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

ABSTRACT

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.

v

ABSTRAK

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.

vi

TABLE OF CONTENTS TITLE

CHAPTER 1

CHAPTER 2

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

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

LITERATURE REVIEW

2.0

Introduction

10

2.1

Gear standards

11

2.2

Gear tooth rating according to AGMA

2.3

and JGMA

12

Spur gear failures

13

vii

CHAPTER 3

CHAPTER 4

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

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)

4.1.6

4.2

Discussion for JGMA results

38 40

AGMA results

42

4.2.1

Material selection and properties

42

4.2.2

A576-1050 Carbon Structured Steel (1500 rpm)

4.2.3

A322 5135 Alloy Structured Steel / Tooth face hardened (1500 rpm)

4.2.4

4.2.6

51

42CrV6 Alloy Structured Steel (1500 rpm)

4.2.5

43

60

A322-5135 Alloy Structured Steel / Heat Treated (1500 rpm)

68

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

LIST OF TABLE

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.

4.2

26

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

4.5

33

Allowable torque value of SUS Stainless Steel for bending strength and surface durability for gear module 1.0 – 3.0 and number of teeth 15 – 70

4.6

37

Allowable torque value of S45C Carbon Steel for bending strength and surface durability for gear module 1.0 – 6.0 and number of teeth 15 – 70

4.7

Gear materials and its properties for AGMA standard

4.8

39

42

Parameter settings for Autodesk Inventor 2013 gear generator software

42

x

LIST OF TABLE

TABLE NO.

4.9

TITLE

PAGE

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)

4.10

45

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 4.0)

4.11

Calculation results for gear module 3.0 and 1500 rpm for gear ratio 2.0

4.12

49

Calculation results for gear module 3.0 and 1500 rpm for gear ratio 4.0

4.13

45

50

Allowable torque value of A322-5135 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)

4.14

53

Allowable torque value of A322-5135 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)

4.15

Calculation results for gear module 2.5 and 1500 rpm for gear ratio 2.0

4.16

58

Calculation results for gear module 2.5 and 1500 rpm for gear ratio 4.0

4.17

54

58

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

TABLE NO.

4.18

TITLE

PAGE

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)

4.19

Calculation results for gear module 2.5 and 1500 rpm for gear ratio 2.0

4.20

66

Calculation results for gear module 2.5 and 1500 rpm for gear ratio 4.0

4.21

62

67

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

4.22

71

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

LIST OF FIGURES

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.

4.2

Maximum torque of surface durability vs gear module for SCM415 Alloy Steel.

4.3

29

Maximum torque (Nm) for threat combination curve: Module 2.5

4.6

29

Maximum torque vs number of teeth for gear module 2.5

4.5

28

Maximum torque vs number of teeth of SCM415 Alloy Steel for gear module 1.0 – 2.5

4.4

27

30

SCM415 Alloy Steel spur gear selection chart for module 2.5

31

xiii

LIST OF FIGURES

FIGURE NO.

4.7

TITLE

PAGE

Maximum torque of bending strength vs gear module for S45C Carbon Steel.

4.8

Maximum torque of surface durability vs gear module for S45C Carbon Steel.

4.9

40

Maximum torque of bending strength vs gear module for A576-1050 Carbon Structured Steel (Gear Ratio 2.0)

4.20

39

Maximum torque vs number of teeth of S45C Carbon Steel (No heat treatment) for gear module 1.0 – 6.0

4.19

38

Maximum torque of surface durability vs gear module for S45C Carbon Steel.( No heat treatment)

4.18

37

Maximum torque of bending strength vs gear module for S45C Carbon Steel (No heat treatment)

4.17

36

Maximum torque vs number of teeth of SUS 303 Stainless Steel for gear module 1.0 – 3.0

4.16

36

Maximum torque of surface durability vs gear module for SUS 303 Stainless Steel.

4.15

35

Maximum torque of bending strength vs gear module for SUS Stainless Steel

4.14

35

S45C Carbon Steel spur gear selection chart for module 2.5

4.13

34

Maximum torque (Nm) for threat combination curve: Module 2.5

4.12

34

Maximum torque vs number of teeth for gear module 2.5

4.11

33

Maximum torque vs number of teeth of S45C Carbon Steel for gear module 1.0 – 4.0

4.10

32

43

Maximum torque of bending strength vs gear module for A576-1050 Carbon Structured Steel (Gear Ratio 4.0)

43

xiv LIST OF FIGURES

FIGURE NO

4.21

TITLE

PAGE

Maximum torque of surface durability vs gear module for A576-1050 Carbon Structured Steel (Gear Ratio 2.0)

4.22

44

Maximum torque of surface durability vs gear module for A576-1050 Carbon Structured Steel (Gear Ratio 4.0)

4.23

44

Maximum torque vs number of teeth of A576-1050 Carbon Structured Steel for gear module 1.0 – 4.0 and gear ratio 2.0

4.24

46

Maximum torque vs number of teeth of A576-1050 Carbon Structured Steel for gear module 1.0 – 4.0 and gear ratio 4.0

4.25

Maximum torque vs number of teeth for gear module 3.0/ gear ratio 2.0

4.26

49

A576-1050 Carbon Structured Steel spur gear selection chart for module 3.0 and gear ratio 2.0

4.31

48

Combination threat curve for all modules (Gear ratio 2.0)

4.30

48

Maximum torque (Nm) for threat combination curve: Module 3.0 and ratio 4.0

4.29

47

Maximum torque (Nm) for threat combination curve: Module 3.0 and ratio 2.0

4.28

47

Maximum torque vs number of teeth for gear module 3.0/gear ratio 4.0

4.27

46

50

A576-1050 Carbon Structured Steel spur gear selection chart for module 3.0 and gear ratio 4.0

51

xv

LIST OF FIGURES

FIGURE NO

4.32

TITLE

PAGE

Maximum torque of bending strength vs gear module for A322-5135 Alloy Structured Steel (Gear Ratio 2.0)

4.33

51

Maximum torque of bending strength vs gear module for A322-5135 Alloy Structured Steel (Gear Ratio 4.0)

4.34

52

Maximum torque of surface durability vs gear module for A322-5135 Alloy Structured Steel (Gear Ratio 2.0)

4.35

52

Maximum torque of surface durability vs gear module for A322-5135 Alloy Structured Steel (Gear Ratio 4.0)

4.36

53

Maximum torque vs number of teeth of A322-5135 Alloy Structured Steel for gear module 1.0 – 2.5 and gear ratio 2.0

4.37

54

Maximum torque vs number of teeth of A322-5135 Alloy Structured Steel for gear module 1.0 – 2.5 and gear ratio 4.0

4.38

Maximum torque vs number of teeth for gear module 2.5/ gear ratio 2.0

4.39

56

Maximum torque (Nm) for threat combination curve: Module 2.5 and ratio 4.0

4.42

56

Maximum torque (Nm) for threat combination curve: Module 2.5 and ratio 2.0

4.41

55

Maximum torque vs number of teeth for gear module 2.5/ gear ratio 4.0

4.40

55

57

Combination threat curve for all modules (Gear ratio 2.0)

57

xvi

LIST OF FIGURES

FIGURE NO

4.43

TITLE

PAGE

A322-5135 Alloy Structured Steel spur gear selection chart for module 2.5 and gear ratio 2.0

4.44

A322-5135 Alloy Structured Steel spur gear selection chart for module 2.5 and gear ratio 4.0

4.45

59

59

Maximum torque of bending strength vs gear module for 42CrV6 Alloy Structured Steel (Gear Ratio 2.0)

4.46

60

Maximum torque of surface durability vs gear module for 42CrV6 Alloy Structured Steel (Gear Ratio 2.0)

4.47

60

Maximum torque of bending strength vs gear module for 42CrV6 Alloy Structured Steel (Gear Ratio 4.0)

4.48

61

Maximum torque of surface durability vs gear module for 42CrV6 Alloy Structured Steel (Gear Ratio 4.0)

4.49

61

Maximum torque vs number of teeth of 42CrV6 Alloy Structured Steel for gear module 1.0 – 2.5 and gear ratio 2.0

4.50

63

Maximum torque vs number of teeth of 42CrV6 Alloy Structured Steel for gear module 1.0 – 2.5 and gear ratio 4.0

4.51

Maximum torque vs number of teeth for gear module 2.5/ gear ratio 2.0

4.52

64

Maximum torque vs number of teeth for gear module 2.5/ gear ratio 4.0

4.53

63

64

Maximum torque (Nm) for threat combination curve: Module 2.5 and gear ratio 2.0

65

xvii LIST OF FIGURES

FIGURE NO

4.54

TITLE

PAGE

Maximum torque (Nm) for threat combination curve: Module 2.5 and gear ratio 4.0

4.55

Combination threat curve for all modules (Gear ratio 2.0)

4.56

67

42CrV6 Alloy Structured Steel spur gear selection chart for module 2.5 and gear ratio 4.0

4.58

66

42CrV6 Alloy Structured Steel spur gear selection chart for module 2.5 and gear ratio 2.0

4.57

65

68

Maximum torque of bending strength vs gear module for A322-5135 Alloy Structured Steel- Heat Treated (Gear Ratio 2.0)

4.59

69

Maximum torque of surface durability vs gear module for A322-5135 Alloy Structured Steel – Heat Treated (Gear Ratio 2.0)

4.60

69

Maximum torque of bending strength vs gear module for A322-5135 Alloy Structured Steel – Heat Treated (Gear Ratio 4.0)

4.61

70

Maximum torque of surface durability vs gear module for A322-5135 Alloy Structured Steel – Heat Treated (Gear Ratio 4.0)

4.62

70

Maximum torque vs number of teeth of A322-5135 Alloy Structured Steel – Heat Treated for gear module 1.0 – 2.5 (ratio 2.0)

4.63

72

Maximum torque vs number of teeth of A322-5135 Alloy Structured Steel – Heat Treated for gear module 1.0 – 2.5 (ratio 4.0)

72

xviii

LIST OF SYMBOLS

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) √

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

xx

xxi

LIST OF APPENDICES

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)

CHAPTER 1

1.1

INTRODUCTION

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) Straight bevel gear, Spiral bevel gear Screw gear, Worm gear

Intersecting axes gears Nonparallel and nonintersecting

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)

1.6

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

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

Project title selection

Planned Actual

Preparation and submission of project proposal 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

*

2

3

4

5

6

7

*

*

8

9

10

11

12

13

14

Planned Actual

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

Data collection for JGMA Data collection for AGMA Data analysis Discussion with supervisor Preparations/writings of project report Submission of project 2 report Preparation of presentation slide

Project 2 presentation

*

2

3

4

5

Planned Actual Planned Actual Planned Actual Planned Actual Planned Actual Planned Actual Planned Actual Planned Actual

6

7

8

9

10

11

12

13

* *

Meeting with supervisor on the 9th and 10th November 2013 for progress evaluation and discussion in Kuching.

14

CHAPTER 2

LITERATURE REVIEW

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.

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.

CHAPTER 3

METHODOLOGY

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

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

0.5 1.0 1.25 1.5 2.0 2.5 3.0 10.0

Diametral pitch,

50.8 25.4 20.32 16.93 12.7 10.16 8.46 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, allowable tangential force at the working pitch circle,

must not exceed the 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, exceed the allowable bending stress at the root, (3.15)

The formula for

(kgf) is: (

)

(3.16)

.

must not

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, stress,

must not exceed the allowable Hertz

. (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.

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

Plot charts/graphs for result and make conclusion

END

NO

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