A course paper submitted on Design and construction of Bevel gear

1. Design & Construction of a Pair of Bevel gear
A report submitted to the Department of Mechanical Engineering, Khulna University of
Engineering & Technology in partial fulfillment of the requirements for the
“Course of ME 3218”
Supervised by Submitted by
Dr. Mohammad Mashud Md. Shariful Islam
Professor Roll: 1205004
Department of Mechanical Engineering Section: A
Khulna University of Engineering & Technology
January 2016
Department of Mechanical Engineering
Khulna University of Engineering & Technology
Khulna 9203, Bangladesh

2. i
Acknowledgements
All the praises to the almighty who makes author capable to complete this Special
work successfully. The author is very much indebted to his course teacher
Dr. Mohammad Mashud, professor of Department of Mechanical Engineering, Khulna
University of Engineering & Technology, Bangladesh, for his wise inspiration to do such
extraordinary work. The author expresses the heart- felt respect to him for his proper
guidance and all kind of support to perform and complete this special study.
The author is extremely grateful to Prof. Dr. Nawsher Ali Moral ,Head of the department of
Mechanical Engineering Khulna University of Engineering & Technology, Bangladesh,
to provide such a good opportunity to do the project work and for providing all other
supports.
May ALLAH bless the course teacher.
“Author”

3. ii
Abstract
A gear, simply put, is an extension of the wheel. A gear is a rotating machine part having
cut teeth, which mesh with another toothed part to transmit torque. The main function of a
gear is to transmit power of rotating shaft.
Bevel gears are used to connect intersecting shafts, usually but not necessarily at 900
. Bevel
gears are most often mounted on shafts that are 90 degrees apart, but can be designed to work
at other angles as well. The pitch surface of bevel gears is a cone.
In this project work a couple of bevel gear(gear & pinion) was designed, and number of
teeth, pitch, face, material of gear and finally heat treatment of gear material also determined.
Finally the Gears were made by Mild Steel, which is low cost and available in every
workshop.

4. iii
CONTENTS
Page
Acknowledgement………………………………………………………….…………….…i
Abstract……………………………………………………………………….….….………ii
List of Figures………………………………………………………………………………..v
CHAPTER-І: INTRODUCTION
1.1 Introduction……………………………………………………………………………..2
1.2 Objectives……………………………………………………….……………………….2
CHAPTER-ІІ: LITERATURE REVIEW
2.1 Historical Background………………………………………………………...................4
2.2 What is Gear?…………….….………….………………………………………….…….4
2.2.1 Basic Purpose Of Use Of Gears.…….……………………………………..…..5
2.2.2 General Applications Of Gears.………………………………………………..5
2.2.3 Types Of Gears……………………………………………………………..…..5
2.3 Bevel Gear ……………….……………………………………………………………….7
2.3.1 Types of Bevel Gear …………………………………………………..……..…7
2.3.2 Field of Applications of Bevel gear………………………………………….…7
2.3.3 Advantages of Bevel Gear……………………………………………..……….8
2.3.4 Dis-advantages of Bevel Gear…………………………..………………………8

5. iv
CHAPTER-III
3.1 Problem……………………………..……………………………………………………10
3.2 Solution…………………………………………………………………………………..10
3.3 Our Designed Dimension………………………………………...………………………13
3.4 CAD Design & Rendered View………………………………………………………….14
3.5 Specification Of Gears…………………………………………………………………...15
3.6 Gear materials………………………………………………………………..…………..15
3.7 Selected Material………………………………………………………………………...16
CHAPTER-ІV
4.1 Manufacture Of Gears ………….………………………………………….……………18
4.2 Manufacture of bevel gear………..…….………………………………………….……18
4.3 Finishing of Gear Teeth………..…….………………………………….……….………18
4.4 Final Project…………………………………………………………………….….….…19
CHAPTER- V
5.1 Discussion ………………………………………………………………………..……..21
5.2 Conclusion ………………………………………………………………………………21
References………………………………………………………………………….………..22

6. v
LIST OF FIGURES
Figure Title Page
Figure-1.1 Some typical bevel gear ……………………………………….......................2
Figure-2.2 Nomenclature of a simple gear ……………….………………………………5
Figure-2.2 Schematic arrangement of (a)External (b)Internal Gear …….………………..6
Figure-2.3 Typical view of spur,bevel,skew,helical and worm gear sequentially …..…..6
Figure-3.1 Designed of dimension of gear ……………………………………………....14
Figure-3.2 Designed of dimension of pinion………………………………………….….14
Figure-3.3 CAD Design of Gear and pinion sequentially …………………….………….…..15
Figure-3.4 Rendered view of designed gear…………………….………………….….…..15
Figure-4.1 Developed pair of bevel gear (Gear & Pinion) ……………….………...……19

7. 1
 Introduction
 Objectives
Chapter I

8. 2
1.1 Introduction
A gear or cogwheel is a rotating machine part having cut teeth, or cogs, which mesh with another
toothed part to transmit torque, in most cases with teeth on the one gear being of identical shape,
and often also with that shape on the other gear. Two or more gears working in a sequence (train)
are called a gear train or, in many cases, a transmission. such gear arrangements can produce
a mechanical advantage through a gear ratio and thus may be considered a simple machine.
Geared devices can change the speed, torque, and direction of a power source. The most
common situation is for a gear to mesh with another gear; however, a gear can also mesh with a
linear toothed part, called a rack, thereby producing translation instead of rotation.
Bevel gears are gears where the axes of the two shafts intersect and the tooth-bearing faces of the
gears themselves are conically shaped. Bevel gears are most often mounted on shafts that are 90
degrees apart, but can be designed to work at other angles as well. The pitch surface of bevel
gears is a cone.
Fig 1.1: Some typical bevel gear
The most common gear-cutting processes include hobbing, broaching, milling, and grinding.
Gears are commonly made from metal, plastic, and wood.
1.2 Objectives:
The main objectives of this project work are-
I. To solve a problem related to Bevel Gear
II. To design that Bevel Gear
III. To develop the selected Gear

9. 3
 Historical Background
 What is Gear?
 Types Of Gears
 Bevel Gear
 Field of Applications of Bevel gear
 Advantages of Bevel Gear
 Dis-advantages of Bevel Gear
Chapter II

10. 4
2.1 Historical Background
Early examples of gears date from the 4th century BCE in China (Zhan Guo times - Late
East Zhou dynasty), which have been preserved at the Luoyang Museum of Henan
Province, China. The earliest gears in Europe were circa CE 50 by Hero of Alexandria, but they
can be traced back to the Greek mechanics of the Alexandrian school in the 3rd century BCE and
were greatly developed by the Greek polymath Archimedes (287–212 BCE).
Examples of further development include:
 Ma Jun (c. 200–265 CE) used gears as part of a south-pointing chariot.
 The Antikythera mechanism is an example of a very early and intricate geared device,
designed to calculateastronomical positions. Its time of construction is now estimated
between 150 and 100 BCE.
 The water-powered grain-mill, the water-powered saw mill, fulling mill, and other
applications of watermill often used gears.
 The first mechanical clocks were built in CE 725.
 The 1386 Salisbury cathedral clock may be the world's oldest working mechanical clock.
2.2 What is Gear ?:
A gear, simply put, is an extension of the wheel. The extension is the teeth on the outer rim of
the wheel, which allows them to be meshed together with other gears for the purpose of
transferring drive from a motor. In a very basic driveshaft, there are three types of gears:
The driver, the idler, and the driven. Due to the laws of motion, coupling two gears together
causes them to rotate in opposite directions. When two gears mesh, and one gear is bigger than
the other (even though the size of the teeth must match), a mechanical advantage is produced,
with the rotational speeds and the torques of the two gears differing in an inverse relationship.

11. 5
Fig 2.1: Nomenclature of a simple gear
2.2.1 Basic Purpose Of Use Of Gears
Gears are widely used in various mechanisms and devices to transmit power and motion
positively (without slip) between parallel, intersecting (axis) or non-intersecting non parallel
shafts,
 without change in the direction of rotation
 with change in the direction of rotation
 without change of speed (of rotation)
 with change in speed at any desired ratio
Often some gearing system (rack – and – pinion) is also used to transform rotary motion into
linear motion and vice-versa.
2.2.2 General Applications Of Gears
Gears of various type, size and material are widely used in several machines and systems
requiring positive and stepped drive. The major applications are:
 Speed gear box, feed gear box and some other kinematic units of machine tools
 Speed drives in textile, jute and similar machineries
 Gear boxes of automobiles
 Speed and / or feed drives of several metal forming machines
 Machineries for mining, tea processing etc.
 Large and heavy duty gear boxes used in cement industries, sugar industries, cranes,
conveyors etc.
 Precision equipments, clocks and watches
 Industrial robots and toys.
2.2.3 Types Of Gears
2.1.4.1 According to configuration
 External gear
 Internal gear

12. 6
Fig 2.2: Schematic arrangement of (a)External (b)Internal Gear
2.1.4.2 According to axes of transmission
 Spur gears
 Bevel gears
 Helical gears
 Skew gears
 Worm gears
Fig 2.3: Typical view of spur,bevel,skew,helical and worm gear sequentially
2.1.4.3 According to pattern of motion
 Rotation to rotation
 Rotation to translation or vice versa – e.g. rack and pinion

13. 7
2.3 Bevel Gear:
2.3.1 Types of Bevel Gear:
Bevel gears are classified in different types according to geometry:
 Straight bevel gears have conical pitch surface and teeth are straight and tapering
towards apex.
 Spiral bevel gears have curved teeth at an angle allowing tooth contact to be gradual and
smooth.
 Zerol bevel gears are very similar to a bevel gear only exception is the teeth are curved:
the ends of each tooth are coplanar with the axis, but the middle of each tooth is swept
circumferentially around the gear. Zerol bevel gears can be thought of as spiral bevel
gears, which also have curved teeth, but with a spiral angle of zero, so the ends of the
teeth align with the axis.
 Hypoid bevel gears are similar to spiral bevel but the pitch surfaces are hyperbolic and
not conical. Pinion can be offset above, or below,the gear centre, thus allowing larger
pinion diameter, and longer life and smoother mesh, with additional ratios e.g., 6:1, 8:1,
10:1. In a limiting case of making the "bevel" surface parallel with the axis of rotation,
this configuration resembles a worm drive. Hypoid gears were widely used in automobile
rear axles.
2.3.2 Field of Applications of Bevel gear
The bevel gear has many diverse applications such as locomotives, marine applications,
automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection
machines, etc.
For examples, see the following articles on:
 Bevel gears are used in differential drives, which can transmit power to two axles
spinning at different speeds, such as those on a cornering automobile.
 Bevel gears are used as the main mechanism for a hand drill. As the handle of the
drill is turned in a vertical direction, the bevel gears change the rotation of the chuck
to a horizontal rotation. The bevel gears in a hand drill have the added advantage of
increasing the speed of rotation of the chuck and this makes it possible to drill a range
of materials.

14. 8
 The gears in a bevel gear planer permit minor adjustment during assembly and allow
for some displacement due to deflection under operating loads without concentrating
the load on the end of the tooth.
 Spiral bevel gears are important components on rotorcraft drive systems. These
components are required to operate at high speeds, high loads, and for a large number
of load cycles. In this application, spiral bevel gears are used to redirect the shaft
from the horizontal gas turbine engine to the vertical rotor.
2.3.3 Advantages of Bevel Gear
 This gear makes it possible to change the operating angle.
 Differing of the number of teeth (effectively diameter) on each wheel
allows mechanical advantage to be changed. By increasing or decreasing the ratio
of teeth between the drive and driven wheels one may change the ratio of
rotations between the two, meaning that the rotational drive and torque of the
second wheel can be changed in relation to the first, with speed increasing and
torque decreasing, or speed decreasing and torque increasing.
2.3.4 Dis-advantages of Bevel Gear
 One wheel of such gear is designed to work with its complementary wheel and no
other.
 Must be precisely mounted.
 The shafts' bearings must be capable of supporting significant forces.

15. 9
 Problem
 Solution
 Our Designed Dimension
 CAD Design & Rendered View
 Specification Of Gears
 Gear materials
 Selected Material
Chapter III

16. 10
3.1 Problem
Decide upon the pitch, face, Ng , material, and heat treatment of a pair of straight
Bevel gears to transmit continuously and indefinitely a uniform loading of 5 hp at
900 rpm of the pinion, reasonable operating temperature, high reliability;
mg≈1.75 ; Dp ≈ 3.333in. Pinion overhangs, gear is straddle mounted.
3.2 Solution
L=(rp
2
+rg
2
)1/2
tan
ᵞp =1/mg=1/1.75
ᵞp=29.7º
L sin
ᵞp=rp
L sin
29.7º
=3.333/2
L=3.358in
Ft=(33,000hp/vm) lb
vm=(π*Dp *np/12)=(π*3.33*900/12)=785.1 fpm
Ft=(33,000*5/785.1)=210lb
Fd=(VF)*Nsf *Km *Ft
VF=(50+vm
1/2
)/50=(50+785.41/2
)/50
One gear straddle, one not
Km=1.2
Table 15.2, for uniform loading
Nsf=1.0

17. 11
Dynamic load
Fd=(1.56)*(1.0)*(1.2)*(210)=393lb
Wear load
Fw=Dp *b*I *(scd
2
/C2
)*(Cl/Kt*Cr)2
Dp=3.333in
b = 0.3L=0.3(3.358)=1.0in
Temperature factor
Kt=1.0, reasonable operating temperature
Life factor for wear
Ct=1.0 for indefinite life
Reliability factor for wear
Cr=1.25 high reliability
Geometry factor for wear, Fig. 15.7
Assume I=0.080
Elastic coefficient (Table 15.4)
Steel on steel, Ce =2800
Fw=Fd
(3.333)*(1.0)*(0.08)*{(scd)2
/(2800)2
}*[1.0/(1.0)*(1.25)]2
=393
scd= 134,370 psi

18. 12
Table 15.3, use Steel, (300)
scd= 135ksi
Strength of bevel gears
Fs=(sbbj/Pd)*{Kt/(Ks *Kt*Kr)}
Size factor, assumeKs=0.71
Life factor for strength
Kl=1, for indefinite life
Temperature factor,
Kt=1, good operating condition
Reliability factor
Kr=1.5 high reliability
Geometry factor for strength (Fig. 15.5)
Assume J=0.240
b =1.0in
sd = design flexural stress
Min. BHN = 300
sd =19ksi
Fs=Fd
(19,000)*(1.0)*(0.240)/Pd*[1/{(0.71)*(1)*(1.5)}]=393

19. 13
Pd=110
Say Pd=10
So that b =10/Pd=10/10=1.0in
Dg=DP*mg=(3.333)*(1.75)=5.833in
Ng=Pd *Dg= (10)*(5.833)=58.33
Say Ng=58
Use Pd =10, b=1.0 in, Ng= 58
Material = steel, minm
BHN = 300
3.3 Our Designed Dimension
Answer:
Ng=58 Pd =10
b=1.0 in BHN = 300
Material: steel (Mild)

20. 14
Fig 3.1:Designed of dimension of gear
Fig 3.2:Designed of dimension of pinion
3.4 CAD Design & Rendered View

21. 15
Fig 3.4: Rendered view of designed gear
3.5 Specification Of Gears
Fig 3.3: CAD Design of Gear and pinion sequentially

22. 16
Gears are generally specified by their
 Type; e.g. spur, bevel, spiral etc.
 Material
 Size or dimensions
 Geometry
 Special features, if any.
3.6 Gear materials
The material for any gear is selected based on,
 The working condition ie, power, speed and torque to be transmitted
 Working environment, i.e., temperature, vibration, chemical etc.
 Ease of manufacture
 Overall cost of material and manufacture
The materials generally used for making gears are :
 Ferrous metals – for high loads
 Grey cast iron – preferred for reasonable strength and wear resistance, ease of
casting and machining and low cost
 Forged or rolled high carbon steels and alloy steels (Ni-Cr, Mo etc.) which are
either fully hardened or surface hardened for use under high stresses and speed.
 Non ferrous metals – for light load
 Aluminum, bronze and brass are used for making gears having fine teeth and
working at very light load – e.g., in equipments, toys etc. or against hard steel mating
gears.
 Aluminum alloys like aluminum bronze, Zinc – Al. alloy etc.
 Non-metals – widely used for light load, non-precision and noiseless operation.
Polymers (plastics) : both thermoplastic and thermosetting type and various
composites (metals, graphite, wood dust or ceramic powders dispersed in
thermosetting plastics).
3.7 Selected Material
Considering cost, strength, ease of access taken into account the selected material for this design
is MILD STEEL.

23. 17
 Manufacture Of Gears
 Manufacture of bevel gears
 Finishing of Gear Teeth
 Final Project
Chapter IV

24. 18
4.1 Manufacture Of Gears
Manufacture of gears needs several processing operations in sequential stages depending upon
the material and type of the gears and quality desired. Those stages generally are :
 Performing the blank without or with teeth
 Annealing of the blank, if required, as in case of forged or cast steels
 Preparation of the gear blank to the required dimensions by machining
 Producing teeth or finishing the preformed teeth by machining
 Full or surface hardening of the machined gear (teeth), if required
 Finishing teeth, if required, by shaving, grinding etc.
 Inspection of the finished gears.
4.2 Manufacture of bevel gears
In manufacture Straight toothed bevel gear
 Forming by milling cutter – low productivity and quality hence employed for
production requiring less volume and precision
 Generation – high accuracy and finish, hence applied for batch to mass
production.
Production of gear teeth by form milling are characterised by :
 use of HSS form milling cutters
 use of ordinary milling machines
 low production rate for
⎯ Need of indexing after machining each tooth gap
⎯ slow speed and feed
 low accuracy and surface finish
 Inventory problem – due to need of a set of eight cutters for each module –
pressure angle combination.
 End mill type cutters are used for teeth of large gears and / or module.
4.3 Finishing of Gear Teeth
For smooth running, good performance and long service life, the gears need
 to be accurate in dimensions and forms
 to have high surface finish and
 to be hard and wear resistive at their tooth flanks
Common methods of gear teeth finishing
Gear teeth, after preforming and machining, are finished generally by:

25. 19
 for soft and unhardened gears
 gear shaving
 gear rolling or burnishing
 for hard and hardened gears
 grinding
 lapping
 for soft but precision gears
 shaving followed by surface hardening and then lapping
4.4 Final Project
Fig 4.1: Developed pair of bevel gear (Gear & Pinion)

26. 20
 Discussion
 Conclusion
Chapter V

27. 21
5.1 Discuusion
Gears have a principal use in the transformation of power of rotating shaft. This project work
includes design and development of a problem from text book of machine design.Our problem
was related to bevel gear. According to the instruction the bevel gear of selected problem was
designed then developed. Considering cost, strength, ease of access taken into account the
selected material for this design as MILD STEEL.
5.2 Conclusion
Mechanical design is a complex undertaking, requiring many skills. Design and fabrication of a
Pair of bevel was done in this project work. In designing problem number of gear teeth was
determined. The pitch, face, material and heat treatment of gear material were also determined.
The application of bevel gears also studied in this project work.

28. 22
References:
[1]: www.nptel.ac.in/courses/112105127/pdf/LM-31.pdf
[2]: http://www.merriam-webster.com/dictionary/gear
[3]: http://www.myoops.org