GUIDE TO LOADANALYSIS FORDURABILITY INVEHICLE ENGINEERING

GUIDE TO LOADANALYSIS FORDURABILITY INVEHICLE ENGINEERING

Editors

P. JohannessonSP Technical Research Institute of Sweden, Sweden

M. SpeckertFraunhofer Institute for Industrial Mathematics (ITWM), Germany

This edition first published 2014 by John Wiley & Sons, Ltd© 2014 Fraunhofer-Chalmers Research Centre for Industrial Mathematics

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Library of Congress Cataloging-in-Publication Data

Guide to load analysis for durability in vehicle engineering / editors, Par Johannesson, Michael Speckert ;contributors, Klaus Dressler, Sara Loren, Jacques de Mare, Nikolaus Ruf, Igor Rychlik, Anja Streit andThomas Svensson – First edition.

1 online resource. – (Automotive series ; 1)Includes bibliographical references and index.

Description based on print version record and CIP data provided by publisher; resource not viewed.ISBN 978-1-118-70049-5 (Adobe PDF) – ISBN 978-1-118-70050-1 (ePub) – ISBN 978-1-118-64831-5

(hardback) 1. Trucks–Dynamics. 2. Finite element method. 3. Trucks–Design and construction.I. Johannesson, Par, editor of compilation. II. Speckert, Michael, editor of compilation.

TL230629.2′31 – dc23

2013025948

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

ISBN: 978-1-118-64831-5

Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India

1 2014

Contents

About the Editors xiii

Contributors xv

Series Editor’s Preface xvii

Preface xix

Acknowledgements xxi

Part I OVERVIEW

1 Introduction 31.1 Durability in Vehicle Engineering 41.2 Reliability, Variation and Robustness 61.3 Load Description for Trucks 71.4 Why Is Load Analysis Important? 91.5 The Structure of the Book 10

2 Loads for Durability 152.1 Fatigue and Load Analysis 15

2.1.1 Constant Amplitude Load 152.1.2 Block Load 162.1.3 Variable Amplitude Loading and Rainflow Cycles 162.1.4 Rainflow Matrix, Level Crossings and Load Spectrum 182.1.5 Other Kinds of Fatigue 20

2.2 Loads in View of Fatigue Design 232.2.1 Fatigue Life: Cumulative Damage 232.2.2 Fatigue Limit: Maximum Load 232.2.3 Sudden Failures: Maximum Load 242.2.4 Safety Critical Components 242.2.5 Design Concepts in Aerospace Applications 24

vi Contents

2.3 Loads in View of System Response 252.4 Loads in View of Variability 27

2.4.1 Different Types of Variability 272.4.2 Loads in Different Environments 28

2.5 Summary 29

Part II METHODS FOR LOAD ANALYSIS

3 Basics of Load Analysis 333.1 Amplitude-based Methods 35

3.1.1 From Outer Loads to Local Loads 363.1.2 Pre-processing of Load Signals 373.1.3 Rainflow Cycle Counting 403.1.4 Range-pair Counting 493.1.5 Markov Counting 513.1.6 Range Counting 533.1.7 Level Crossing Counting 553.1.8 Interval Crossing Counting 563.1.9 Irregularity Factor 563.1.10 Peak Value Counting 563.1.11 Examples Comparing Counting Methods 563.1.12 Pseudo Damage and Equivalent Loads 603.1.13 Methods for Rotating Components 673.1.14 Recommendations and Work-flow 70

3.2 Frequency-based Methods 723.2.1 The PSD Function and the Periodogram 733.2.2 Estimating the Spectrum Based on the Periodogram 743.2.3 Spectrogram or Waterfall Diagram 793.2.4 Frequency-based System Analysis 793.2.5 Extreme Response and Fatigue Damage Spectrum 853.2.6 Wavelet Analysis 863.2.7 Relation Between Amplitude and Frequency-based Methods 873.2.8 More Examples and Summary 87

3.3 Multi-input Loads 913.3.1 From Outer Loads to Local Loads 923.3.2 The RP Method 943.3.3 Plotting Pseudo Damage and Examples 953.3.4 Equivalent Multi-input Loads 993.3.5 Phase Plots and Correlation Matrices for Multi-input Loads 1013.3.6 Multi-input Time at Level Counting 1043.3.7 Biaxiality Plots 1043.3.8 The Wang-Brown Multi-axial Cycle Counting Method 105

3.4 Summary 105

Contents vii

4 Load Editing and Generation of Time Signals 1074.1 Introduction 107

4.1.1 Essential Load Properties 1084.1.2 Criteria for Equivalence 108

4.2 Data Inspections and Corrections 1104.2.1 Examples and Inspection of Data 1104.2.2 Detection and Correction 112

4.3 Load Editing in the Time Domain 1154.3.1 Amplitude-based Editing of Time Signals 1154.3.2 Frequency-based Editing of Time Signals 1264.3.3 Amplitude-based Editing with Frequency Constraints 1364.3.4 Editing of Time Signals: Summary 138

4.4 Load Editing in the Rainflow Domain 1394.4.1 Re-scaling 1394.4.2 Superposition 1414.4.3 Extrapolation on Length or Test Duration 1434.4.4 Extrapolation to Extreme Usage 1504.4.5 Load Editing for 1D Counting Results 1544.4.6 Summary, Hints and Recommendations 154

4.5 Generation of Time Signals 1564.5.1 Amplitude- or Cycle-based Generation of Time Signals 1564.5.2 Frequency-based Generation of Time Signals 163

4.6 Summary 167

5 Response of Mechanical Systems 1695.1 General Description of Mechanical Systems 169

5.1.1 Multibody Models 1705.1.2 Finite Element Models 172

5.2 Multibody Simulation (MBS) for Durability Applications or: from SystemLoads to Component Loads 1735.2.1 An Illustrative Example 1735.2.2 Some General Modelling Aspects 1755.2.3 Flexible Bodies in Multibody Simulation 1785.2.4 Simulating the Suspension Model 181

5.3 Finite Element Models (FEM) for Durability Applications or: fromComponent Loads to Local Stress-strain Histories 1865.3.1 Linear Static Load Cases and Quasi-static Superposition 1885.3.2 Linear Dynamic Problems and Modal Superposition 1895.3.3 From the Displacement Solution to Local Stresses and Strains 1925.3.4 Summary of Local Stress-strain History Calculation 192

5.4 Invariant System Loads 1935.4.1 Digital Road and Tyre Models 1945.4.2 Back Calculation of Invariant Substitute Loads 1965.4.3 An Example 199

5.5 Summary 200

viii Contents

6 Models for Random Loads 2036.1 Introduction 2036.2 Basics on Random Processes 206

6.2.1 Some Average Properties of Random Processes∗ 2076.3 Statistical Approach to Estimate Load Severity 209

6.3.1 The Extrapolation Method 2106.3.2 Fitting Range-pairs Distribution 2106.3.3 Semi-parametric Approach 213

6.4 The Monte Carlo Method 2156.5 Expected Damage for Gaussian Loads 218

6.5.1 Stationary Gaussian Loads 2196.5.2 Non-stationary Gaussian Loads with Constant Mean∗ 223

6.6 Non-Gaussian Loads: the Role of Upcrossing Intensity 2246.6.1 Bendat’s Narrow Band Approximation 2246.6.2 Generalization of Bendat’s Approach∗ 2256.6.3 Laplace Processes 228

6.7 The Coefficient of Variation for Damage 2306.7.1 Splitting the Measured Signal into Parts 2306.7.2 Short Signals 2316.7.3 Gaussian Loads 2326.7.4 Compound Poisson Processes: Roads with Pot Holes 233

6.8 Markov Loads 2356.8.1 Markov Chains∗ 2406.8.2 Discrete Markov Loads – Definition 2426.8.3 Markov Chains of Turning Points 2436.8.4 Switching Markov Chain Loads 2446.8.5 Approximation of Expected Damage for Gaussian Loads 2476.8.6 Intensity of Interval Upcrossings for Markov Loads∗ 248

6.9 Summary 249

7 Load Variation and Reliability 2537.1 Modelling of Variability in Loads 253

7.1.1 The Sources of Load Variability: Statistical Populations 2547.1.2 Controlled or Uncontrolled Variation 2557.1.3 Model Errors 255

7.2 Reliability Assessment 2567.2.1 The Statistical Model Complexity 2567.2.2 The Physical Model Complexity 257

7.3 The Full Probabilistic Model 2587.3.1 Monte Carlo Simulations 2597.3.2 Accuracy of the Full Probabilistic Approach 263

7.4 The First-Moment Method 2637.5 The Second-Moment Method 264

7.5.1 The Gauss Approximation Formula 2647.6 The Fatigue Load-Strength Model 265

7.6.1 The Fatigue Load and Strength Variables 265

Contents ix

7.6.2 Reliability Indices 2667.6.3 The Equivalent Load and Strength Variables 2677.6.4 Determining Uncertainty Measures 2717.6.5 The Uncertainty due to the Estimated Damage Exponent 2737.6.6 The Uncertainty Measure of Strength 2757.6.7 The Uncertainty Measure of Load 2777.6.8 Use of the Reliability Index 2797.6.9 Including an Extra Safety Factor 2817.6.10 Reducing Uncertainties 283

7.7 Summary 284

Part III LOAD ANALYSIS IN VIEW OF THE VEHICLE DESIGNPROCESS

8 Evaluation of Customer Loads 2878.1 Introduction 2878.2 Survey Sampling 288

8.2.1 Why Use Random Samples? 2888.2.2 Simple Random Sample 2898.2.3 Stratified Random Sample 2908.2.4 Cluster Sample 2908.2.5 Sampling with Unequal Probabilities 2918.2.6 An Application 2928.2.7 Simple Random Sampling in More Detail 2938.2.8 Conclusion 294

8.3 Load Measurement Uncertainty 2958.3.1 Precision in Load Severity 2958.3.2 Pair-wise Analysis of Load Severity 3018.3.3 Joint Analysis of Load Severity 301

8.4 Random Sampling of Customers 3038.4.1 Customer Survey 3038.4.2 Characterization of a Market 3048.4.3 Simplified Model for a New Market 3068.4.4 Comparison of Markets 308

8.5 Customer Usage and Load Environment 3088.5.1 Model for Customer Usage 3108.5.2 Load Environment Uncertainty 312

8.6 Vehicle-Independent Load Descriptions 3148.7 Discussion and Summary 318

9 Derivation of Design Loads 3219.1 Introduction 321

9.1.1 Scalar Load Representations 3219.1.2 Other Load Representations 3229.1.3 Statistical Aspects 322

x Contents

9.1.4 Structure of the Chapter 3239.2 From Customer Usage Profiles to Design Targets 324

9.2.1 Customer Load Distribution and Design Load 3249.2.2 Strength Distribution and Strength Requirement 3249.2.3 Defining the Reliability Target 3269.2.4 Partial Safety Factor for Load-Strength Modelling 3289.2.5 Safety Factors for Design Loads 3299.2.6 Summary and Remarks 331

9.3 Synthetic Load Models 3339.4 Random Load Descriptions 335

9.4.1 Models for External Load Environment 3359.4.2 Load Descriptions in Design 3369.4.3 Load Description for Testing 336

9.5 Applying Reconstruction Methods 3369.5.1 Rainflow Reconstruction 3369.5.2 1D and Markov Reconstruction 3399.5.3 Spectral Reconstruction 3399.5.4 Multi-input Loads 340

9.6 Standardized Load Spectra 3419.7 Proving Ground Loads 3429.8 Optimized Combination of Test Track Events 342

9.8.1 Optimizing with Respect to Damage per Channel 3439.8.2 An Instructive Example 3469.8.3 Extensions∗ 3519.8.4 Hints and Practical Aspects 353

9.9 Discussion and Summary 354

10 Verification of Systems and Components 35710.1 Introduction 357

10.1.1 Principles of Verification 35710.1.2 Test for Continuous Improvements vs. Tests for Release 35810.1.3 Specific Problems in Verification of Durability 35910.1.4 Characterizing or Verification Tests 36010.1.5 Verification on Different Levels 36110.1.6 Physical vs. Numerical Evaluation 36310.1.7 Summary 363

10.2 Generating Loads for Testing 36310.2.1 Reliability Targets and Verification Loads 36410.2.2 Generation of Time Signals based on Load Specifications 36410.2.3 Acceleration of Tests 365

10.3 Planning and Evaluation of Tests 36510.3.1 Choice of Strength Distribution and Variance 36610.3.2 Parameter Estimation and Censored Data 36810.3.3 Verification of Safety Factors 37110.3.4 Statistical Tests for Quantiles 373

10.4 Discussion and Summary 379

Contents xi

A Fatigue Models and Life Prediction 383A.1 Short, Long or Infinite Life 383

A.1.1 Low Cycle Fatigue 383A.1.2 High Cycle Fatigue 383A.1.3 Fatigue Limit 384

A.2 Cumulative Fatigue 384A.2.1 Arguments for the Palmgren-Miner Rule 384A.2.2 When is the Palmgren-Miner Rule Useful? 386

B Statistics and Probability 387B.1 Further Reading 387B.2 Some Common Distributions 387

B.2.1 Normal Distribution 387B.2.2 Log-Normal Distribution 388B.2.3 Weibull Distribution 388B.2.4 Rayleigh Distribution 388B.2.5 Exponential Distribution 388B.2.6 Generalized Pareto Distribution 388

B.3 Extreme Value Distributions 389B.3.1 Peak over Threshold Analysis 389

C Fourier Analysis 391C.1 Fourier Transformation 391C.2 Fourier Series 392C.3 Sampling and the Nyquist-Shannon Theorem 393C.4 DFT/FFT (Discrete Fourier Transformation) 394

D Finite Element Analysis 395D.1 Kinematics of Flexible Bodies 395D.2 Equations of Equilibrium 396D.3 Linear Elastic Material Behaviour 397D.4 Some Basics on Discretization Methods 397D.5 Dynamic Equations 399

E Multibody System Simulation 401E.1 Linear Models 401E.2 Mathematical Description of Multibody Systems 402

E.2.1 The Equations of Motion 403E.2.2 Computational Issues 404

F Software for Load Analysis 407F.1 Some Dedicated Software Packages 407F.2 Some Software Packages for Fatigue Analysis 408F.3 WAFO – a Toolbox for Matlab 408

Bibliography 411

Index 423

About the Editors

Par Johannesson (SP Technical Research Institute of Sweden, Sweden) received his PhDin Mathematical Statistics in 1999 from Lund Institute of Technology, with a thesis onstatistical load analysis for fatigue. During 2000 and 2001 he worked as a PostDoc atMathematical Statistics, Chalmers, on a joint project with PSA Peugeot Citroen, where hestayed one year in the Division of Automotive Research and Innovations in Paris. From2002 to 2010 he was an applied researcher at the Fraunhofer-Chalmers Research Centre forIndustrial Mathematics in Goteborg, and in 2010 he was a guest researcher at Chalmers. Heis currently working as a research engineer at SP Technical Research Institute of Sweden,mainly on industrial and research projects on statistical methods for load analysis, reliabilityand fatigue.

Michael Speckert (Fraunhofer Institute for Industrial Mathematics (ITWM), Germany)received his PhD in Mathematics from the University of Kaiserslautern in 1990. From 1991to 1993 he worked at TECMATH in the human modelling department on optimization algo-rithms. From 1993 to 2004 he worked at TECMATH and LMS in the departments for loaddata analysis and fatigue life estimation in the area of method as well as software devel-opment. Since 2004 he has been working at the department for Dynamics and Durabilityat Fraunhofer ITWM as an applied researcher. His main areas of interest are statistical andfatigue-oriented load data analysis and multibody simulation techniques.

Contributors

Klaus Dressler (Fraunhofer ITWM, Kaiserslautern, Germany) received his PhD in Mathe-matical Physics from the University of Kaiserslautern in 1988. From 1990 to 2003 he ledthe development of load data analysis and simulation software for the vehicle industry atTECMATH and LMS International. In that period he initiated and organized the coopera-tion workgroups ‘load data analysis’ and ‘customer correlation’ of the German automobilecompanies AUDI, BMW, Daimler, Porsche and Volkswagen. Since 2003 he has been themanager of the department for Dynamics and Durability at Fraunhofer ITWM with 35researchers, working on load data analysis and simulation topics. He is also coordinat-ing the Fraunhofer innovation cluster on ‘commercial vehicle technology’ where leadingcompanies like Daimler, John Deere, Volvo and Liebherr cooperate with Fraunhofer onusage variability and virtual product development.

Jacques de Mare (Department of Mathematical Sciences at Chalmers University of Technol-ogy and University of Gothenburg, Goteborg, Sweden) received his PhD in mathematicalstatistics in 1975 from Lund University. He worked at Umea University from 1976 to1979 before securing a position at Chalmers University of Technology. He became aprofessor there in 1995. He was a visiting researcher at the University of North Carolinain 1982, at the University of California, Santa Barbara, in 1989, and at Kyushu Universityin Fukuoka, in Japan, in 2004. He is a member of the International Statistical Instituteand was one of the founders of UTMIS (the Swedish Fatigue Network) and a memberof the first board. He is currently working with statistical methods for material fatigue inco-operation with SP Technical Research Institute of Sweden. At Chalmers he has alsoworked in different ways to bring the mathematical and engineering disciplines closertogether.

Sara Loren (School of Engineering at University of Boras, Boras, Sweden) received herPhD in mathematical statistics in 2004 from Chalmers University of Technology: with athesis entitled ‘Fatigue limit, inclusion and finite lives: a statistical point of view’. From2005 to 2010 she was an applied researcher at Fraunhofer-Chalmers Research Centrefor Industrial Mathematics, working with statistical methods for material fatigue. She iscurrently at the School of Engineering at University of Boras.

Nikolaus Ruf (Fraunhofer ITWM, Kaiserslautern, Germany) studied mathematics at theUniversity of Kaiserslautern. He obtained a degree in mathematics in 2002 with a specialtyin optimization and statistics, and a doctoral degree (Dr. rer. nat.) in 2008 for his work onstatistical models for rainfall time series. He has worked as a researcher at ITWM since

xvi Contributors

2008 and focuses on the analysis of measurement data from technical systems, in particularregarding the durability, reliability, and efficiency of vehicles and their subsystems.

Igor Rychlik (Department of Mathematical Sciences at Chalmers University of Technologyand University of Gothenburg, Goteborg, Sweden) is Professor in Mathematical Statisticsat Chalmers University of Technology. He earned his PhD in 1986, with a thesis entitled‘Statistical wave analysis with application to fatigue’. His main research interest is infatigue analysis, wave climate modelling and in general engineering applications of thetheory of stochastic processes, especially in the safety analysis of structures interactingwith the environment, for example, through wind pressure, ocean waves, or temperaturevariations. He has published more than 50 papers in international journals, is the co-author of the text book Probability and Risk Analysis. An Introduction for Engineers, andhas been visiting professor (long-term visits) at the Department of Statistics, ColoradoState University; the Center for Stochastic Processes, the University of North Carolinaat Chapel Hill; the Center for Applied Mathematics, Cornell University, Ithaca; and theDepartment of Mathematics, University of Queensland, Brisbane, Australia.

Anja Streit (Fraunhofer ITWM, Kaiserslautern, Germany) received her PhD in Mathematicsfrom the University of Kaiserslautern in 2006, with a thesis entitled ‘Coupling of differentlength scales in molecular dynamics simulations’. Since 2007 she has been working in thedepartment for Dynamics and Durability at Fraunhofer ITWM as an applied researcher.Her main areas of work are statistical and fatigue-oriented load data analysis.

Thomas Svensson (SP Technical Research Institute of Sweden, Boras, Sweden) received hisPhD in mathematical statistics in 1996 from Chalmers, with a thesis entitled ‘Fatiguelife prediction in service: a statistical approach’. He was a research engineer at SP ofSweden, 1990–2001, Fraunhofer-Chalmers Research Centre for Industrial Mathematics,2001–2007, and returned to work at SP in 2007. He has been Adjunct Professor inMathematical Statistics at Chalmers University of Technology since 2010, and a memberof the Editorial Board for the journal, Fatigue and Fracture of Engineering Materialsand Structures. Since 2008, he has been the chairman of UTMIS (the Swedish FatigueNetwork).

Series Preface

The automotive industry is one of the largest manufacturing sectors in the global community.Not only does it generate significant economic benefits to the world’s economy, but theautomobile is highly linked to a wide variety of international concerns such as energyconsumption, emissions, trade and safety.

The primary objective of the Automotive Series is to publish practical and topical booksfor researchers and practitioners in industry, and postgraduate/advanced undergraduates inautomotive engineering. The series addresses new and emerging technologies in automotiveengineering supporting the development of more fuel efficient, safer and more environmen-tally friendly vehicles. It covers a wide range of topics, including design, manufacture andoperation, and the intention is to provide a source of relevant information that will be ofinterest and benefit to people working in the field of automotive engineering.

In 2006, six leading European truck manufacturers (DAF, Daimler, Iveco, MAN, Scania,and Volvo) commissioned a research project to produce a guide to load analysis orientedtowards fatigue design of trucks. The project was run by Fraunhofer-Chalmers ResearchCentre for Industrial Mathematics (FCC) in collaboration with Fraunhofer ITWM, the SPTechnical Research Institute of Sweden, Mathematical Sciences at Chalmers University ofTechnology, and the industrial partners.

The project included an investigation of the current practice and future needs withinload analysis, together with a survey on the state-of-the-art in load analysis for automotiveapplications. This book, Guide to Load Analysis for Durability in Vehicle Engineering, isthe result of this research.

The guide presents a number of different methods of load analysis, explaining theirprinciples, usage, applications, advantages and drawbacks. A section on integrating loadanalysis into vehicle design aims at presenting what methods are useful at each stage of thedesign process.

The Guide to Load Analysis for Durability in Vehicle Engineering covers a topic usuallypresented in separate works on fatigue, safety and reliability; signal processing, probabilityand statistics. It is up-to-date, has been written by recognized experts in the field and is awelcome addition to the Automotive series.

Thomas KurfessAugust 2013

Preface

This work is the result of a collaboration between researchers and practitioners with aninterest in load analysis and durability but with different backgrounds, for example, math-ematical statistics, applied mathematics, mechanics, and fatigue, together with industrialexperience of both load analysis problems and specific fatigue type problems. The projectstarted in 2006 when the six European truck manufacturers: DAF, Daimler, Iveco, MAN,Scania, and Volvo, commissioned a research project to produce a Guide to Load Analysisoriented towards fatigue design of trucks. The project was run by Fraunhofer-ChalmersResearch Centre for Industrial Mathematics (FCC) in collaboration with Fraunhofer ITWM,SP Technical Research Institute of Sweden, Mathematical Sciences at Chalmers Universityof Technology, and the industrial partners. All the research groups involved have long expe-rience and profound knowledge of load analysis for durability, where the Swedish group(FCC, SP and Chalmers) has the key competencies in statistics and random processes, andthe German group (Fraunhofer ITWM) are experts in mathematical modelling of mechanicalsystems. The complete Guide was available in 2009, as planned, after a joint effort of tenstaff years.

Transport vehicles are exposed to dramatically different operating conditions in differentparts of the world and in different transport missions. The ultimate goal for the manufactureris to make a design that exactly meets the needs of the customers, neither too strong nortoo weak. The requirements need to be converted into, for example, a certain small risk offailure, a proper safety factor, or an economical expected life. In order to make a robustdesign it is as important to have a good working knowledge of the properties of the customerloads, as it is to have good working knowledge of the mechanical behaviour of the materialand structure in question.

In the process of designing a robust and reliable product that meets the demands of thecustomers, it is important not only to predict the life of a component, but also to investigateand take into account the sources of variability and their influence on life prediction. Thereare mainly two quantities influencing the life, namely, the load the component is exposedto, and the structural strength of the component. Statistical methods present useful tools todescribe and quantify the variability in load and strength. The variability in the structuralstrength depends on both the material scatter and the geometrical variations. The customerload distribution may be influenced by, for example, the application of the truck, the driverbehaviour, and the market.

The development of information technology and its integration into vehicles have pre-sented new possibilities for in-service measurements. Further, the design process has alsomoved to the computer. Both these tasks, together with demands for lightweight design

xx Preface

and fuel efficiency, require a refined view on loads and lead to a renewed interest in loadanalysis.

During 2006 an initial one-year project was carried out, with the aim of preparing theground for a Guide to Load Analysis. The project included an investigation of the currentpractice and future needs within load analysis, together with a survey of the state of the artin load analysis for automotive application.

The main project that developed the Guide in 2007–2009 also included several seminarsat the companies, with the aim of spreading the knowledge within the companies. Thethemes of the seminars were Basics on load analysis in 2007, Methods for load analysis in2008, and Load analysis in view of the vehicle design process in 2009.

The Guide presents a variety of methods for load analysis but also their proper use inview of the vehicle design process. In Part I, Overview, two chapters present the scopeof the the book as well as giving an introduction to the subject. Part II, Methods for LoadAnalysis, describes useful methods and indicates how and when they should be used. Part III,Load Analysis in View the Vehicle Design Process, offers strategies for the evaluation ofcustomer loads, in particular the characterization of the customer populations, which leadsto the derivation of design loads, and finally to the verification of systems and components.Procedures for generation and acceleration of loads as well as planning and evaluation ofverification tests are also included. All through the book, the methods are accompanied bymany illustrative examples.

To our knowledge there is no other comprehensive text available covering the samecontent, but most of the results and methods presented in this Guide are distributed inbooks and journals in various fields. Partial information on load analysis for durability ismainly found in journals on mechanics, fatigue and vehicle design as well as in text bookson fatigue of engineering materials, but also in conference and research papers in otherareas, such as signal processing, mathematics and statistics.

Our intended readership is those interested in designing for durability. The audience isprobably advanced design engineers and reliability specialists. Especially, people interestedin durability, fatigue, reliability and similar initiatives within the automotive industry, are thetarget group. The Guide should provide a better understanding of the currently used methodsas well as inspire the incorporation of new techniques in the design and test processes.

Par JohannessonGoteborg, March, 2013

Michael SpeckertKaiserslautern, March, 2013

Acknowledgements

This book springs from the four-year project (2006–2009) Guide to load analysis for auto-motive applications commissioned by six European truck manufacturers: DAF, Daimler,IVECO, MAN, Scania, and Volvo. The project was run by Fraunhofer-Chalmers ResearchCentre for Industrial Mathematics (FCC) in Gothenburg, Sweden, together with FraunhoferITWM in Kaiserslautern, Germany, SP Technical Research Institute of Sweden in Boras,Sweden, and Mathematical Sciences at Chalmers University of Technology in Gothenburg,Sweden.

We are most grateful for the financial support from the industrial partners, as well asthe valuable feedback on the Guide during the project. Among the many people involved,we are especially grateful to Peter Nijman at DAF, Christof Weber at Daimler, MassimoMazzarino at IVECO, Manfred Streicher at MAN, Anders Forsen at Scania, and BengtJohannesson at Volvo.

The Swedish Foundation for Strategic Research has supported the Swedish researchteams through the Gothenburg Mathematical Modelling Centre (GMMC), which is gratefullyacknowledged.

Part OneOverview

1Introduction

The assessment of durability is vital in many branches of engineering, such as the automo-tive industry, aerospace applications, railway transportation, the design of windmills, andoff-shore construction. A fundamental element of the discussion is the very meaning ofdurability. A rather general definition is the following:

Durability is the capacity of an item to survive its intended use for a suitablelong period of time.

In our context, durability may be defined as the ability of a vehicle, a system or a com-ponent to maintain its intended function for its intended service life with intended levels ofmaintenance in intended conditions of use.

The analysis of durability loads is discussed with truck engineering in mind, however,most of the contents are applicable also to other branches of industry, especially for applica-tions in the automotive context. Properties of loads that cause fatigue damage are emphasizedrather than the properties of extreme crash loads or acoustic loads. The fatigue damage mech-anisms are assumed to be similar to those encountered in metal fatigue, but a few commentsconcerning rubber and composite material are given in Section 2.1.5.

In vehicle engineering the purpose of load analysis is:

• to evaluate and quantify the customer service loads;• to derive design loads for vehicles, sub-systems, and components;• to define verification loads and test procedures for verification of components, sub-

systems, and vehicles.

The Guide is divided into three parts, where the introductory part sets the scope. Part II,Methods for Load Analysis, presents different methods with the aim of providing an under-standing of the underlying principles as well as their usage. It is important to know whereand when each method is applicable and what merits and disadvantages it has. Part III,Load Analysis in View of the Vehicle Design Process, is organized according to the bul-let list above, and describes what methods are useful in the different steps of the vehicleengineering process.

Guide to Load Analysis for Durability in Vehicle Engineering, First Edition. Edited by P. Johannesson and M. Speckert.© 2014 Fraunhofer-Chalmers Research Centre for Industrial Mathematics.

4 Guide to Load Analysis for Durability in Vehicle Engineering

Concept

system

subsystem

systemCAE + test

subsystemCAE + test

componentCAE + test

components

CAD /DMU

CAE /physics

CAE /manufacturing

anal

ysis

and

optim

izatio

n

Functional

specification and

target loads

Figure 1.1 The vehicle engineering process

1.1 Durability in Vehicle Engineering

In vehicle engineering the aim is to design a vehicle with certain physical properties. Suchproperties can be specified in the form of ‘design targets’ for so-called ‘physical attributes’such as durability, NVH (Noise Vibration Harshness), handling, and crash safety. Designvariants are analysed, optimized, and verified by means of physical tests and numericalsimulations for the various attributes. An often used view of the vehicle engineering processis illustrated in Figure 1.1, and can be summarized as follows:

1. Concept for the new vehicle (class of vehicles, market segment, target cost, size, weight,wheel base, etc.).

2. Overall targets and benchmarks are defined for the physical properties of the vehicle(performance, durability, safety (crash), acoustics, vibration comfort, etc.).

3. Target cascading: Design targets for the sub-systems and components are derived (chassissuspension, engine, transmission, frame, body, etc.); those targets are again related todifferent physical attributes (durability, NVH, handling, crash, etc.).

4. Design of components, sub-systems and the full vehicle.5. Design verification and optimization by means of physical tests and numerical simulations

on the various levels for the various attributes.6. Verification on vehicle level.

Especially for trucks, durability is one of the most important physical attributes for thecustomer, and therefore durability needs to be highlighted in the development process.The vehicle engineering process in Figure 1.1 needs to be implemented with respect toload analysis for durability. The process illustrated in Figure 1.2 is frequently used in theautomotive industry.

Introduction 5

Requirement ⇒ Design Target ⇒ Verification

customerregionusage

load severityrainflow matrix

PSD

test tracktest rig

CAE simulation

Example of design re-quirements: satisfy cus-tomers in long-distanceoperation in Europe,with design life of 2 mil-lion kilometres, and re-liability index of 3.8.

Derive targets in formof engineering quantitiessuch as load severity,histogram, PSD or testtrack schedule. Repre-sent the load targets interms of time signals.

For example, set up arig test or make a CAEsimulation, in order toverify the design target.

Figure 1.2 An implementation of the vehicle engineering process with respect to load analysis

0 10 20 30 40 50 60 70 80 90 100−100

0

100

200

300

400

Time / min

Load

/ M

Pa

Figure 1.3 A measured service load of a truck transporting gravel

Metal fatigue and other durability phenomena are degradation processes in the sense thatan effect builds up over time. A certain force applied to a structure once or a few timesmay cause no measurable effect, but if it is applied a million times, the structure may fail.Loads in durability engineering need to be studied with regard to the fatigue phenomenonas well as with regard to the vehicle dynamics and the variation in customer usage.

Loads may be displacements (linear or rotational), velocities, accelerations, forces, ormoments. They may represent road profiles, wheel forces, relative displacements of compo-nents, frame accelerations, or local strains. When we talk about load signals, we mean one-or multi-dimensional functions of time as they appear in the vehicle, for example, duringcustomer usage, on test tracks, in test benches, or in virtual environments. Figure 1.3 showsan example of a measured service load, where a stress signal has been recorded for about100 minutes on a truck transporting gravel. There we can observe different mean levelsas well as different standard deviations of different parts of the load. The changes in themean level originate from a loaded and an unloaded truck while the changes in the standarddeviation derive from different road qualities.

6 Guide to Load Analysis for Durability in Vehicle Engineering

1.2 Reliability, Variation and Robustness

The overall goal of vehicle design is to make a robust and reliable product that meets thedemands of the customers; see Bergman and Klefsjo [22], Bergman et al. [23], O’Connor[172], Davis [64] and Johannesson et al. [126] on the topic of reliability and robustness. Inorder to achieve this goal it is important not only to predict the life of a component, butalso to investigate and take into account the sources of variability and their influence on lifeprediction. There are mainly two quantities influencing the life of the component, namely,the load the component is exposed to, and the structural strength of the component. Statisticalmethods provide useful tools to describe and quantify the variability in load and strength, seeFigure 1.4. The variability in the structural strength depends on both the material scatter andgeometrical variations. The customer load distribution may be influenced by the applicationof the vehicle, the driver behaviour, and the market. From a component designer’s point ofview, the varying vehicle configurations on which the component, for example, a bracket,is to be used are yet another variation source. For example, for trucks, the same designmay well be used on semi-trailer tractors as well as on two- and three-axle platform trucks.This adds to the load variation, as these truck configurations have considerably differentdynamic properties. Further, the verification is often performed using test track loads, whichrepresent conditions that are more severe than those of a normal customer. Even though thetest track conditions are well controlled, they also exhibit variation, which is illustrated byits distribution in Figure 1.4.

The conventional strategy for reliability improvement has been to utilize feedback fromtesting and field usage in order to understand important failure mechanisms and to findengineering solutions to avoid or reduce the impact of these mechanisms. Based on pastexperience it has also been the practice to perform predictions of future reliability perfor-mance in order to find weak spots and subsequently make improvements already in theearly design stages. However, the conventional reliability improvement strategy has stronglimitations, as it requires feedback from usage or from testing. Thus, it is fully applicable

Severity

Probabilitydensity

customer loads(service load)

test track loads

structural strength(material + geometry)

Figure 1.4 Distributions of customer loads, test track loads and structural strength