ASSOSA UNIVERSITY 12.docx

ASSOSA UNIVERSITY
COLLEGE OF ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
MACHINE DESIGNPROJECT 2
PROJIECT TITLE;DESIGN OF GEAR BOX
PREPARED BY MUSSIE TILAHU ID 0517/12
MARCH, 2023 – JANUARY, 2024
APPROVED BY MR, DESALEGN. A
ASSOSA,ETHIOPIA

i
ACKNOWLEDGEMENT
First of all we would like to thank the Almighty God for giving the strength to prepare this design project.
Secondly we would like to express our sincere appreciation and special gratitude to MR DESALEGN
(MSc.) for his lecture and guidance throughout the project period which is very essential for our future
designing tasks. And also we would like to express our great thank to assosa university as well as text book
reference owners. The last but not the least we would like to express our sincere appreciation for all
individual who invested their time, energy and resources to help us.

ii
ABSTRACT
The gearbox is the second element of the power train in automobile. It is used to change the speed
and torque of vehicle according to variety of road and condition. Transmission box change the engine
speed into torque when climbing hails and other uses depending on the condition. Sliding mesh gear
box is one of most commonly used types of gear box which is used most of the time in automobile
mainly in oldest version for less speed and high torque application like tractor. There are several
problems associated with this device which is mainly arise due to material selection and faulty design
specially on the gears(tooth) and shaft because it is subjected to excessive load , wear and heat. This
later will create problems such as noise, incable of proper gear shifting and improper meshing which
finally leads the machine not to operate properly. The main aim of the paper is to design gear box
with with the appropriate material. For the design we collect necessary information or data about gear
box and survey some literatures, select appropriate materials, perform detail design calculations,
model and analysis based on given specification. The design is safe from different point of view and
the problem related with the machines are solved. For modelling of 2D and 3D we use
SOLIDWORK 2018 for analysis.

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Table of Contents
AKNOLOGMENT ...........................................................................................................................................i
Abstract.......................................................................................................... Error! Bookmark not defined.
CHAPTER ONE..............................................................................................................................................1
INTRODUCTION TO DESIGN OF GEAR BOX .........................................................................................1
1.1 General overview of the project .............................................................................................................1
1.2 Background............................................................................................................................................1
1.3 Definition of gear box ............................................................................................................................2
1.3.1 Purpose of a gearbox:..........................................................................................................................3
1.3.2Types of gearbox..................................................................................................................................3
1.4 In this type of gearbox, ..........................................................................................................................6
1.4.1. Synchromesh gearbox.....................................................................................................................7
1.5 Epi-cyclic gearbox..................................................................................................................................9
1.5.1 Advantage of epicyclical gearbox....................................................................................................9
4.5.2 Main component gearbox..............................................................................................................10
1.5.3 Gears..............................................................................................................................................10
1.6 General classification of gears..............................................................................................................11
1.7 Shafts...................................................................................................................................................13
1.7.1 Types of transmission shafts..........................................................................................................14
2,Counter shaft........................................................................................................................................14
3,Output shaft .........................................................................................................................................14
1.8 Bearing.................................................................................................................................................15
1.8.1 Classification of bearing................................................................................................................15
1.9 Problem statement................................................................................................................................16
Objective of the project..................................................................................................................................16
1.10 General objective ...............................................................................................................................16
1.10.1 Specific objectives.......................................................................................................................16
1.11 Methodology......................................................................................................................................17
1.12 Scope and limitation of the project ....................................................................................................18
1.12.1 scope of project............................................................................................................................18
1.12.2 limitation of project .....................................................................................................................18
2.1 Literature Review.................................................................................................................................19
CHAPTER 3..................................................................................................................................................20
MARERIAL SELECTION............................................................................................................................21

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Material selection.......................................................................................................................................21
3.1.1 Shaft material ...............................................................................................................................21
3.3.2 Advantage of bearing ...................................................................................................................22
CHAPTER 4..................................................................................................................................................23
4. DESIGN ANALYSIS................................................................................................................................23
4.1 Design of a Gear Box...........................................................................................................................23
.1 Guide lines for choice the type of gear drives....................................................................................24
4.1.2 How to select type gears for gear box...........................................................................................24
4.1,3 Gear Material.................................................................................................................................24
4.1.4 Power and Torque Requirements ..................................................................................................25
4.1.5 Gear and pinion teeth calculation..................................................................................................26
4.1.6 Calculation of module for first stage.............................................................................................28
4.1.7 Calculation of module for second stage ........................................................................................29
4.1.8 Contact Ratio calculation for first stage........................................................................................31
4.1.9 pinion and gears parameter calculation.........................................................................................31
4.1.10 Design for the pinion and gear for first stage..............................................................................32
4.1.11 Calculation for pinion in stage two .............................................................................................33
4.1.12 Design for the pinion and gear for second stage .........................................................................34
4.1.14 Gear one Bending and Wear calculationGear tooth wear ...........................................................41
4.1.15 Pinion two Bending and Wear calculationPinion two tooth wear...............................................42
4.1.16 Gear two Bending and Wear calculationGear tooth wear ...........................................................42
4.2 SHAFT DESIGN .................................................................................................................................43
4.2.1 general layout of shaft...................................................................................................................43
4.2.2 Definition of shaft .........................................................................................................................43
4.2.3 Stresses in Shafts...........................................................................................................................45
Force Analysis ...............................................................................................................................................45
4.2.4 Manufacturing method of Shafts...................................................................................................46
4.2.5 Stresses in Shafts...........................................................................................................................47
4.2.6 Endurance Limit Modifying Factors on Shaft...............................................................................47
4.2.7 Stress Concentration and Notch Sensitivity..................................................................................50
4.2.8 DESIGN OF INPUT SHAFT ...............................................................................................................51
4.2.9 Shaft Loading for minimum diameter calculation.........................................................................51
4.2.10 S.F.D, TD AND B.M.D FOR INPUT SHAF..............................................................................53
4.2.11 Reaction force for Vertical Loads.......................................................................................................53
4.2.12 FOR HORIZONTAL LOADS....................................................................................................55
4.2.13 Shear force and bending Moment Diagram for resultant Loads..................................................56

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4.2.13 Shear force and bending moment Diagram for Vertical Loads...................................................56
4.2.15 Shear force and bending Moment Diagram for Horizontal Loads .............................................57
4.2.16 Stress Concentration Factors for in put shaft ..............................................................................57
4.2.17 DESIGN OF INTERMEDIATE SHAFT....................................................................................58
4.2.18 Shaft loading for minimum diameter calculation........................................................................59
4.2.19 S.F.D and B.M.D for output SH..................................................................................................59
4.2.20 CALCULATION OF EXTERNAL REACTION FORCES .......................................................60
4.2.21 FOR VERTICAL LOAD S.........................................................................................................60
4.2.22 FOR HORIZONTAL LOADS....................................................................................................62
4.3 KEY DESIGN......................................................................................................................................65
4.3.1 Introduction ...................................................................................................................................65
4.3.2 Key Design for intermediate shaft................................................................................................67
4.3.3 Key Design for 0utput shaft ..........................................................................................................68
4.4 BEARING SELECTION.....................................................................................................................68
4.4.1 BALL BEARIN.............................................................................................................................68
4.4.2 BEARING SELECTION FOR INPUT SHAFT ..........................................................................68
4.4.4 BEARING SELECTION FOR OUTPUT SHAFT ......................................................................72
4.5 DESIGN OF CASTING REDUCER CASING AND OTHER REQUIREMENTS IN DESIGNOF
GEAR BOX ...............................................................................................................................................73
4.5.1 DESIGN OF CASTING................................................................................................................73
4.5.2 BEARING SELECTION...............................................................................................................75
4.5.3 Ball bearing ...................................................................................................................................75
CHAPTER FIVE ...........................................................................................................................................76
RESULT AND DISCUSTION.....................................................................................................................76
5.1 RESULT DISCUSTION......................................................................................................................76
CHAPTER SIX..............................................................................................................................................78
CONCLUSTION AND RECOMMENDATION..........................................................................................78
Conclusion .................................................................................................................................................78
5.2 Recommendation .................................................................................................................................79
REFERENCES..............................................................................................................................................80
APPENDIX ...................................................................................................................................................81
2D DRAWING..............................................................................................................................................81
3D drawing and assembly drawing ...............................................................................................................85

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LIST OF FIGURES
Figure 1.1 Gearbox with housing ....................................................................................................................1
Figure 1.2 gear box coupling...........................................................................................................................3
Figure 1.3 Gear position of SMG....................................................................................................................5
Figure 1.4 Constant mesh gear box with dog clutch ......................................................................................7
Figure 1.5 The working of synchromesh gearbox...........................................................................................8
Figure 1.6 Epi-cyclic gear box .......................................................................................................................9
Figure 1.7 spur gear wheels...........................................................................................................................11
Figure 1.9 helical gear wheel.........................................................................................................................12
Figure 1.10 bevel gear wheel.........................................................................................................................12
Figure 1.11 Worm and worm wheel .............................................................................................................13
Figure 1.12 spiral bevel gear .........................................................................................................................13
Figure 1.13vcrosed helical gear gear.............................................................................................................13
Figure-4.1 Interference of meshing gears......................................................................................................27
Figure-4.2. Contact Ratio between two gears................................................................................................30
Figure 4.3 layout of shaft for two stages gear bo ..........................................................................................44
Figure 4.4 resultant load ................................................................................................................................53
Figure 4.5 vertical load critical locations ......................................................................................................54
Figure 4.6 Horizontal loads ...........................................................................................................................55
Figure 4.7 diagram of resultant loads ............................................................................................................56
Figure 4.8 diagram of vertical loads..............................................................................................................57
Figure 4.9 diagram of horizontal loads..........................................................................................................57
Table 4.9 moment of different location.........................................................................................................57
Figure 4.10 output SH for resultant load .......................................................................................................59
Figure 4.11 output SH for vertical load........................................................................................................61
Figure 4.12 output SH for horizontal load.....................................................................................................62
Figure 4.13 moment diagram for resultant load ............................................................................................64
Figure 4.14 moment diagram for resultant load ............................................................................................64
Figure 4.15 housing layout............................................................................................................................74
Figure 1 drawing of main shaft......................................................................................................................81
Figure 2 Bill of material ................................................................................................................................81
Figure 3 spur gear 2D drawing.....................................................................................................................82
Figure 4 main shaft 2D ..................................................................................................................................82
Figure 5 hub 2D............................................................................................................................................83
Figure 6 drive shaft 2D..................................................................................................................................83
Figure 7 dog clutch 2D ..................................................................................................................................84

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Figure 8 2d drawing of counter shaft.............................................................................................................84
Figure 9 d drawing of counter shaft..............................................................................................................85
Figure 10 3d drawing of main shaft..............................................................................................................85
Figure 11 3d drawing of input shaft .............................................................................................................86
Figure 12 Assymbly drawing of counter shaft and gear................................................................................86
Figure 13 Assembly drawing of main shaft and gear....................................................................................86
Figure 14 Assembly drawing of input shaft and gear....................................................................................87
Figure 15 3d drawing of bearing ...................................................................................................................87
Figure 16 exploded Side view ......................................................................................................................87
Figure 17 Upper housing...............................................................................................................................88
Figure 18 Lower housing...............................................................................................................................88
Figure 19 assymblly of gear box ...................................................................................................................88
Figure 20 Extrude view of gear box ..............................................................................................................89
Figure 21 assembled Right view ...................................................................................................................89
Figure 22 exploded Top view 1.....................................................................................................................90
Figure 23 Exploded top view 2......................................................................................................................90

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LIST OF TABLES
Table 3.1 grey cast iron table.........................................................................................................................21
Table-4.1According with the load to be transmitted .....................................................................................24
Table-4.2 According to the velocity..............................................................................................................25
Table 4.3. Summary table about gears ..........................................................................................................35
Table-4.4 Reliability Factors .........................................................................................................................39
Table-4.5 Mechanical properties of steels used for shafts.............................................................................46
Table-4.6Temperature Factor ........................................................................................................................49
Table 4.7 Reliability Factor..........................................................................................................................50
Table-4.8 Combined shock and fatiguefactors..............................................................................................52
Table 4.9 moment of different location.........................................................................................................57
Table 4.10 Summary for bending moment at critical locationShear force and bending................................63
Table 4.11 Proportions of standard parallel rectangular keys........................................................................66
Table 4 .12 Basic capacities .........................................................................................................................70
Table 4.13 Basic capacities............................................................................................................................71
Table 4.14 Basic capacities............................................................................................................................73

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Nomenclature
A
Bb
Z
dp
Wf
Vf
Np
E
F
I
Zn
Addendum
Dedendem
Numbr of teath
Diameter of pinion
Transitional load
Pich circle radius pinion
Pinion speed
Modules eslasticsity
Face width for narow
Geometric factor
Stress cycle factor
Pichcircleradiuspinion
Sc
Zn
Va
Sb
T
Kw
z
b
Cv
W
Te
Wt
zm
Wr
Contact stress
Stress cycle factor
Pitch circle radius gear
Bending stress
Tangential stress
Power
number of teeth
Shape parameter
Velocity factor
Tangential speed
Tooth factor
Tooth head
Pitch circle
Watton

x
Wr
YN
Yϴ
Yz
CH
KT
KB
Re
Xo
B
X
Vbcr
Sb
Px𝜇
μ
∅
∅t
Kt
Ks
Pn
Kb
Ra
Kf
E
V
Radial component
Stress cycle
Temperature factor
Reliability factor
Ratio factor
Temperature factor
Thickness factor
Reliability
Guaranty
Shape parameter
Life measure dimension less
Gas diagram surface
Bending stress
Axial pitch
Coefficient of friction
Pressure angle
Transverse pressure angle
Temperature factor
Size factor
Normal base pitch
Rim contact thickness
Root mean surafce
Factor stress consent
Module elastic
Velocity

1
CHAPTER ONE
INTRODUCTION TO DESIGN OF GEAR BOX
1.1 General overview of the project
Cars need a transmission (gearbox) because the engines binary itself isn’t capable of create different
relations of velocity and binary. The engine has a rotation limit (redline) that cannot be passed for the
good of the engine. So, we need to create a way of using the available rotation of the engine, creating
different relationships between engine and the wheels.
A transmission is a machine in a power transmission system, which provides controlled application
of power. Often the term 5- speed transmission refers simply to the gearbox that uses gears and gear
trains to provide speed and torque conversions from a rotating power source to another device. Many
machines that are used today are made up of a power source and a gearbox
Gearboxes are essential in vehicles because without a gearbox cars would have very limited top
speed. A gearbox can be used in many different applications such as, industrial, power generation
and construction.
A gear box is a device for converting the speed of a shaft from one speed to another. In process the
torque is also changed. A gearbox can be simple or complex and is a machine that is used to transfer
rotational energy from a motor to another device.
When transmitting power from a source to the required point of application, a series of devices is
available including gears, belts, pulleys. Generally if the distances of power transmission are large,
gears are not suitable and chains and belts can be considered which are introduced.
Figure 1.1 Gearbox with housing
1.2 Background
The first transmission system was given by French Inventors Louis-Rene and Emile Leaser who
invented the world largest ever transmission system with 3-speed sliding mesh transmission in
1894.Gear ratio is achieved by sliding the required gears to bring it with appropriate mating gears. T
he advanced gearbox of today has reverted to what it was back in 1928 three-speed and non-

2
synchromesh. At least that is the way it is for Volvo trucks. The development span between that first
gearbox and the very latest the I-shift encompasses a huge amount of work and many landmark
accomplishments
.The gearbox in the new truck series was a robust four-speed unit specially designed for heavy
vehicles. The new trucks also had sturdy rear axles with a reduction gear. In these non-synchromesh
gearboxes, it was necessary to press the clutch twice to change gears. This heavy double-declutching
and shifting of gears solely by manual force put considerable physical strain on the driver.
That is why it was hailed as an important leap ahead when synchromesh gearboxes appeared on the
market in the 1950s. “During the 1950s, Volvo also started experimenting with automatic
transmissions.
That at least is the view of mart magi, former professor of automotive technology at the
Chalmers university of technology in Goteborg, Sweden “from a technological development
perspective, the inclusion of additional mechanical gears behind and in front of the base gearbox was
only a minor step in overall progress.
1.3 Definition of gear box
A gear box, also known as a gear case or gear head, is a gear or a hydraulic system responsible for
transmitting mechanical power from a prime mover in to some form of useful output motor
connected to one end of the gearbox and, through the gearbox's internal configuration, provides a
given output torque and speed determined by the gear ratio.
A gearbox is a transmission device used between the engine's output shaft and the final drive to
transfer the torque and power required for the vehicle's wheels, the gearbox consists of a set of gears
(i.e. spur, helical, bevel, worm And epicycle depending on the types of gearboxes used.
Connected to one end of the gearbox and, through the gearbox's internal configuration, provides a
given output torque and speed determined by the gear ratio. A gearbox is a transmission device used
between the engine's output shaft and the final drive to transfer the torque and power required for the
vehicle's wheels, the gearbox consists of a set of gears (i.e. spur, helical, bevel, worm And epicycle
depending on the types of gearboxes used.Gear drives consist of rears as main transmission elements
mounted on shafts supported by bearings. In open gear drives the bearings caring shafts are supported
in rigged frames while in closed gears drives bearing are supported in the casing or body, normally
made in two halves and may be cast or welded.The casing also stores lubricant at the bottom and is
designed to keep the body cool, drain the oil for oil change. Hook for lifting and windows for
observing the gears. Gear drives are mainly used for reducer which may be made in single, double or
triple stages. Single, two and three stage reducer may appear with its shaft in parallel also two stages
with power bifurcation or with co-axial input and output shafts.

3
Figure 1.2 gear box coupling
1.3.1 Purpose of a gearbox:
The gear box is necessary in the transmission system to maintain engine speed (or torque) at
the most economical value under all conditions of vehicle movement. An ideal gear box
would provide an infinite range of gear ratios, so that the engine speed should be kept at or
near that the maximum power is developed whatever the speed of the vehicle.
Basically the gearbox serves the following purposes:
 Provides speed and torque conversions because of the limitations of internal combustion
engines.
 Also facilitates change of direction of output shaft for reversing.
 Automotive gearboxes are used to reduce load on the engine by manipulating torque and
speed.
 They have the option to select one of several different gear ratios.
 Most gearboxes are used to increase torque & reduce the speed of output shaft. This
produces a mechanical advantage
 Automotive gearbox also have the provision to do the opposite i.e. provide an increase in
output shaft speed with a reduction of torque (overdrive)
 Multiply (or increase) the torque (turning effort) being transmitted by the engine.
1.3.2Types of gearbox
 Manual /Selective type

4
 Sliding mesh
 Constant mesh
 synchromesh
 Progressive type
 Epicyclical type
Selective type gear box it is a transmission in which any speed may be selected from the
neutral position. In this type of transmission, neutral position has to be obtained before
selecting any forward or reverse position
Advantages:
Simple in construction
 Relatively free from troubles
 Light and small
 Low production costs. Disadvantages:
 Gear ratios not being continuous but being in steps (3 to 5 steps), making it
necessary to shift gears each time when vehicle running conditions change.
 Noisy in operation.
1.3.2.1 Sliding mesh gearbox
Sliding Mesh Gearbox was the first gearbox or transmission system invented of an
automobile. It is the gearbox in which the required gear ratio is achieved by sliding the
required gears to bring into mesh with the appropriate mating gear. Since the gears are to be
slide axially and brought into contact the gears have to be necessarily be spur gears. Gear
ratio is achieved by sliding the required gears to bring it with appropriate mating gears.
The main components are:
1 Shafts: There are 3 shafts present in Sliding Mesh Gearbox:
a) Disengaging clutch which is mounted at the engine end. A gear is mounted over this
shaft known as clutch gear which is used to transmit rotational motion to lay shaft.
b) Lay Shaft or Counter Shaft: After the input shaft comes the Lay Shaft. Lay shaft is an
intermediate shaft between the Clutch Shaft and Main Shaft. In the lay shaft, the gears
are rigidly fixed and rotate with the lay shaft.

5
c) Main Shaft: This splined output shaft carries spur gearwheels that slide along the shaft to
engage with the appropriate lay shaft gears.
2. Gears: Usually two types of gears were used in sliding mesh gearbox. They are:-
i. Spur gear: Spur gears have straight teeth that are produced parallel to the axis of gear.
These gears are most economical types of gear but tend to vibrate and become noisy at
high speed. ii. Helical gear:
3. Gear lever: It is used slide the gears in the main shaft to obtain appropriate gear ratio. It is
operated by the driver. Working of SMG
 At first, the clutch shaft is driven by engine. It carries the engine output and rotates in
the same direction as that of engine. The gear connected to the clutch shaft also rotates.
 As gear of clutch shaft rotates, the lay shaft gear which is connected to the clutch shaft
gear also rotates but in opposite direction.
 So the lay shaft rotates due to rotation of lay shaft gear that is rigidly fixed in the lay
shaft. Due to rotation of lay shaft other gears of lay shaft also rotates as all the gears in
lay shaft are rigidly fixed including the reverse gear.
 The gears of main shaft are internally and the main shaft is also, so the gears of main
shaft can slide over it. The gear of main shaft are shifted and meshed with different
gears of lay shaft to obtain different gear ratios required to face different road
problems.
.
Figure 1.3 Gear position of SMG

6
Neutral - All main shaft gearwheels are positioned so that they do not touch the lay shaft
gears. A drive is taken to the lay shaft, but the main shaft will not be turned in neutral position
First gear- By operating gearshift lever, the larger gear on main shaft is made to slide and
mesh with first gear of countershaft.
Main shaft turns in the same direction as clutch shaft in the ratio of 3:1
Second gear- By operating gear shift lever, the smaller gear on the main shaft is made to slide
and mesh with second gear of counter shaft. A gear reduction of approximately 2:1 is
obtained.
Third gear - In the third gear, the gearbox provides low torque and high speed when
compared to 2nd gear
Top gear- By operating gearshift lever, the combined second speed gear and top speed gear is
forced axially against clutch shaft gear. External teeth on clutch gear mesh with internal teeth
on top gear and the gear ratio is 1:1.
Reverse gear- By operating gearshift lever, the larger gear of main Shaft meshed with reverse
idler gear. The reverse idler gear is always on the mesh with counter shaft reverse gear.
Interposing the idler gear, between reverse the main shaft turns in a direction opposite to
clutch shaft.
1.4 In this type of gearbox,
all the gears of the main shaft are in constant mesh with corresponding gears of the
countershaft. The gears on the main shaft which are bushed are free to rotate. The dog
clutches are provided on main shaft. The gears on the lay shaft are, however, fixed.
Similarly, movement of the right dog clutch to the left results in low gear and towards right in
reverse gear. Usually the helical gears are used in constant mesh gearbox for smooth and
noiseless operation. For the smooth engagement of dog clutches, it is required that the speed
of main shaft gears and the dog clutch must be equal. Therefore to obtain lower gear, the
speed of the lay shaft, clutch shaft, and the main shaft must be increased.
The shifting of gears was not at all an easy task and only a skilled driver can drive such a
vehicle and the special technique required was Double-de-clutching (there are usually two
dog clutches in a Constant Mesh Gear Box)

7
Figure 1.4 Constant mesh gear box with dog clutch
1.4.1. Synchromesh gearbox
This type of gearbox is similar to the constant mesh type gearbox. Instead of using dog clutches
here synchronizers are used. The modern cars use helical gears and synchromesh devices in
gearboxes, that synchronize the rotation of gears that are about to be meshed
This type of gearbox is similar to the constant mesh type in that all the gears on the main shaft
are in constant mesh with the corresponding gears on the lay shaft..
This is the provision of synchromesh device which avoids the necessity of double
declutching. The parts that ultimately are to be engaged are first brought into frictional
contact, which equalizes their speed, after which these may be engaged smoothly. In most of
the cars, however, the synchromesh devices are not fitted to all the gears as is shown in this
figure.
Figure 4Lline diagram of synchromesh gearbox
They are fitted only on the high gears and on the low and reverse gears ordinary dog clutches
are only provided. This is done to reduce the cost. In figure A is the engine shaft, Gears B, C,
D, E are free on the main shaft and are always in mesh with corresponding gears on the lay
shaft. Thus, all the gears on main shaft as well as on lay shaft continue to rotate so long as
shaft A is rotating.
Members F1 and F2 are free to slide on spines on the main shaft. G1 and G2 are ring shaped
members having internal teeth fit onto the external teeth members F1 and F2 respectively. K1
and K2 are dogteeth on B and D respectively and these also fit onto the teeth of G1 and G2.
S1 and S2 are the forks. T1 and T2 are the balls supported by spring.
These tend to prevent the sliding of members G1 (G) on F1 (F2). However, when the force
applied on G1 (G2) slides over F1 (F2), these are usually six of these balls symmetrically

8
placed circumferentially in one synchromesh device.
M1, M2, N1, N2, P1, P2, R1, R2 are the frictional surfaces. To understand the working of this
gearbox, consider figure which shows in steps how the gears are engaged.
Figure 1.5 The working of synchromesh gearbox
In the synchromesh gearbox, the Lay shaft is connected to the engine directly, but it rotates
freely when the clutch is disengaged. Because the gears have meshed all the time, the synchro
brings the lay shaft to the right speed for the dog teeth to mesh to achieve the desired speed of
the output shaft.
i) Working of First Gear: For the first gear, the ring shaft member and the sliding members
i.e., G2 and F2 moves towards the left till the cones P1 and P2 rub each other. Then
friction makes their speed equal. Once their speeds are equal G2 is further pushed towards
the Left and it engages with the teeth L2. A motion is carried from clutch gear B to the lay
shaft gear U1.
ii) Working of Second Gear: For second gear the ring shaft and the sliding members i.e., G1
and F1 moves towards the right till the cones N1 and N2 rub each other. Then the friction
makes their speed equal. G1 is further pushed towards the right so that it meshes with the
gear. The motion is transferred from clutch gear B to the lay shaft gear U1 F1. Then it
goes to the main shaft for the final drive.
iii)Working of Top Gear: For top gear or direct gear, the motion is shifted directly from
clutch gear B to the sliding member F1. Then from F1 to the main shaft, this is done by

9
moving G1 and F1 to the left.
iv)Working of Reverse Gear: For reverse gear, the motion is transferred from clutch gear A
to the lay shaft gear U1.
1.5 Epi-cyclic gearbox
The basic of epi-cyclic gear is that it has a sun gear, planetary gears and Ring Gears. This type
of gear mechanism is used in the PTO shaft of the Tractors and automatic gear boxes
Figure 1.6 Epi-cyclic gear box [2]
An epicyclical gearbox consists of two, three or even four epi-cyclic or planetary gear sets. A
simple gear set has a sun gear, about which planets turns around. These planet gears are
carried by a carrier and a shaft and are also in mesh with a ring gear.
1.5.1 Advantage of epicyclical gearbox
 It provides a more comfort unit operating about a common central axis, because they
planetary gear operate within a ring gear its external surface of cylindrical form.
 The planetary gears are in constant mesh and hence dog clutches or sliding gears are not
used.
 The gear and gear housings are comparatively smaller in overall dimensions.
 Instead of having the load on only one pair of gears, it is distributed over several gear
wheels.
 External contrasting hand brackets or multiple clutches of relatively small dimensions are
used for changing the gears.

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4.5.2 Main component gearbox
Some of the components used in gear box are:
 Gears
 shafts
 Bearing
 Selector Forks
 Housing
 Synchronizer/dog clutch
1.5.3 Gears
Gear is defined as a machine element used to transmit motion and power between rotating
shafts by means of progressive engagement of projections called teeth. Gear is a part, as a
disk, wheel, or section of a shaft, having cut teeth of such form; size and spacing that they
mesh with teeth in another part to transmit or receive force and motion the gears in a
transmission are analogous to the wheels in a pulley. An advantage of gears is that the teeth of
a gear prevent slipping. Gears are the most common means used for power transmission.
For mechanical power transmission, gears are generally categorized into three distinct types:
1. Those transmitting power and motion between parallel shafts, namely, spur and ordinary
helical gears;
2. Those for shafts with intersecting axes, the angle between the shafts being generally go,
e.g. Bevel gears.
3. Those where the shafts are neither parallel nor intersecting, the axes generally making 90’
(or some other angle) to each other but in different planes, e.g. Worm and worm-wheel,
crossed helical gears, and hypoid gears.
Fixed Gears: These gears are attached to lay shaft for a proper mesh with the gears of the
main shaft. As they are fixed, if one gear rotates then all the gears rotate along with lay shaft
also.
Movable Gears:
These gears are attached to the Main shaft and are independent. It means, if one gear rotates,

11
then other gears do not rotate with respect to the shaft. As the vehicle has to move in any of
one gear (might be 1st, 2nd, and 3rd), so there is no need for the rotation of another gear.
Idler Gear: This gear is used when the vehicle needs to move in the reverse direction. This
gear places its position in the center of lay shaft gear and main shaft gear and thus the reverse
action is taking place in the vehicle.
Clutch Gear: This gear is attached at the end of the clutch shaft for transmitting power from
the engine to the lay shaft and main shaft respectively.Gears of constant mesh gearbox come
in pairs.
All gears of lay shaft or counter shaft are always paired with gears of main shaft or output
shaft.
These paired gears of counter shaft and main shaft provide different gear ratio which can be
transmitted to main shaft by engaging dog clutch with appropriate gear ratio required.
1.6 General classification of gears
Depending upon the relation between the axes, shape of the solid on which the teeth are
developed, curvature of the tooth-trace and any other special features, gears are categorized
into the following types.
1 Spur gears, spur gears are used to transmit rotary motion between parallel shafts. They are
cylindrical, and the teeth are straight and parallel to the axis of rotation and also they are used
to transmit motion from one shaft to another the most common gears are spur gears and are
used inSeries for large gear reductions. Spur gears are used in washing machines,
screwdrivers, windup alarm clocks, and other devices.
Figure 1.7 spur gear wheels
2 Helical gears, helical gears are used to transmit motion between parallel or nonparallel shafts.
Helical gears operate more smoothly and quietly compared to spur gears due to the way the teeth

12
interact. The teeth on a helical gear cut at an angle to the face of the gear. The typical range of
the helix angle is about15to30deg.
Figure 1.9 helical gear wheel
3 Bevel gears, Bevel gears are used to transmit rotary motion between intersecting shafts. The
tooth of the bevel gears can be cut straight or spiral. Have teeth formed on conical surfaces and are
used mostly for transmitting motion between intersecting shafts. The figure actually illustrates
straight-tooth bevel gears. Spiral bevel gears are cut so the tooth is no longer straight, but forms a
circular arc. Hypoid gears are quite similar to spiral bevel gears except that the shaftsare offset and
nonintersecting.
Figure 1.10 bevel gear wheel
4 Worm gears, Worm gear sets are used to transmit rotary motion between nonparallel and
nonintersecting shafts consist of a worm and a worm wheel.. Worm gear drives are used for shafts,
the axes of which do not intersect and are perpendicular to each other. Worm gear drives are
characterized by high speed reduction ratio. The direction of rotation of the worm gear, also called
the worm wheel, depends upon the direction of rotation of the worm and
upon whether theworm teeth are cut right-hand or left-hand. Worm gear sets are also made so that
the teeth of one or both wrap partly around the other. Such sets are called single enveloping and
double- enveloping worm gear sets. Worm gear sets are mostly used when the speed ratios of the

13
two shafts are quite high, say, 3 or more
Figure 1.11 Worm and worm wheel [2]
5 Spiral bevel gears,In this type of bevel gears, the tooth elements are curved in the shape of a
spiral so that the contact between the inter meshing teeth begins gradually and continues smoothly
from one end to the other.
Figure 1.12 spiral bevel gear
6 Crossed helical gears, These are cylindrical helical gears, but their axes are at an angle when in
mesh and do not intersect. Crossed helical gears are also sometimes termed as“spira1gears” and
“screw gears’’ but such names are discouraged as they are rather confusing.
Figure 1.13vcrosed helical gear gear
1.7 Shafts
A shaft is a rotating machine element which is used to transmit power from one place to another.
The power is delivered to the shaft by some tangential force and the resultant torque (or twisting

14
moment) set up within the shaf permits the power to be transferred to various machine linked up to
the shaft.
The following stresses are induced in the shafts:
1.Shear stresses due to the transmission of torque (i.e. due to torsional load).
2.Bending stresses (tensile or compressive) due to the forces acting upon machine element like
gears, pulleys etc.
3.Stresses due to combined torsional and bending loads
1.7.1 Types of transmission shafts
Transmission shafts can be found in a manual transmission gearbox. The purpose of a transmission
gearbox is to transfer the high output of an automobile's engine to the wheels, and in the process
reduce it to a compatible speed Gearbox does this through a complex arrangement of gears and
shaft
1,Input shaft
The automobile's engine crankshaft turns and creates power. This mechanical energy must first go
through the transmission gearbox before it eventually reaches the wheels. The first component to
receive this energy is the input shaft. It can be engaged or disengaged through the mechanism of the
clutch. Typically in a rear-wheel drive car, the input shaft is designed to lie along the same line as
the output shaft, forming what seems like a singular component that is sometimes called a main
shaft
2,Counter shaft
The counter shaft lies parallel to the main shaft and is driven by the input shaft through a pinion
gear. In a basic manual transmission design, the transmission gears are attached to the counter
shaft permanently spinning along with it. In front-wheel-drive cars, the input and counter shafts is
actually the same thing. I bears the clutch mechanism, which connects it to the engine and
transfers power to the output shaf through the gears that lie along it.
3,Output shaft
The final component that carries the power out of the transmission gearbox and on to the wheels is
the output shaft. A set of transmission gears parallel to those on the counter shaft are arranged along

15
the output shaft; it is driven by the counter shaft through these gears. Both output and counter shaft
gears are usually already meshed but the output shaft gears are not permanently attached to it.
1.8 Bearing
A bearing is a machine element which supports another moving machine element (known as
journal). It permits a relative motion between the contact surfaces of the members, while carrying
the load. A little consideration will show that due to the relative motion between the contact
surfaces, a certain amount of power is wasted in overcoming frictional resistance and if the rubbing
surfaces are in direct contact, there will be rapid wear. In order to reduce frictional resistance and
wear and in some cases to carry away the heat generated, a layer of fluid (known as lubricant) may
be provided. The lubricant used to separate the journal and bearing is usually a mineral oil refined
from petroleum, but vegetable oils, silicon oils, greases etc., may be used
1.8.1 Classification of bearing
Bearings may be classified as given below
 Depending upon the direction of load to be supported. The bearing under this group are classified
as:-
 Radial bearings: the load acts perpendicular to the direction of motion of the moving
element.
 Thrust bearings: the load acts along the axis of rotation.
 Depending upon the nature of contact. The bearing under this group are classified as: Sliding
contact bearings sliding takes place along the surface of contact between the moving element and
the fixed element. The sliding contact bearing are also knows as plain
Selector Fork
The shifter fork and fork rods have a mechanism using a plunger with a ball in it and is supported
with a slide able ball bearing. The detent mechanisms give the driver distinctive detent feeling
and the sliding ball bearings help reduce the shift lever operating force. All shifter forks are made
of aluminum die casting and the shifter arm shaft i formed as a hollow type to minimize the overall
weight of the transmission.
Housing
It consists of the parts; the gear box housing was sided from the extension by a lover. The foxing

16
point for the lef assembly braket is locating at the gear box housing the attachment point for self
aligning of the gear box.
Dog clutch
Among many different types of clutches, a dog clutch provides non slip coupling of two rotating
members. It is not at all suited to intentional slipping, in contrast with the foot operated friction
clutch of a manual transmission car Gear selector does not engage or disengage the actual teeth
which are permanently meshed. Rather, the action of the gear box selector is to lock one of the
freely spinning gears to the shaft that runs through its hub. The shaft then spins together with that
gear.
1.9 Problem statement
The strength, efficiency, life and durability of the gear train can be fully controlled by the
gear designer and all are related to the following:
o the material and tooth proportions
o the mounting of the gears, the bearings used and the casing design
o the heat treatment and finish of the gear teeth
o the accuracy of the teeth in mesh
o the type of lubrication system used
Objective of the project
1.10 General objective
The general objective of this project is to design four speed sliding mesh gearbox with power 7.5
KW, speed of 1500 rpm and speed ratio 10
1.10.1 Specific objectives
The specific objectives of this project are:
To design each/individual components of sliding mesh gearbox, such as:
a. Gear
b. Shaft
 Main shaft
 Input shaft
 Counter shaft

17
c. Bearing
d. Key way
e. Housing
 To select the appropriate material for the components
 To solve geometrical analysis of sliding mesh gearbox
 To compute force and stress analysis
 To select bearing
 To draw the 3D modeling
 To analyze the result
1.11 Methodology
This project has 5 main chapters. And we can classify them in to two major parts. The first part is
an introductory part and the second part is literature review part and other part will be analysis of
the project by using the force analysis, geometrical analysis as well as the detail drawing. Finally
this project design is focus on the gear box design which is different parameters such as force;
stresses etc. are calculated by numerical method. Generally describe by using block diagram of
methodology as follow

18
1.12 Scope and limitation of the project
1.12.1 scope of project
The scope of this design project is to design a sliding mesh type four speed, manual transmission
gearbox based on 7.5kw and @ 1000 rpm within system component part of gearbox is made more
suitable material that available know a day and using optimization concept, to provide the speed
control mechanisms of gearbox. It is applicable for automotive vehicle type. The cad software that
is solid work is used to perform the drawing parts of component as well as final assembled object
with in good performance capacity
1.12.2 limitation of project
The limitation of this project is there no enough software skill (like Ansys, solid work, Catia),
internet access (due to limited signal), also can’t discuss and design each type and subordinate
components for the gearbox like that of reverse 1st, 2nd , 3rd , 4th, and etc. And has no extra
guidance other than Mr.DESALEGN to design the gearbox in most precision or accuracy manner of
examination as well as execution of the desired

19
CHAPTER 2
2.1 Literature Review
Literature cited revealed that for speed control mechanism like lab testing setups of engagement and
dis engagement power transmission controlling mechanism under safe condition. There is different
scope for design and development of gearbox for use free longer life. This type of gear d should be
more heat resistance ability, less or no effect on to the society as well as environment, more
economical, light, easy to install and maintain.
has presented in his paper a gear box with 7 forward gears and 2 reverse gears has been described
and the detailed 3D parametric model was developed in Sold works so that the design modifications
and creation of a family of parts can be performed in remarkably quick time thereby avoiding
redrawing as required by traditional CAD.
The geometry created in Solid Works & was imported to ANSYS workbench for performing stress
analysis & results were comparable with theoretical calculations. A normal 7 speed MT requires 8
gear pairs to provide 7 forward and 1 reverse gear but, on his paper, presents a novel 7 speed MT
designed with just 6 gear pairs giving 7 forward and 2 reverse gears thereby saving both the
material cost as well as meeting the space constraints.
has presented on [Design and study of four speed gear box] shows that in their paper deals with
understanding of the gear transmission system principles with its design and working. Different
types of gears are used in automobiles.
Gears have teeth which mesh with each other to transmit the drive.
A detailed CAD (Computer-aided design) model has also been developed according to the
theoretical calculations to validate the design and a brief study of the four-speed sliding mesh gear
box and finally they conclude that the aim of their paper is that they have undertaken in their
engineering course is to improve our practical knowledge in design and fabrication of a particular
component in a technical manner. This improves not only their practical skills, but also their various
managing functions such as planning the project design, fabrication and erection and cost analysis
etc.
Their paper is planned and completed as per the schedule and regulations. And In addition to that,
by accomplishing this project of “FOUR SPEED GEARBOXES” successfully they felt that they
have obtained enough knowledge regarding this topic, with full of satisfaction and forward the
project to concerned.
Gearbox Noise and Vibration Prediction and Control by mussie tilahun: his paper will review
practical techniques and procedures employed to quiet gearboxes and transmission units.

20
The author prefers solving the gear noise problem at the very source to introduce an enclosure as a
means to reduce radiated noise, which seems to be easy but its effect on the sound pressure level is
small.
Components. The sum of the power contributions of the tooth meshing harmonic components
results in the noise level of an individual gear pair. Averaging the acceleration signal in the time
domain, synchronized by revolutions and tooth-pitch rotations, results in an averaged tooth mesh
response serving to compare the effects of improving gear design. Gear design and accuracy may
be tested by the transmission error measurement. The effect of the most efficient improvements
reducing noise excited by gears, as well. Concerning the gearbox noise problem, one can conclude
that a low noise gearbox requires sufficiently rigid housing, shafts and gears.
Modeling of an Automated Manual Transmission system] shows that vehicles with automated
manual Transmissions (AMT) for gear shift control offer many advantages in terms of reduction of
fuel consumption and improvement of driving comfort and shifting quality.
Complexity, nonlinearity and high-order dynamics of the automated driveline, combined with strict
requirements for high performance gear shifts, demand the development of driveline models, which
include a detailed description of the actuators.
These models can be useful for different purposes: during system development, to evaluate the
achievable performance and its dependency on system properties The simulation results prove the
advantages in terms of gearshift quality and ride comfort of the analyzed transmission.
From the analysis of the AMT ACL transmission it is possible to state that the assist clutch proves
useful during up shifts, downshifts (Kick Down) and motoring mode. From the pre-researched
journals, we concluded that the great cause of gearbox failure especially gear and gear tooth is the
wear which is initiated by the high friction due to continues meshing of gear.
CHAPTER 3

21
MARERIAL SELECTION
Material selection
The first step in the gearbox design process is to select the material. A material is to be
selectedby doing intensive research on the properties of the various materials.
3.1.1 Shaft material
A shaft is a rotating machine element which is used to transmit power from one place to
another. The power is delivered to the shaft by some tangential force and the resultant torque
(or twisting moment) set up within the shaft permits the power to be transferred to various
machines linked up to the shaft. In other words, we may say that a shaft is used for the
transmission of torque and bending moment. The various members are mounted on the shaft
by means of keys or splines.
Material Used for Shafts the material used for shafts should have the following properties:
 It should have high strength.
 It should have good machinability.
 It should have low notch sensitivity factor.
 It should have good heat treatment properties.
 It should have high wear resistant properties.
The material used for ordinary shafts is carbon steel of grades 40 C 8, 45 C 8, 50 C 4 and 50
C12. The mechanical properties of these grades of carbon steel are given in the following
table
Table 3.1 grey cast iron table

22
For the gear
For the gear selected material for the same as shaft The material used for ordinary gear is carbon steel
of grades 40 C 8, 45 C 8, 50 C 4 and 50 C12. The mechanical properties of these grades of carbon steel
are given in the above table1.When a shaft of high strength is required, then an alloy steel such as
nickel, nickel-chromium or chrome-vanadium steel is used 45C8 carbon steel is selected as shaft
material due to its better mechanical properties
Casting Design
An engineer must know how to design the castings so that they can effectively and efficiently render
the desired service and can be produced easily and economically. In order to design a casting, the
following factors must be taken into consideration.
 The function to be performed by the casting,
 Soundness of the casting,
 Strength of the casting,
 Ease in its production,
 Consideration for safety, and
 Economy in production
3.3.2 Advantage of bearing
Low starting and running friction except at very high speeds.
 Accuracy of shaft alignment.
 Low cost of maintenance, as no lubrication is required while in service.
 Small overall dimensions.
 Easy to mount and erect.
 Cleanliness.

23
CHAPTER 4
4. DESIGN ANALYSIS
4.1 Design of a Gear Box
A. Specification
i. Power [kw]:- 7.5 KW
ii. Input Speed [rpm]: 1500
iii. Total Gear Ratio:-10:1
iv. Arrangement :-perpendicular drive
v. Driving Machine: Electric Motor
vi. Driven Machine:-simple grinding machine
vii. Housing Design:- casting sheet metal
B. Main Task of the Project
1. Select the best alternative for gears carrying out preliminary calculation
2. Calculate precisely the geometry of the selected alternative so that the
relative slippagesat the boarder points of the length of engagement are
equalized.
3. Check the strength of the pair of gears.
4. Check the strength of the shafts and key joints.
5. Select the proper type of bearings that fulfill the requirement Lh = 12000 hrs
6. Construct the gearbox in 1:1 and trace with ink. The main fitted and
calculated sizesshould be given in the drawing.
7. Check critical speeds of the shafts
8. Select an appropriate lubrication
9. Prepare a design report of the gearbox containing the assumptions, considerations,
calculations and remarks concerning the project

24
.1 Guide lines for choice the type of gear drives
For a two-stage gear reducer, the distribution of the speed ratio between the two stages is as
follows: Due to above standards my design of gear box is double stage gear box withhelical
gear
Iinput=(1.2 to 1.25) √itotal and ioutput =
𝑖𝑡𝑜𝑡𝑎𝑙
𝑖inpu𝑡
1.25√10 =3.95 taking 4
ioutput =
10
4
=2.5
4.1.2 How to select type gears for gear box
At the beginning of the design, in order to select the type of gear teeth, we may use the
formulaof the empirical velocity given by: v = 0.114 HinputNinputNoutput .where H is power in
kW
V=0.11 4√7500 × 1500 × 100 × 60²/ (2𝜋) ²
V=8.14m/s
Then for velocities smaller than 8.14 m/s perpendicular spur gears are used, for values greater
than 8.14 m/s helical gears must be used. In cases of speed ratio from 6 to 8 and velocity
greater than 5 m/s helical gears must be used. For my design helical gear with two stage is
selected.
4.1,3 Gear Material
Type of the load acting on the gear drive and materials selection for the gears
Table-4.1According with the load to be transmitted
Input power/output
rpm
Load Materials for gears Hardness
0,1 Light Carbon steel or Cast iron BHN 350
0,1 to 0,3 Medium Carbon or Alloy steel BHN>350
>0,3 Heavy Alloy steel BHN>350

25
Tabl
e-4.2
Acc
ordi
ng to
the
velo
city
Depending on the above table material for all gears can be selected For both gear and
Pinion,of first stage
 Direct Hardening Steel C45
 Tensile Strength σp= 700 N / mm2
 Hardness = 340BHN Bending Strength σb 234 N / mm2For Gear and pinion in second
stage
 Cast steel Grade 25
 Tensile strength σ = 590 N / mm2
 Hardness = 175 BHN
 Bending Strength σb = =196 N / mm2

The total gear ratio is=12.5 since my design of gear box is two stage gear box I must
distributethe gear ratio in to two stages. 10= (7.14*2.5)
 Output speed=1500/10=150rpm
 Speed in first stage=1500/7.14=210rpm
 Speed in second stage=210/2.5=84rpm
4.1.4 Power and Torque Requirements
Power transmission systems will typically be specified by a power capacity, for example,a40-
Velocity in m/s Load Materials for gears Hardness
< 2 Light Carbon steel or Cast iron BHN 350
2 to 6 Medium Carbon or Alloy steel BHN > 350
> 6 Heavy Alloy steel
Heat Treatment steel
BHN > 350
HRC  60

26
horsepower gearbox. This rating specifies the combination of torque and speed that the unit
can endure. Remember that, in the ideal case, power in equals power out, so that we can refer
tothe power being the same throughout the system. In reality, there are small losses due to
factorslike friction in the bearings and gears. In many transmission systems, the losses in the
rolling bearings will be negligible. Gears have a reasonably high efficiency, with about 1 to 2
percent power loss in a pair of meshed gears.
Thus in the double reduction gearbox with two pairs of meshed gears the output power is
likely to be about 2 to 4 percent less than the input power. Since this is a small loss, it is
common to speak of simply the power of the system, rather than input power and output
power.
Torque, on the other hand, is typically not constant throughout a transmission System.
Remember that power equals the product of torque and speed. Since power in Power out, we
know that for a gear train with a constant power, a gear ratio to decrease the angular velocity
willsimultaneously Increase torque
Calculated from T =
60𝑝′
2.314𝑛output =
60∗300
2∗3.14∗100 =286Nm
 The angular speed became,
Ѡ = 2/60
Ѡ =2*3.14N/60
=2*3.14*100/60
=10.5rad/sec
4.1.5 Gear and pinion teeth calculation
The governing equations are: Z3/Z4=4
Z5/Z4=2.5
Z2+Z3=Z4+Z5
With three equations and four unknown numbers of teeth, only one free choice is available of
thetwo smaller gears, Z2 and Z4, the free choice should be used to minimize Z2 since a greater
gear ratio is to be achieved in this stage. To avoid interference assuming the minimum for Z2
is 14 Applying the governing equations yields
Z3 = 6Z2 = 6(14) = 70
Z2 + Z3 = 14 + 70= 84 = Z4 + Z5
Substituting Z5 = 2.5Z4 gives

27
84 = 2.5Z4 + Z4 = 3.5Z4
Z4 = 84/3.5 = 24
Z5=2.5*24=60
Then the four numbers of teeth are;
Z2=14 Z3=70
Z4=24 Z5=60
Interference
The contact of portions of tooth profiles that are not conjugate is called interference.Consider
Fig Illustrated . The initial and final points of contact are designated A and B, respectively,
and are located on the pressure line. Now notice that the points of tangency of the pressure
line with the base circles C and D are located inside of points A and B. I
nterference is present.Contact begins when the tip of the driven tooth contacts the flank of the
driving tooth. Inthis case the flank of the driving tooth first makes contact with the driven
tooth at point A, andthis occurs before the involutes portion of the driving tooth comes within
range. In other words,contact is occurring below the base circle of gear 2 on the non-involute
portion of the flank.
The smallest number of teeth on a spur pinion and gear,1 one-to- one gear ratio, which can
exist without interference is NP . This number of teeth for spur gears is
Figure-4.1 Interference of meshing gears
Interference can be eliminated by using more teeth on the pinion. However, if the pinion is to

28
transmit a given amount of power, more teeth can be used only by increasing the pitch
diameter. Interference can also be reduced by using a larger pressure angle. This results in a
smaller base circle, so that more of the tooth profile becomes involutes. The demand for
smallerpinions with fewer teeth thus favors the use of a 20◦ pressure angle even though the
frictional forces and bearing loads are increased and the contact ratio decreased.
The interference can be checked by,
I=
𝑍3
𝑍2
X
𝑍5
𝑍4
10x =
60
6
X
70
7
= 10
10=10
4.1.6 Calculation of module for first stage
We know that torque transmitted by the gear,
We know that the torque transmitted by the pinion in first stage
T=
60
2𝜋𝑁𝑃
T=
60∗300𝑊
2𝜋∗1500
=19Nm
Wt=
𝑇
𝑀𝑧/2
=
2∗19000
14𝑚
=
2714
𝑚
N
V=𝜋
𝐷𝑁
60
=
𝜋𝑍𝑀𝑁
60
=
𝜋14𝑀𝑥1500
60
=1099MM/s
Let us take velocity factor,
CV=
15
15+𝑉
=
15
15+1099
=0.1346
TE=
14
𝑐𝑜𝑠335
=26
Tooth form factor for the pinion for 20° stub teeth
y'=0.135-
0.841
𝑍𝑒
y'=0.135-
0.841
26
=0.14265=0.105
We know that tangential tooth load,
Wt= (σo × Cv) b.π m.y' = (σo × Cv) 3pN × π m × y'
2714
𝑚
= (σo × Cv) × 10m × π m × y'

29
2714
𝑚
= (σo × Cv) ×10m × π m × y'
2714
𝑚
=193x
15
15+1099𝑚
×10m×πm×0.105
2714(15+1099
m
=
19663m3
=46290+3009976m
Solving this equation by hit and trial method, we find that
m = 4.7 say 5 mm
4.1.7 Calculation of module for second stage
We know that the torque transmitted by the pinion in second stage
T=
60𝑃
2𝜋𝑁𝑃
T=
60𝑥300𝑊
2𝜋𝑥250
=114NM
Wt=
𝑇
𝑚𝑧/2
=
2𝑥114000
24𝑚
=9500
V=
𝜋𝐷𝑁
60
=
𝜋𝑍𝑚
60
=
𝜋𝑥24𝑚𝑥375𝑁
60
=471mm
Let us take velocity factor,
CV=
15
15+𝑉
=
15
15+471
=0.3086
TE=
24
𝐶𝑂𝑆335
=44
Tooth form factor for the pinion for 20° stub teeth
y' =0.175-
0.841
𝑍𝑒
y' =0.175-
0.841
44
=0.155
We know that tangential tooth load,
WT = (σo × Cv) b.π m.y' = (σo × Cv) 3pN × π m × y'
9500
𝑚
=(σo × Cv) × 12.5m × π m × y'
9500
𝑚
= (σo × Cv) ×12.5 m × π m × y'
9500
𝑚
=196×
15
115+471
=×10m× π m×0.155
9500(15+471𝑚)
𝑚
=19237

30
19,237=192,375=1,923,750
Solving this equation by hit and trial method, we find thatm = 5.57 say 6 mm
b = 10 m ,Pressure angle = 20˚
Select Module for first stage m = 5 And for the second stage m=6 Helix angle for first
stage=35˚, Helix angle for second stage=25
Contact Ratio calculation
The zone of action of meshing gear teeth is shown in Fig. We recall that tooth contact begins
and ends at the intersections of the two addendum circles with the pressure line. In Fig. below
initial contact occurs at a and final contact at b. Tooth profiles drawn through these points
intersect the pitch circle at A and B, respectively. As shown, the distance AP is called the arc
of approach qa , and the distance P B, the arc of recess qr . The sum of these is the arc of
action qt . Now, consider a situation in which the arc of action is exactly equal to the circular
pitch, that is, qt = p. This means that one tooth and its space will occupy the entire arc AB..
Figure-4.2. Contact Ratio between two gears
Thus, for a short period of time, there will be two teeth in contact, one in the vicinity of A
andanother near B. As the meshing proceeds, the pair near B must cease contact, leaving only
a single pair of contacting teeth, until the procedure repeats itself. Because of the nature of
this tooth action, either one or two pairs of teeth in contact, it is convenient to define the term
contactratio mc as
Mc=
𝑞𝑡
𝑝
= pc = 𝜋 x m) and qt =1.2p

31
a number that indicates the average number of pairs of teeth in contact. Note that this ratio is
also equal to the length of the path of contact divided by the base pitch. Gears should not
generally bedesigned having contact ratios less than about
4.1.8 Contact Ratio calculation for first stage
Mc=
𝑞𝑡
𝑝
Pc= 𝜋 m) =3.14*5 =15
Qp =1.2p 1.2*15=18
Mc=
18
15
=1.2
Contact Ratio calculation for first stage
Mc=
𝑞𝑡
𝑝
Pc= 𝜋 m) =3.14*6 =15
Qp =1.2p 1.2*15=19
Mc=
18
15
=1.22
4.1.9 pinion and gears parameter calculation
Calculation for pinion in stage one
Pitch circle diameter=
𝑍𝑚𝑛
csc 𝛽
=Zm=
14𝑥5
csc𝑝
= 85𝑚𝑚
Tip circle diameter = d + 2 rn=86+2*5=96
Root circle diameter = d - 2 x 1.25 m=86-2*1.25=83.5mm
Clearance=0.25Mn=0.25*5=1.25mm
Addendum circle =module Dedendum=1.25Mn=1.25*5=6.25mm
Calculation for gear in stage one
Number of teeth z=70
Pitch circle diameter=
𝑍𝑚𝑛
csc 𝛽
=Zm=
70∗5
𝑐𝑜𝑠35
= 428mm

32
Tip circle diameter = d + 2 rn=428+2*5=438mm
Root circle diameter = d - 2 x 1.25 m=428-2*1.25=425.5mm
Clearance=0.25Mn
=0.25*5=1.25mmAddendum circle =module=5 Dedendum=1.25Mn=1.25*5=6.25mm
𝐶𝑒𝑛𝑡𝑟𝑒 Distance and Tooth thickness on pitch are respectively
A=
𝑑1+𝑑2
2
and SN=
𝜋𝑀𝑛
2
86+428
2
=257mm and
𝑆𝑁 =
3.14𝑥5+𝑑2
2
=7.85Nm
4.1.10 Design for the pinion and gear for first stage
We know that the torque transmitted by the pinion
T=
60𝑃
2𝜋𝑁𝑝
T=
60∗3000𝑊
2𝜋1500
=19Nm
Wt=
𝑇
2/𝐷
=
19000
43
=441N
Since both the pinion and gear are made of the same material (i.e. steel C45), therefore the
pinion is weaker. Thus the design will be based upon the pinion. We know that formative or
equivalent number of teeth, in helical gears, the contact between mating teeth is gradual,
startingat one end and moving along the teeth so that at any instant the line of contact runs
diagonally across the teeth.
Therefore in order to find the strength of helical gears, a modified Lewis equation is used. It
isgiven by
Where WT = Tangential tooth load,σo = Allowable static stress,
Cv = Velocity factor,b = Face width,
m = Module, and
y' = Tooth form factor or Lewis factor correspond
The value of velocity factor (Cv) may be taken as follows:
Cv =6/6 C x V for peripheral velocities from 5 m / s to 10 m / s.
=15/15 C x V for peripheral velocities from 10 m / s to 20 m / s

33
=0.75/0.75 C x V For peripheral velocities greater than 20 m / s
TE=
𝑇𝑝
𝑐𝑜𝑠3𝛼
V=
𝜋∗86∗1500
60
=6.7
CV=
0
6+𝑣
=
0
6+𝑣
=0.675
Since the maximum face width (b) for helical gears may be taken as 8 m to 20 m, where m is
the module, therefore let us take
b = 8m b=8*5=40
= 234*0.516*40*3.14*5*0.14265
=10.8KN
The pressure angle υn in the normal direction is different from the pressure angle υt inthe
direction of rotation, because of the angularity of the teeth. These angles are relatedby the
equation
Cosψ=tan υn/tan υt
υt= tan−1 tan υn/cosψ= tan−1( tan 20◦/cos 25◦) = 22◦
The transmitted load is calculated before which is found by total transmitted torque.
T=60P/2πNout 60*3000/2π*100=286 Wt=286/43=6.66Nmm=6662NmWt =6662N
From above equation we find
Wr= Wt tan υt= (6662) tan24◦ = 2966NWa= Wt tanψ= (6662) tan 35◦ = 4665N
W =Wt/cosυncosψ=6662/cos 20◦cos 35◦ = 8654N
4.1.11 Calculation for pinion in stage two
Pitch circle diameter r=
𝑍𝑚𝑛
𝑐𝑜𝑠𝛽
=Zm=
24∗6
𝑐𝑜𝑠25
=159mm
Tip circle diameter = d + 2 rn=159+2*5 =169mm
Root circle diameter r = d - 2 x 1.25 m=159-2*1.25*6=144mmClearance =0.25Mn
=0.25*6=1.5mm

34
Addendum circle =module=6 Dedendum=1.25Mn=1.25*6=7.5mm
Calculation for gear in stage two
Pitch circle diameter =
𝑍𝑚𝑛
𝑐𝑜𝑠𝛽
=Zm=
60∗6
𝑐𝑜𝑠25
=398mm
Tip circle diameter = d + 2 rn=398+2*5=408mm
Root circle diameter = d - 2 x 1.25 m=398-2*1.25*6=383mm
Clearance =0.25Mn =0.25*6=1.5mm
Addendum circle =module=6 Dedendum
=1.25Mn=1.25*6=7.25mm
A=
𝑑1+𝑑2
2
A=
159+392
2
=278.5mm and the tooth tickhnes become
SN= A=
𝜋𝑀𝑛
2
= A=
3.14+6
2
=9.4mm
4.1.12 Design for the pinion and gear for second stage
We know that the torque transmitted by the pinion
T=
60𝑃
2𝜋𝑁𝑝
T=
60∗3000𝑊
2𝜋∗375
=127KN/m
𝑇
𝑑/2
=
19000
79.5
=238N
T=60P/2πNout
T=60*3000/2π*100=286
Wt=
𝑇
𝑑𝑝/2
Wt=286/79.5=3.6kN=3597N
Wt =3597N
Since both the pinion and gear are made of the same material (i.e. cast steel), therefore the

35
pinion is weaker. Thus the design will be based upon the pinion.
Where WT = Tangential tooth load,σo = Allowable static stress,
Cv = Velocity factor,b = Face width,
m = Module, and
y' = Tooth form factor or Lewis factor correspond
Since the maximum face width (b) for helical gears may be taken as 8 m to 20 m, where m
Is Module therefore let us takes b = 8m b=8*6=48
= 196*0.516*48*3.14*6*0.151 =2.5KN
A three dimensional view of the forces acting against a helical gear tooth. The point of
application of the forces is in the pitch plane and in the center of the gear face. From the
geometry the three components of the total (normal)
Tooth force W is
Wr= W sin υnWa= Wttanυn
Where W = total force
Wr= radial component
Wt = tangential component, also called transmitted load
Wa = axial component, also called thrust load
The pressure angle υn in the normal direction is different from the pressure angle υt in
The direction of rotation, because of the angularity of the teeth. These angles are related by
theequation Cosψ=tan υn/tan υt
Φt= tan−1 tan υn/cosψ= tan−1( tan 20◦/cos 35◦) = 24◦ The transmitted load is calculated
before Wt =3597N
From above equation we find
Wr= Wt tan υt= (3597) tan24◦ = 1602N Wa= Wt tanψ= (3597) tan 25◦ = 2518.64N
W= 𝖶𝑡 =3597/cos 20◦cos25◦ =4673
𝑐𝑜𝑠 𝜑𝑛 𝑐𝑜𝑠ƒ
Table 4.3. Summary table about gears

36
Name Pinion -1 Gear -2 Pinion -1 Gear -2
1 Number of teeth 14 60 24 70
2 Direction right left right left
3 Helix angle 35 35 25 25
4 Module 5 5 6 6
5 Pitch circle diameter 86 428 159 398
6 Root circle diameter 83.5 425.5 144 383
7 Tip circle diameter 96 438 169 408
8 Clearance 1.25 1.25 1.5 1.5
9 Tooth thickness 7.85 7.85 9.4 9.4
Fandamental Stress Equations
Two fundamental stress equations are used in the AGMA methodology, one for bending
stress and another for pitting resistance (contact stress). In AGMA terminology, these are
called stressnumbers, as contrasted with actual applied stresses.
σ=Wt KoKvKs=(
1
𝑏𝑚𝑡
) (
𝑘ℎ𝑘𝑏
𝑓𝐽
)
Where for U.S. customary units (SI units),the name of each symbols are given in table-3
These items include issues such as
• Transmitted load magnitude
• Overload
• Dynamic augmentation of transmitted load
• Size
• Geometry: pitch and face width
• Distribution of load across the teeth
• Rim support of the tooth
Lewis form factor and root fillet stress concentration
Where Wt, Ko, Kv, Ks, Km, F, and b are the same terms as defined (SI units), theadditional
terms are( ZE) is an elastic coefficient√𝑁/𝑚𝑚2)(ZR) is the surface condition factor
(dw1) is the pitch diameter of the pinion, in (mm)I (ZI)is the geometry factor for pitting

37
resistanceThe equation for the allowable bending stress is
𝑆𝑡 𝐹𝑁
𝑓𝐽𝑓𝑧𝑓∅
Where for U.S. customary units (SI units),
St is the allowable bending stress, (N/mm2)
YN is the stress cycle factor for bending stress(Yθ) is the temperature factors
(YZ)is the reliability factors
SF is the AGMA factor of safety, a stress ratioThe equation for the allowable contact stress
σc,all is
𝑆𝑡 𝐹𝑁
𝑓𝐽𝑓𝑧𝑓∅
Where;Sc is the allowable contact stress N/mm2
ZN is the stress cycle life factorZWis the
hardness ratio factors for pitting resistanceYθare the temperature factorsYZis the reliability
factorsSH is the AGMA factor of safety, a stress ratio
Allowable stress numbers (strengths) for bending and contact stress are for
• Unidirectional loading
•10 million stress cycles
• 99 percent reliabil
Contact stress analysis in helical gear and factors
Continue the design by specifying appropriate gears, including pitch diameter, diametric
pitch, face width, and material. Achieve safety factors of at least 1.2 for wear and bending.
Bending-Strength Geometry Factor J
The load-sharing ratio Mn is equal to the face width divided by the minimum total length of
the lines of contact. This factor depends on the transverse contact ratio mp, the face-contact
ratio mFthe effects of any profile modifications, and the tooth deflection. For spur gears,
MN= 1.0. Forhelical gears having aface contact ratio mF >2
Dynamic Factor Kv
As noted earlier, dynamic factors are used to account for inaccuracies in the manufacture and
meshing of gear teeth in action. Transmission error is defined as the departure from uniform
angular velocity of the gear pair. Some of the effects that produce transmission are:

38
Inaccuracies produced in the generation of the tooth profile; these include errors in tooth
spacing, profile lead, and run out
• Vibration of the tooth during meshing due to the tooth stiffness
• Magnitude of the pitch-line velocity
• Dynamic unbalance of the rotating members
• Wear and permanent deformation of contacting portions of the teeth
• Gear shaft misalignment and the linear and angular deflection of the shaft
• Tooth friction
KV =
A = 50 + 56(1 −B)
B = 0.25(12 −Qv) 2/3
Transmission accuracy level number Qv could be taken as the same as the quality number.
The following equations for the dynamic factor are based on these Qv numbers: These
numbersdefine the tolerances for gears of various sizes manufactured to a specified accuracy
Load-Distribution Factor Km
The load-distribution factor modified the stress equations to reflect nonuniform distribution
of load across the line of contact. The ideal is to locate the gear “midspan” between two
bearings atthe zero slope place when the load is applied. However, this is not always Possible
The following procedure is applicable to
• Net face width to pinion pitch diameter ratio F/d ≤2
• Gear elements mounted between the bearings
• Face widths up to 60mm
• Contact, when loaded, across the full width of the narrowest member.
• The load-distribution factor under these conditions is currently given by the face load
distribution factor, Cmf, where
• Km = Cmf= 1 + Cmc(Cp f Cpm+ CmaCe)Cmc=1 for uncrowned teeth 0.forcrowned teeth Cp
f= F/10d −0.025 F ≤1mm
• Cp f= 1 for straddle-mounted pinion with S1/S <0.175
• 1.1 for straddle-mounted pinion with S1/S ≥0.175Cma= A + BF + CF2
• Ce= 0.8 for gearing adjusted at assembly, or compatibility 686is improved by lapping, or

39
both1 for all other conditions
• From graph the value of Km =1.3 may be taken
Overload Factor Ko
The overload factor Ko is intended to make allowance for all externally applied loads in
excess of the nominal tangential load Wt in a particular application Examples include
variations in torque from the mean value due to firing of cylinders in an internal combustion
engine or reaction to torque variations in a piston pump drive. There are other similar factors
such as application factor or service factor. These factors are established after considerable
field experience in a particular application most of the time Ko=1
Reliability Factor 𝑌𝑍
The reliability factor accounts for the effect of the statistical distributions of materialfatigue
failures. Load variation is not addressed here. The gear strengths St and Scarebased on a
reliability of 99 percent. The functional relationship between KR and reliability is highly
nonlinear. Wheninterpolation is required, linear interpolation is too crude. A log
transformationto eachquantity produces a linear string. A least-squares regression fit is
KR= 0.658 −0.0759 ln(1 −R) 0.5 <R <0.99=0.50 −0.109 ln(1 −R) 0.99 ≤R ≤0.99999
Table-4.4 Reliability Factors
Reliability (YZ)
0.9999 1.50
0.999 1.25
0.99 1.00
0.09 0.85
0.50 0.70
Surface Condition Factor (ZR)
The surface condition factor ZR is used only in the pitting resistance equation, It depends on
• Surface finish as affected by, but not limited to, cutting, shaving, lapping, grinding.
• Residual stress

40
• Plastic effects (work hardening)
Standard surface conditions for gear teeth have not yet been established. When a detrimental
surface finish effect is known to exist, AGMA specifies a value of ZR greater than unity.
Hardness-Ratio Factor CH
The pinion generally has a smaller number of teeth than the gear and consequently is
subjected to more cycles of contact stress. If both the pinion and the gear are through-
hardened, then a uniform surface strength can be obtained by making the pinion harder than
the gear
The hardness-ratio factor CH is used only for the gear. Its purpose is to adjust the surface
strengths for this effect. The values of CH are obtained from the equation
CH = 1.0 + A′ (mG−1.0)
A′ = 8.98(10−3) HBP/HBG−8.29(10-3
)1.2 ≤HBP/HBG ≤1.7
The terms HBP and HBG are the Brinell hardness (10-mm ball at 3000-kg load)
of the pinionand gear, respectively. The term mG is the speed ratio and is given
by HBP/HBG<1.2, A′ = 0 HBP/HBG>1.7, A′ = 0.006 98
Since both pinion and gear are made up of the same material HBP/HBG=1 SO
Hardness-A′=0then hardness-Ratio Factor CH= 1.0+A (mG−1.0)CH =1
Temperature Factor KT (Yθ)
For oil or gear-blank temperatures up to (120°C), use KT = Yθ= 1.0. For higher
temperatures,the factor should be greater than unity. Heat exchangers may be used to ensure
that operating temperatures are considerably below this value, as is desirable for the lubricant.
Rim-Thickness Factor KB
When the rim thickness is not sufficient to provide full support for the tooth root, the location
ofbending fatigue failure may be through the gear rim rather than at the tooth fillet. In such
cases, the use of a stress-modifying factor KB or (tR) is recommended. This factor, the rim-
thickness factor KB, adjusts the estimated bending stress for the thin-rimmed gear. It is a
function of the backup ratio mB then from table KB=1.3
Stress Cycle Factors YN and ZN
The purpose of the load cycle factors YN and ZNis to modify the gear strength for lives other
than 107 cycles. Values for these factorsare given YN = ZN = 4 on eachgraph. Note also that
the equations for YN and ZN change on either side of 107 cycles.For life goals slightly

41
higher than 107 cycles, the mating gear may be experiencingfewer than 107 cycles and the
equations for (YN )Pand (YN )G can be different. Thesame comment applies to (ZN )Pand
(ZN)G Safety Factors SF and SH
The safety factor SF guarding against bending fatigue failure and safety factor SH guarding
against pitting failure.The definition of SF ,
SF
𝑆𝑡𝐹𝑁/(𝐾𝑇𝑅𝐾)
ϭ𝐶
Pinion tooth bending and wear
σ=Wt KoKvKs =
(1) 𝐾𝐻 𝐾𝐵
𝑏𝑚𝑡 𝐹𝐺
σ=6662× 1 × 1.25 × 1
1
40𝑋5
1.3𝑋1.2
2
= σ =32.5KN
The surface endurance strength of cast steel can be estimated fromAllowable bending stress
numbers for nit riding steel gears St. The SI equationsare St = 0.594HB + 87.76MPa
St= 0.59× 340 + 87.76 = 288.36N/mm2
Contact-fatigue strength Sc at 107 cycles and 0.99 reliability for through hardened steel gears.
The SI equations areSc= 2.22HB + 200 MPa,Sc= 2.22×340 + 200 MPa, =954.8N/mm²
Note, that the denominator of the second group of terms contains four elastic constants, two
forthe pinion and two for the gear. As a simple means of combining and tabulating the results
for the same combinations of pinion and gear materials,
CP =
1
𝐸𝑃+𝐸𝐺
𝐸𝑝 𝑎𝑛𝑑 𝐸𝐺Are elastic modulas
From table vp=0.3 and vg=0.2
Since both gear and pinion are made of the same material they have the same modules’ of
elasticity =207GB Cp==110 Mpa
r1 =dPsin υ/2=86𝑠i𝑛 20/2=14.7 r2 =dGsin υ/2 =428𝑠i𝑛 20/2 =73.2
σC= -187710*
∗ 53×6662
40 cos 20°
(1
47
+
1 )
73.2
=2300Mpa
SH=
(955∗4∗1.1/0.851)
2300
= 2.5
4.1.14 Gear one Bending and Wear calculationGear tooth wear
T=60P/2πNout T=60*3000/2π*100=286

42
Wt =
𝑇
𝐷𝑝/2
Wt=286/214=1.34kN=1336.45N
Wt =1336.45N
σc=ZE√𝑡𝑠
𝑘𝑧 𝑚𝑟
𝑑𝑤𝑏 𝑍𝐽
ZE =4
( 𝜋 )
𝑃
=4(π/8)=1.6
σc=1.6√1336.45 × 1 × 1.25 × 1*
1.2∗2
428∗40∗1
= 1140N/mm2
Sc=SHσc/ZN =1140× 1.2/0.85 =1609N/m²σc.all= ScZN /SH = 1609×2.5/0.85 =4732N/m²
The factor of safety for wear of pinion one becamenc=σc,all/σc =4732/1140 =4
4.1.15 Pinion two Bending and Wear calculationPinion two tooth wear
T=60P/2πNout
T=60*3000/2π*100=286
Wt =
𝑇
𝐷𝑝/2
= t = 286/79.5 = 3.6kN = 3600N
Wt = 3600N
4.1.16 Gear two Bending and Wear calculationGear tooth wear
T=60P/2πNout T=60*3000/2π*100=286
𝑇
𝐷𝑔/2
= Wt=286/199=1.44kN=1440NWt =1440N
σc=ZE√𝑡𝑠
𝑘𝑧 𝑚𝑟
𝑑𝑤𝑏 𝑍𝐽
ZE =4
( 𝜋 )
𝑃
=4(π/16)=0..79
σc=1.6√1440 × 1 × 1.25 × 1*
1.2∗2
428∗40∗1
= 386N/mm2
Sc=SHσc/ZN =386× 1.2/0.85 =545N/mm²
σc.all= ScZN /SH = 545×2.5/0.85 =1600N/m𝑚²

43
The factor of safety for wear of pinion one became nc=σc,all/σc =1600/545 =2.9Gear two
tooth bending.
Wt KV
𝑃𝐷
𝐹
( 𝜋𝐾𝑀 )
𝐽
=1440 × 1.25×
398
1.6
×
1.3
2
=232830N/mm²
σall= StYN =288000 ×1=288000N/mm²
The factor of safety for bending of pinion one isn =σall /σ =288000/232830 =1.
4.2 SHAFT DESIGN
4.2.1 general layout of shaft
4.2.2 Definition of shaft
Shaft is a rotating member, usually of circular cross section, used to transmit power
ormotions. It provides the axis of rotation, or oscillation, of elements such as gears, pulleys,
flywheels, cranks, sprockets, and the like and controls the geometry of their motion. An axle
is a no rotating member thatcarries no torque and is used to support rotating wheels, pulleys,
and the like.. The design of the machine itself will dictate that certain gears, pulleys,bearings,
and other elements will have at least been partially analyzed and their size andspacing
tentatively determined. In this chapter, details of the shaft itself will be examined, including
the following:
 Material selection
 Geometrical layout
 Stress and strength
 Static strength
 Fatigue strength
 Deflection and rigidity
 Bending deflection
 Torsion deflection
 Slope at bearings and shaft-supported elements
 Shear deflection due to transverse loading of short shafts

44
Shaft Materials
Deflection is not affected by strength, but rather by stiffness as represented by the modulus of
elasticity is essentially constant for all steels. For that reason, rigidity cannot be controlled by
materialdecisions, but only by geometric decisions.
The material used for shafts should have the following properties:
 It should have high strength.
 It should have good Machinability.
 It should have low notch sensitivity factor.
 It should have good heat treatment properties.
 It should have high wear resistant properties.
Shaft Layout
Before deciding the overall dimensions of the casing it is necessary determined its inside
dimensionsas follows: dimensions of gears (pitch diameters and face width) calculated from
strength considerations. Distances of two gears in the sameshaft is kept as 10 to 15 mm,inner
periphery boundary of the reducer is drawn at 10 to 15 mm away from the edge ofpinion -
gear pair and for the ends of pinion of the first stage and gear of the last stage.
Figure 4.3 layout of shaft for two stages gear bo
Length of the shaft
Adding it all up gives the intermediate shaft length as 193mm .this means; Assume bearing

45
thickness (H=B) =30mm, D=10mm which is face width of gears in first stage F=8mm
which is face width of gears in second stage C=E=G=15mm which is the space between
two gears in intermediate shaft gears, which is standard in gear box design itsvalueis between
(10mm to 15 mm) for my design thisvalue15mm
The total length of shafts became;
L=30+30+15+15+15+10+8=108mm
4.2.3 Stresses in Shafts
1. Shear stresses due tothe transmission of torque (i.e, due to torsion load).
2. Bending stresses (tensile or compressive) due to the forces acting up on machine
elements like gears,pulleys etc. as well as due to the weight of the shaft itself.
3. Stresses due to combined torsion and bending loads.
Maximum Permissible Working Stresses for Transmission Shafts
According to American Society of Mechanical Engineers (ASME) code for the design of
transmission shafts, the maximum permissible working stresses in tension or compression
may be taken as
 112Mpa for shafts without allowance for key ways.
 84Mpa for shafts with allowance for key ways.
For shafts purchased under definite physical specifications, the permissible tensile stress (σt)
may be taken as 60 per cent of the elastic limit in tension (σel), but not more than 36 percent
of the ultimate tensile strength (σu). In other words, the permissible tensile stress,
σt= 0.6σel or 0.36σu, whichever is less.
The maximum permissible shear stress may be takenas
 56Mpa for shafts without allowance for key ways.
 42Mpa for shafts with allowance for key ways.
Force Analysis
Once the gear diameters are known, and the axial locations of the components are set, the
free- body diagrams and shear force and bending moment diagrams for the shafts can be
produced. With the known transmitted loads, determine the radial and axial loads transmitted
through the gears. From summation of forces and moments on each shaft, ground reaction

46
forces at thebearings can be determined. For shafts with gears and the forces and moments
will usually have components in two planes along the shaft. For rotating shafts, usually only
the resultant magnitude is needed, so force components at bearings are summed as vectors.
Shear force and bending moment diagrams are usually obtained in two planes, and then
summed as vectors at any point of interest. A torque diagram should also be generated to
clearly visualize the transfer of torque from an input component, through the shaft, and to an
output component
Shaft Materials
The material used for shafts should have the following properties :
 It should have high strength.
 It should have good mach inability.
 It should have low notch sensitivity factor.
It should have good heat treatment properties.
It should have high wear resistant properties.
The material used for ordiary shafts is carbon steel of grades 40 C 8, 45 C 8, 50 C 4 and 50
C 12. The mechanical properties of these grades of carbon steel are given in the following
table.
Table-4.5 Mechanical properties of steels used for shafts.
Table-5 Mechanical properties of steels used for shafts.
Standard designation Ultimate tensile strength, MPa Yield strength, MPa
40 C 8 560 – 670 320
45 C 8 610 - 700 360
50 C 4 640 – 760 370
50 C12 700 390
When a shaft of high strength is required, then an alloy steel such as nickel, nickel-chromium
or Chrome vanadium steel is us .For my design C-45 with Yield strength 360 MPa and
Ultimate tensile strength 660Mpa selected
4.2.4 Manufacturing method of Shafts

47
Shafts are generally manufactured by hot rolling and finished to size by cold drawing or
turning and grinding. The cold rolled shafts are stronger than hot rolled shafts but with higher
residual stresses. The residual stresses may cause distortion of the shaft when it is machined,
especially when slots or keyways are cut.
4.2.5 Stresses in Shafts
 Shear stresses due to the transmission of torque (i.e. due to torsional load).
 Bending stresses (tensile or compressive) due to the forces acting upon machine
elementsLikegears as well as due to the weight of the shaft itself.
 Stresses due to combined torsion and bending loads.Most shafts serve to transmit
torque from an input gear or pulley, through the shaft, toan output gear or pulley. Of
course, the shaft itself must be sized to support the torsion stress and torsion
deflection.
It is also necessary to provide a means of transmitting the torque between theshaft and the
gears. Common torque-transfer elements are:
 Keys
 Spines
 Setscrews
 Pins
 Press or shrink fits
 Tapered fits
4.2.6 Endurance Limit Modifying Factors on Shaft
Bending, torsion, and axial stresses may be present in both midrange and alternating
components. For analysis, it is simple enough to combine the different types of stresses into
alternating and midrange von Mises stress It is sometimes convenient to customize the
equationsspecifically for shaft . Axial loads are usually comparatively very small at critical
locations where bending and torsion dominate, so they will be left out of the following
equations.
The fluctuating stresses due to bending and torsion are given by;

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