-
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
bending strength and surface durability for gear
module 1.0 – 3.0 and number of teeth 15 – 70 37
4.6 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 39
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
TABLE NO. TITLE PAGE
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
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) 45
4.11 Calculation results for gear module 3.0 and
1500 rpm for gear ratio 2.0 49
4.12 Calculation results for gear module 3.0 and
1500 rpm for gear ratio 4.0 50
4.13 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) 53
4.14 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) 54
4.15 Calculation results for gear module 2.5 and
1500 rpm for gear ratio 2.0 58
4.16 Calculation results for gear module 2.5 and
1500 rpm for gear ratio 4.0 58
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
TABLE NO. TITLE PAGE
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
4.19 Calculation results for gear module 2.5 and
1500 rpm for gear ratio 2.0 66
4.20 Calculation results for gear module 2.5 and
1500 rpm for gear ratio 4.0 67
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
4.10 Maximum torque vs number of teeth for gear
module 2.5 34
4.11 Maximum torque (Nm) for threat combination
curve: Module 2.5 35
4.12 S45C Carbon Steel spur gear selection chart for
module 2.5 35
4.13 Maximum torque of bending strength vs gear
module for SUS Stainless Steel 36
4.14 Maximum torque of surface durability vs gear
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
4.16 Maximum torque of bending strength vs gear
module for S45C Carbon Steel (No heat treatment) 38
4.17 Maximum torque of surface durability vs gear
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
4.22 Maximum torque of surface durability vs gear
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
4.24 Maximum torque vs number of teeth of A576-1050
Carbon Structured Steel for gear module 1.0 – 4.0
and gear ratio 4.0 46
4.25 Maximum torque vs number of teeth for gear
module 3.0/ gear ratio 2.0 47
4.26 Maximum torque vs number of teeth for gear
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
4.28 Maximum torque (Nm) for threat combination curve:
Module 3.0 and ratio 4.0 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
chart for module 3.0 and gear ratio 4.0 51
LIST OF FIGURES
-
xv
FIGURE NO TITLE PAGE
4.32 Maximum torque of bending strength vs gear
module for A322-5135 Alloy Structured Steel
(Gear Ratio 2.0) 51
4.33 Maximum torque of bending strength vs gear
module for A322-5135 Alloy Structured Steel
(Gear Ratio 4.0) 52
4.34 Maximum torque of surface durability vs gear
module for A322-5135 Alloy Structured Steel
(Gear Ratio 2.0) 52
4.35 Maximum torque of surface durability vs gear
module for A322-5135 Alloy Structured Steel
(Gear Ratio 4.0) 53
4.36 Maximum torque vs number of teeth of A322-5135
Alloy Structured Steel for gear module 1.0 – 2.5
and gear ratio 2.0 54
4.37 Maximum torque vs number of teeth of A322-5135
Alloy Structured Steel for gear module 1.0 – 2.5
and gear ratio 4.0 55
4.38 Maximum torque vs number of teeth for gear module
2.5/ gear ratio 2.0 55
4.39 Maximum torque vs number of teeth for gear module
2.5/ gear ratio 4.0 56
4.40 Maximum torque (Nm) for threat combination curve:
Module 2.5 and ratio 2.0 56
4.41 Maximum torque (Nm) for threat combination curve:
Module 2.5 and ratio 4.0 57
4.42 Combination threat curve for all modules
(Gear ratio 2.0) 57
LIST OF FIGURES
-
xvi
FIGURE NO TITLE PAGE
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
4.45 Maximum torque of bending strength vs gear
module for 42CrV6 Alloy Structured Steel
(Gear Ratio 2.0) 60
4.46 Maximum torque of surface durability vs gear
module for 42CrV6 Alloy Structured Steel
(Gear Ratio 2.0) 60
4.47 Maximum torque of bending strength vs gear
module for 42CrV6 Alloy Structured Steel
(Gear Ratio 4.0) 61
4.48 Maximum torque of surface durability vs gear
module for 42CrV6 Alloy Structured Steel
(Gear Ratio 4.0) 61
4.49 Maximum torque vs number of teeth of 42CrV6
Alloy Structured Steel for gear module 1.0 – 2.5
and gear ratio 2.0 63
4.50 Maximum torque vs number of teeth of 42CrV6
Alloy Structured Steel for gear module 1.0 – 2.5
and gear ratio 4.0 63
4.51 Maximum torque vs number of teeth for gear module
2.5/ gear ratio 2.0 64
4.52 Maximum torque vs number of teeth for gear module
2.5/ gear ratio 4.0 64
4.53 Maximum torque (Nm) for threat combination curve:
Module 2.5 and gear ratio 2.0 65
LIST OF FIGURES
-
xvii
FIGURE NO TITLE PAGE
4.54 Maximum torque (Nm) for threat combination
curve: Module 2.5 and gear ratio 4.0 65
4.55 Combination threat curve for all modules
(Gear ratio 2.0) 66
4.56 42CrV6 Alloy Structured Steel spur gear selection
chart for module 2.5 and gear ratio 2.0 67
4.57 42CrV6 Alloy Structured Steel spur gear selection
chart for module 2.5 and gear ratio 4.0 68
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
for A322-5135 Alloy Structured Steel – Heat Treated
(Gear Ratio 4.0) 70
4.61 Maximum torque of surface durability vs gear module
for A322-5135 Alloy Structured Steel – Heat Treated
(Gear Ratio 4.0) 70
4.62 Maximum torque vs number of teeth of A322-5135
Alloy Structured Steel – Heat Treated for gear module
1.0 – 2.5 (ratio 2.0) 72
4.63 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
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
-
xx
-
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