil-bleeding Eq. 14.9 and in the oil loss Eq. 14.16, that is, η/(n2d2

s ) where ds = 2Rc isthe diameter of the sealing contact. In the film thickness Eq. 14.7 this group is divided by the


contact radius, giving: η/(n2ds). The influence of the size of the grease reservoir is includedby defining

tc = [C1 Ar + C2]

[η

n2ds

], (14.17)

where Ar = WH0, with H0/W = 2. An excellent fit to the model calculations gives: C1 =2 × 1015, C2 = 6 × 106. The simplified engineering model, Eq. 14.17, is a simple methodto predict the time until the mixed lubrication regime is reached. More advanced pumpingmodels could be included by, for example, including the actual seal lip geometry. However,since the pumping phase is short compared to the phase where the film thickness decays, andsince the maximum film thickness is at least a few times higher than the critical film thickness,the pumping rate has little effect on the predicted critical time to mixed lubrication.

14.7 Some Examples Showing the Importance of Sealing and Grease

Sealing in grease lubricated bearings is not necessarily done through elastomer (contacting)seals. Labyrinth seals, in a wide variety of designs are also used. Labyrinth seals are noncon-tacting seals where a long and thin gap in a small volume is created by means of a labyrinth.The sealing action, preventing contaminant ingress, is provided by the grease.

Figure 14.16 from Winter [617] shows examples of sealed grease lubricated bearings invibrating screens using such labyrinth seals.

a b

Figure 14.16 Left: Grease-lubricated labyrinth seal with effective damp barrier through a contactingseal. Right: Labyrinth seal designed to exclude stone dust [617].


Figure 14.17 Left: Conventional arrangement with a grease valve and incorporating a cylindrical rollerbearing. The arrows indicate the passage of grease. Right: Modified arrangement with plugged drain andno facility for relubrication. Reproduced from Bengtsson and Ekberg, 1979.

To facilitate relubrication, bearing housings are often equipped with a grease drain, Fig-ure 14.17. Bengtsson and Ekkberg [75] investigated the effect of making such an openingin grease lubricated bearings used in auxiliary machinery such as the fan and pump motorsof a Swedish power plant. All machines were located indoors in a clean dry environmentfavourable to the lubrication of the bearings. The field tests performed by Bengtsson andEkkberg consisted of monitoring the grease quality extracted from 43 bearings consisting ofvarious sizes of ball bearings, cylindrical roller bearings and spherical roller bearings for eightyears. Grease samples were extracted once per year and chemically analysed to characterizeany possible degradation process that could have taken place. Given the favourable cleanand dry environment, frequent grease relubrication to avoid moisture or debris penetration inthe bearing housing was considered unnecessary and therefore the conventional arrangementincorporating a grease drain was modified by plugging and sealing the drain as shown inFigure 14.17.

This modification was introduced in order to reduce the leakage of the base oil from thehousing grease. The preservation of the base oil and its evaporation products in the housingwas found to extend the service life of the bearing. Indeed during the eight years in which


the grease conditions of all 43 bearings were monitored it was found that in many casesthe lubrication properties of the grease sample extracted from the bearing housing in closeproximity to the rolling elements were only marginally reduced. This has prompted a change inthe recommended relubrication procedures in use at that power plant. Time intervals betweenrelubrication were extended to up to twenty times the generally recommended time. Thisillustrates the importance of sealing on grease performance.

15Condition Monitoringand Maintenance

15.1 Condition Monitoring

Condition monitoring of rolling bearings is well established. The various methods for detec-tion and diagnosis of bearing damage can be broadly classified as vibration and acousticmeasurements, temperature measurements and wear debris measurement [571]. Vibration, butmore and more acoustic emission techniques, are used for measuring the bearing conditiononline. Today these techniques are primarily used for detecting bearing faults or damage [330,505, 527, 571]. However, with these techniques it is also possible to measure the quality ofthe lubricating film.

Acoustic emission is low when the bearing is well lubricated, whereas it increases signif-icantly in the case of lubricant film breakdown. In the case of grease lubrication, a surplusof grease will also give an acoustic emission signal. The acoustic emission (AE) techniqueis generally applicable to lubrication in rolling bearings and it will therefore be only brieflydescribed here. In this chapter more emphasis will be given to specific grease conditionmonitoring techniques where various grease analysis techniques will also be described.

Actually, the condition of grease usually varies throughout the bearing. As an example, in amedium speed, medium temperature operating bearing, the grease in the tracks will be heavilydegraded whereas fresh grease can be found on the seals. This also makes monitoring the con-dition of grease online very difficult, and therefore generally off-line techniques are employedwhere grease samples are taken from the bearing and analysed in a laboratory. Consistent sam-pling of grease from specific locations in the bearing where aging has taken place is crucial.

Previously, relatively large samples of grease were required for doing a proper analysis.Therefore grease analysis was historically done for quality control and product acceptance.With modern analytical equipment it is possible to analyse also smaller samples (milligrammes,Herguth [254]). Grease condition monitoring can be used to improve grease selection, get animpression of the remaining grease life or find root cause failures.

It is possible to reduce the grease analysis efforts by only measuring those properties that arerelevant to the expected failure mode. For instance, in the case of low temperature applications



Table 15.1 Some deterioration index limitsas given by Tomaru et al. [574].

Indices Limits

Total Acid Number, TAN 3 mg KOH/gLeakage 50%Bleeding 40%Fe Wear 0.1%

one could decide to monitor only the bearing temperature and change in grease consistency[386]. Tomaru et al. [574] and Suzuki et al. [563] propose methods for residual grease lifein ball bearings using deterioration indices such as antioxidant content, total acid number,grease leakage rate, oil-bleeding rate and wear amount. Tomaru et al. [574] give deteriorationindexes, listed in Table 15.1.

These values are empirical and obviously for indication only. Other conditions, grease typesand/or bearing types/sizes may give different levels. The work that has been done so far inthis area is very limited and no absolute criteria for remaining grease life exists today. It istherefore up to the reader to define such criteria. However, the work described in this chaptermay be of some help.

A new technique to monitor the condition of (grease lubricated) bearings is ‘ultrasound’[634]. Here a high frequency ultrasonic transducer is mounted on the outer-ring of a bearing.The transducer is focused on the contact between rolling element and inner-ring and measuresthe reflection coefficient from the lubricant in the contact. This technique is promising but stillin the laboratory phase.

In the next sections the bearing monitoring techniques such as acoustic emission (AE) willbe described followed by the grease monitoring techniques.

15.2 Vibrations and Acoustic Emission

Rotating rolling bearings produce vibrations and noise. Vibrations are caused by variation instiffness, such as in a radially loaded bearing where the rolling elements vary their positionin the loaded zone. Other causes of vibrations are caused by ‘damage’, such as cracks, spallsand particles. Various sources in the bearing can create vibration signals, such as the dynamiccontact between rolling elements and raceway but also grease thickener material travellingthrough the contacts.

Effects of roughness and contaminant particles only occur in the case of insufficient lubrica-tion where asperities or particles interact with the surface of its mating element. This interactionresults in rapid changes in contact pressure, generating a pulse of short duration, which againgenerates vibrations and noise. The vibration spectra can roughly be divided into the rangesshown in Table 15.2. These vibrations may be detected by accelerometers and are measuredas overall vibration levels.

Bearing damage at an early stage is difficult to detect because the damage originated signalscombine with the larger rotational vibrational signals which results in poor signal to noiseratios. Normal acceleration measurements are therefore not effective for picking up the earlystages of failure. By contrast, acoustic emission techniques are effective for this and could

Condition Monitoring and Maintenance 329

Table 15.2 Vibration spectra in rolling bearings.Reproduced with permission from Miettinen andAndersson, 2000 C© Sage Publications.

Frequency Sources

>50 kHz Inside material effects20–50 kHz Ultra-sonic frequencies0.1–20 kHz Natural frequencies

0.001–1 kHz Rotational defect frequencies

be used to detect early failure in (grease) lubrication (see Figure 15.1). The basic differencebetween vibration measurement and AE is that AE techniques are based on measuring pulsesor spikes rather than (high frequency) vibrations.

In both vibration and acoustic emission time domain and frequency domain approaches areapplied. In the time domain, statistical parameters are calculated from the probability densitycurves of acceleration such as the statistical moments or kurtosis. Time domain signals thatcontain only bearing defect frequencies can be obtained by means of enveloping. Envelopeanalysis is essentially a demodulation process on a time domain vibration signal, whichcontains a series of impulses, each corresponding to a rolling element passing a damagedarea. The impulses become clearer by removing background noise by filtering to leave onlysignals in a pass band, for acoustic emission typically 100–500 kHz. This signal is rectifiedand then smoothed to give a time domain signal that no longer contains 100–500 kHz, onlythe repetition frequency of the impulses, that is the bearing defect frequency. This can betransformed into the frequency domain for analysis. However, in certain circumstances it is ofvalue to examine the time domain envelope data, particularly with low speed bearings [546].This method is widely used today and makes it possible to detect possible damage at an early

Acoustic emission enveloping

Warning time

Long Short

TimeWorse

Good

Condition

Acceleration enveloping

Unfiltered acceleration Velocity

Listenandfeel

Figure 15.1 Various techniques to detect bearing damage. Courtesy of SKF.


1.2

1

0.8

0.6

0.4

0.2

0–1.5 –1 –0.5 0 0.5

X

H

P

1 1.5

1.2

1

0.8

0.6

0.4

0.2

0–1.5 –1 –0.5 0 0.5

Y

H

P

1 1.5

(a) Along the running track. (b) Across the running track.

Figure 15.2 Pressure distribution in a (fully flooded condition) grease lubricated contact. Reproducedwith permission from Åstrom and Venner, 1994 C© Sage Publications.

stage, see Figure 15.1. So acoustic emission is effective in detecting lubrication problems andbearing problems at an early stage, before they lead to mechanical damage.

Acoustic emission and vibration are commonly applied as trending tools and changes inbehaviour would trigger intervention. An indication of contamination or lack of lubricationare largely independent of the bearing, but if the technique is used to identify bearing damage,it relies on knowing defect frequencies, that is bearing operational conditions. The signal isanalysed by means of counting pulses exceeding some predefined values or by measuring ther.m.s. The r.m.s. of the ‘continuous’ Acoustic Emission Enveloping (AEE) has a relationshipwith the κ , that is the quality of lubrication. When the “spikes” in AEE become periodic witha bearing defect frequency it means that damage is occurring at one or more fixed locationshence the start of defect that will then be picked up by acceleration enveloping once it hasdeveloped further.

Particles are not only formed by contamination. The grease thickener material may alsoform particles in the form of solid crystals or agglomerates [197]. In addition, the greaseproperties vary throughout the bearing. The film thickness measurements from Section 9.4.1,Figure 9.8 clearly show that grease particles may enter the contact. Such particles generatepressure perturbations in the contact, see Figure 15.2, leading to excitation and therefore (highfrequency) vibrations and noise.

These particles give rise to noise, called ‘grease noise’. This noise is measured by ‘GreaseNoise Testers’, which typically operate at 50 Hz–10 kHz (Bichler [81], Miller [422], Wunsch[621]). For a description, see Section 16.2.22.

Miettinen and Andersson [420] performed acoustic emission measurements on grease lubri-cated bearings using the so-called ‘pulse count method’, where pulses are counted exceedinga defined voltage level. They showed that the method is very suitable for measuring contami-nation levels in grease lubricated bearings but also for indicating the level of starvation [421].An example is shown in Figure 15.3 where the acoustic emission signal (pulse count rate) isplotted versus time. The bearing was initially lubricated with a grease with a base oil viscosityof 150 cSt. After some time grease with lower base oil is added to the bearing. Clearly theAE-pulse rate is reduced indicating an improved lubrication situation.


5000

Pulses/s

4000

3000

2000

1000

20:43

Grease G2(150 mm2/s)

Grease G4(22 mm2/s)

Addition ofgrease G4

21:09Time

21:34 22:00 22:26 22:51 23:170

AE

pul

se c

ount

rat

e

Figure 15.3 Example showing an acoustic emission signal where a grease with low base oil viscosityis added to a bearing. Reproduced with permission from Miettinen, Andersson, and Wikstrom, 2001 C©Sage Publications.

15.3 Lubcheck

The thickness of a lubricant film can be measured by means of the electrical capacitanceof the contact. In the case that the film is smooth and parallel, the capacitance is inverselyproportional to the film thickness. This assumption no longer holds in the case that the filmthickness approaches the roughness. However, when the film breaks down, the method isvery useful again. In this case, occasional metal-to-metal contact can again be measured bymeans of the capacity, which in this case vanishes. In a rotating bearing the contact intensityis dynamic and (individual) asperity contact will therefore be very short in time only. In 1982SKF developed a technique (capacitative voltage divider) to measure the degree of surfaceseparation in rolling bearings, which materialized in a apparatus called ‘Lubcheck’ [253]. Thedevice was designed such that it is very sensitive to disturbances caused by asperity contact,and fast asperity contact can be observed. The Percentage Metallic Contact Time fraction(PCT) can be used to identify the intensity of contact. Figure 15.4 illustrates the ability tomeasure a ‘κ-like’ parameter on this device. The figure shows the measured PCT versus speedfor a radially loaded (1 kN) 6204 deep groove ball bearing lubricated with a few drops of ISOVG 100 oil. The figure also shows the film thickness–roughness ratio � for the highest loadedouter-ring–ball contact.

The method is an excellent tool to measure the quality of the lubricant film. Unfortunately,it is not always possible to electrically isolate the bearing, which makes it often difficult toapply in practice.

15.4 Consistency Measurement

The standard for consistency measurement is the cone penetration test according to ISO 2137,as described in Section 16.2.1. For this test, large volumes are necessary and it is thereforenot possible for condition monitoring. Instead a small volume can be spread between two


100PCTbrg

(%)

80

60

40

20

00 20

1 1.5 2.5 3.5

Theoretical curve

Typical chart recording

Envelope of3 chart recordings

3

Λ or ball 1

2

40 60 80 100 Inner ringspeed

Figure 15.4 Calculated and measured metallic contact time fraction (PCT) versus inner ring speed.Reproduced from Heemskerk, Vermeiren and Dolfsma, 1982 C© Taylor and Francis Group.

glass plates where the plates are loaded by a calibrated dead weight. The consistency can beobtained by measuring the spread of the grease after, for instance 15 seconds, (SKF GreaseTest Kit [418, 542]).

15.5 Oil Bleeding Properties

The standardized grease bleeding test (DIN 51817, Section 16.2.6) cannot usually be applieddue to the required large volume of grease. An alternative method is available in the SKFGrease Test Kit [418, 542]. Here a small volume of grease is put on a piece of blotting paperwhere the base oil will separate from the grease into the paper. The paper is put on a heater toaccelerate the bleeding process. By measuring the oil stain diameter and comparing this witha fresh sample the bleeding properties can be evaluated.

15.6 Oil Content

Bearings fail when the oil is lost from the grease. Booser [91, 93] and Tomrau [574] observedbearing lubrication failure when grease lost half of its oil content. The remaining oil in a greasecan be obtained by weighing the grease sample, dissolving the grease in a solvent, for examplepetroleum ether, filtering out the thickener material, extracting the solvent again and weighingthe remaining oil.

15.7 Particle Contamination

The simplest way to measure contamination in grease is by spreading grease between twoglass plates and inspecting the grease using optical microscopy.


Weak

Magnetic field

Magnetic field

Magnet

Strong

Lubircant flow

Slide

Figure 15.5 Principle of ferrography. The lubricant is flowing over an inclined slide such that themagnetic field is weaker at the entry point than at the exit side. Due to the gradient in magnetic fieldstrength the particles in the lubricant will deposit along the slide.

Direct collection of particles through filters is not possible with grease. Today, the mostestablished technology for measuring particles is Ferrography, established in the 1970s [522].Here, the particles are separated from the lubricant on a ferrogram slide, mounted on an anglesuch that the lubricant will flow and a gradient in magnetic force is created, as shown inFigure 15.5. Next, washing and fixing removes the residual lubricant. After drying the slide isanalysed in a so-called ‘Ferroscope’, giving the size shape and number of particles. In the caseof grease a solvent system must be used to obtain a fluid with a low viscosity such that the fluidwill flow on the slide. A mixture of toluol/hexane has been found to be a good general solventand can be used to obtain a suitable viscosity [370]. An example can be found in Cousseauet al. [140].

Ferrography can measure particles in the range 1–100 μm. The quantity, size distribution,morphology and composition can be measured [504].

15.8 Spectroscopy

Spectrometric techniques are by far the the most common methods for measuring contamina-tion for particles smaller than about 10 microns [370]. Here samples are excited and radiationis then split up in a spectrum and the relevant wavelengths are identified according to elementsand chemical bonds. This radiation can have any wavelength, for example visible light, X-ray,infrared and so on.

15.8.1 Infrared (IR) Spectroscopy

Infrared spectroscopy is widely used to determine contamination, identification and depletionof additives and to measure the state of oxidation of grease. It can also measure water contami-nation [370]. In infrared spectroscopy, matter absorbs energy through covalent chemical bondvibrations in a molecule causing them to vibrate by stretching and contracting (as opposed


Table 15.3 Infrared Spectroscopy of Li-hydroxystearate and tetraurea thickener and base oil[112, 128, 282].

Adsorption, ν cm−1 Origin Component

3300–3500,1600 OH stretch Water3335 (centre broad peak) OH-stretch Li thickener3360–3260 NH stretch Urea thickener2953 CH asymmetric stretch (CH3) Oil2921 CH asymmetric stretch (CH2) Oil2851 CH asymmetric stretch (CH2) Oil1747 Ester group Additive1631 Amide I band (C=O), med. Urea thickener1565 Amide II band (C-N & N-H), med. Urea thickener1579 COO− asymmetric stretch Li thickener1560 COO− asymmetric stretch Li thickener1464/1455 CH deformation (CH2) Oil1310–1175 CH2 twist and rock Oil1377 CH deformation (CH3) Oil1300–1000 O-C(H2) stretch Li thickener1233 & 1302 Amide III (N-C=O & N-H) doublet Urea thickener1002 ZDDP P-O-C Additive721 (CH2)n in phase rocking Oil

to ionic bonds). Absorption of energy can only occur if there is an exact match between thewavelength of vibration of a molecule and the wavelength of the radiation. For molecules withdifferent kinds of bonds (e.g. C-H, C=O), such as in greases, different absorption bands willbe found. These are referred to as ‘wavenumbers’ (number of waves in one centimetre), whichis more convenient than the frequency of the absorbed radiation. The technique is usuallycalled Fourier Transform Infrared Spectroscopy, FTIR, because Fourier techniques are usedto convert the raw data in a spectrum. Table 15.3 shows the most salient absorbtion peaks forLi-hydroxystearate and urea thickened grease and of water. Figure 15.6 shows an example ofthe spectrum of two typical Li-greases (Cann [112], Figure 15.6). Grease A is additive free,grease B contains various additives, amongst which is ZDDP. Here the main thickener bondsare at 1580 and 1560 cm−1 (carboxylate stretch). The 1460 and 1377 cm−1 peaks are due tovibrations mainly by the base oil. The 1002 peak is caused by the ZDDP vibrations.

Areas of change in the grease can be identified by subtracting the spectra of fresh and usedgrease. For making a thorough evaluation an expert is needed. To illustrate this: some of thepeaks are caused by thickener and base oil where overlap takes place. Changes in only one ofthem are therefore hard to detect.

15.9 Linear Voltammetry

For higher temperature operation, where oxidation will be the main cause of failure, a methodcalled Voltammetry can be used to measure the antioxidants left in the grease. Van den Kommerand Ameye [340] used the RULER C© instrument for this and showed that, for the cases studied,the antioxidants were almost used up at about half of the lifetime of the grease. This techniquecan therefore be used to measure the remaining grease life.


700 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 Wavenumber [cm–1]

Abs

orba

nce

1580

1560

1460

1377

1002 722Grease B

Grease A

Figure 15.6 Infrared absorbance spectra for two Li-soap greases (limited wavenumber range). Repro-duced from Cann et al, 2007 C© Taylor and Francis Group.

The Linear Voltametry method is an electroanalytical method where the grease is mixedwith an electrolyte and a solvent in an electrolytic cell. Subsequently, a linear increase involtage with time is applied over the cathode and anode while the current as a function of thisvoltage is measured. With increasing voltage the antioxidants oxidize electrochemically andthe measured current signal is a measure for the presence of certain additives.

The method is easy to use, requires only very small grease samples (max 200 mg), isportable, quick (less than 5 minutes) and detects all present antioxidants (including ZDDP)[340, 524].

15.10 Total Acid Number

The total acid number is determined by Potentiometric Titration (ASTM D 664-95). It is thetotal amount of potassium hydroxide in milligrams that is needed to neutralize the acids in onegram of oil (so the unit is mg/g). An increase of TAN is ascribed to the formation of oxidativeproducts, see also Section 8.2, p. 179.

Figure 15.7 illustrates the similarity of using the Acid Number technique and the LinearVoltammetry method. In this case a sample of grease was aged in an oven at 125 ◦C. Thefigure shows that initially the antioxidants remain constant (up to 80 minutes). Next depletionof antioxidants takes place (up to 150 minutes). Finally, after 150 minutes degradation of thebase oil takes place where the acidity increases and oxidation products are formed leading toan increase of the acidity [31].

15.11 DSC – Differential Scanning Calorimetry

In DSC the heat flow resulting from chemical reactions is measured. A grease sample is heatedto a sufficiently high temperature for oxidation to occur. The overall grease oxidation chemicalreaction is exothermal, meaning that heat will be produced as soon as the oxidation starts. The


120

100

80

60

40

20

00 50 100 150

Time [min]200

0

0.5

1

1.5

2

% Antioxidants

% A

ntio

xida

nts

Acid number

Aci

d nu

mbe

r

2.5

3

Figure 15.7 Example of the use of the Linear Voltammetry and Acid Number measurement techniquesmeasuring the condition of grease that is thermally aged in an oven (data from Aranzabe et al. [31]).

time at which this happens OIT, Oxidation Induction Time is then a reference for fresh greaseand is measured through the detection of heat emission. The condition of the grease can bemeasured by measuring used grease and comparing to the reference time [31].

A variant of this method is PDSC, Pressure Differential Scanning Calorimetry, where thesample is not only heated but also pressurized, typically at a pressure of 3.5 MPa (35 bar). Theadvantage of measuring under high pressure is that oxidation is no longer diffusion controlled.This accelerates the oxidation process and increases the repeatability (Reyes–Gavilan andOdorisio [492]. For an extensive description and application to grease the reader is referred toRhee [494–496].

15.12 Oxidation Bomb

Another method for monitoring the chemical aging of grease is the oxidation bomb. In thistest the grease is stored in a sealed system at high temperature and pressurized with oxygento 7.6 bar (110 psi). Next it is placed in an oil bath at 99 ◦C while rotating. The pressure isrecorded for 100 hours (ASTM D942). Oxidation will decrease the pressure and the pressuredrop is therefore a measure of the amount of oxygen consumed in the oxidation reactions. Ahigh pressure drop indicates a high oxidation rate.

15.13 Water

Water is one of the most common contaminants in grease. Free water is available as humidity.Condensation may take place, especially with bearings experiencing frequent stops and starts.


Abs

orba

nce

Wave number [cm–1]

0.00

0.2

5

0

.50

0.7

5

1

.00

1.2

5

1

.50

3800 3700 3600 3500 3400 3300 3200 3100 3000

1.84%

0.99%

0.57%

0.43%

0.26%

Figure 15.8 FTIR spectrum of water in a medium temperature grease (0.26, 0.43, 0.57, 0.99 and 1.84%water. Courtesy of SKF.

Water has an impact on the aging of the grease through, for example, depletion/passivationof additives or increased oxidation. However, most important is the formation of free waterleading to corrosion which accelerates wear.

The most widely used method to measure water content is the ‘Karl–Fischer’ titrationmethod (ASTM D 17744). Here a chemical reaction occurs between water and a mixture ofsulfur dioxide and iodine. The reaction scheme in its simplest form is:

I2 + 2H2 O + SO2 → HI + H2SO4. (15.1)

The reaction takes place in the presence of a base (pyridine) and a solvent (methanol) where theiodine is added (the Karl–Fischer reagent). There is a strict stoichiometry of 1:1 between waterand ionide. Titration should end as soon as free ionide is liberated, which may be registeredpotentiometricly or by colour indication. The water content can now easily be determined fromthe amount of iodine that was used during the titration (equal). The Karl–Fischer reagent maynot only react with water but also with additives. This may introduce serious errors especiallyfor aged lubricants containing degradation products, [201]. For lubricating grease, there isspecial Karl–Fischer equipment with an oven to transfer water from a grease sample to thetitration vessel.

An alternative is water content measurement by FTIR spectroscopy. Water is identified in theFTIR spectrum by the broad and strong OH-group absorption from 3150–3500 cm−1, centredon 3400 cm−1. This is convenient because it is outside the regions of the other components. Itis a strong IR absorber and therefore relatively easy to detect. Figure 15.8 shows an exampleof a water measurement and illustrates the impact of water concentration on the measuredIR spectrum.

16Grease Qualification Testing

16.1 Introduction

Grease testing can be roughly divided into 3 categories, that is, functional testing, life testingand grease property testing. In functional testing, the functionality of the grease in the bearingis tested. This can be, for example, friction torque or corrosion resistance. In life testing thegrease is run in a bearing until it is ‘exhausted’. Testing or measuring properties of the grease isoften done outside the bearing environment. This can be done for quality control or for greasescreening purposes. Here, a relationship between the grease properties and grease performanceis assumed. Examples are the measurement of consistency and base oil viscosity.

First, an overview will be given of the ‘standard’ test methods. Some of these are accordingto standards (ISO, DIN, ASTM) and some of them simply commonly used. After this, somebearing single component test methods will be described and finally some qualification criteriafor which testing is used.

16.2 Standard Test Methods

16.2.1 Penetration/Grease Consistency

Outline of the Test

Simple, aged, but sturdy characterization of grease on stiffness.

Reference to Standard(s)

ISO 2137 / ASTM D217.

Test Conditions

A standard cone is allowed to sink into the grease at 25 ◦C for 5 seconds (see Figure 16.1a). Ahigher penetration value means a softer grease. When sufficient grease is available, a full sizecone is preferred. Alternatives are half size and quarter size cones. Penetration depths can berecalculated into full cone penetration, but are less accurate.



(a) Consistency test. (b) Worked penetration. Grease is pumpedthrough holes in a plate, which mechanicallyages the grease.

Figure 16.1 Consistency test equipment. Photos: H. Sloof.

Outcome

The depth of penetration is reported in tenths of a mm (10−1 mm). Lubricating greases areclassified by the NLGI consistency number, indicating that the penetration is in a specifiedrange, see Table 5.3.

Relevance

The penetration depth does not have a straight correlation with performance of greases inbearings. For different greases with the same penetration result, the actual rheology canbe quite different (elastic/plastic characteristics). Nevertheless, in most grease specificationsthe NLGI number is given as the first parameter. The penetration change of a grease afterbeing subjected to mechanical shear is often more important for bearing applications, seeSection 16.2.2.

Utilization

The penetration value/NLGI classification is used for:

• Indication of grease stiffness level;• quality control parameter (comparison of batches versus originally qualified batch);• estimation of suitability for applications where the grease flow plays a role (vibrating

applications, vertical shaft, pumpability, etc.).

Grease Qualification Testing 341

16.2.2 Worked Penetration

Outline of the Test

Penetration change of a grease after being subjected to mechanical shear in a grease worker(see Figure 16.1b) for a certain number of strokes.


ISO 2137, ASTM D217.

Test Conditions

The grease is worked by a specified number of double strokes (once per second) in a full size,half size or quarter size grease worker (see Figure 16.1b). The penetration is measured afterconditioning at room temperature. Typical conditions for the working treatment are:

• Unworked (this is a poorly defined condition, as the minor shear that is applied when fillingthe equipment can already affect the results).

• 60 strokes (base value, better defined than unworked).• 100 000 strokes (also called ‘prolonged penetration’).

Outcome

Penetration change, that is the increase or decrease of penetration, expressed in 10−1 mm.Both values (before and after working) must be measured with the same cone size.

Relevance

The 60 strokes worked penetration is used for the NLGI classification (see Section 16.2.1).The 100 000 strokes (change) value is used as an indication for the thinning tendency of

greases during the churning processes that can occur in freshly lubricated bearings (beforegrease has settled in the unswept volume) or when conditions prohibit settling of grease.

Utilization

The penetration change after 100 000 strokes is one of the criteria for judgement of suitabilityfor vertical applications. The penetration change after 100 000 strokes is also widely used as aquality control parameter. The penetration change after 1000 strokes is used for determinationof compatibility with residual process fluids, for example, preservative oils and so on (mixturesubjected to test).

16.2.3 Shell Roll Stability

Outline of the Test

Penetration change of a grease after being subjected to mechanical shear in a Shell roll tester(see Figure 16.2) for certain temperature, time and filling degree.


Figure 16.2 Roll stability test ASTM D1831


ASTM D1831

Test Conditions

The grease is rolled for a certain time at selected temperature and filling quantity. After the test,the penetration is measured after conditioning at room temperature. Typical rolling conditionsare

• fill 50 g;• temperature 80 ◦C;• duration 50 hours.

The outcome is not reliable when the grease is too stiff to allow the roller to rotate freely inthe cylinder.

Outcome

Penetration change, that is increase or decrease of penetration depth, expressed in 10−1 mm.Both values (before and after working) must be measured with the same cone size (greasequantity matches best with half cone size).

Relevance

The roll stability (change) value is used as an indication of the thinning tendency of greasesduring the churning processes that can occur in freshly lubricated bearings (before grease hassettled in the unswept volume) or when conditions prohibit settling of grease. The test is moresevere than worked penetration and therefore more relevant for bearing applications.


Utilization

The roll stability is used for

• Judgement of suitability for vertical applications;• an alternative method for determination of suitability for vibrating applications (lower rating

levels only);• an alternative test for stability in presence of water (roll stability grease + water mix);• a quality control parameter.

16.2.4 Dropping Point

Outline of the Test

Determination of high temperature limit where grease starts flowing spontaneously, see Sec-tion 4.3.


ISO 2176 (automated method).

Test Conditions

Automated test with a commercial instrument (Figure 16.3). Heating performed at a pro-grammed rate until the first drop falls through the outlet.

Outcome

Temperature at which the first drop falls.

Figure 16.3 Dropping point test. Photo: H. Sloof.


Relevance

The dropping point should never be exceeded, otherwise the grease structure is permanentlydamaged.

Utilization

The dropping point is the primary definition for the HTL (High Temperature Limit, seeSection 4.3).

16.2.5 Emcor

Outline of the Test

Test on capability of grease to protect against corrosion when steel bearings are in contactwith water, see Figure 16.4.


ISO 11007, DIN 51802, IP 220, NF T-60135.

Test Conditions

Bearing type 1306K/236725 (special bearing with stamped steel cage)1307 EKTN9 (different ball set (larger balls) and a polyamide cage)

Speeds 80 rpm during 8 hours in the first 3 days, followed by 108 hours stop.Loads No loadTemperatures AmbientGrease fill 10 gMonitoring N.A.Strategy 2 bearings per grease, each housing is filled with 20 ml of distilled water after 30

minutes of running in.Evaluation After dismounting, outer rings are visually inspected for presence of rust spots

and rated according to the standardSpecial options Variants with salt water and/or larger quantity of flowing water

Figure 16.4 Emcor test.


0

1

2

3

4

5

Figure 16.5 Emcor test, qualification of rust inhibition.

Outcome

Visual rating, varying from 0 (no corrosion spot visible with the naked eye) to 5 (>10% ofsurface covered by corrosion), see Figure 16.5.

Relevance

No corrosion with distilled water is a sufficient indication that the grease provides protectionwhen condensation occurs (rating 0). The other ratings from 1 to 5 indicate that the grease isless suitable.

Utilization

Primary parameter securing protection against corrosion.

Remark

Some users of Emcor make tests with standard catalogue bearings, instead of the specialbearings prescribed in the standard. Results can be different.


16.2.6 Oil Separation

Outline of the Test

Evaluation of grease on tendency to bleed oil.


DIN 51817 IP 121 [168] (sieve material may differ from DIN, giving different results)A similar ASTM test exists [196].

Test Conditions

A specified quantity of (unworked) grease is placed in a wire screen cone and is lightly loadedby a metallic cap giving a pressure of 161 Pa (Figure 16.6). The unit is kept at a constanttemperature (in most cases 40 ◦C) for 168 hours (1 week). The amount of oil separated isweighed and converted to percentage oil bleed. The DIN norm prescribes 40 ◦C. However,very often other temperatures are used.

Outcome

Percentage (weight/weight) of oil bleeding at the selected temperature, typically 0.5–4% at40 ◦C.

Relevance

• The result (at 40 ◦C) is considered an indication of the stability of the grease with regard tooil separation during storage.

• The result is also useful for predicting lubricating ability at the selected temperature.

Note

There is also an ASTM D 6184 oil separation standard available for this. In this standard ahigher temperature and shorter time is used.

Utilization

An upper limit for oil separation (at 40 ◦C) is specified in view of storage stability (also calledshelf life). A minimum value for oil separation is often specified in view of lubricating ability

Dead weight(pressure on grease)

Sieve

Separated oil

Figure 16.6 Oil separation test.


and for securing LTPL (with different requirements for roller bearings and ball bearings at aselected temperature, see Section 7.2).

Alternative Methods

• Pressurised ASTM D1742.• FTMS 791-321, cone test, more relevant for high temperature tests (result also affected by

evaporation loss).

16.2.7 Water Resistance

Outline of the Test

Evaluation of grease on its ability to withstand emulsification by water.

Reference to Standard

DIN 51807 part 1 (static test).

Test Conditions

A 1 mm thick grease film on a glass plate is submersed in water at selected temperature(standard 90 ◦C) for three hours, see Figure 16.7. The dimensions of the test tube, the cleanlinessof the glass surface, the water volume and the total amount of grease applied are critical.For heating, only the water bath method is recommended to quickly reach the equilibriumtemperature. After the test, the diffusion/absorption of the water into the grease layer andthe degree of emulsification is visually evaluated according to the standard and reported withvalues between 0 (no change) and 3 (major change).

Outcome

Visual rating

Glass or metal plate

Thin layer of greaseon plate

Distilled water

Temperature controlledbath e.g. 90 ± 1 °C

Figure 16.7 DIN 51 807 rating for degree of grease deterioration in water.


Relevance

The result can be used to evaluate a grease on its suitability for application under wet conditions.A severe emulsification tendency (rating 3) makes a grease unsuitable for use under wetconditions. A slight water absorption (rating 1) is not considered a problem. The water canevaporate when conditions are better. In a closed system, a zero water absorption is not alwaysadvantageous, as free water inside a bearing can initiate rust.

Utilization

Included in almost every grease specification.

16.2.8 Low Temperature Torque

Outline of the Test

Determination of break away torque and rotational resistance of grease lubricated bearings atlow temperature in order to assess the Low Temperature Limit.


IP 186, using standard 7204 BEP bearing.

Test Conditions

Bearing type 7204 BEPSpeeds 1 rpmLoads 45 N axialTemperature To be selected, steps of 10 ◦CGrease fill 100%Monitoring Break away torque (at start of bearing rotation)

Running torque after 10 minutes

Outcome

Starting torque and running torque (mNm) at selected temperature.

Relevance

If the starting and/or running torque is too high at a low temperature, bearings may be damagedwhen elements cannot rotate.

Utilization

Determination of LTL (Low Temperature Limit).


16.2.9 Flow Pressure

Outline of the Test

Determination of pressure at which grease can be pushed through a defined nozzle at selectedtemperature.


DIN 51805.

Test Conditions

The gas pressure above the grease filled nozzle (equilibrated at selected temperature) isincreased step-wise (30 seconds, step height specified) until the grease starts flowing.

Outcome

Flow pressure in mbar at the selected temperature.

Relevance

Some correlation is reported with low temperature torque test(s). Sometimes used as a measurefor pumpability, see Section 17.11.1.

Utilization

For bearing applications, the low temperature torque test with a bearing is preferred.

16.2.10 4-Ball Weld Load

Outline of the Test

Evaluation of Extreme Pressure properties by determination of a critical load where weldingof sliding balls occurs (see Figure 16.8).


ISO 11008, DIN 51350/4, IP 239, ASTM D2596 (standards not completely identical, differentstep sizes and also different rotational speeds due to power supply frequencies).

Test Conditions

Rotational speed: 1450 rpm (Europe)Special balls: RB 12.7/310995ALoad steps: 200 N (DIN)Duration: Max 1 minute, or shorter when welding occurs


Welding

noEP2

1400 2000

With EP

AW effect

Wea

r sc

ar (

mm

)

1

EP effect

(a) 4-ball working principle. Three balls areloaded against a fourth ball.

(b) 4-ball test machine.

Figure 16.8 4-ball test method. Photos: H. Sloof.

Outcome

• Load [N] where no welding occurs (‘OK load’).• Load [N] where welding occurs (Weld load / Weld point).

Greases with a weld point ≥2800 N are considered full EP greases. Greases with a weldpoint > 2000 N are considered to have basic EP characteristics.

Relevance

Best available standard laboratory test to classify EP greases on wear prevention. However,there is no correspondence with bearing fatigue life with modern additives. The test seemedto work better with the former lead-based EP additives. The test has been the basis for theevaluation of lead-free EP additives of which the chemistry is sometimes suspected to befatigue promoting.

Utilization

For classification of EP greases.

Remark

Special balls from a lime finishing process are required. Balls from other finishing processesmay give significantly different results.

16.2.11 4-Ball Wear Scar

Outline of the Test

Evaluation of wear preventive properties by determination of the dimension of the wear scarcreated between sliding balls.



DIN 51350/5, IP 239, ASTM D2266 Modified load and duration.

Test Conditions

The preferred test conditions are: Load 1400 N, duration 1 min. Background: the loads specifiedby the original standard(s) are too low to provoke initial seizure effects. Moreover, the balancein the sliding contact is achieved within 1 minute, thus avoiding long tests.

Outcome

Wear scar diameter, average of 2 x 3 balls minimal.

Relevance

Indication for wear prevention characteristics.

Utilization

For classification of EP greases, with following criteria:

Wear scar Judgement

< 1.0 mm very good EP / anti-wear characteristics< 1.6 mm reasonable EP / anti-wear characteristics> 2.0 mm poor EP / anti-wear characteristics

16.2.12 High Speed Grease Life Testing, RHF1

For high speed, the standard test rigs (R0F/FE9) may be modified. However, there is also adedicated rig generally available for this: the RHF1 (see Figure 16.9).

Outline of the Test

• Grease life in ball bearings.• Simulation of conditions typical for high speed applications (up to ndm = 3 600 000

mm/min).• Full statistical evidence for lifetime lubrication.


R0F grease test method, described in machine manual.


Figure 16.9 High speed grease tester RHF1.

Test Conditions

Bearing type: 7005CE/HCP4A62042Z/C3S2VM104

Grease fill: Small quantity (less than 1 g)Speed: variable

n · dm up to ndm = 3 600 000 mm/minLoad: 50–1100 N pure axialTemperature: To be selected for the subject greaseStrategy: At least 4 groups of each 2 bearings run until failureEvaluation: Weibull calculation

Outcome

• Calculated grease life (L01, L10, L50) and 90% confidence interval, and Weibull slope forselected speed and temperature.

• Residual grease quantity/quality after test.

Relevance

The test rig is specially designed for high speed (high temperature) testing.


16.2.13 R0F

Outline of the Test

• Grease life in ball bearings, see Figure 16.12.• R0F: simulation of conditions typical for electric motor applications.• Full statistical lifetime lubrication.


The R0F grease test method is described in the machine manual and in references [377, 378].

Test Conditions

Bearing type DGBB 6204-2Z/C3Grease fill Normal quantity (1.4 g)Speed 10 000 (standard) and 5600, 15 000, 20 000 rpm

n*dm in range ≈190 000–670 000Load 100 N axial and 50 N radial (C/P ≈ 65)Temperature To be selected for the subject grease, aiming for L50 of minimally 1000 hours

(for the 10 000 rpm test)Strategy 5 groups of each 2 bearings run until failureEvaluation Weibull calculation

The loads are so low that fatigue failures will not occur (see Figure 2.4).

Outcome


• Residual grease quality/quantity after test.

Relevance

Determination of grease life in lubricated-for-life deep groove ball bearings. Test results haveshown good correlation with grease performance in electric motors. When the test temperatureis selected within the ‘green zone’ (traffic light concept) and within speed capability for thegrease, then the results can be directly extrapolated to deep groove ball bearings operatingunder different conditions within the green zone.

Utilization

The R0F test is the basis for the definition of the high temperature performance limit (HTPL)for factory fill greases for deep groove ball bearings and for determination of the GreasePerformance Factor (GPF). Also, the high speed capability can be determined by testing atdifferent speeds.


Figure 16.10 R0F + grease life tester.

16.2.14 R0F +Outline of the Test

• Grease life in small ball and roller bearings.• Possibility of varying operating conditions.• Full statistical lifetime lubrication.

The R0F + (see Figure 16.10) is an upgrade of the R0F test rig.


The R0F + grease test method is described in the machine manual and in references [377,378].

Figure 16.11 Grease life tester R2F.


Figure 16.12 R0F grease life tester.

Test Conditions

Bearing type 6204-2Z/C3, NJ204/C3, 22205E/C3, 30304 J2/Q, 7204Grease fill 6204 : 1.4 g, 22205E: 2.5 g, 30304 J2/Q: 2.5 g.Speed 3500–25 000 rpm

n · dm in range ≈117 000–840 000 mm/minLoad 100–1100 N axial and 50–900 N radial per bearing (C/P for 6204 ≈ 8–65)Temperature room temperature −230 ◦C,Standard Strategy 5 groups of each 2 bearings run till failure, but is flexible.Evaluation Weibull calculation

The loads should be chosen such that no fatigue failures will occur. Other than R0F, R0F +is not belt-driven which makes it saver to operate than R0F. This makes it possible to replacebearings from individual units while other units are running, for example. It is also possible torun individual units under different conditions. This makes the machine very flexible in use, avariety of test strategies can be applied.

Outcome


• Residual grease quantity/quality after test.

Relevance

Determination of grease life or relubrication intervals for deep groove ball bearings/cylindricalroller bearings/spherical roller bearings/tapered roller bearings/angular contact ball bearings.

Utilization

The R0F(+) test is the basis for the definition of the HTPL for factory fill greases for deepgroove ball bearings and for determination of the Grease Performance Factor (GPF). Also, thehigh speed capability can be determined by testing at different speeds.

The tests are used to identify the effect of load, speed, temperature and bearing type ongrease life.


16.2.15 R2F, Using the Special Spherical Roller Bearing

Outline of the Test

• Lubricating ability/durability/wear prevention of grease in spherical roller bearings, seeFigure 16.11.

• Simulation of conditions relevant for roller bearings in housing arrangements.• Acceptance procedure.


R2F method, described in machine manual. Obsolete standard DIN 51806 (latest version draftJune 1988) is followed.

Test Conditions

Bearing type 22312 EWMA/C3P VQ420 (special cage, controlled parameters, run-in prior totest)

Speeds 1500 rpm (heated) or 2500 rpm (unheated)Loads 8.34 kN radialTemperatures Unheated (A-test) or heated (B-test, up to 160 ◦CGrease fill Bearing + partly fill of housing volumeMonitoring Temperature, vibration, Lubcheck (to detect film breakdown, Heemskerk [253])Strategy Running for fixed period (480 h) or until serious eventEvaluation Weight loss of rolling elementsSpecial options Determination of first occurrence of film breakdown (monitoring)

Alternative method: procedure with standard catalogue bearing (cost savings onbearings, omission of running in and weighing)

Outcome

• Weight loss of rolling elements and comparison with acceptance criteria.• Weight loss of cages and comparison with acceptance criteria.• Monitored incidents.

Acceptance criteria for weight loss: DIN 51806 (obsolete).

Max roller wear per bearing 25 mg 50 mgMax cage wear per bearing 50 mg 100 mg

Relevance

A pass rating in the heated test (e.g. at 120 ◦C for a Li-soap grease) means that the RelubricationInterval Diagram (Figure 4.5) may be applied for the subject grease in larger bearings in housingarrangements. A pass rating at a higher temperature indicates an elevated High TemperaturePerformance Limit. A pass rating in the unheated test means that the grease is able to maintain


a lubricant film in a larger rolling bearing at normal temperature, also in a low vibratingapplication.

Utilization

• Aftermarket greases for industrial applications.• Railway greases.

16.2.16 R2F, Using Standard Bearings

Outline of the Test

• Lubricating ability/durability/wear prevention of grease in spherical roller bearings.• Simulation of conditions relevant for roller bearings in housing arrangements/acceptance

procedure.


R2F method is described in the machine manual and in the following obsolete standard DIN51806 (latest version draft June 1988). Possible deviation of standard: no special bearings, norunning in of bearings and no weighting.

Test Conditions

Bearing type 22312 E C3 (standard catalogue bearing)Speeds 1500 rpm (heated) or 2500 rpm (unheated)Loads 8.34 kN radialTemperatures unheated (A-test) or heated (B-test, up to 160 ◦C)Grease fill bearing + partly fill of housing volumeMonitoring Temperature, vibration, Lubcheck (to detect film breakdown, Heemskerk et al. [253])Strategy Running for fixed period (480 h)Evaluation Qualitative inspection of rollers and raceways after test (bearing can not be

disassembled for weighing before the test)Special options Determination of the first occurrence of film breakdown (monitoring)

Outcome

• Visual rating for condition of rolling elements and cages after test.• Monitored film build-up.

Relevance

A pass rating in the heated test (e.g. at 120 ◦C for a Li-soap grease) means that the RelubricationInterval Diagram (Figure 4.5) may be applied for the subject grease in larger bearings inhousings. A pass rating at a higher temperature indicates an elevated High TemperaturePerformance Limit. A pass rating in the unheated test means that the grease is able to maintaina lubricant film in a larger rolling bearing at normal temperature, also in a low vibratingapplication.


The reproducibility of this alternative method is worse compared to the test with the specialbearing. Bearing design and parameters for catalogue bearings are subject to changes.

Utilization

This variant of the R2F test is not often used in grease specs (only reference to R2F test withthe special bearing).

16.2.17 V2F

Outline of the Test

Determination of mechanical stability of a lubricating grease, by determination of the greaseleakage through the labyrinth seal from a railway axlebox when subjected to accelerativeforces that are typical for passing over railtrack joints.


V2F method, Standard: SIS 3653; Draft by CEN/TC 256/SC2/WG12 (part of railway standardEN 12081).

Test Conditions

Bearing type Spherical roller bearing 229750/C3 in W4A axleboxSpeeds 72 hours at 500 rpm, followed by 72 hours at 1000 rpmLoad Bearing and shaft weight and belt tension acceleration

Impact ≈12–15 g once per secondTemperature Self-inducedGrease fill 60% of volume, i.e. 1369 cm3 (1300 g for grease with density 0.95)Monitoring Self-induced temperatureEvaluation Grease leakage through labyrinth in initial period, after 72 hours at 500 rpm and

after additional period of 72 hours at 1000 rpmSpecial options Additional measurement of grease penetration at relevant positions and analysis

of grease behaviour on the basis of temperatures

Outcome

Leakage [g] after period at 500 rpm and after period at 1000 rpm, comparison with acceptancecriteria for both periods.

Relevance

Greases which pass the full test can be recommended for arrangements subjected to strongvibrations; greases that pass only the mild first part of the test can be recommended forarrangements subjected to moderate vibrations. Good correlations are found for railway andheavy industry.


Utilization

For vibrating arrangements, especially for railway axlebox greases.

16.2.18 FE8

Outline of the Test

• Wear prevention/durability of grease in axially loaded bearings.• Simulation of wide range of conditions for various applications.• Acceptance procedure.


The FE8 method is described in the machine manual. Standard DIN 51819.

Test Conditions

Bearing type Angular contact ball bearings, tapered roller bearings or cylindrical roller thrustbearings (d = 60 mm)

Speeds 7.5 / 75 /750 / 1500 / 3000 / 4500 [rpm]n · dm in range ≈1000–430 000 mm/min

Loads 5 - 80 kN axial C/P down to ≈2Temperatures Ambient or heated up to 200 ◦CGrease fill High fillingMonitoring Bearing temperatures, friction torqueStrategy Running with 2 bearings for fixed period; optional running-in

Duplicate test is recommendedEvaluation Weight loss of rolling elements and cages in milligrams

Friction torque and actual temperature during testResidual grease quantities

Special options Tests with circulating oil (instead of grease)Tests with cooling

Outcome

• Weight loss of rolling elements.• Weight loss of cages.• Graphs for friction torque and measured bearing temperatures.

Relevance

Lubricating ability (capability to maintain lubricant film and/or to prevent wear; durability offormulation) of grease in axially loaded bearings, especially when at least one condition (load,speed or temperature) or a combination thereof is critical.

Utilization

Greases for larger tapered roller bearings.Greases for railway bearings (FE8 standard will be referred to in EN 12081).


16.2.19 FE9

Outline of the Test

Grease life in angular contact ball bearings under various conditions.


DIN 51821 [17].

Test Conditions

Bearing type 7206B, special execution FAG 529689Speeds 3000 or 6000 rpmLoads 1500 / 3000 / 4500 N axial (C/P=26/13/9)Temperatures 120–200 (steps by 20 ◦C; max 250 ◦C)Sealing 3 variants:

A = open, B = shielded both sides, C = open 1 side + depotGrease fill 2 cm3 in bearingMonitoring recording of running hoursStrategy 5 single bearings running until failure.

Evaluation with Weibull statistics

Outcome

Grease life (L10,L50) for selected operating temperature.

Relevance

Comparison of greases at selected operating conditions. As the temperatures are often chosenoutside the green zone, the results may not be extrapolated to normal temperatures. This makesgrease ‘ranking’ only valid for selected conditions.

Utilization

Utilization of the method is similar to that of R0F/R0F + , see 16.2.13/16.2.14 and Table 16.1.A comparison between R0F and FE9 is given in Section 16.2.29.

16.2.20 A-Frame Cycle Test

Outline of the Test

Evaluation of greases for automotive hub bearing units (ball bearing types) in actual hubbearing unit at temperature cycle and cornering simulation.


Not a standard.


Test Conditions

Bearing type HBU 2, BAF-4104A / BAF-4104 BBSpeeds 1000 rpm, rotating outer ringLoads ± 0.5 g (30s/30s) corneringTemperatures Cycle 12 hours: composed of 10 h baseline (100 ◦C) followed by 2 h peak.

The peak starts at 130 ◦C and is increased in the next cycle by10 ◦C, up to max 200 ◦C, with further peaks at 200 ◦C

Grease fill 9.5 gStrategy running in groups of 2 until failureEvaluation Failure mode (operating conditions can provoke lubricant failure as well as

rolling contact fatigue)

Outcome

Time to failure (Weibull evaluation possible for min. 4 groups) and leakage (by weight loss).

Relevance

Relevant for operation of grease in modern automotive hub bearing units (ball bearing types)where high peak temperatures can occur due to compact design and disk breaks.

Utilization

Specific performance test for qualification of greases for automotive hub bearing units (ballbearing types).

16.2.21 Cold Chamber Test

Outline of the Test

Testing of lubricating ability of greases in rolling bearings under low ambient temperatures.Simulation of bearing operation.


Not a standard.

Test Conditions

Bearing type 22310 / 22312 and 6310 / 6312Speeds frequency controlled, max 1600 rpmLoads 0–15 kN radialTemperatures simulation of ambient temperature range −40 ◦C to + 20 ◦CConfiguration bearing in housing or sealedMonitoring bearing temperature, Lubcheck, shaft speedStrategy Starting at room temperature with stepwise decreasing of temperature by 10 ◦C

each 24 hours, until failure occursEvaluation Time (temperature) until failure


Figure 16.13 Grease noise tester BeQuiet + .

Outcome

Low Temperature Performance Limit, that is, lowest temperature where the lubricant canmaintain a lubricant film.

Relevance

For grease lubricated rolling bearings operating for longer period at low ambient temperature(�20 ◦C).

Utilization

Greases for lubrication of rolling bearings at low temperature.

16.2.22 BeQuiet +Outline of the Test

Testing of noise level generated by grease in low noise bearings.


Figure 16.14 V2F test.


The BeQuiet + method is not standardized. The measurement procedure has been laid downin ISO 15242 and ANSI/ABMA 13-1987. The standards define the suitable frequency bandsand other boundary conditions (see also Bichler [80, 81]).

Test Conditions

Bearing type: Small size, low noise deep groove ball bearings, e.g. 608 QE4, or standard6202

Basic instrument: Extension of VKL bearing noise analyser as used inSKF factories.

Speed: 1800 rpmLoad: 30 N axial for 608 bearingGrease fill: Automated dosing via linear actuator, repeated 10 times after intermediate

cleaning by automatic blow offMeasuring: Highest peaks during 10 sequential periods of each 3 seconds (after run in for

10 seconds) (and optional also vibration in Low, Medium and High-band)Strategy Collection of 10 peak values for 10 dosingsEvaluation Classification of measured peaks, in classes for subject bearingSpecial options Measurement of damping by the grease (comparison with vibration levels in

the bearing reference condition, i.e. lubricated with clean oil).Cleanliness control / measurement of damaging effect on bearing surfaces by

particles in the grease by consecutive tests with suspected grease and withknown clean grease


Outcome

Grease noise level class, GN-class.

Details for Classification

GN ratings vs. BQ peak readings

BQ1 BQ2 BQ3 BQ45 μm/s 10 μm/s 20 μm/s 40 μm/s GN class

>95% GN1>95% >98% GN2

>95% >98% =100% GN3>95% >98% =100% =100% GN4

QE vs. BQ Ratings

Acceptance level

Qualification of grease for % BQ1 %BQ2 %BQ3 %BQ4

608-QE4 ≥95 >98 100608-QE5 >95 >98 100608-QE6 >95 >98

Relevance

Good statistical evidence for noise level characteristics of a lubricating grease sample. Moreinformation can be found in Bichler [81].

Utilization

1. Qualification of greases for low noise application.2. Batch release testing for low noise greases.

16.2.23 Fafnir Friction Oxidation Test

Outline of the Test

Determination of protection by grease against false brinelling in an oscillating thrust ballbearing.


ASTM D4170.


Test Conditions

Bearing type Thrust ball bearing INA / Andrews P/N W-5/8 (06x65), nontumbledOscillation 30 Hz (USA) or 25 Hz (Europe) on an arc of 120

Load 2450 N axialTemperature Room temperature, or cooled environmentStrategy Running 2 tests with each 2 bearings for 22 hoursEvaluation Average weight loss per bearing

Outcome

Wear (average per bearing) in mg, and preferably also details for individual bearings. SeeFigure 16.15.

Relevance

Suitable to distinguish greases on their capability to give temporary protection againstbrinelling/fretting corrosion, for example in hub bearing units during transport of cars ontrucks or on ships.

Utilization

1. Qualification of greases for automotive hub bearing units.2. Batch release parameter greases for automotive hub bearing units.

16.2.24 Copper Corrosion Test

Outline of the Test

Accelerated laboratory test on compatibility between grease and copper alloy (cage) material.

Figure 16.15 Tested bearings from the Fafnir test. Photo: H. Sloof.



DIN 51811, IP 154, ASTM D130 / ASTM D4048.

Test Conditions

Immersion of specified copper strip in grease at selected temperature for 24 hours.

Evaluation

Comparison with described discolouration/tarnishing in the standard. Photographic referencesare available.

Ratings from 1 (slight tarnish) to 4 (corrosion).

Relevance

Reasonable indication on reactivity of grease towards copper alloy cage material (copperalloys are less susceptible than the pure copper that is used in the test; the use of copper in thisstandard test allows speeding up of testing).

Utilization

Used for greases for industrial bearing applications where copper alloy cages are in use.

16.2.25 EP Reaction Test

Outline of the Test

Accelerated laboratory test on aggressiveness of EP additives towards bearing steel at elevatedtemperature.


Not a standard.

Test Conditions

Immersion of balls (4-ball test) in grease at a selected temperature over 24 hours.

Evaluation

Rating Discolouration of balls

0 no colour change1 yellow colour2 shiny black colour on 50% of the surface3 shiny black colour on 80% of the surface4 shiny black colour on 100% of the surface5 matt black colour


Relevance

Indication of aggressiveness of EP additives. High ratings indicate fatigue promoting.

Utilization

Exclusion of fatigue promoting greases for critical applications (EP grease high temperatureand heavy load). Alternative definition for HTL.

16.2.26 Compatibility with Preservatives/Process Fluids

Outline of the Test

Determination of negative effect caused by preservative oils or residual process fluids (frombearing manufacturing process) on grease performance, defined in terms of shear stability loss.


Grease worker, see Section 16.2.2 in this chapter.

Test Conditions

Mixtures are subjected to 1000 working strokes.

Evaluation

Evaluation on penetration change. Typical acceptance limits for factory fill greases:

Concentration (% of fluid in grease) Maximum change penetration value

10% + 20 points20% + 30 points

Relevance

Contamination of greases must be kept as low as possible. The acceptance limits are specifiedin view of excessive quantities of fluids that may be present after accidents in the manufacturingprocess.

16.2.27 Compatibility Tests for Polymeric Materials

Outline of the Test

Accelerated laboratory test on compatibility between grease and polymeric materials used forbearing cages and seals.


International standards for testing properties of polymeric materials.


Test Conditions

Immersion of test pieces/plates in grease at selected temperature during specified time.

Evaluation

Evaluation of changes in various parameters for the polymeric material after immersion.

Relevance

Selection of proper grease/material combinations for bearings.

Utilization

For many bearing applications compatibility is specified. Requirements appear in greasespecifications as well as in polymeric materials specifications, which makes this parameterrather complicated.

16.2.28 Remaining Oil Percentage, or Thickener/Oil Ratio

Outline of the Test

Analytical and diagnostic investigation of grease after being used for certain a time, sampledfrom defined position in the bearing arrangement.


No standard.

Test Method

Separation of oil phase and thickener by dispersing the grease in a suitable solvent, followedby filtering, removal of solvent and weighing of separated phases.

Outcome

Oil content in fresh grease and oil content in used grease.

Relevance

Rule of thumb: a grease is considered to have reached the end of life when half of the originaloil quantity in the grease is consumed/has disappeared.

Utilization

Only for analytical/diagnostic purposes of grease after use in bearings.


16.2.29 ROF/ROF +The SKF standard for testing grease life is the R0F/R0F + method. SKF classifies its rigsin sizes, from R0 (rig with smallest bearings) to R5 (very large bearing). For grease testrigs, the character F is added, which refers to ‘Fett’, which is Swedish for grease. Here, fivepairs of bearings are tested at a controlled temperature where a pair is stopped as soon as thetemperature of one of the two exceeds a pre-defined value (one failure and one suspendedbearing, referred to as sudden death) or when increased friction causes motor overload (thermalswitch). This number is considered large enough for a statistical (Weibull) analysis. However,if the Weibull slope is low, say β < 1.5, more bearings need to be tested to get acceptable 95%confidence intervals. Figure 16.16 shows the drawing of the test head of the R0F machine. Inthe R0F, the test bearings (6204-2Z) are mounted on a shaft, which is driven by a flat belt. Theradial load is fixed to 50 N per bearing and imposed by a dead weight. The shaft is axiallyloaded by a spring giving a load of 100 N per bearing. The temperature of the outer rings iscontrolled to pre-set values. The speeds can be varied by changing pulleys with a range from5600 rpm to 20 000 rpm.

Recently, a new generation R0F has been developed, denoted by R0F + . This rig is themodern variant of the R0F. The basic set-up was maintained: two test bearings per unit,five units per battery. The belt-drive has been replaced by a direct drive. The speed can becontinuously varied. Support bearings have been introduced, which are cooled by compressedair. The support bearings will therefore be running at a relatively low temperature, providingthem with a long grease life. Therefore identical bearings can be used for test and supportbearings. In order to ensure grease failures, rather then bearing failures, relatively light loadsare applied in grease life testing. The R0F + makes it possible to test at heavy loads as well.

Figure 16.16 Drawing of the R0F-test head with two 6204-2Z ball bearings, axially loaded by a spring.


Figure 16.17 Photograph of the R0F + test rigs at SKF Engineering & Research Centre, Nieuwegein,The Netherlands.

The maximum radial and axial load is 900 N and 1100 N respectively per bearing, whichmakes it possible to also test other bearing types such as tapered roller bearings, sphericalroller bearings and angular contact ball bearings.

The 6204 2Z bearings are shielded and filled with approximately 30% of the free volume ofthe bearing, which is in this case 1.4 grammes. The rig is designed such that the test bearinghousing is small and seals off at the end face of the test bearings, that is the test bearingscan be regarded as having shields at the side face. For testing with such an ‘open bearings’configuration a larger volume of grease needs to be chosen. The standard test procedurefor deep groove ball bearings is to start running the bearings at the pre-set speed withoutpre-heating. This means that the bearing temperature will rise from room temperature to thepre-set temperature by both heat generated by friction and by the heaters. Only at higher speeds(20 000 rpm), is running-in applied such that the bearings will go through the churning phasewithout too much mechanical work on the grease.

The test data is evaluated with the Weibest program, which calculates the Ln life and Weibullslope. The calculation of grease life, by incorporating the suspended bearings, is not trivial.If a test is suspended at some time t , then the grease life of this particular bearing is longerthan t . This time t can be used to calculate a correction for the life distribution, as describedin Chapter 12, Section 12.4.2.

16.2.30 R2F and FE8 Comparison

Table 16.2 shows a comparison between the R2F and FE8 machines. Both R2F and FE8machines are designed for running somewhat larger bearings than those in the R0F/R0F + /FE9


Table 16.1 Comparison R0F and FE9.

Parameter R0F FE9 CommentsStandard DIN51821

Bearing typedetailsdDB

DGBB6204 steel cage204714

ACBB7206B (FAG 529689)306216

Both types are radialball bearings forwhich grease lifeconsidered verysimilar

standard speeds(rev/min) andcorrespondingndm (mm/min)

10 000 (335 000)15 000 (500 000)20 000 (670 000)

3000 (138 000)6000 (276 000)

The ndm range forR0F is morecorresponding withwide range ofelectrical motorapplications thanfor FE9

loads(correspondingC/P)

100 N axial; 50 N radial(≈60)

1500/3000/4500 Naxial(≈28/≈14/≈9.3)

Grease life is assumedto be affected whenload C/P<15

Sealing metal shields (2Z) Different config.A = nonshieldedB = shielded both

sidesC = shielded one side+ depot open side

Test temperatures(◦C)

70–170 120–200

Test strategy 5 groups of 2 brgs,sudden death

5 bearings in singleruns

Failure detection running temp >5 ◦Cover set point orthermal switch-off

increase of motorpower consumption(by factor 2)

Evaluation Weibull WeibullReporting L50, L10, L01 (& 90%

confidence intervals);β; residual grease %

F50 and F10 L50 and F50 differentterminology for50% survival life

Test conditions Preferably L50 >1000 h(10 000 rpm test) inorder to stay withingreen zone trafficlight concept)

No minimumspecified manyreported results arein range F50 =50–300 h;

See comments abouttesting outsidegreen is notpreferred

Comments onrelevance

Comments on convertedto electricalapplications(lubricated-for-lifedeep groove ballbearings)

Config. C is relevantfor sealed bearings.Config A isrelevant forhousing with freegrease escape.Config. B is nearestto R0F


Table 16.2 Comparison of R2F and FE8.

Parameter R2F FE8 Comments

Standard No standardDIN 51806;latest issue draft 1988,obsolete

FAG methodDIN 51819draft 1997(for grease testing)

Bearing types

detailsd /D/B [mm]

22312special EWMA/C3P VQ420or catalogue bearing60 / 130 / 46

731231312CRTB60 / 130 / various

R2F typical forradially loadedbrgs

FE8 typical foraxially loaded brgs

standard speeds(rev/min)

15002500

7.5 / 75 / 750 / 1500 /3000 / 4500

Low speeds in FE8aim at boundarylubricationconditions

Loads C/P 8.34 kN, radial 28 5–80 kN axial downto 2

Testtemperatures

unheated, or heated up to160 ◦C

unheated, or heatedup to 200 ◦C

Configuration Bearing housing,representative for industrialapplications

Test strategy Acceptance procedure,Running 2 bearings for 480hours

Running 2 bearingsfor 500 hours (forgrease testing)

FE8 requiresduplicate test R2Fmust be repeated incase of inconsistentresults

Failuredetection

Vibration, temperature andoptional Lubcheck

friction torque,temperature

Evaluation andreporting

Special brg: Weight loss andoccurrence lubricationincident(s)

Weight loss, frictionand temperaturebehaviour

Resolution of mg ontotal mass >500gneeds specialexpertise.

Catalogue brg: visualinspection and lubricationincidents

Surface layersseverely interferewith weightanalysis.

Theoretical life,SKFcataloguediagram

L01@70 ◦C/2500 rpm≈2100 hL01@120 ◦C/1500 rpm≈600 h

Very wide range ofconditions andcalculated lives

Comments onrelevance

Failure within test periodindicates that grease hasinsufficient lubricatingability, incompatibility withbearing materials ortendency to formation ofdeposits

Multitude of testconditions makes itdifficult to defineFE8 as standardmethod (also oiltesting options)

Weight loss should benegligible whenrunning under fullfilm conditions.


machines. The main difference between the two test rigs is that the R2F is designed for runningradially loaded bearings and FE8 is designed for axially loaded bearings. Neither type ofmachine is generally used for running bearings to failure, but are instead used for monitoring(functional testing versus life testing).

16.2.31 ASTM D 3527 Life Performance of Wheel Bearing Grease

In this test two tapered roller bearings are rotated at 1000 rpm at 160 ◦C. The bearings run inrepeated cycles of 20 hours and 4 hours with no rotation until the power consumption is fourtimes the steady state value. Outcome is the number of hours.

16.2.32 ASTM D 5483 Oxidation Induction Time of Lubricating Greasesby Pressure Differential Scanning Calometry

This test was developed by the US army in 1990 as an oxidation stability test for greases, Rhee[495]. Pressure Differential Scanning Calometery (PDSC) is a thermal analytical techniqueusing the differential heat flow between sample and reference thermocouples under varioustemperatures and pressures. Rhee [495] designed the method such that a test would be com-pleted between 10 and 120 minutes. For this the test is performed under high temperatures(155, 180 and 210 ◦C) and pressure (500 psig, 35 bar, 3.5 kPa) where an oxygen flow is ledover the grease sample until an oxidation exotherm is observed on a thermal analyser scan.The times for other temperatures can be found through

t = A exp

(17 500

T

), (16.1)

where A is the oxidation coefficient for the grease, t is the time in minutes and T is thetemperature. More information is given in Section 8.3.

16.2.33 Linear Sweep Voltammmetry

Linear sweep voltammetry (Kauffman [314]) directly extracts the antioxidants out of the baseoil. A controlled voltage ramp is applied through the electrode inserted into a diluted greasesample resulting in a current that will peak at the oxidation potential of the antioxidationadditive in the sample. The height of the peak is related to the concentration of the antioxidantadditive. The method is used to determine the remaining life of a grease in a bearing, [340],where it is assumed that the antioxidants are consumed by half the lifetime of the grease.

16.3 Some Qualification Criteria for Grease Selection

16.3.1 Low Temperature Limit

The Low Temperature Limit (LTL) is determined by the ability to start-up a bearing under verylow temperatures when the viscosity/yield stress of the grease has become too high to make


this possible without ‘difficulty’ [4]. It is part of the traffic light concept (see Section 4.3). Thequalification parameter for this is the ‘low temperature torque test’, Section 16.2.8. Startingup is considered to be safe when the starting torque has ≤1000 mNm and running torque≤100 mNm. Alternatively, the yield stress can be measured on a rheometer. However, forthis no specifications are available. The value of the penetration may also give an indication,although the measurement for this is made at room temperature.

A qualitative comparison with other greases can be made based on base oil viscosity/typeand/or thickener type.

16.3.2 Low Temperature Performance Limit

The Low Temperature Performance Limit (LTPL) is defined in the traffic light concept (seeSection 4.3). It is the temperature at which the grease will operate reliably and where grease lifecalculations can be made. It is different for different bearing types. The primary qualificationparameter for the LTPL is the ability to bleed oil. The oil separation test (Section 16.2.6) isapplicable here. For ball bearings the acceptance level is the temperature where bleeding is≤0.5%. For roller bearings this is ≤3%.

An alternative would be to run the specific bearing (-type) at low temperatures (e.g. in acold chamber) and measure the film formation using the Lubcheck system (see Section 15.3).The acceptance limit would be the temperature at which the bearing can maintain a lubricantfilm.

Other greases can be compared by studying the oil separation at 40 ◦C, the NLGI class,base oil viscosity, base oil type, thickener type and/or thickener content.

16.3.3 High Temperature Performance Limit

The High Temperature Performance Limit (HTPL) is defined in the traffic light concept (seeSection 4.3). Above this temperature grease will age and oxidize at an increasing rate andgrease life calculations do not apply.

The primary qualification method for the HTPL is the R0F test for deep groove ball bearings(Page 388) where the HTPL is approximately 10 ◦C below the temperature where L50 ≈ 1000 hin a 10 000 rpm test. For roller bearings the R2F is used (Section 16.2.16), where the bearingis heated and where the HTPL is approximately 10 ◦C below the temperature where a passrating is obtained. As an alternative, a screening test could be done in the R0F with a reducednumber of bearings.

Comparison with other greases can be made on the basis of composition and primaryphysical parameters.

16.3.4 High Temperature Limit

The High Temperature Limit (HTL) is defined in the traffic light concept (see Section 4.3). Itis determined by the type of thickener and the dropping point. This point is accepted as beingthe maximum temperature at which the grease can be exposed without losing its structure. Forsafety reasons this is reduced by 15–20 ◦C.


Sometimes an EP reaction test is used (Section 16.2.25). This is particularly applicable tohigh load greases where the chemistry of the grease my be activated by the ambient bearingtemperature rather than the contact temperature. Alternatives are PDSC (Section 16.2.32),evaporation loss or the bomb oxidation test. It is important to realize that there is no correlationwith the High Temperature Performance Limit. This is confirmed by the tests from Coe [132]who found no correlation between dropping point and dynamic tests, that is tests using bearings.

16.3.5 Minimum Speed

The minimum speed is determined by the ability to build-up a hydrodynamic lubricant filmand the ability to form ‘protective tribo-layers’. There is no test available for this other thanfunctional tests where bearings or ball-on-disc devices are run at low speeds followed bysurface inspection. Usually, the base oil viscosity is used as a qualifier for this, low speedsrequire a high base oil viscosity. So called ‘EP-greases’ are specially designed for low speed.

16.3.6 Maximum Speed

The maximum speed is determined by the ability of the grease not to generate excessive heat.As a rule of thumb, this requires a low viscosity and higher consistency class (see Section 4.7.2).The maximum speed can sometimes be determined on the R0F + /FE9 machines. Bearingsmay be run under self-induced temperatures where the speed is increased stepwise until thetemperature exceeds an accepted value. However, this only applies to conventional greasesand the speed range is often too small for this. The RHF1 test rig can be used to very highspeeds (Section 16.2.12).

16.4 Pumpability

Pumpability is both a grease and lubrication system property. As an example, for the pumpa-bility though simple pipes, a dependency in pipe diameter and grease consistency exists.For this reason grease pumpability tests are described in the Chapter ‘Lubrication systems’,Section 17.12.

Images in this chapter are courtesy of SKF unless otherwise indicated.

17Lubrication Systems

P.M. Lugt, R. Stockhammer and P. Conley

As extensively described in the preceding chapters, lubricating grease has a limited life and reli-able long-term operation is often only possible in the case that rolling bearings are relubricatedwith fresh grease. Other reasons for relubrication are the washing out of contamination and/orwater. The amount of grease is very critical. Too little will not provide sufficient lubrication andtoo much grease leads to excessive heat development and/or damage to seals. Relubricationis done through lubrication systems, which are manually, automatically or semi-automaticallycontrolled and should deliver the lubricant, in the right amount, at the right time, to the rightlubrication point. What the bearing needs is different to what the lubrication system needs. Astiff grease that can bleed readily can be considered a good grease from the bearing or greasemanufacturer’s point of view and a bad grease from a lubrication system manufacture’s pointof view. It would be very desirable from a bearing manufacturer’s point of view to have a stiffgrease for good sealing, and yet bleed out the oil readily to prevent starvation in the lubricationcontact zone. Because it is more difficult to pump a stiff grease and one that bleeds the oil outreadily, the application has to take into account both the lubrication system pump ability andthe lubrication requirements of the bearing.

This is why the choice/design of a good lubrication system may be as important as theselection of the right grease.

In grease lubrication for rolling bearings, always so called ‘total loss lubrication systems’ areapplied. This means that no recirculation takes place and that the lubrication points are alwayssupplied with fresh lubricant. It also means that these systems generate waste, which obviouslyneeds to be minimized. The design and lubricant selection for lubrication systems becomingtherefore increasingly important from both an economic and an environmental point of view.

Research in lubrication systems is aimed at gaining knowledge about the design and manu-facturing of lubrication system components and system design. Lubrication system engineeringis a special field in mechanical and systems engineering that a limited number of experts havemastered. Designers and development engineers have to rely on just a few companies that arespecialized in this equipment. The available technical literature is sparse, often oriented to



the respective manufacturer, and rarely contains the criteria that make it possible to choosethe equipment required for performance of the task at hand. This is why the number of ref-erences in this chapter is very few and most of the contents in this chapter come from theauthors’ company.

The basis for the design and operation of (the centralized) lubrication systems used forrelubrication is the lubrication knowledge of the bearing system and expected operational con-ditions. This defines the requirements, that is how much, where and which lubricant to be used.

Relubrication can be done manually or by a lubrication system, which can be automatedor centralized or automated and centralized. Automated means that the lubrication interval(event) is actuated by a control unit. Centralized means that all distributors (the elementsfeeding the lubrication points) are actuated and refilled from a single source (pump unit withlubricant reservoir).

Figure 17.1 illustrates the effect of manual lubrication. Applying too much grease will causeexcessive churning and often the excess is pushed through the seals, causing housekeeping andenvironmental and safety hazards. This represents the top area in Figure 17.1. The lower zonerepresents the danger zone where insufficient grease is supplied to the bearing. The greasemay have lost its ‘lubricity’ (see Chapter 4, grease life) or the grease may be contaminatedsuch that the bearing will be damaged. In fact, preferably, the lubricant is to be delivered insmall portions, such that excessive churning is avoided, Figure 17.2.

In addition, the physical limits of the system components utilized in the (centralized)lubrication system should be well known. The use of lubrication systems also complicates thegrease technology: in addition to appropriate lubrication properties, the grease pumpabilityshould also be taken into account. This can be done through adding this boundary conditionto the selection of the grease or making it inherent to the design of the lubrication system.

Lubrication can be done using a wide variety of methods, from simple single point tocomplex multi-point centralized systems. In this chapter the different lubrication methods andsystem components such as pumps, valves and distributors will be described. For optimumperformance in lubrication systems the grease needs the proper ‘pumpability’ properties,which will also be treated.

Manual lubrication cyclesBearingsealbreached

Too muchgrease

Max. Bearingcapacity

Right amountgrease

Too littlegrease

Contaminationbegins

0 1 2 3 4

Missed lubeevent

Bearing starvedsevere ware

Am

ou

nt

of

lub

rica

nt

dis

pen

sed

Time between lubrication eventsdays/weeks/months

Extreme over/underlubricationOver / under lubricationOptimum lubrication amt.Maximum bearingLubricant capacity

Figure 17.1 Effect of manual lubrication. Reproduced from Conley and Grach, 2006 C© Taylor &Francis Group.

Lubrication Systems 379

Am

ount

of l

ubri

cant

dis

pens

ed

Too much

Automated lubrication cycles

Time between lubrication eventsin hours

Max. Bearingcapacity

Right amount

Too little

Extreme over/underlubricationOver/under lubricationOptimum lubrication amt.

Maximum bearingLubricant capacity

0 2 4 6 8 10

Figure 17.2 Automated lubrication. Reproduced from Conley and Grach, 2006 C© Taylor & FrancisGroup.

For sealed rolling bearings, relubrication intervals are very infrequent and may not warrantan automatic lubrication system. When a lubrication system is used, it is recommended to usea vent fitting or pressure relieving fitting, which is attached to the seal bearing housing.

It is very important to notice that the relubrication intervals related to grease life, as describedin Chapter 4, do not apply here. In Chapter 4 the relubrication interval is the time when 1% ofa large population of bearings will fail caused by the fact that the grease is no longer able tolubricate the bearing. In this case, an amount of fresh grease was placed in a thoroughly cleanedbearing. In the case of lubrication systems this is more complex. Here, the bearings are notcleaned before relubrication. Bearings are ‘topped up’ with grease and part of the aged greasemost probably will remain inside the bearing. For this reason, the terminology ‘relubrication’ isavoided and the terms ‘lubrication event’ or ‘lubrication interval’ are used instead. Obviously,the frequency of ‘lubrication events’ or the length of the ‘lubrication interval’ is much shorterthan expected, based on the relubrication theory from Chapter 4.

17.1 Single Point Lubrication Methods

Single point lubrication is normally used when only a few lubrication points are located on amachine and these are far away from each other. In this case a centralized lubrication systemis not economical. Another reason to use single point lubrication is when several lubricantsare used. In this case the lubricant cannot be supplied from a common reservoir.

If only such single points need to be lubricated, either manual lubricators or ‘automatic lubri-cators’ are used. Manual lubrication is typically done with grease guns, Figure 17.3a, whichare manual pumps with an extension pipe with a hydraulic gripping nozzle. An alternativeto manual lubrication are the single-point (or multi-point) automatic lubricators. An exam-ple are the so-called ‘SYSTEM 24’ lubricators, which are automatic gas-driven single-pointlubricators, as shown in Figure 17.3b. A time-setting slot enables the adjustment of lubricantflow. The pressure to a piston is provided by an electrochemical gas cell that produces inertgas. Other versions are electromechanically driven. The piston pumps the grease towards thefitting, mounted on, for example, a bearing housing.


(a) Grease gun. (b) Single point automatic lubricator.

Figure 17.3 Single point lubricators. Courtesy of SKF.

Some versions, known as multi-points, can supply a few points at the same time. Multi-points are used when a few points are lubricated with the same lubricant and share the samefrequency, quantity and lubrication interval.

More complex configurations exist where the pressure is for example time-controlled orwhere lubrication is provided to multiple points.

17.2 Centralized Grease Lubrication Systems

By definition, ‘centralized lubrication’ means all soft- and/or hardware that is necessary tooperate, control and/or monitor the lubrication of any type of lubrication point from a centrallocation.

In a centralized lubrication system a pump pressurizes a so-called ‘main line’, leading tovalves and distributors, which again supply lubricant to the ‘secondary lines’ leading to thelubrication points.

Centralized lubrication helps to eliminate often unsafe manual lubrication and to optimizelubrication in terms of volume size and lubrication interval. Centralized lubrication systemsfeed lubricant from a central source to the connected lubrication points on a machine ormachining system automatically or via manual trigger. Most lubrication systems are triggeredby a preset timer in the lubrication controller that turns it on and off. Feedback from asensor indicating that the lubrication system has completed a cycle can also be used as aninput to turn the lubrication pump off. Pump units for centralized lubrication system areavailable with or without integrated control and monitoring units. Important advantages ofcentralized lubrication systems in comparison with single-point lubricating systems are thatthe reservoir for all lubrication points are located at the same place and that monitoring canbe easily installed. Usually, centralized lubrication systems are more or less built as stand-alone ‘intelligent systems’ with integrated control and monitor units available for workingautonomously in any kind of application, although centralized lubricating systems withoutcontrol and monitoring functionality also exist.

Centralized lubricating systems differ in the way the lubricant is delivered and distributed.


Usually, the lubricant is not directly provided by the pump. In this case, the pump provideslubricant under pressure to distributors, components that contain valves/pistons, which deliverthe grease to the lubrication points. There are essentially four different types of lubricationsystem which will be briefly described below.

The following types of systems are customary for grease lubrication today:

• Single-line systems;• progressive systems;• dual-line systems;• multi-line systems.

The oldest are the progressive and dual-line systems, which were originally developed inthe late 1800s during the Industrial Revolution. Single-line systems were developed in thelate 1930s as an enhancement of the progressive and dual-line systems [134]. Ever since,continuous improvements in design and components have taken place, which have led to themodern lubrication systems that will be described below.

Single-Line

In single-line systems the lubricant is metered by the distributor by means of a fixed dis-placement of pistons. The flow rate is not controlled by the pump pressure at each lubricationinterval.

Progressive

While single-line piston distributors discharge a metered quantity of lubricant to the lubricationpoints almost simultaneously during the run time (lubrication interval) at one time, progressivefeeders deliver the lubricant feed to the lubrication points in sequence during the run time andin the ratios of the individual metered volumes of each section. Here too, as with pistondistributors, each outlet port of a feeder can supply only one respective lubrication point withlubricant.

Dual-Line

Dual line distributors need two main lines in order to function. These lines are alternatelysupplied with lubricant by a pump unit. While one main line is pressurized, the other is relieved.For a complete lubrication cycle both main lines have to be pressurized and relieved one afterthe other. The distributors meter out an adjustable amount of lubricant per lubrication cycle.The lubricant is either fed directly to the lubrication point or is discharged by a secondarydistributor, usually a progressive feeder. Each lubrication point must be provided with aseparate distributor port.

Multi-Line

Each output port inside the pump is assigned to a separate delivery piston that simultaneouslymeters the lubricant (but is adjustable). The lubrication lines lead directly from the pump tothe lubrication points or to a progressive feeder that further divides up the respective delivery


rates of the connected outlet ports. The outlet ports of the multi-piston pumps can be combinedinternally or can be shut down (by setting the delivery stroke to ‘0’).

In all types of lubrication systems, monitoring of the system performance is very important.Every type of lubrication system has some provisions for monitoring. This varies from visualindicators to full electronic transducer feedback monitoring.

Before going into the details of the various systems, a short description of the variouscomponents of the system will be given.

17.3 Pumps

In automatic grease lubrication systems, one common component is the pump unit. The pumpunit must be able to remain primed (to avoid cavitation) and deliver the correct amount ofvolume within the specified operating limits and under back pressure. A back pressure iscreated to overcome the yield pressure and the flow resistance in the supply line.

Almost all grease pumps operate with pistons to deliver the grease. In some applicationsscrew spindle pumps are used when large amounts of grease volume have to be delivered.Gear pumps or gerotor pumps are only used for oil or very low consistency greases. If thestiffness (yield stress) or if the apparent viscosity of the grease is too high, grease may notflow into the delivery chamber or cannot totally fill it during the time that the piston createsan under-pressure. When this happens, the pump cavitates, which should be avoided as it cancause premature pump failure. Moreover, a pump that is cavitating cannot pump enough greaseinto the system, resulting in a malfunction of the lubrication system.

The pumps could be either electrically, pneumatically or hydraulically driven. Only in rarecases are mechanically operated pumps used. The piston pumps contain either one or, moreoften, several pump elements, which are actuated by the pump drive. It is these elements thatdeliver the lubricant and determine the dosing during each delivery stroke.

17.3.1 Shovel Pump for Pumping High Viscous Grease

A common heavy industrial pump has a shovel type action. This is illustrated in Figure 17.4.Positive displacement double-acting shovel pumps are most often used for pumping viscous

material. The pumps are described as double acting because they output grease when pumpingin both the up and down stroke. There are two pumping chambers, one for the up stroke andone for the down stroke. Positive displacement pumps create suction in their action. The pumpsoperate in a piston/cylinder arrangement. The piston displacement creates a vacuum, this vac-uum is used to create a pressure differential causing grease to flow. Because there is only 1 barvacuum pressure possible, this may not be enough to produce flow from the grease reservoir tothe pumping chamber. To overcome this situation, a mechanical shovel is used to mechanicallypush the grease into the pumping chamber. Below is a description of how they work.

The operation of a double acting shovel pump produces the same output when the pistonis in the up or down stroke. After the pump is inserted in a grease reservoir, the pump is firstprimed by turning on the pump and removing any air from the pump. When the pump is turnedon, the pump in the up stroke uses the mechanical shovel to force the grease into the pumpingchamber. All the volume of grease entering the pump occurs on the up stroke only. The pumpdoes not accept grease on the down stroke.


Greaseout

Outletcheck

First pumpchamberTwice volume ofchamber 2

Mechanicalshovel

(a) (b)

Lowerinlet

check

Greaseout

Outletcheck

Secondpump chamber1/2 volume of 1stpump chamber

Mechanicalshovel

Lowerinlet

check

Figure 17.4 Shovel pump in up and down stroke configuration. Courtesy of Lincoln.

There are two pumping chambers within double-acting shovel pumps. The grease that entersthe pump tube first enters the first pumping chamber. The inlet check opens during the up strokecycle. Simultaneously, the second pump chamber volume is compressed, forcing lubricant outof the pump.

During the down stroke, the outlet check closes and the pump piston fills the second pumpingchamber while dispensing lubricant out of the pump. Because the displaced volume of the first


Figure 17.5 Shovel pump in a standard grease drum. Courtesy of Lincoln.

pump chamber is twice that of the second pump chamber, the grease fills the second pumpchamber as it dispenses.

It is important that a pump produces the same amount of pressure and flow on the downstroke as the up stroke. If the pump ratio is say 1:50, the pump should be able to generate thesame pressure on either the up and down stroke at that ratio.

17.3.2 Method to Create a Positive Head Pressure by Using aFollower Plate

A follower plate can be used to create an additional pressure head, which will prevent a voidfrom forming around the pump inlet, see Figure 17.5. If the grease is too stiff, and the pumpdraws in grease, a void could be created. This void will cause cavitation. The principal behindthis is the techniques using differential pressure produced by the pump’s ability to produce avacuum. When the pump displacement causes a vacuum, some grease will flow into the pumpchamber. Simultaneously, this will create a pressure differential across the follower plate. Thepressure differential across the follower plate may be small, but the net force produced becomeslarge, creating a positive head that will prevent voids or pockets. This simple relationship canbe illustrated as follows. A typical follower plate for a 200-litre refinery drum may be 60 cmin diameter. This results in an area of 2826 cm2. If the pump can produce just a small vacuumof 0.14 bar, the net force acting on the follower plate will be 4 kN. This net downward forcewill cause any void in the grease to collapse.

17.4 Valves

The choice of valves depends on the following criteria:

• Grease type;• delivery rate;


• pressure;• function.

The valves can be built into the system as stand-alone devices, or they can be integrated in thepump units or reservoir units in the form of valve combinations.

Valves can be classified based on their function as:

• Intake valves (ball valves, conical seat valves or port controls in the case of grease pumps);• delivery valves or check valves in the form of outlet valves (ball valves, conical seat valves

with elastic seals, piston valves with elastic sealing rings);• bleed valves (ball valves);• pressure regulating or pressure limiting valves (ball valves, piston valves, conical seat valves);• relief valves (sleeve valves, piston valves, ball valves);• residual pressure valves.

Table 17.1 shows a selection of valves together with their technical data and use.

Table 17.1 Types of valves that are used for grease in lubrication systems.

NLGI PressureType <1 >1 range (bar) Flow rate Application

Sleeve X 0 0–5 <15 cm3/stroke Relief and residual pressure valve inpiston pumps

Ball X X 0–15 <1000 cm3/stroke Intake valve, delivery (outlet) valve inpiston pumps

Check valve in progressive feeders(frequent actuation with small pressuredifferentials and low delivery rates).Overpressure valve in devices andsystems (infrequent actuation at highpressure differentials)

Conical seatwith elasticseal

X X 0–25 <10 l/min Intake and delivery (outlet) valve inpiston pumps.

Host couplings.Check valves with small pressure

differentials.Relief valves.

Conical seatwith metallicseal

X 0 0–25 <20 l/min Pressure regulating valve, overpressurevalve

Valve with hydraulic damping, nearlyvibration free for frequent actuation

Piston X 0 0–5 <15 l/min Valve with little leakage (depending onviscosity)

Piston (slide)valve

0 0–40 <20 l/min 4/2 way valve for oilChange-over valve for dual-line systems

Valve comb. X – 0–4 <5 l/min Total loss lubrication systems for fluidgreases


17.5 Distributors

The pump provides the grease, through the main line, to the ‘distributors’. The distributorsare devices that actually provide the dosing/metering, that is, they deliver a specific andpredetermined amount of grease every pump cycle. Distributors are designed such that themetering is normally not directly influenced by the type of lubricant (fluid grease or grease),system pressures or operating temperatures.

The main types of distributors used in centralized lubrication systems for grease are:

• Single-line distributors;• progressive feeders;• dual-line distributors.

They will be described in more detail in the next sections. As mentioned above, the type ofdistributor that has to be used is determined by the type of lubrication system. The description ofdistributor type is therefore encapsulated in the description of the different types of lubricationsystems. It is only in multi-line lubrication systems that various types of distributors are used.

17.6 Single-Line Centralized Lubrication Systems

Figure 17.6 shows a typical single-line system where a pump supplies the lubricant to thelubricant distributors via the main feed line or supply line. The distributor consists of anumber of injectors, which each ‘injects’ a metered amount to the secondary lines or feedlines down to the lubrication points. As with all lubricating system types, the pump can bepneumatically, hydraulically or electrically powered.

The lubrication cycle is initiated by a controller, which starts the pump by opening ansolenoid valve, in the case of a pneumatic or hydraulic driven pump, or by switching on anelectric motor. The pump will build up a grease-pressure in the main line. At a certain criticalpressure the injectors will meter a predetermined amount of lubricant to a bearing. The pressurein the main line will still increase until a pressure sensor, usually located farthest away fromthe pump, gives a signal to the controller indicating that a sufficiently high pressure has beenobtained here so that the pump can be turned off. Next, a three way valve is activated, whichallows excess grease due to line expansion, for example to directly flow back to the reservoir.This reduces the pressure in the system. This pressure relief process is also known as ventingand allows the injectors to reset again and be ready for the next lubrication event.

Single-line systems are mainly used for fluid greases and oil. They are suitable for thenumerous lubrication points on small and medium-sized machines, machine groups and sys-tems operated on an intermittent basis. However, there are also systems for large systems andNLGI 2 greases.

Single-line distributors consist of ‘injectors’, sometimes called ‘metering elements’ or‘metering valves’. It is these injectors that supply the necessary lubricant precisely meteredto the lubrication points. Distributors can be classified into pre- and relubrication distributorswhere the lubricant is delivered to the lubrication point during or after the build-up of pressurein the main line. So the lubricant is delivered either when the pump is switched on or after ithas been switched off.


1

2

34

5

5

5 6

Figure 17.6 Single line lubrication system using an electrical pump. 1 = pump unit; 2 = controller;3 = pressure relief valve with pressure regulating valve; 4 = main lubricant line; 5 = single linedistributor, 6 = pressure switch. Courtesy of SKF.

17.6.1 Single-Line System and Venting

The traditional limitation of a single-line system is the necessity of the lubricant to vent backdown under the system pressure in order for the injector to reset (so as to depressurize).The value of this pressure is sometimes called ’venting pressure’. This value differs for thedifferent types of injectors. Typical venting pressure values are between approximately 7 MPa(1000 psi) to 4 MPa (600 psi). Because of this, grease single-line systems today can have alsolong main lines from the pump to the furthest distributors. The maximum supply line length(with given diameter) can be approximately determined using the results from pumpabilitytests, which will be described in Section 17.12. The grease viscosity determines its flowability and therefore the time needed to fill up the measuring chamber and the time neededto pressurize and depressurize the grease in the supply line. The time between successivelubrication events in single line lubrication systems is mainly determined by this ventingprocess in the supply line.

17.6.2 Prelubrication Distributors

‘Prelubrication’ denotes the fact that a pre-metered quantity is supplied to the lubricationpoints during the pressure build-up in the supply line at each lubrication cycle. The quantity is


(a) Courtesy of SKF. (b) Courtesy of Lincoln.

Figure 17.7 Single line, multi-point lubricant distributor for a centralized lubrication system consistingof several injectors.

given by a pre-determined volume of each stroke of a piston in the distributor and is thereforefixed and not given by the pump pressure, temperature or grease consistency.

Typical Prelubrication Injector

There are two main types of prelubrication injectors, one being the MonoFlex VR- and onebeing the SLV-type. These are shown in Figure 17.7.

The MonoFlex VR and SLV distributors consists of 6 and 2 or 1 and 6 injectors respectively.Each injector provides lubricant to a lubrication point by means of pistons, loaded by springs.

The SLV type is more suited for very large industrial applications such as steel mills, cementfactories and so on, where long lines and distances from the pump to the lubrication pointsexist, mainly because of the venting and resetting features. The VR type is typically used formobile and smaller industrial equipment.

Figure 17.8 illustrates the functioning of the VR piston distributor and injector.

(a) The measuring chamber is filled with lubricant from the previous cycle. This is the ’normal’position when the pressure is released.

(b) The pump pressurizes the main line and the control piston opens. This allows the greaseto flow into the lower piston chamber.

(c) While the pressure builds up to its maximum value in the main line, the metering volumewhich was present in the upper piston chamber is driven into the outlet towards thelubrication point.


Control pin

Upper piston chamber

Outlet

H = metering stroke

H

Piston

Lower piston chamber

Control piston

Control piston socket

Inlet

Main line relieved:Distributor in normal position

(a) Main line relieved: Distributor innormal position.

(b) Pressure builds up in the main line: Control piston opens inlet to lower piston chamber.

(c) Pressure builds up to max pressure in the main line: The metering volume is expelled and the lower piston chamber is filled.

(d) Pressure relief in the main line: Control piston returns to the normal position and connects the lower piston chamber with the upper piston chamber. The piston moves lubricant from the lower to the upper piston chamber.

Figure 17.8 Single-line distributor (MonoFlex VR piston distributor). Courtesy of SKF.


(d) Next, when the pressure is relieved (venting) the larger spring pushes the piston back.Meanwhile, due to the low pressure in the inlet, the control piston returns to the normalposition and connects the lower piston chamber with the upper piston chamber. The pistonnow moves lubricant from the lower to the upper piston chamber. When the piston is down,at the end of its maximum stroke, the upper chamber is filled with grease giving again ametered volume which is then ready for the next pump stroke.

Figure 17.9 illustrates the functioning of the SLV piston distributor and injector. The corre-sponding stages of operation are described below.

(a) The discharge chamber is filled with lubricant from the previous cycle. Under the pressureof incoming lubricant, lubricant is directed to both sides of the measuring piston through theslide valve. The port to the bearing is closed in this position which prevents the measuringpiston from moving. The indicator stem will be at its innermost position, having pulledaway from the stop in the adjusting screw.

(b) Pressure has built-up and has moved the slide valve into the position shown. This closesthe flow passage to the upper side of the piston (larger diameter) while simultaneouslyopening the port to allow lubricant to flow out of the injector to the bearing. Pressure fromthe supply line continues to apply pressure to the lower portion of the measuring piston,which causes a pressure difference across the measuring piston thus allowing it to moveupward.

(c) Movement of the measuring piston is shown, caused by the pressure on the lower side ofthe measuring piston dispensing lubricant to the bearing. The indicator stem will moveup against the stop in the adjusting screw when all the lubricant has been delivered to thebearing.

(d) As the pressure in the supply line is vented down to 70 bar (7 MPa), the slide valve movesback to its rest position. Flow of lubricant to the bearing is closed and simultaneouslyallows lubricant to flow to the upper (larger diameter) of the piston. The displacement offluid on the lower side of the measuring chamber is also allowed by the slide valve to flowto the upper side of the piston. The injector is recharged by the residual pressure in thesupply line to the upper portion of the measuring chamber.

17.6.3 Relubrication Distributors

Relubrication distributors are typically used for oil and fluid-grease application only. Withrelubrication distributors, lubricant is fed into the storage chambers of the distributors whilethe pump is running and is not dispensed until the main line has been relieved of pressure(relubrication effect). During the storage process, a compressed spiral spring is used to providethe required delivery pressure. After the pressure in the main line is relieved, the lubricant isdischarged to the lubrication point by a spring-loaded accumulator piston in the distributor.The discharge pressures for the lubrication point are determined by the spring force andpiston surface, which can match the feed pump’s maximum working pressure. A relubricationdistributor performs the function of a spring energy store, which has an advantage over theprelubrication distributor in some applications.

This principle is used predominantly in the commercial vehicle sector. Relubrication may bebeneficial when the lubrication point is not continuously open. The pressure in the secondary


Injectorstem

Dischargechamber

Measuringpiston

Slidevalve

(a) Phase 1 (b) Phase 2

(c) Phase 3 (d) Phase 4

Figure 17.9 Operation of single line injector (SLV). Courtesy of Lincoln.


Distributor in initial positionsystem is non-pressurized

Metering nipple

Piston spring

Piston

O-ring

Main line

Collar withsupport ringValve spring

Plug-in connector

Max. delivery pressureof relubrication distributors13.5 bars independent ofpump feed pressure

to lubricationpoint

Valve clearance

Distributor pressurizedmain line pressurized by pump

Distributor feedingmain line relieved of pressure

Figure 17.10 Relubrication injector and the three phases of operation. Courtesy of SKF.

line is maintained until the lubricant can be taken up. Figure 17.10 shows the principle ofrelubrication.

Relubrication distributors feed grease to the lubrication points if the pressure is relieved inthe main line. The maximum pressure is given by the spring which is generally lower thanthe pump pressure. These distributors can therefore only be used for soft greases. For stiffergreases (NLGI 0 and higher), a prelubrication distributor should be used.

17.6.4 Strengths and Weaknesses of Single-Line Systems

Weaknesses

• The venting process limits the maximum distance between the pump and the last distributor/injector. Compared to progressive or two line systems, larger pipe diameters are usuallyrequired.

• Monitoring is more difficult because a separate transducer would have to be placed at eachindividual injector.

• The injectors use elastomer seals which deteriorate faster with contamination.

Strengths

• Each injector services only one lubrication point which is more reliable and precise.• If adjustable distributors are used each injector output can be tuned for each specific bearing.• Having only a single main line makes the installation and design (calculation) relatively

simple.• The system is very flexible. Lubrication points can be added or removed at any point by

adding or removing injectors.• Greases that contain solid lubricants such as molybdenum disulfide or graphite can be used.• The system is not continuously under a high back-pressure which reduces the risk of base

oil separation.


17.7 Dual-Line Lubrication Systems

17.7.1 Description

Dual-line central lubrication systems are designed for medium-sized or large machines witha large number of lubrication points, long lines and harsh operating conditions. Applicationsinclude heavy industry, metal working plants, pulp and paper, mining, mineral processing andcement factories, deck cranes, power plants and more. The system requires two main lines thatare alternately supplied with lubricant. They can be used for higher consistency greases andwhen the distance to the pumping unit is long – up to 100 m or more.

Dual-line distributors need two main lines in order to function. These lines are alternatelysupplied with lubricant by a pump unit. While one main line is pressurized, the other isrelieved. For a complete lubrication cycle both main lines have to be pressurized and relievedone after another. The distributors meter out an adjustable or predefined amount of lubricantper lubrication cycle. The lubricant is either fed directly to the lubrication point or is dischargedby a secondary distributor, usually a progressive feeder (see Section 17.8). Each lubricationpoint must be provided with a distributor port of its own. Figure 17.11b shows a dual-linedistributor. Figure 17.12 shows the sequence of operations in a complete lubrication cycle.During the lubrication pause the metering and control pistons are in their lower end position(Figure 17.12a). First the control piston and then the metering piston move into their upperend positions as soon as main line 1 is pressurized and main line 2 simultaneously relievedby the changeover of the dual-line system (Figure 17.12b). The lubricant displaced by themetering piston is pressed through the control system’s ring groove to the upper outlet port.The lubricant displaced by the control piston is relieved into main line 2. The lubricant pressurein main line 1 remains pending until the dual line system changes over.

After the change over, main line 2 is pressurized and main line 1 relieved in the secondhalf cycle (Figure 17.12c). As a result, first the control piston and then the metering piston arereturned to their initial positions.

(a) System. (b) Distributors.

Figure 17.11 Dual-line central lubrication system. Courtesy of SKF.


Main line 2

Metering piston

Control piston

Main line 1

Plug Lower outlet port

Upper outlet port

Main line 2

Main line 1

Lower outlet port

Upper outlet port

Main line 2

Main line 1

Lower outlet port

Upper outlet port

(a) Initial position. (b) First half cycle. (c) Second half cycle.

Figure 17.12 Sequence of operation in a dual-line distributor.

The lubricant displaced by the metering piston is pressed through the lower groove of thecontrol piston to the outlet port. The lubricant displaced by the control piston is relieved intomain line 1. The lubricant pressure in main line 2 remains pending until the dual-line systemchanges over again.

By removing the plug (Figure 17.12a), the delivery rates of both output ports can becombined forming one output port. One output port then has to be closed by a screw plug anda washer (this is called cross-porting). It is important to note that a port should never be closedwithout removing the plug. This would block the metering piston.

17.7.2 Strengths and Weaknesses of the Dual-Line System

Strengths

• High consistency greases may be used (up to NLGI 4).• The maximum distance between pump and the last distributor/injector can be large.• Lubricant points can be added without changing the main lubrication lines.• A large number of lubrication points are possible.• There are no elastomer seals that may wear.

Weaknesses

• Requires two main lines and double the amount of fittings and mounting hardware.• Metal-to-metal sealing prohibits the use of lubricants with solid additives and decreases the

reliability of the system in the case of contamination.

17.8 Progressive Lubrication Systems

17.8.1 Description

Figure 17.13a shows the layout of a progressive lubrication system. Again, a pump deliversgrease to the main line connected to a distributor, which is now called a progressive feeder ordistributor. In single-line and dual-line lubrication systems the distributors deliver a metered


(a) System layout. (b) Progressive distributor.

Figure 17.13 Progressive lubrication system. Courtesy of SKF.

quantity of grease to the lubrication points almost simultaneously. Progressive feeders deliverthe grease in sequence to the lubrication points.

In progressive systems master and secondary feeders are distinguished.In the case of progressive lubrication the pump provides a nearly constant grease flow

delivered to a master feeder, which again distributes the lubricant to the secondary feeders.From there, the lubricant flows to the lubrication points. This means that the delivered greasevolume depends only the delivery rate of the pump unit. Figure 17.14 shows how progressivefeeders work. The inlet passageway, denotes by the arrow, is connected to all piston chambers1–8 at all times with only one piston free to move at any time. With all pistons at the far right,lubricant from the inlet flows against the right end of the piston A (Figure 17.14a). The lubricantflow shifts piston A from right to left, dispensing lubricant through connection passages tooutlet 2. Then piston B shifts from right to left, dispensing lubricant through outlet 7. Thelubricant flow is directed against the right side of piston C (Figure 17.14c). Subsequently,piston C shifts from right to left, dispensing lubricant through outlet 5. Now lubricant flow isdirected against the right side of piston D. Then piston D shifts from right to left, dispensinglubricant through outlet 3. Piston D’s shift directs lubricant through a connecting passage tothe left side of piston A (Figure 17.14d).

Lubricant flow against the left side of piston A begins the second half cycle, which shiftspistons from left to right, dispensing lubricant through outlets 1, 8 and 4 of the divider valve.

Outputs from adjacent outlets may be combined by installing a closure plug in one or moreoutlets as shown in Figure 17.14e. Lubricant from a plugged outlet is redirected to the nextadjacent outlet in descending numerical order. Outlets 1 and 2 must not be plugged since theyhave no crossport passage to the next adjacent outlet. In Figure 17.14e, outlets 5 and 3 arecross-ported and directed through outlet 1. In this example, outlet 1 will dispense three times


7

5

3

1

A

B

C

D

8

6

4

2

7

5

3

1

A

B

C

D

8

6

4

2

7

5

3

1

A

B

C

D

8

6

4

2

7

5

3

1

A

B

C

D

8

6

4

2

5

3

7

1

(a) (b)

(c) (d)

(e)

Figure 17.14 Schematic and operation of progressive feeders or distributors. The inlet passagewayis connected to all four piston chambers at all times with only one piston free to move at any time.Each of these four pistons consists of three lobes ‘forming a spool valve’ connected to each other by agroove which has a diameter smaller than the cylinder bore, which makes it possible to create connectingpassages. All chambers and lines are always filled with grease but only occasionally pressurized. Thedark lines denote the areas which are pressurized and where flow (will) occur. Courtesy of Lincoln.


as much lubricant as outlet 7. The tube ferrules in outlets 1 and 7 block the cross-port passageso that lubricant flow is only directed through outlets.

System monitoring is important for progressive systems because of the many pistons. Visualsystems and sensors are available for this.

17.8.2 Strengths and Weaknesses of Progressive Systems

Weaknesses

• The whole system may be disabled by blockage of one single outlet.• Large systems will need a complex design and complex calculations.• Adding or removing lubrication points is very difficult.• Adjusting the lubricant output to a bearing is very difficult once the system is set up.• The output grease setting to a bearing is in multiples of the outlet volume of the measuring

piston.• The amount of grease flow through one distributor is limited.• Progressive distributors may lock up when solid additives, such as molybdenum disulfide,

graphite or copper are used.• Progressive distributors may block when the grease becomes hardened due to oil separation

(Oil-Bleeding).• The distributors have to make complete cycles to distribute grease to any connected bearing.

Strengths

• System monitoring can detect a fault if one lubrication point is blocked.• Venting is not needed.• No elastomer seals.

17.9 Multi-Line Lubrication System

In a multi-line lubrication system, the lubricant is delivered from a central reservoir (tank)with a piston pump unit (generally electrically-powered) which is equipped with several pistonpump elements, Figure 17.15.

Multi-line systems are in principle single-point lubricators, whereby the lubrication pointsare supplied from just one pump and from a single reservoir. As a result, all of the lubricationpoints are supplied with the same lubricant. A differentiation, that is, the utilization of differentlubricants, is not possible here. This also applies to lubrication intervals, which are orientedto the same base, dependent on time or load. The pressure losses to be anticipated in thelubrication lines are higher with multi-line systems, due to the spatially larger dimensions incomparison to single-point lubrication and pump delivery rates/time.

17.10 Cyclic Grease Flow

The grease flow characteristics are important factors in the design of lubrication systems. Thelubricating points may vary from a few to 1000 and the length of the piping from a few to


Figure 17.15 Multi-line lubrication system with a progressive distributor. Courtesy of SKF.

150 m, [150]. Other than in the bearing contacts, shear rates are low here. The non-Newtonianfluid behaviour therefore results in a relatively high resistance to flow.

The stationary flow of grease through pipes was described in Section 6.1. The modelsthat were mentioned there are applicable to the pipe flow in lubrication systems. Start-up ofgrease flow associated with yield stress of grease is a challenging problem in intermittentpumping systems where often increasing pumping pressure is required to initiate flow. On theother hand, occasionally less pressure is required after the grease has started to flow due towall-slip [127]. Obviously, this does not apply to very thin greases. Wall-slip is caused by oilseparation close to the wall and the difference between the two pressures depends thereforeon the thickness of the oil layer and the viscosity of the base oil [100]. For the design of thepumping system, the pump should be designed to at least overcome the frictional resistanceposed by the start-up stress [127] and the pressure required for the distributors.

17.11 Requirements of the Grease

17.11.1 Grease Pumpability

Pumpability is the ability of a grease to be pumped or pushed through a system. Morepractically, pumpability is the ease with which a pressurized grease can flow through lines,nozzles and fittings of grease-dispensing systems, [620]. It is one of the most importantcharacteristics of the grease in lubrication systems.


It is not usually possible to derive a statement regarding pumpability in centralized lubrica-tion systems from grease data sheets. Still, in practice, the consistency class specified by themanufacturer is often applied as the single criterion for determining the pumpability of thelubricant, which is obviously weak. A better qualification of pumpability is by the ‘apparentviscosity’, which is determined by measuring the flow rate by pressurized grease in long pipes,see for example Wyllie [622]. In addition, the pressure is measured at various positions alongthe length of the pipe, which gives:

η = π D4�p

128LQ, (17.1)

with �p the pressure drop over a length L , D the pipe diameter and Q is the volume flow.Note that the viscosity is strongly dependent on the temperature and that the pressure losses

increase with decreasing temperature.If the viscosity is not at hand, it may be estimated from the Cone-penetration test (Sec-

tion 16.2.1, p. 339):

ln η = 16.5882 − 5.88. ln Pen. (17.2)

However, this is not accurate.As an indication for the pumpability of greases the so called ‘flow pressure’ can sometimes

be found on lubricant data sheets, Kesternich as per DIN 51805. Here a lubricating grease ina test nozzle is exposed to steadily increasing pressure until a pressure is reached where thegrease emerges from the test nozzle, which is then called the flow pressure for the lubricant(see also Section 16.2.9). However, the dimensions of the test nozzle are very different from thediameters of pipelines and bore holes present in centralized lubrication system components.The results should therefore be regarded as for indication only.

Experience has shown that flow pressures of ≤700 mbar in the operating temperature rangeof the centralized lubrication system may be a good indication for pumpability. However,depending on the grease chemical composition, it could be that a grease with a flow pressureof 400 mbar at −25 ◦C could not be delivered by a pump. So flow pressure as the singleindicator for assessing the pumpability of lubricating grease in the centralized lubricationsystem is not sufficient.

To predict the pumpability of grease in centralized lubrication systems more informationthan flow pressure and pressure loss in the pipe is needed. This will be shown later inSection 17.12.

17.11.2 Venting Pressure for Single-Line Systems

For single-line systems, which use injectors to dispense grease in a measured amount toa bearing, these are activated by pressure and deactivated by a depressurization or ventingprocess. The venting process occurs when some of the grease in the supply line is allowed toflow back to the reservoir. Thus venting of grease is needed for the injectors to set and resetthemselves for the next lubrication cycle. The ventability of a grease is primarily determinedby the remaining pressure in the pipes when the pump pressure is back to nearly zero and


3000

2500

2000

1500

1000

500

00 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

1817180317411889206924942081168414951583

Time [s]

Tra

nsdu

cer

pres

sure

[P

sig]

Figure 17.16 Venting process starting at different pressures [136].

grease is allowed to freely flow back into the reservoir. This remaining pressure is given bythe yield stress of the grease. Figure 17.16 shows the result of venting starting at differentpressures. Note that the remaining pressure is a function of the yield stress only and thereforeindependent of the initial pressure.

17.11.3 Oil Separation/Bleeding

Oil and thickener may separate (bleed, see Chapter 7), which leads to a (local) consistencychange (hardening). The tendency to oil separation is lubricant-specific but it is acceleratedby external factors such as vibrations, temperature and pressure. Assuming that grease can beregarded as a porous medium, Darcey’s law applies, which means that the oil flow throughgrease is proportional to the applied pressure and inversely proportional to the base oil viscosity.

This hardening may lead to problems. First of all, the pressure losses of the affectedcomponents and connections with lubricant feed increase, ultimately leading to blockage ofthe feed-through [76] and the failure of the lubricant feed and possibly the breakdown of thelubrication system.

17.11.4 Cleanliness

The lubricant must be generally free of foreign substances. Contaminants cause and acceleratewear and corrosion at the contact points of the components of the centralized lubricationsystem.

Experience has shown that the improper storage of opened drums is the main source ofcontamination of lubricating greases. Collection of moisture in the drum should be avoided atany time and drums should be stored at temperature ranging between 5 ◦C and 35 ◦C.


17.11.5 Compressibility

Lubricating grease may contain air pockets, which could be visible as air bubbles. However,these air pockets are usually so small and dispersed that they are not visible to the nakedeye. Even though the lubricant manufacturers use venting equipment in the process during themanufacture of the lubricant, it can as a basic rule be assumed that air pockets are present in thelubricants. For the grease in the bearing, the air bubbles are squeezed out from the inlet of theEHL rolling element–ring contacts. Hence, they will not be present inside the EHL contactsand therefore not contribute to the compressibility of the lubricant here. In lubrication systemsthis does not apply. Here these bubbles could lead to uncontrolled system behaviour in thecentralized lubrication system, just as they do in almost every hydraulic system. Particularlyaffected are the functions connected with the priming and feeding of the lubricant, the pressurebuild-up ([164]) and the time required for this purpose, as well as to system monitoring.

Air bubbles in the priming area of the pump, depending on the size of the air pockets, couldlead to a reduced feed quantity or even to the breakdown of the feed. In the case of large airpockets, it is sometimes not possible with piston pumps to compress the air up to the pressurevalue, which is necessary for opening the discharge valve of the pumps, due to the labyrinthseals which are usually found in the feed area of the pump (seals over fitted pistons). The airis pressed back into the reservoir through the sealing gap of the fitted piston with the pressuregenerated with the delivery stroke. The lubricant film which is as a rule present between thepiston and the piston bore hole and which normally provides an additional seal is often not ofhelp here either.

Smaller air pockets are usually delivered together with the lubricant into the main line andthen from there into the conventionally branched network of main and lubrication lines. The airwhich is fed in the system increases the ‘compressibility’ of the enclosed air–grease mixture,with the result that the time required for the pressure build-up can be prolonged considerably.

Special attention must be paid to the correct functioning of filling aids. The reservoirs for thelubricant pump should contain as few air bubbles as possible. Furthermore, it is advisable tocheck the lubricating grease in the container from which filling is to take place for air pockets.Filling with ladles or grease spatulas is not advisable.

17.11.6 Homogeneity

The lubricant must exhibit a uniform consistency and may not be divided up into liquid,semi-fluid and solid phases. Occasionally pools of oil will be seen on the surface of openeddrums, the source of which is to be found in oil separation. Under no circumstances shouldan attempt be made to ‘stir down’ the oil with a spatula or other aid. As a rule, the oil–thickener composite would thereby only be seemingly restored, and the effect would not belasting. Furthermore, air becomes mixed in with the lubricating grease during stirring, whichincreases the compressibility (Section 17.11.5).

17.11.7 Additives

A wide range of additives are used in lubricating greases. Examples are antioxidants, metaldeactivators, anti-corrosion protection, anti-wear protection and so on. Furthermore, additives


such as solid lubricants and adhesion enhancers/tackifiers are also used. The influence ofadditives/tackifiers (Section 5.10), with the exception of solid lubricants, has not yet beensystematically investigated.

Solid substance additives such as graphite or molybdenum disulfide (MoS2) can for theirpart lead to deposits in the lubrication vessels, in the pump, in the valves and in the distributors.Care should be taken to ensure that the number and particle size are such that they remain insuspension in the lubricant. Filters should not intercept these additives.

As a rule of thumb, the particle size should be smaller than 10 μm and the concentrationless than 8%.

17.11.8 Compatibility

Similarly to bearing seals and cage materials, seals and plastics in lubrication systems maynot be compatible with the lubricant either. The reader is referred to Section 14.5.

17.11.9 Delivery Resistance or Pressure Losses

The pressure that is required to deliver the lubricant to the lubrication points is called the‘pressure loss‘ and depends on many parameters but essentially on the lubricant and itsconsistency/viscosity, the internal diameter of the pipes used and on the amount of lubricationdelivered per time unit by the lubricant pump. The pressure required to actuate the distributorand to overcome the flow resistance in the secondary lines towards the lubrication point shouldbe added to this.

The consistency/viscosity of the lubricant depends also on the ambient temperature, sodifferent resistances (pressures) may not only arise for different lubricants at identical temper-atures but also for the same lubricant with changing temperatures.

Knowledge of the anticipated pressure losses is of great importance for the design, par-ticularly with large-area centralized lubrication systems. After all, the pressure loss largelydetermines the restrictions on pipeline lengths, diameter of the pipelines and, last but not least,the dimensioning of the feed pump.

For cost reasons and to minimize the stored grease in the system, the diameter of pipelines ischosen to be as small as possible. Smaller volumes in the pipes make it possible to replace thegrease more rapidly and will reduce the risk of aging of the grease (Chapter 8). In addition, thelubricant will have less time available for oil separation. However, if this leads to considerablyhigher pressures, then the latter may be counteracted again by increased oil separation due tohigher pressures.

A description of the various tests related to grease flow resistance, flow ability and and oilseparation will be given in the next section.

17.12 Grease Pumpability Tests

The header ‘pumpability’ refers to all requirements for a lubricant to make it suitable foroperation in a lubrication system.


There are no standardized test methods for qualifying a grease for a lubrication system.As mentioned above, the flow pressure test (DIN 51805) is mainly used. Alternatives usingrheology are new developments, [453], but not established. In this chapter the SKF greasepumpability test R© will be described. The test consists of the following aspects:

1. Flow ability:(a) Flow resistance (FTG5);(b) compressibility (FTG1);(c) pressure venting (FTG3 and Lincoln Ventmeter).

2. Delivery(a) Flow pressure;(b) unworked penetration;(c) deliver index for the pump unit (FTG4);(d) functioning of the pump unit.

3. Oil separation (and hardening): grease hardening under pressure (FTG2).

Flow ability comprises flow resistance, compressibility and pressure venting. The delivery testaddresses the flow rates and pumps. In the oil separation test the ability of the grease to notblock the system by means of ‘thickener separation under high pressure’ is measured. In thenext sections the test will be described in more detail.

17.12.1 Flow Ability

Flow Resistance

The FTG5 test set-up consists of three metre-long pipes, with inner diameters 7, 16 and 24 mm,where the pressure is measured at the entrance, in the middle and at the end of the pipe. Thepressure drop is measured for flow rates of 1, 2, 5, 10, 50, 100 and 200 ml/min, each attemperatures of at least 20 ◦C, 0 ◦C and −20 ◦C. The results provide valuable informationfor the selection of the pump units and the dimensioning of the main lines of the lubricationsystem. Figure 17.17 shows an example of the delivery resistance test for a lubricant at varioustemperatures, depending on the mass flow and the inner diameter of the pipes. Similar testscan be found in, for example, Wyllie [622]. The results from the FTG5 test can also beused to calculate the grease viscosity. As described in Section 6.1.2, for power-law fluidsd ln P/d ln �Q = n, which is the slope of the curves in Figure 17.17. The viscosity at thewall of the pipe reads:

ηw = τw

γw

= π D4�p

32LQ

[3 + d ln Q

d ln �p

]−1

. (17.3)

Through having this viscosity, the same equation can now be used to design the pipe diameterand pipe length for any pressure gradient.


Grease Deliver Resistance (FTG5) 20°C

Pre

ssur

e dr

op [b

ar/m

]

10.0

0.1

0.01

1.67

0.32

0.07

2.23

0.47

0.07

0.58

0.10

0.67

0.10

0.83

0.10

2.50 2.97 3.67 3.97

0.97

0.13

4.37

1.10

0.13

5 20 50 100 200 [g/min]10

10 x 1,5mm/20°C

22 x 3mm/20°C

30 x 3mm/20°C

1.0

Figure 17.17 Example of the FTG5 flow resistance test for three pipes with different diameters.

Compressibility

As was described in Section 17.11.5, grease may contain air pockets making it compressibleat already lower pressures. Compressibility is a function of lubricant type, its air content,pressure and temperature. An example is shown in Figure 17.18.

The compressibility can be measured with the FTG1 set-up, Figure 17.19, where the cylindercontaining the grease sample is closed at one end and pressurized by a piston at the other end.The compressibility is calculated from the displacement of the piston.

4.5%

4.0%

3.5%

3.0%

2.5%

2.0%

Com

pres

sion

1.5%

1.0%

0.5%

0.0%10 20 30 40 50

Pressure [bar]

V5

V1

60 70 80 90

V1 – V2

V1

Figure 17.18 Example of measured compressibility in the FTG1 test set-up for a Li grease with mineralbase oil at 25 ◦C. V1 is the original volume, V2 is the compressed volume and V5 is the compression set,see Figure 17.20.


Figure 17.19 Grease compressibility test FTG1. Courtesy of SKF.

The pressure is normally increased in steps from 10 bar to 90 bar where a pressure relief iscarried out before each step. The pressure can be relieved to 0 bar or to pressure correspondingto the residual pressure to be expected in the lubrication system. The test volume is deliberatelykept small in order to avoid errors caused by air pockets which are more likely to be presentwhen larger-sized volumes are used.

The decompression rate is also measured. Figure 17.20 schematically shows the compressionand pressure relief. A sample with volume V1 is compressed, leading to a volume V2. When thepressure is released the volume V2 grows with a volume V4 to V3 due to elastic compression.

Sample volume

V1

Pressurized

V2

Pressure released

V3

V4

V5Compression setF

Elastic part

Figure 17.20 Schematic representation showing compression and decompression of grease. Courtesyof SKF.


The volume difference between the original volume V1 and the volume after pressure releaseV2 is caused by nonreversible compression of the solid material in the grease, that is thickenermaterial and additives.

Pressure Venting

The pressure relief characteristic describes the pressure decay after pressurizing the greasein the lubrication system (see Section 17.10). The dominating parameters are outlet pressure,inner pipe diameter, pipeline length, temperature and lubricant type.

Ventmeters such as the Lincoln Ventmeter and the FTG3, Figure 17.21, were developedas an instrument to measure the flow limits of grease. They are more precise than the classicNLGI number rating. The Lincoln Ventmeter was developed in the early 1950s and since 1965has been used extensively in determining acceptable performance out of a single line injectortype centralized lubrication system [502].

Actually the instruments measures the yield stress of the grease, which is a measure forthe ventability of the grease, that is the ability of the grease to facilitate a pressure reliefin the lubrication system after the lubrication event. Figure 17.22 shows the schematic ofFigure 17.21a and Figure 17.23 a typical measurement result from the FTG 3 unit.

In the Lincoln Ventmeter the sample of grease is charged to 12.4 MPa through a greasegun. Next, a relief valve (Valve 1 in Figure 17.22) is opened and the grease is discharged.The discharge of the grease will reduce the pressure. The pressure left in the system is read30 seconds after the relief valve is opened.

(a) Lincoln Ventmeter [134]. Courtesyof Lincoln.

(b) FTG3 Ventmeter. Courtesy of SKF.

Figure 17.21 Some examples of Ventmeters.


Checkvalve

Pump(lever gun)

Valve 1

25 ft. Ø 1/4 in.coiled tubing

Pressureguage

Valve 2

Figure 17.22 Lincoln Ventmeter schematic. Reproduced from Conley and Grach, 2006 C© Taylor &Francis Group.

If the pressure gauge reading goes to zero within the 30 seconds, this is an indication thatthe grease has effectively no yield limit. Very light viscous grease behaves like oil and can beconsidered Newtonian. With lower temperatures or stiffer greases, the pressure gauge readingwill be some value other than zero. Even for relatively stiff lubricating greases, 30 seconds isenough time to reach such low shear rates that the shear stress is very close to the yield stress.After these 30 seconds, the pressure gauge reading is the Ventmeter pressure pv or ‘yield stresspressure’. The test is conducted normally at ambient, −1 ◦C and −18 ◦C. Tests are often doneat progressively lower temperatures to establish a value when the grease ceases to flow. Withthe FTG3 the tests are normally done at 25 ◦C, 0 ◦C and −25 ◦C.

The yield stress (or pressure) is given by

τy = pv D

4L, (17.4)

with D the diameter of the tube, pv the Ventmeter pressure and L length of the tube. Fora single-line system, after the system is charged the grease must vent back to the reservoir.

140

120

100

80

60

40

20

00.02 0.20 2.00

Time [s]

Pre

ssur

e [b

ar]

20.00

Figure 17.23 Typical test result from FTG3 at 25 ◦C, 0 ◦C and −25 ◦C. Courtesy of SKF.


Injectors used in most single-line systems reset after the system pressure has vented downbelow 4100 kPa (600 psig). This means that the yield pressure should be lower than this valueto allow the system to vent down below 4100 kPa (600 psig), and to reset the injectors for thenext lubrication cycle.

More information can be found in Conley and Grach [134], Conley and Shah [136] and Heand Conley [251].

The Lincoln Ventmeter also offers the possibility of estimating the grease viscosity [251].A reasonable assumption is that the shear stress at a shear rate γ = 1 is a factor 1.5 higher(see e.g. Gow [230]). In that case, assuming a power fluid

τ = K γ n−1. (17.5)

K = 1.5τy . So

η = 1.5τy γn−1. (17.6)

Recently a method has been developed to also measure the shear thinning exponent n with thisinstrument [135]. However, this may also be guessed. Experience has taught that the powerlaw index n = 0.20 when the Lincoln Ventmeter reading is P ≤ 300 psi and n = 0.25 whenthe Lincoln Ventmeter reading is 300 < P ≤ 500 psi.

Example: Determine the yield stress of the grease

The Lincoln Ventmeter uses a 1/4 inch (0.635 cm) diameter tube and a length of 300 inches(7.62 m). The Ventmeter is charged to 1800 psig (12.4 MPa). After opening the valve, allowingthe grease to vent, the pressure drops to 400 psig (2.76 MPa) after 30 seconds. So the yieldstress is

τy = 2.76 × 106 × 0.00635

4 × 7.62= 575 Pa. (17.7)

Example: Determine the venting pressure in a single-line system

In the case that a lubrication system is used with a pipe of 25 metres and diameter of 1 cm,the venting pressure would be

pv = 4Lτy

D= 4 × 25 × 575

0.01= 5.75 MPa. (17.8)

17.12.2 Delivery Test

The delivery test consists of several individual tests, all related to ‘grease delivery’. Normallythe tests are done at three temperatures: 25 ◦C, 0 ◦C and −25 ◦C and always with the samepump. Obviously for applications running under more extreme conditions it is necessary torun such a test at other temperatures.


Flow Pressure

The flow pressure measurements can be carried out according to DIN 51805 (as earlierdescribed in Section 17.11.1). The flow pressure test is relatively simple and can therefore alsobe used to to find quality deviations for different charges/batches. The limiting values of flowpressure that are sometimes specified for lubrication systems should be used as guidelinesonly. They cannot be used to determine the overall grease pumpability.

Grease Unworked Penetration

Grease in the reservoir is unworked and grease that has passed a pump could be regarded as‘worked grease’. Therefore both worked and unworked penetration values are relevant. Mea-surements are usually done at temperatures of 25 ◦C, 0 ◦C, −10 ◦C and −25 ◦C. The tempera-ture decrease is stopped as soon as the flow pressure has reached 1000 mbar. The worked pene-tration is measured according to DIN ISO 2137 (as earlier described in Section 16.2.1) and canbe measured only at 25 ◦C to compare the results with the given values from the grease supplier.

In addition to these well-known test procedures some more tests are necessary to determinethe degree of grease filling in the delivery chambers of the pump elements at changing ambienttemperatures.

Delivery Index for the Pump Unit

The filling grade of the delivery chamber of a piston pump is given by its design, its operationand by the rheological properties of the grease. For example for a very stiff/high viscous greasethere may not be enough time for the delivery chamber in a piston pump to fill during thedownwards stroke of the piston. The filling grade of the delivery chamber of the pump is mea-sured by means of the ‘grease delivery index’. It is defined by the ratio of the volume of greasedelivered at the output during one minute and the theoretical maximum volume. Figure 17.24shows typical test results for two different pump units at two operating temperatures.

1.20

1.10

1.00

0.90

0.80

0.70

0.60

0.50

Gre

ase

deliv

er in

dex

0.40

0.30

0.20

0.10

0.001 10 100

Time [minutes]

Pump A at –30 °C

Pump B at –30 °C

Pump B at –25 °C

Pump A at –25 °C

Figure 17.24 Typical test results of the delivery index test for two different pump units at two operatingtemperatures.


Oil Separation Test

Oil separation in lubrication systems should be tested under pressure. Examples can be foundin Wyllie [623], for example, who tested separation using a system pressurized by a springloaded piston, or in Miller [422] where a short description of 16 different oil separation testscan be found. Ideally, to test oil separation for modern lubrication progressive systems the testpressure should be about 20 bar, which is a typical value of the back pressure when the pumpis stopped.

Figure 17.25 shows the FTG2 oil separation test unit, which is based on the work of Marawe[398, 399]. This set-up simulates the thin gap of the piston ring in a centralized lubricationprogressive system. A cylinder is filled with a defined grease volume which is compressed bya piston to 20 bar. The cylinder is sealed by means of a thrust plate with a test filter placedon top. A hard core is formed which grows from the bottom towards the piston. The base oilwhich separates is collected on the thrust plate and in the filter.

Normally after 24 hours the displacement of the piston is measured and multiplied with thepiston surface to determine the oil separation. At the end of the test the pressure is released, avalve is opened and the remaining grease is pushed out until the piston touches the hardenedcore, mainly consisting of thickener material. Again the displacement is measured, giving theheight of the hardened core. With this, the volume of thickener from which the oil has beenbled out can be calculated, assuming a 100% oil separation. There may be some residual oilleft in the crusted residual grease. However, this can be neglected. The ratio of this volumeand the original grease volume is called the ‘percentage thickener material’.

Figure 17.26 shows the various modes of operation. Excessive oil separation under pressureshould be avoided. This means that ideally the hardened thickener core (percentage greasethickener material) should be small and that the hardening (displacement of the the pistonduring the test) should also be small. Figure 17.26 also shows the results of measurementscarried out on three samples of the same lubricating grease of the same batch at temperatures

Valve

Piston

Grease

Hardened grease core

Base oil

Thrust plate

Test filter

(a) FTG2. (b) Schematic presentation FTG2.

Figure 17.25 Oil separation test. Courtesy of SKF.


Operation not recommended

25 °C

30 °C

40 °C

50 °C

Har

deni

ng

Qualified operation possible

Standard operation

Percentage thickener material [%]0 5 10 15 20 25 30

Figure 17.26 FTG2 test: hardening is measured by the displacement of the piston, which is causedby oil bleeding. Percentage grease thickener denotes the volume fraction of thickener that remains inthe cylinder after the test. The measurement points have been carried out for a specific grease and showincreased bleeding with increasing temperature.

25 ◦C/50 ◦C, 25 ◦C/40 ◦C and 25 ◦C/30◦C. The diagram shows that the critical ‘hardening’ isexceeded above 30 ◦C. Hence, this lubricant would already be critical operating above 30 ◦Cdue to excessive oil separation. Therefore, to prevent oil–thickener separation, excessivelyhigh residual pressures and long lubrication interval times should be avoided in the lubricationsystem with this grease.

ACharacteristics of ParaffinicHydrocarbons

Table A.1 Characteristics of paraffinic hydrocarbons. Modified from Briant, Denis and Parc, 1985 C©Editions Technip.

Visc. (cSt.) Visc. (cSt.) Visc. Pour PointFormula Name 40 ◦C 100 ◦C index (◦C)

n C24H50 n-tetracosane 8.68 2.74 175 50.6n C26H54 n-hexacosane 10.73 3.24 188 56.2C26H54 Ethyl 3-tetracosane 10.8 3.23 182 30.1C26H54 n-butyl 5-docosane 10.6 2.97 141 20.8C26H54 n-butyl 7-docosane 10.4 2.87 128 3.2C26H54 n-butyl 9-docosane 9.92 2.76 124 1.3C26H54 n-butyl 11-docosane 9.65 2.73 128 0C26H54 Di n-butyl 5,14-octadecane 11.24 2.78 83 5.7C26H54 n-amyl 11-heneicosane 9.37 2.68 126 −9.1C26H54 di-n- amyl 6,11-hexadecane 10.9 2.68 70 −16.2C26H54 Pentyl 3, 11-heneicosane 9.64 2.69 120 −40C26H54 Neopentyl 11-heneicosane 10.9 2.83 104 −21C26H52 Cyclohexyl 1-eicosane 15.15 4.05 180 47.9C26H52 Cyclohexyl 2-eicosane 16.3 4.07 162 13.1C26H52 Cyclohexyl 4-eicosane 15.7 3.71 126 16C26H52 Cyclohexyl 9-eicosane 16.1 3.68 115 −2.2C26H52 Cyclopentyl 1-eicosane 13.1 3.72 187 45C26H52 Cyclopentyl 11-eicosane 11.65 3.04 122 −12.7n C28H58 n-octacosane 13.14 3.75 191 61.2n C32H66 n-dotriacontane 18.95 4.92 203 69.2n C36H74 n-hexatriacontane 26.6 6.27 200 75.9n C44H90 n-tetratetracontane 51.3 9.44 170 86.0


References

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Index

π -effect, 124

Abrasive wear, 61Acoustic emission, 96, 328Additives, 4, 25, 28, 29, 36, 37, 56, 61, 68, 117,

145, 179, 304, 401, 406anti-corrosion, 61, 62anti-foam, 40antioxidants, 16, 36, 59, 62, 64, 180, 183bismuth, 65EP/AW, 16, 31, 36, 40, 61–63, 65, 66, 91,

295–299, 301graphite, 66lead, 65molybdenum disulfide, 66tackifiers, 35, 133–135, 402thickener modifiers, 35, 62, 67, 68VI-improvers, 35, 38ZDDP, 65, 298ZnO, 66

Adhesion, 2, 8, 35, 38, 58, 60, 66, 133, 134, 297,402

Aging, 4, 5, 14, 18, 75, 78, 171, 207, 260, 327chemical, 336, 337EHL, 172mechanical, 134, 172, 175–178, 223oxidation, 179shear aging, 104, 149shelf life, 58, 59, 97, 346, 402softening, 172, 176, 319

Air flow, 10, 21, 179, 194, 228

Air in grease, 121, 137, 144, 401, 404Alkanes, 27Alkenes, 27Alkylated aromatic synthetic hydrocarbons, 36Aluminium complex, 59Aluminium soap, 58American Petroleum Institute, 27Angular contact ball bearings, 10, 71, 78, 83, 85,

89, 91, 225, 231, 294, 355, 359, 360,370

Antiwear properties, 40Apparent viscosity, 241Application temperature, 57, 158Aromatic hydrocarbons, 27Aromatics, 27, 29Automatic lubricators, 379Axlebox bearings, 292, 358

Ball versus roller bearings, 91, 158Barus, 46, 47, 204, 218Bearing factors, 71, 76, 78, 79, 81, 91Bearing life, 5, 10, 17, 18, 20, 71, 89, 94, 184,

247, 257, 258, 264, 279, 283, 286, 291,292, 294–298, 300, 301, 304–306

Bearing type, 20, 91Bentonite, 50, 61BeQuiet+, 362Bingham model, 11, 15, 99, 113, 139, 153, 211,

212, 224Bingham number, 141Biodegradability, 26, 32, 65


440 Index

Bleeding, 2, 4, 5, 8–10, 13, 16, 19–21, 50, 52, 59,67–69, 73, 85, 90, 91, 97, 157–159, 161,163, 164, 166, 168, 170, 172, 175, 176,180, 191, 248, 249, 294, 332, 346, 400,402. See Oil separation

from the covers, 159from under the cage, 159oxidation, 161test, 158

Brinelling, 285, 364, 365

Cage, 7, 10, 13, 85, 99, 149, 150, 153, 157, 159,161, 205, 228, 239, 240, 246, 285, 328

bar, 7, 10, 179, 192, 248brass, 16, 190, 365clearance, 151compatibility, 402failure, 40guidance, 85, 95, 151material, 16, 90, 155, 320pocket, 7, 9, 13polymer, 9, 304scraping, 10, 13, 151, 227, 239, 308steel, 190strength, 82temperature, 13

Calcium, 3complex, 51, 53, 59soap, 58sulfonate, 58sulphonate complex, 59

Carbon black, 23, 50Carboxylic acid, 33, 50, 182, 183Casson model, 113, 177, 224Censoring, 267

mixed censoring, 268type I right censoring, 267type II right censoring, 268

Centralized lubrication systems, 4, 379, 380, 399,400, 406

Ceramics, 78, 85, 91Challenging, 152Channelling, 83, 134

grease, 152Characteristic life, 264, 266Characteristic time, 101, 111, 233, 234Churning, 7, 134, 149Clay, 25, 52, 57, 61, 67Cleanliness, 283, 288, 289, 300, 347, 363, 400Clearance, 13, 40, 150, 151, 239, 240

Clearing grease, 152see Channelling, 152

Cohesion, 38, 133Compatibility, 1, 31, 67, 320, 341, 367Compressibility, 35, 47–49, 144, 145, 215, 219,

401, 403, 404Condition monitoring, 96, 180, 327Cone penetration test, 14, 120–122, 331, 339,

358, 374, 399, 403, 409worked, 122, 149, 177, 341, 342

Consistency, 4, 6, 7, 13, 14, 19, 20, 23, 37, 55, 56,58, 59, 66–68, 72, 74, 83, 85, 95, 104, 115,120–122, 134, 145, 152, 157, 162, 166,171, 172, 179, 254, 295, 306, 328, 331,339, 375, 382, 388, 393, 399, 401, 402

index, 15, 115, 131, 146, 209, 223Contamination, 86, 285, 288, 289, 309, 312, 330,

333, 367, 377, 392, 400moisture, 72particles, 286, 288, 305, 313, 316, 317, 319,

328, 332, 333water, 72, 305, 333

Copper, 16, 64, 90, 181, 365, 397Conversion cSt to Pa · s, 43Corrosion, 4, 26, 41, 59, 66, 184, 297, 298, 306,

337, 339, 344, 345, 365, 400, 401inhibitors, 62, 64, 65

Cox-Merz rule, 125Crossover stress, 111, 126Crystallization, 105Cylindrical roller bearings, 1, 7, 10, 12, 17, 78,

91, 95, 149, 159, 160, 229, 241, 245, 246,292, 325, 355

Cylindrical roller thrust bearings, 8, 359

Definition grease, 23Degradation, see Aging, 11Density, 29, 41, 43, 45, 47, 49, 54, 106, 166, 205,

217Depressurization, 387, 399Differential Scanning Calorimetry, 335

Pressure DSC, 188, 336, 373Diffusion, 157, 303, 336, 347Doraiswamy rule, 126Dropping point, 19, 50, 52, 57–59, 61, 67, 72, 73,

92, 120, 175, 343, 374

Elasto-Hydrodynamic Lubrication, 3, 25, 186,192, 257, 287, 291, 304, 401

Electric motors, 157, 296, 353

Index 441

Electrical capacitance, 7, 8, 17, 241, 245,331

Electrical resistance, 12, 249, 255, 295Energy density, 131Entrance length, 145Envelope, 329EP grease, 58EP greases, 16, 66, 97, 350Ester

phosphate, 25phthalate, 34trimellitic, 34

Esters, 24, 25, 27, 30–33, 38, 42, 62, 186,334

dibasic, 32dibasic acid, 32organic, 31phosphate, 35, 65phospites, 65phthalate, 33polyol, 32, 33synthetic polymeric, 35wax, 26

Evaporation, 10, 12, 21, 30, 75, 185–187, 191,227, 309, 325, 347, 375

Extracting oil from grease, 332

Failure probability rate, 257, 259, 280Falling ball viscometer, 102Fatty acids, 30, 33, 50, 51, 53, 55FE8, 17, 71, 359, 370FE9, 17, 71, 89, 157, 246, 247, 279, 351, 360,

370, 371, 375Fibers, 58

breakdown, 10, 16dimensions, 6, 23visualisation, 24

Filling, 7, 13, 21, 82, 83, 90, 94, 95, 150, 170,249, 255, 341, 342, 401, 409

Film thickness, 8, 191Filter, 333, 368, 402, 410

noise, 329Finger test, 133, 136Flow, 152, 155, 349, 403, 409Flow pressure, 349, 399, 403

test, 399, 403, 409Flow pressure test, 403Fracture, 103, 125Free space, 94, 95, 153Fretting, 285, 365

Friction, 1, 3, 4, 7, 10, 13, 14, 24, 32, 36, 44, 45,62, 65, 66, 74, 82, 83, 95, 117, 131, 142,152, 163, 179, 194, 241, 246, 247, 253,257, 275, 285, 359, 370, 372

Darcy friction factor, 142, 143seals, 310, 311, 323start-up, 6, 75

FTIR, 8, 333, 334, 337

Gel, 23, 61, 183point, 112

Graphite, 38, 66, 397Grease definition, 6Grease drain, 325Grease flow, 7, 13, 14, 19–21, 123, 137–139, 142,

145, 149, 152, 153, 208, 317, 319, 340,395, 397, 402

Grease lifeBall versus roller bearings, 158temperature, 75

Grease noise, 65, 67, 198, 330, 362Grease Performance Factor, 77, 353, 355Grease worker, 14, 68, 118, 121, 149, 173,

176–178, 341

Hardening, 179, 400Hazard function, 259, 268Hazard plotting, 268Helix structure, 55Herschel-Bulkley model, 15, 113, 115, 131, 140,

145–148, 208, 210, 223, 224, 314Herschel–Bulkley model, 11, 14, 113High speed, 6, 10, 33, 39, 58, 61, 67, 76, 82, 83,

85, 90, 95, 105, 134, 161, 171, 175, 218,351, 355

test rig RHF1, 352High temperature, 3, 19, 21, 25, 30, 32–34, 36,

38–41, 50, 52, 58, 59, 61, 75, 76, 90, 96,97, 161, 171, 186, 248, 336, 347, 373

High temperature limit, 19, 72, 74, 171, 343, 344,374

High temperature performance limit, 73, 111,357, 374

Homogeneity, 401Homogenization, 105Housing, 7, 9, 13, 94, 95, 149, 151, 152, 155, 288,

290, 295, 296, 306, 325, 344, 356, 357,361, 370–372, 379

Hydrogenation, 27Hysteresis, 104, 105, 132

442 Index

Induction time, 188, 336Inertia effects, 106Inlet shear heating, 210Isoparaffins, 27

Kurtosis, 329

Lacquers, 186Large size bearings, 11, 85, 94, 292, 293, 369Leakage, 3, 12–14, 95, 99, 103, 105, 108, 125,

150, 152, 175, 197, 203, 319, 325, 328,358, 385

Linear voltammetry, 334–336, 373Lithium, 52, 55, 58, 68, 69, 82, 97, 115, 175, 180,

184, 241, 243, 247, 254, 291, 318, 334,335, 356, 357

complex, 51, 52, 59, 88, 147, 179, 306rust inhibitor, 63

Loss modulus, 99, 109–111, 126, 184Low speed, 6, 16, 61, 80, 85, 94, 95, 171, 207,

210, 213, 224, 226, 229, 241, 293–295,297, 306, 375

Low temperature, 19, 27–32, 36, 39, 40, 52, 67,69, 73–75, 119, 120, 131, 327, 348,349

Low temperature limit, 59, 72, 74, 348, 373Low temperature performance limit, 73, 75, 362,

374Lubcheck, 331, 356, 357, 361, 372, 374Lubrication event, 379Lubrication interval, 379Lubrication pump, 378–388, 393, 395, 397,

401–403, 409Lubrication systems, 131, 140, 377

crossporting, 394distributors, 386dual-line, 381injectors, 386main line, 380metering element, 386metering valve, 386monitoring, 382pRelubrication, 387progressive, 381pumpability, 4, 57, 59, 61, 119, 120, 349, 375,

378, 387, 398Relubrication, 390secondary line, 380single line, 381single line distributors, 386

total loss lubrication, 377venting, 386, 399

Lyapunov exponents, 252–255

Magnus effect, 145Maintenance, 327Manual lubrication, 379Maximum likelihood, 269, 272, 276, 280, 281Maximum speed, 82, 85, 90, 95, 375Mean life, 261, 263, 264Mechanical degradation, see Aging, 134Mechanical stability, 14, 20, 32, 50, 58, 59, 61,

67, 69, 90, 152, 171, 173, 176, 183, 225,367

Meniscus, 11, 43, 212–214, 221Metallic contact time fraction, 331Mineral oils, 26, 29, 287, 318Minimum life, 258, 261, 265, 280, 281, 292Minimum load, 76, 82, 89, 236Minimum lubrication, 8Minimum temperature, 57Molybdenum disulfide, 38, 66, 397, 402

Nano tubes, 3Nanotechnology, 66Naphthenes, 27, see NaphthenicNaphthenic, 27–29, 37, 42, 55, 111, 183NLGI number, see Consistency, 104, 121Normal stresses, 126, 316

Oil content, 10, 159, 160, 175, 179, 332, 368Oil life, 187Oil retention, 56Oil separation, 68, 97, 157, 161, 171, 397, 398,

400–403test, 158, 346, 374, 410

Olefins, 28, 29Oswald-de Waele relationship, 115Outer ring rotation, 11, 12, 21, 90, 229Oxidation, 4–6, 10, 12, 13, 16, 18, 19, 26, 29–31,

60, 61, 65, 72, 75, 86, 90, 157, 159, 170,171, 179, 181, 183, 185, 188, 189, 191,333–335, 375

bomb, 336stability, 28, 33, 34, 36, 38–40, 50, 59, 62, 180stability test, 373test, 364

Paint, 33, 36Palacios and Palacios model, 15, 113, 116, 128

Index 443

PAO, 25, 27, 30, 32, 34, 36, 41, 42, 75, 301,318

Paraffinic oils, 27, 42, 44, 55, 413Particles, 105, 145, 179, 316, 402

brass, 90wear, 90, 179, 285, 295

Percentile life, 264, 275Perfluoropolyalkylether, 25, 30, 40, 75PFPE, see Perfluoropolyalkylether, 25Phosphoric acid, 35Pipe flow, 99, 100, 131, 137, 147, 149, 153, 178,

316, 398Polarity, 16, 29, 31, 36, 50, 124, 184Polyalkylene glycols PAG, 25, 31Polybutylene, 38Polybutylene glycols, 31Polyethylene, 61, 66Polyisobutenes; PIBs, 38, 40, 134Polymer grease, 3, 67–69Polymerization, 10, 35, 36, 180, 183, 185–187,

191, 228Polyphenyl ethers, 36, 39Polytetrafluoropolyethers, see PTFE, 61Polyurea, 3, 25, 52, 57, 59, 60, 67, 75, 91, 179,

183, 306Pour point, 25, 28, 29, 31, 33–37, 39, 41, 75, 413Power law model, 14, 15, 116, 128, 139, 140

index, 403, 408Pressure-viscosity coefficient, 25, 42, 102, 103,

204, 304Pressure–viscosity coefficient, 39, 41, 46Probability density, 18, 259–262, 266, 329Prolonged penetration, see Cone penetration

test/worked, 341PTFE, 61Pumping action, 233

R0F, 8, 17, 18, 20, 69, 71, 234, 246, 247, 275,278, 351, 353, 369–371, 374

R0F+, 20, 263, 267, 269, 275, 277, 278, 354, 369,370, 375

R2F, 9, 17, 69, 71, 253, 277, 357, 370, 374Radiation, 37, 39Railway, 358Railway bearings, 173, 292, 357, 359Reaction layers, 301Reduced radius, 200Relaxation time, 102Reliability, 71, 72, 79, 241, 257, 259, 264, 270,

281, 285, 292

Relubrication, 5, 71, 152, 153, 296, 325intervals, 5, 71, 94, 246, 288, 379

Remaining grease life, 327, 328, 334Remaining life, 264, 373Replenishment, 4, 5, 8, 12, 17, 19, 158, 191, 213,

219, 222, 224, 225, 228–230, 234, 243, 255Reynolds’ viscosity equation, 44Rhee-Eyring, 15Rheology models, 115Roelands, 46Roll stability, see Mechanical stability, 173Roll stability test, 173, 341Roughness, 15, 85, 124, 125, 133, 143, 146, 147,

198, 284, 292, 294, 299, 306, 308, 310,311, 323, 328, 331

Ruler, 180, 334, 373

Seal swell, 33Sealing, 296, 309Sealing action of grease, 133, 312Sealing and film thickness, 320Sealing and service life, 324Sealing mechanisms, 309Seals, 31, 78, 152, 309

compatibility, 367Shear modulus, 100, 108Shear stability, see Mechanical stability, 20Shear thinning, 14, 112, 117, 131Shelf life, 58, 59, 97, 171, 179, 346Shields, 296, 306, 309, 371Shock loads, 11, 21, 66, 96Shrinkage, 36, 320Silica, 23, 25, 50, 52, 61Silicones, 25, 30, 39, 48, 66, 75, 123Sisko model, 14, 113, 177Size base oil molecules, 27Size thickener, 23Slow rotation, 11, 295Sludge, 62, 180, 183, 185Soap fiber size, 56Sodium, 3, 50, 58, 241, 291, 292, 306

complex, 59nitrite, 62

Solid lubricants, 62, 66Solidification, 44, 48, 49, 187Solubility, 36, 50, 183Solvability, 16Solvency, 28, 33, 34, 36Space applications, 3, 61, 186Speed range, 6, 82, 241

444 Index

Speed ratings, 82Spherical roller bearings, 1, 2, 7, 8, 10, 12, 17, 77,

78, 94, 153, 199, 231, 233, 241, 245, 292,301, 325, 355, 356, 370

Start-up pressure, 144Start-up torque, 6, 7, 13, 72, 73, 75, 119, 131,

150, 348, 374Starvation, 11, 295Starved lubrication, 212Statistical moments, 329Stirring, 401Storage modulus, 99, 109, 184Storage of grease, 400Stringiness, 134Sudden death, 267, 273, 275–277, 369Swelling, 320Syneresis, 176Synthetic oils, 30System life, 281

Tackiness, 133Tapered roller bearings, 10, 13, 91, 92, 150, 153,

158, 179, 200, 231–233, 293, 298, 300,305, 309, 355, 359, 370, 373

Teflon, 25, 66Temperature window, 6Thermal aging, see Oxidation, 5Thixotropy, ix, 15, 98, 124, 128, 130–132, 144Total Acid Number, 180, 328, 335Tracer material, 9Traction

coefficient, 32, 33, 36fluid, 37, 42motor, 10

Traffic light concept, 72, 343, 344, 353,374

Transient effects, 144Triglyceride, 26Tube viscosmeters, 102Twisted fibers, 55

Vacuum, 186Varnish, 62, 183, 186Varying operating conditions, 132

starts and stops, 10, 132, 336Vegetable oils, 187Vertical shaft, 13, 21, 91, 95, 99, 120, 340VI index, 75Vibrations, 11, 13, 17, 21, 96, 120, 132, 155, 171,

198, 205, 245, 328, 330, 358, 400Visco-elastic material, 99Viscometers, 102Viscosity, 41, 403Viscosity Index, 25Viscosity–pressure–temperature, 45Viscosity–temperature, 44Visualization, 24Vogel’s viscosity equation, 45Volatility, 35

Wall slip, 15, 122–124, 137, 139, 143, 145, 147,149, 153, 398

Walther’s viscosity temperature equation, 45,163

Water, 31, 50, 86, 133, 184, 189, 304, 306Water Spray Off, 133Water-in-oil, 304Weissenberg effect, 127, 136Wetting, 38

marangoni effect, 10Wheel bearings, 373White grease, 66White oils, 28Wohler, 175

Yasutomi, 47Yield Index, 119Yield stress, 14–16, 90, 111, 112, 118–122, 125,

126, 128, 139, 145, 146, 153, 155, 163,172–175, 177, 208, 209, 211, 212, 223,225, 373, 398, 400, 406–408