maximum torque of combination threats for spur … · tooth bending failure (breakage) and tooth...

MAXIMUM TORQUE OF COMBINATION THREATS FOR SPUR GEAR

BASED ON AGMA AND JGMA STANDARDS

WU JIA HANG

A project report submitted in partial

fulfilment of the requirement for the award of the

Degree of Master of Mechanical Engineering

Faculty of Mechanical and Manufacturing Engineering

Universiti Tun Hussein Onn Malaysia

JANUARY 2014

iv

This thesis is an approach to investigate the transformation curve of gearing

safety. Two types of tooth failures are known to happen to spur gears. There are

tooth bending failure (breakage) and tooth surface pitting failure. The focus of this

study however will be on the JGMA and AGMA standards of gearing. Different

methods were used to gather relevant data from both standards. JGMA data were

gathered from a source in the internet while AGMA data were calculated with the aid

of Autodesk Inventor spur gear component generator 2013. The most important data

is the allowable torque applied on the gear tooth which can be distinguished into

causing either one of the tooth failures mentioned above. Several materials selected

from the JGMA and AGMA standards with high value of allowable contact stress

compared to its allowable bending stress have a transformation curve from surface

durability to bending strength when its torque values are plotted against number of

teeth. This allows the forming of a combination threats curve for the material. The

curves are useful in determining the maximum torque that can be applied on the spur

gear before failures occur. The threat combination curves are then further developed

into charts that include other parameters like power, angular velocity and pitch

diameters.

ABSTRACT

v

Tesis ini merupakan satu pendekatan untuk mengkaji lengkung perubahan

keselamatan bagi gear taji. Dua jenis kegagalan yang boleh berlaku pada gigi gear

taji telahpun dikenalpasti. Kegagalan tersebut adalah tooth bending failure ( patah )

dan tooth surface pitting failure . Fokus kajian ini walabagaimanapun adalah kepada

standard gear JGMA dan AGMA sahaja . Kaedah yang berbeza yang digunakan

untuk mendapatkan data yang relevan dari kedua-dua standard. Data JGMA telah

dikumpulkan dari sumber di internet manakala data AGMA dikira dengan bantuan

Autodesk Inventor spur gear component generator 2013. Data yang paling penting

ialah daya kilasan maksimum yang dikenakan pada gigi gear yang boleh dibezakan

kepada daya yang akan menyebabkan salah satu daripada kegagalan gigi yang

dinyatakan di atas . Beberapa bahan yang dipilih dari standard JGMA dan AGMA

dengan nilai allowable contact stress yang tinggi berbanding dengan allowable

bending stress mempunyai lengkung transformasi daripada surface durability kepada

bending strength apabila nilai kilasannya diplot terhadap jumlah gigi gear. Ini

membolehkan pembentukan lengkung ancaman gabungan untuk bahan-bahan

tersebut. ( combination threats curve) . Lengkung ini adalah berguna dalam

menentukan daya kilas maksimum yang boleh digunakan pada gear taji sebelum

kegagalan berlaku. Lengkung ancaman gabungan ini kemudiannya akan

dibangunkan seterusnys ke dalam bentuk carta yang akan menggabungkan

parameter- parameter lain seperti kuasa , halaju sudut dan pitch diameter gear.

ABSTRAK

vi

TITLE PAGE

STUDENT DECLARATION ii

ACKNOWLEDGEMENTS iii

ABSTRACT iv

ABSTRAK v

TABLE OF CONTENT vi

LIST OF TABLES ix

LIST OF FIGURES xii

LIST OF SYMBOLS xviii

LIST OF APPENDICES xxi

CHAPTER 1 INTRODUCTION

1.1 Introduction to gears 1

1.2 Background of study 5

1.3 Problem statement 5

1.4 Objectives of study 6

1.5 Scopes and limitations of study 7

1.6 Project planning 7

CHAPTER 2 LITERATURE REVIEW

2.0 Introduction 10

2.1 Gear standards 11

2.2 Gear tooth rating according to AGMA

and JGMA 12

2.3 Spur gear failures 13

TABLE OF CONTENTS

vii

CHAPTER 3 METHODOLOGY

3.1 Gear tooth calculations 15

3.2 AGMA stress equations 16

3.3 JGMA stress equations 19

3.4 The Autodesk Inventor 2013

Gear component generator 22

3.5 Project flowchart 24

3.6 Expected outcome 25

CHAPTER 4 RESULTS AND DISCUSSION

4.1 JGMA Results 26

4.1.1 Material selection and properties 26

4.1.2 Material i) SCM 415 Alloy Steel 27

4.1.3 Material ii) S45C Carbon Steel 32

4.1.4 Material iii) SUS303 Stainless Steel 36

4.1.5 Material iv) S45C Carbon Steel

(No heat treatment) 38

4.1.6 Discussion for JGMA results 40

4.2 AGMA results 42

4.2.1 Material selection and properties 42

4.2.2 A576-1050 Carbon Structured Steel

(1500 rpm) 43

4.2.3 A322 5135 Alloy Structured Steel /

Tooth face hardened (1500 rpm) 51

4.2.4 42CrV6 Alloy Structured Steel

(1500 rpm) 60

4.2.5 A322-5135 Alloy Structured Steel /

Heat Treated (1500 rpm) 68

4.2.6 Discussion for AGMA results 74

viii

CHAPTER 5 CONCLUSION AND RECOMMENDATION

5.1 Conclusion 76

5.1.1 Introduction 76

5.1.2 Result conclusion 77

5.1.3 Recommendation 78

REFERENCES 79

APPENDICES 80

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

Appendix G

Appendix H

ix

TABLE NO. TITLE PAGE

1.1 Types of gears and their categories 2

1.2 Gantt chart for Project 1 8

1.3 Gantt chart for Project 2 9

3.1 Comparison of module and diametral Pitch 16

4.1 Gear materials and its properties for JGMA

standard. 26

4.2 Allowable torque value of SCM415 Alloy Steel

for bending strength and surface durability for

gear module 1.0 - 2.5 and number of teeth 17 – 50 28

4.3 Calculation results for gear module 2.5 and 2000 rpm 31

4.4 Allowable torque value of S45C Carbon Steel for

bending strength and surface durability for gear

module 1.0 – 4.0 and number of teeth 15 – 80 33

4.5 Allowable torque value of SUS Stainless Steel for



4.6 Allowable torque value of S45C Carbon Steel for



4.7 Gear materials and its properties for AGMA

standard 42

4.8 Parameter settings for Autodesk Inventor 2013 gear

generator software 42

LIST OF TABLE

x

LIST OF TABLE


4.9 Allowable torque value of A576-1050 Carbon

Structured Steel for bending strength and surface

durability for gear module 1.0 – 4.0 and number

of teeth 17 – 70 (Gear ratio 2.0) 45

4.10 Allowable torque value of A576-1050 Carbon


durability for gear module 1.0 – 4.0 and number of

teeth 17 – 70 (Gear ratio 4.0) 45

4.11 Calculation results for gear module 3.0 and

1500 rpm for gear ratio 2.0 49



4.13 Allowable torque value of A322-5135 Alloy




4.14 Allowable torque value of A322-5135 Alloy








4.17 Allowable torque value of 42CrV6 Alloy Structured

Steel for bending strength and surface durability for

gear module 1.0 – 2.5 and number of teeth

17 – 70 (Gear ratio 2.0) 62

xi

LIST OF TABLE


4.18 Allowable torque value of 42CrV6 Alloy Structured

Steel for bending strength and surface durability for

gear module 1.0 – 2.5 and number of teeth

17 – 70 (Gear ratio 4.0) 62





4.21 Allowable torque value of A322-5135 heat treated

alloy structured steel for bending strength and

surface durability for gear module 1.0 – 2.5 and

number of teeth 17 – 60 71

4.22 Allowable torque value of A322-5135 heat treated

alloy structured steel for bending strength and

surface durability for gear module 1.0 – 2.5 and

number of teeth 17 – 60 71

xii

FIGURE NO. TITLE PAGE

1.1 Spur gear 2

1.2 Spur rack 2

1.3 Internal gear 2

1.4 Helical gear 3

1.5 Herringbone gear 3

1.6 Straight bevel gear 3

1.7 Spiral bevel gear 4

1.8 Screw gear 4

1.9 Worm gear 4

2.1 Gear tooth breakage 14

2.2 Gear tooth surface pitting 14

3.1 Nomenclature of spur gear teeth 15

3.2 Spur gear generator (design interface) 23

3.3 Spur gear generator (result interface) 23

4.1 Maximum torque of bending strength vs gear

module for SCM415 Alloy Steel. 27

4.2 Maximum torque of surface durability vs gear

module for SCM415 Alloy Steel. 28

4.3 Maximum torque vs number of teeth of SCM415

Alloy Steel for gear module 1.0 – 2.5 29

4.4 Maximum torque vs number of teeth for gear

module 2.5 29

4.5 Maximum torque (Nm) for threat combination

curve: Module 2.5 30

4.6 SCM415 Alloy Steel spur gear selection chart for

module 2.5 31

LIST OF FIGURES

xiii

FIGURE NO. TITLE PAGE

4.7 Maximum torque of bending strength vs

gear module for S45C Carbon Steel. 32

4.8 Maximum torque of surface durability vs

gear module for S45C Carbon Steel. 33

4.9 Maximum torque vs number of teeth of

S45C Carbon Steel for gear module 1.0 – 4.0 34


module 2.5 34


curve: Module 2.5 35

4.12 S45C Carbon Steel spur gear selection chart for

module 2.5 35


module for SUS Stainless Steel 36


module for SUS 303 Stainless Steel. 36

4.15 Maximum torque vs number of teeth of SUS 303

Stainless Steel for gear module 1.0 – 3.0 37


module for S45C Carbon Steel (No heat treatment) 38


module for S45C Carbon Steel.( No heat treatment) 39

4.18 Maximum torque vs number of teeth of S45C Carbon

Steel (No heat treatment) for gear module 1.0 – 6.0 40

4.19 Maximum torque of bending strength vs gear module for

A576-1050 Carbon Structured Steel (Gear Ratio 2.0) 43

4.20 Maximum torque of bending strength vs gear module for

A576-1050 Carbon Structured Steel (Gear Ratio 4.0) 43

LIST OF FIGURES

xiv

FIGURE NO TITLE PAGE

4.21 Maximum torque of surface durability vs

gear module for A576-1050 Carbon Structured

Steel (Gear Ratio 2.0) 44


module for A576-1050 Carbon Structured Steel

(Gear Ratio 4.0) 44

4.23 Maximum torque vs number of teeth of A576-1050

Carbon Structured Steel for gear module 1.0 – 4.0

and gear ratio 2.0 46


Carbon Structured Steel for gear module 1.0 – 4.0



module 3.0/ gear ratio 2.0 47


module 3.0/gear ratio 4.0 47

4.27 Maximum torque (Nm) for threat combination curve:

Module 3.0 and ratio 2.0 48



4.29 Combination threat curve for all modules

(Gear ratio 2.0) 49

4.30 A576-1050 Carbon Structured Steel spur gear selection

chart for module 3.0 and gear ratio 2.0 50

4.31 A576-1050 Carbon Structured Steel spur gear selection


LIST OF FIGURES

xv



module for A322-5135 Alloy Structured Steel

(Gear Ratio 2.0) 51



(Gear Ratio 4.0) 52



(Gear Ratio 2.0) 52



(Gear Ratio 4.0) 53


Alloy Structured Steel for gear module 1.0 – 2.5





4.38 Maximum torque vs number of teeth for gear module

2.5/ gear ratio 2.0 55








(Gear ratio 2.0) 57

LIST OF FIGURES

xvi


4.43 A322-5135 Alloy Structured Steel spur gear

selection chart for module 2.5 and gear ratio 2.0 59

4.44 A322-5135 Alloy Structured Steel spur gear

selection chart for module 2.5 and gear ratio 4.0 59


module for 42CrV6 Alloy Structured Steel

(Gear Ratio 2.0) 60



(Gear Ratio 2.0) 60



(Gear Ratio 4.0) 61



(Gear Ratio 4.0) 61

4.49 Maximum torque vs number of teeth of 42CrV6



4.50 Maximum torque vs number of teeth of 42CrV6








Module 2.5 and gear ratio 2.0 65

LIST OF FIGURES

xvii



curve: Module 2.5 and gear ratio 4.0 65


(Gear ratio 2.0) 66

4.56 42CrV6 Alloy Structured Steel spur gear selection


4.57 42CrV6 Alloy Structured Steel spur gear selection


4.58 Maximum torque of bending strength vs gear module

for A322-5135 Alloy Structured Steel- Heat Treated

(Gear Ratio 2.0) 69

4.59 Maximum torque of surface durability vs gear module

for A322-5135 Alloy Structured Steel – Heat Treated

(Gear Ratio 2.0) 69

4.60 Maximum torque of bending strength vs gear module


(Gear Ratio 4.0) 70

4.61 Maximum torque of surface durability vs gear module


(Gear Ratio 4.0) 70


Alloy Structured Steel – Heat Treated for gear module

1.0 – 2.5 (ratio 2.0) 72


Alloy Structured Steel – Heat Treated for gear module

1.0 – 2.5 (ratio 4.0) 72

LIST OF FIGURES

xviii

Pd = Diametral pitch

m = module

N = Number of teeth

AGMA standards

= Gear bending stress

= Gear bending endurance strength

= Bending factor of safety (AGMA)

= Gear contact stress

= Gear contact endurance strength

= Wear factor of safety (AGMA)

√

LIST OF SYMBOLS

xix

,

JGMA standards

/s)

= Allowable tangential force at the working pitch circle.

= Actual bending stress at the root

= Allowable bending stress at the root

= Actual Hertz stress

= Allowable Hertz stress

xxi

APPENDIX TITLE

A JGMA results – SCM415 Alloy Steel

B JGMA results - S45C Carbon Steel

(Tooth Surfaces Induction Hardened)

C JGMA results – SUS303 Stainless

Steel

D JGMA results – S45C Carbon Steel

(No Heat Treatment)

E AGMA results – A576-1050 Carbon

Structured Steel

F AGMA results – A322-5135 Alloy

Structured Steel (Tooth face Hardened)

G AGMA results – 42CrV6 Alloy

Structured Steel

H AGMA results – A322-5135 Alloy

Structured Steel (Heat Treated)

LIST OF APPENDICES

Gears are defined as toothed wheels or multi-lobed cams which transmit

power and motion from one shaft to another by means of successive engagement of

teeth [1]. Its popularity and usage in various type of machinery as a transmission

component is mainly due to the fact that it is a positive drive and hence the velocity

ratio is constant, it can transmit much larger power as compared to belt and chain

drive, it is especially suitable for transmitting power at low velocity and most of all

the transmission efficiency is very high. Gears range in size from miniature

instrument installations, such as watches, to large powerful gears used in automobiles

and turbine drives for ocean liners.

There are many types of gears and it is common to classify them into 3

categories; parallel axes gears, intersecting axes gears, and nonparallel and

nonintersecting axes gears. Table 1.1 below lists some examples of the gear types

available by axes orientation.

Table 1.1 Types of gears and their categories

Categories of gears Types of gears

Parallel axes gears Spur gear, Spur rack,

Internal gear, Helical gear,

Double Helical gear

(Herringbone gear)

Intersecting axes

gears

Straight bevel gear, Spiral

bevel gear

Nonparallel and

nonintersecting

Screw gear, Worm gear

CHAPTER 1

1.1 INTRODUCTION

2

The gear types in Table 1.1 are further explained below: (From Ref.[2])

a) Spur Gear – This is a cylindrical shape gear, in which the teeth are

arranged parallel to the axis. It is the most commonly used gear with a

wide range of applications and is the easiest to manufacture.

Figure 1.1: Spur gear

b) Spur Rack – This is a linear shaped gear which can mesh with a spur gear

with any number of teeth. The spur rack is a portion of a spur gear with an

infinite radius.

Figure 1.2: Spur Rack

c) Internal gear – This is also a cylindrical shaped gear, but with the teeth

inside the circular ring. It can mesh with a spur gear. Internal gears are

often used in planetary gear systems.

Figure 1.3: Internal gear

3

d) Helical gear – This is a cylindrical shaped gear with helicoid teeth.

Helical gears can bear more load than spur gears, and work more quietly.

They are widely used in industry. A disadvantage is the axial thrust force

caused by the helix form.

Figure 1.4: Helical gear

e) Double helical gear (Herringbone gear) – A gear with both left-hand and

right-hand helical teeth. The double helical form balances the inherent

thrust forces.

Figure 1.5: Herringbone gear

f) Straight bevel gear – This is a gear in which the teeth have tapered conical

elements that have the same direction as the pitch cone base line. The

straight bevel gear is both the simplest to produce and the most widely

applied in the bevel gear family.

Figure 1.6: Straight Bevel gear

4

g) Spiral bevel gear – This is a bevel gear with a helical angle of spiral teeth.

It is much more complex to manufacture, but offers higher strength and

less noise.

Figure 1.7: Spiral bevel gears

h) Screw gear – A pair of cylindrical gears used to drive non-parallel and

nonintersecting shafts where the teeth of one or both members of the pair

are of screw form. Screw gears are used in the combination of screw

gear/screw gear, or screw gear/spur gear. Screw gears assure smooth,

quiet operation. However, they are not suitable for transmission of high

horsepower.

Figure 1.8: Screw gear

i) Worm gear – Worm gear pair is the name for a meshed worm and worm

wheel. An outstanding feature is that if offers a very large gear ratio in a

single mesh. It also provides quiet and smooth action. However,

transmission efficiency is poor.

Figure 1.9: Worm gear

5

1.2 Background of study

In a gear design, one of the most important processes is the determination of a

gear tooth rating. The rating of a gear tooth is determined by the loads the gear tooth

is capable of transmitting. Organizations such as the American Gear Manufacturers

Association (AGMA) and the American Petroleum Institute (API) issue Standards

that define gear rating procedures [3]. These standards are widely used in the United

States and some parts of the world.

AGMA or The American Gear Manufacturers Association is the trade group

of companies in manufacturing gears and gearing. AGMA is accredited by the

American National Standards Institute (ANSI) to write all U.S standards on gearing.

In 1993, AGMA became the Secretariat for Technical Committee 60 (TC 60) of ISO.

TC 60 is the committee responsible for developing all international gearing standards.

In designing a gearbox, the designer must take into consideration at least on 4

design details of the gearbox. The designer must address on the gear tooth rating,

bearing rating, thermal rating and the shaft rating in detail to completely rate a

gearbox. It is the purpose of this thesis to focus on gear tooth rating only because it is

the most important gear design parameter and the first step in determining the

gearbox rating as a whole. Gear tooth rating procedures and its significance will be

discussed further in Chapter 2 and 3.

1.3 Problem statement

Gear design is the process of designing a gear and gear design itself is a part

of gearbox design. Gear design is a time consuming process because it includes the

selection of gear types and the calculation of its geometry. This will then take into

account the gear strength, the wear characteristic of the teeth, the suitable material

selection and its alignment. This step is otherwise known as gear tooth rating. It is

mainly time consuming because it involves tedious calculations when the designer

tries to determine its bending and contact stress value. For a spur gear, the

determination of the maximum torque value applied on the gear tooth before it fails

is also helpful in the design and selection process. Any steps or methods to simplify

the gear tooth rating process will help to shorten the time for gear design.

6

Various gear design software exists in the market to help in the calculations,

selection and visualization of the designed gear but they are expensive. For example,

gear design software like EXCEL-LENTTM

developed by EXCEL GEAR, INC

would cost about USD 995 for a single license purchase. Therefore for individuals

who couldn’t afford these design software, any other method that would assist in the

design process would be appreciated.

Various standards on gear exist in the world today. Among the most popular

are ISO gear standards, AGMA standards, DIN standards, JGMA standards and JIS

standards, etc. The practice and usage of these standards differ in every country

mostly depending on the standards’ country of origin. Most developing third world

countries like Malaysia do not have their own standard for gears yet; therefore the

corresponding industries would normally adopt any of the popular standards like

those mentioned above for their usage. In other words, different industry or

companies might practice different set of standards for gears. Because of this, a

general understanding on some of the standards is important for the local industry

especially on gear tooth design parameters.

1.4 Objectives of study

a) To determine the maximum allowable torque applied on spur gears

before failing due to occurring threats such as bending or contact

stress.

b) To create a spur gear selection chart from maximum torque of

combination threats data developed from objective (a) from selected

gear materials. The selection chart can assist gear designers in their

work.

7

1.5 Scopes and limitations of study

a) All gear tooth design parameters used in this study as well as any

charts developed will be based on AGMA and JGMA standards.

b) The gear tooth design parameters utilized for this study would be

limited to maximum torque, surface durability, bending stress, module

and number of teeth.

c) Only standard addendum spur gears will be considered for this study

and the pressure angle is limited to 20°.

d) The gear design component accelerator in Autodesk Inventor 2013

will be used to assist in developing the charts and graphs for AGMA

standards for objective (a) of this study.

e) The focus of this study will only be on ferrous gear materials.

1.6 Project Planning

The Master’s project or MDC10102 is divided into two parts namely

Project 1 and Project 2 to be completed in two academic semesters as a partial

requirement for the Master’s degree in Mechanical Engineering. For the

duration of project 1, there are 14 weeks in total for the student to complete a

report comprising of chapter 1, 2 & 3 to be submitted by week 12 before a

presentation by week 14.

As part of the project planning and time management, a project Gantt

chart is included hereafter for the duration of Project 1 to show the planned

activities and the time taken to achieve it.

8

Table 1.2: Gantt chart for Project 1

Project 1 Activities Weeks of Semester 2 2012/2013

(4th March 2013 – 16th June 2013)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Project title selection Planned Actual

Preparation and

submission of project

proposal

Planned Actual

Literature review Planned Actual

Discussion with

project supervisor Planned Actual * *

Preparations/writings

of project report Planned Actual

Submission of project

1 report Planned Actual

Preparation of

presentation slide Planned Actual

Project 1

presentation

Planned Actual

* Visited UTHM on 12th

– 15th

April 2013 (during week 6 and 7) for further

discussion and to get guidance from project supervisor.

As for project 2, there are also 14 weeks in total for the student to complete

the project before submission of the project report by week 13 then follow by a

presentation on week 14. The following Gantt chart will show the planned activities

throughout project 2 and the time taken to achieve them.

9

Table 1.3: Gantt chart for Project 2

Project 1 Activities Weeks of Semester 1 2013/2014

(17th September 2013 – 27th December 2013)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Data collection for

JGMA Planned Actual

Data collection for

AGMA Planned Actual

Data analysis Planned Actual

Discussion with

supervisor Planned * Actual *

Preparations/writings

of project report Planned Actual

Submission of project

2 report Planned Actual

Preparation of

presentation slide Planned Actual

Project 2

presentation

Planned Actual

* Meeting with supervisor on the 9th

and 10th

November 2013 for progress

evaluation and discussion in Kuching.

2.0 Introduction (Importance of gear tooth rating)

There are basically two methods of manufacturing gear teeth; by using the

generating process and the forming process. Modern gear design is very much

influenced and based on these manufacturing processes. The generating gear rack

profile is important because the designed gear tooth profile will depend on it. In

designing the gear geometry, the designer will select the gear generating rack

parameters such as pitch, module, and tool profile angle, etc. These pre-selected

(typically standard) tool parameters is limiting the possibility of better gear tooth

profile design and gear performance as a result. This gear design method based on

standard tool parameters provides “universality” but not the best possible

performance because it is constrained by predefined tooling parameters.

The theoretical foundation of modern Direct Gear design was developed by

Dr. E.B. Vulgakov in Theory of Generalized parameters [4] but the engineering

implementation of this theory was called Direct Gear Design [5]. This Direct Gear

Design method emphasizes more on the gear tooth parameters instead of the tool

parameters and the manufacturing processes and therefore can maximize gear

performance. In other words, gear tooth rating and its parameters are important

aspects in gear design for performance with efficiency. That is why the process of

gear tooth rating must be done correctly although time consuming.

CHAPTER 2

LITERATURE REVIEW

11

2.1 Gear standards

Various gear tooth rating standards are in used in the world today. For a given

gear, the rating system that is used can give very different answers in the amount of

torque that can be transmitted because certain rating system may have different terms

and formulas for its calculations. If a used or a gear designer is not specific or does

not have a basic understanding of the different rating systems, the reliability of the

gear/design can be affected.

The basis of gearing standards in the United States has been developed by the

participants in the American Gear Manufacturers Association (AGMA) as introduced

under “Background of Study” in Chapter 1. AGMA, having founded in 1916, has

developed rating standards by consensus using volunteers from the gear

manufacturing companies and other interested parties who wish to participate.

Currently, the basic gear tooth rating formulas are in AGMA 2001 (1995).

In Europe, both the German originated specification DIN 3990 and the

AGMA Standards are used. The International Organization for Standardization (ISO)

modified DIN 3990 and released ISO 6336 in 1996 [6].

JIS or Japanese Industrial Standards specifies the standards used for industrial

activities in Japan. The standardization process is coordinated by Japanese Industrial

Standards Committee (JISC) and published through Japanese Standards Association

(JSA). The Japanese industrial standards are organized into divisions and the

standards associated with gears are under Mechanical Engineering division.

JGMA or Japan Gear Manufacturers Association is the only representative of

Japanese gear and gearing industry. The objectives of JGMA is to contribute to the

development of Japanese economy by promoting technical innovation, streamlining

the management and the machine renovation for gear and gearing industry in

Japan. It was organized 1938 and restarted as an incorporated body in 1958.

12

2.2 Gear tooth rating according to AGMA and JGMA

In determining a gear tooth rating, the gear designer must determine the

bending stress and the surface contact stress of the gear before comparing it to a

material strength and durability rating. This process involves a series of calculation

and reference to a number of related charts according to the gearing standards

utilized. If AGMA standards are intended for use, then the following standards will

define and cover the calculations for a gear tooth rating:-

a) ANSI/AGMA 1012-G05 - Gear nomenclature, definitions of terms with

symbols

b) ANSI/AGMA 2101-D04 - Fundamental rating factors and calculation

methods for involute spur and helical gear teeth (Metric Edition) or

ANSI/AGMA 2001-D04 - Fundamental rating factors and calculation

methods for involute spur and helical gear teeth.

For gear accuracy, JGMA will have to refer to Japan Industrial Standards for

gearing namely B 1702 1976-01:1998 - Accuracy for spur and helical gears and

B 1702 1976-02:1998 - Accuracy for spur and helical gears.These two JIS standards

conform to International Standard Organizations (ISO) standards. For definitions of

tooth profile terms and its related formulas, JIS B 1701-02:1999 - Involute gear tooth

profile and dimensions for spur and helical gears will be used.

As in other standards, to determine the gear strength, one has to consider the

bending strength and surface durability of the tooth design. For this purpose, the

relevant JGMA standards are:-

a) JGMA 401-01 1974 - Calculation of bending strength for spur and helical

gears

b) JGMA 402-01 1975 – Calculation of surface durability for spur and helical

gears

13

2.3 Spur gear Failures

There are two types of gear tooth failures considered for this study.

The first one is known as the tooth bending failure (breakage) and the second

one is known as tooth surface pitting failure. Tooth breakage can be the result

of a fatigue mechanism or an overload which exceeds the gear tooth fracture

strength .Destructive fatigue pitting is a result of repeated stress cycling of the

tooth surface beyond the material’s endurance limit [3].

Bending stress and contact stress (Hertz stress) calculation are the

basic of stress analysis and the design of an effective and reliable gearing

system include its ability to withstand RBS (Root Bending Stress) and SCS

(Surface Contact Stress). [9] Contact stress is generally the deciding factor for

the determination of the requisite dimensions of gears. Research on gear

action has confirmed the fact that beside contact pressure, sliding velocity,

viscosity of lubricant as well as other factors such as frictional forces, contact

stresses also influence the formation of pits on the tooth surface [10].

The bending stress is highest at the fillet and can caused breakage or

fatigue failure of tooth in root region. Whereas contact stresses on the side of

the tooth may causes scoring Wear and pitting fatigue. Contact stress is a

compressive stress occurring at the point of maximum Hertzian stress [11].

Bharat Gupta, Abhishek Choubey and Gautam V. Varde [10] in their journal

paper has concluded through their contact stress analysis that hardness of the

gear tooth profile can be improved to resist pitting failure and module is an

important geometrical parameter during the design of gear because maximum

contact stress decreases with increasing module and it will be higher at the

pitch point.

In this study, the allowable torque value associated with bending

stress is the one that will cause the tooth bending failure while the torque

value associated with contact stress will cause the surface pitting failure. The

spur gear will either fail by tooth breakage or surface pitting depending on

which allowable torque value is lower. These two types of spur gear failures

are best described with diagrams as shown in the next page.

14

Figure 2.1: Gear tooth breakage

Figure 2.2: Gear tooth surface pitting

As computer technology becomes more powerful, complicated gear analysis

and simulations have also improved. The finite element method can be utilized with

computers to perform analysis on gears with regards to failures such as bending and

contact stress. Shinde S.P, Nikam A.A. and Mulla T.S. [12] with their journal

“Static Analysis of Spur Gear Using Finite Element Analysis” generated the profile

of a spur gear teeth and predicted the effect of gear bending using a three

dimensional model and compare the results with conventional calculation method.

They found that the simulation results of the finite element analysis have good

agreement with the theoretical results and concluded that numerically obtained

values of stress distributions on spur gear are credible.

3.1 Gear tooth calculations

The first step in designing a gear is to analyze the tooth meshes. The basic

gear tooth limitations in design that are considered and calculated are the fatigue

phenomena of bending/breakage and pitting. Tooth bending is analyzed by

calculating the bending stress in the root fillet area and comparing it against a

material strength rating. Pitting is analyzed by calculating the compressive stress at

the tooth contact and comparing it against a material durability rating. Both of these

procedures apply to AGMA and JGMA standards but their corresponding formulas

might have differences. The figure below shows the basic spur gear teeth

nomenclature which is universal to most standards.

Figure 3.1 Nomenclature of spur gear teeth

CHAPTER 3

METHODOLOGY

16

Diametral Pitch is Pd is the unit to denote the size of the gear tooth. Diametral

pitch is the ratio of the number of teeth on the gear to the pitch diameter. It is normally

used in AGMA standards. The equivalent unite to indicate tooth size in JGMA is called

module, m. Module is the ratio of the pitch diameter to the number of teeth or the

reciprocal of Diametral Pitch.

(Teeth per inch), (3.1)

or

(3.2)

Where

The conversion from Diametral pitch, to module, m is accomplished by the

following equation:-

(3.3)

The table below shows the comparison in value between some module and diametral

pitch extracted from Ref. (2) page 602.

Table 3.1 Comparison of module and diametral pitch

Module, m Diametral

pitch,

0.5 50.8

1.0 25.4

1.25 20.32

1.5 16.93

2.0 12.7

2.5 10.16

3.0 8.46

10.0 2.54

3.2 AGMA stress equations

Gear failure can be caused by teeth bending failure and tooth surface pitting

failure. Teeth bending failure occur when significant tooth stress equals or exceeds

the gear bending endurance strength. Tooth surface pitting failure occurs when

significant contact stress equals or exceeds the gear surface endurance strength.

17

The AGMA gear bending stress equation in S.I metric unit is:

(3.4)

Where

(3.5)

While the AGMA gear bending endurance strength equation in S.I metric unit is:

(3.6)

Therefore the bending factor of safety is:

(3.7)

where

18

For AGMA gear contact stress/pitting, the equation in S.I metric unit is:

√(

) (3.8)

And the gear contact endurance strength equation is:

(3.9)

Therefore, the wear factor of safety is

(3.10)

Where

√

(normally 1.5 minimum)

19

3.3 JGMA stress equations

For JGMA standards, the equations that define tangential force (kgf),

power P (KW), torque T (kgf.m) and tangential speed of working pitch circle v (m/s)

are:

(3.11)

(3.12)

(3.13)

Where

/s)

The transmitted tangential force at the working pitch circle, must not exceed the

allowable tangential force at the working pitch circle, which is calculated

taking into account the allowable bending stress at the root.

(3.14)

At the same time, the actual bending stress at the root, this is calculated on the

basis of the transmitted tangential force at the working pitch circle, must not

exceed the allowable bending stress at the root, .

(3.15)

The formula for (kgf) is:

(

)

(3.16)

20

The formula for is:

(

) (3.17)

Where

For surface durability, the transmitted tangential force at the reference pitch circle,

must not exceed the allowable tangential force at the reference pitch circle,

which is calculated taking into account the allowable Hertz stress.

(3.18)

At the same time, the actual Hertz stress, that is calculated on the basis of the

tangential force at the reference pitch circle, must not exceed the allowable Hertz

stress, .

(3.19)

The allowable tangential force, (kgf) at the reference pitch circle can be

calculated from:

(

)

(3.20)

21

The Hertz stress is calculated from equation:

√

√ (3.21)

Where the symbol “+” in equations (3.20) and (3.21) applies to two external gears in

mesh, whereas the “-“symbol is used for an internal gear and an external gear mesh

and

All JGMA stress equation are extracted from Ref [2] page 663 & 670

For the purpose of this study, calculations of gear tooth design parameters

like bending strength and surface durability based on JGMA standards for different

modules m, number of teeth n, and gear materials will be extracted from spur gear

catalogs (stock gears) of Kohara Gear Industry Co, Ltd available on this website :

http://www.khkgears.co.jp. The results will be plotted in charts for analysis purposes

together with results from AGMA standards.

http://www.khkgears.co.jp/

22

3.4 The Autodesk Inventor 2013 Gear Component Generator

The Autodesk Inventor 2013 component accelerator is a built-in design tool

in the software itself to assist designer in selecting and designing accurate standard

engineering parts like gears, bearings, shafts, disc cams and etc. The spur gear

component generator is able to calculate dimensions and check strength of external

and internal gearing with straight and helical teeth. It contains geometric calculations

for designing different types of correction distributions, including a correction with

compensation of slips.

The spur gear generator calculates the production, checks dimensions and

loading forces, and performs the strength check based on Bach, Merrit, CSN 01 4686,

ISO 6336, DIN 3990, ANSI/AGMA 2101-D04: 2005, or Legacy ANSI [7].

Some of the functions of the spur gear generator is to:

Design and insert one gear.

Design and insert two gears connection.

Insert gears as components, features, or only calculations.

Design gears based on various entry parameters such as number of teeth or

center distance, for example.

Calculate spur gears according to various strength methods, according to

ANSI or ISO, for example.

Perform the calculation of power, speed, or torque.

Perform the material design of spur gears.

For the purpose of this study, the spur gear generator in Autodesk Inventor

2013 will be used to assist in calculation of gear tooth design parameters like bending

strength and surface durability for different gear modules, number of teeth n and

different gear ratio for different gear materials according to ANSI/AGMA 2101-D04:

2005 standard. The results obtained will be plotted in charts for analysis purposes

with results obtained from calculations using JGMA standards. The figures below

show the user interface of the spur gear generator of Autodesk Inventor 2013.

23

Figure 3.2 Spur gear generator (design interface)

Figure 3.3 Spur gear generator (Result interface)

24

3.5 Project flowchart

Start

Discussion with Project

supervisor

Data gathering from KHK gear catalogues

for JGMA standards and Spur Gear

Component Generator for AGMA standards

Data compilation and analysis

Data verification

with project

supervisor

YES

NO

Plot charts/graphs for result

and make conclusion

END

79

References

1. Dr. S.S Wadhwa, Er. S.S. Jolly. Machine Design, A basic approach. New Delhi :

Dhanpat Rai & Co, 2007, Page 546.

2. Industry, Kohara Gear. Gear Technical References. 1996-2013, Page 595-606.

3. Lynwander, Peter. Gear drive systems, Design and Application. New York :

Marcel Dekker, Inc, 1983. Page 93. ISBN 0-8247-1896-8 .

4. A.L. Kapelevich, R.E. Kleiss. Direct Gear Design for Spur and Helical Involute

Gears, Gear Technology. September/October 2002, Page 29-35.

5. Review of API Versus AGMA Gear Standards/Rating, Data Sheet Completion, and

Gear Selection Guidelines. In Proceedings of the Twenty-Ninth Turbomachinery

Symposium (pp. 191-204). Kenneth O. Beckman, Vinod P. Patel. 2000.

6. Vulgakov, E.B. Gears with Improved Characteristics (in Russian).

Mashinostroenie, Moscow : s.n., 1974.

7. Autodesk Wikihelp : Inventor 2013, Spur gear component generator. Autodesk, Inc

Website. [Online] Autodesk, Inc. [Cited: May 29, 2013.]

http://wikihelp.autodesk.com/Inventor/enu/2013/Help.

8. Chee Kiong Sia, Loo Yee Lee, Siaw Hua Chong, Mohd Azwir Azlan & Nik

Hisyamudin Muhd Nor. "Decision Making with the Analytical Hierarchy Process

(AHP) for Material Selection in Screw Manufacturing for Minimizing

Environmental Impacts." Applied Mechanics and Materials 315 (2013): 57-62.

9. Sushil Kumar Tiwari, Upendra Kumar Joshi. " Stress Analysis of Mating

Involute Spur Gear Teeth." International Journal of Engineering Research &

Technology (IJERT), Vol. 1 Issue 9, November- 2012. ISSN: 2278-0181

10.Bharat Gupta, Abhishek Choubey & Gautam V. Varde. "Contact stress

analysis on spur gear." International Journal of Engineering Research &

Technology (IJERT), Vol. 1 Issue 4, June - 2012. ISSN: 2278-0181.

11. Darle W. Dudley, Practical Gear Design, McGraw-Hill Book Company, 1954

12. Shinde S.P, Nikam A.A. and Mulla T.S. " Static Analysis of Spur Gear Using

Finite Element Analysis” IOSR Journal of Mechanical and Civil Engineering

(IOSR-JMCE), ISSN: 2278-1684, PP: 26-31

maximum torque of combination threats for spur … · tooth bending failure (breakage) and tooth...

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