Design & Analysis of Spur Gears

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A MAJOR PROJECT REPORT ON
MODELLING AND ANALYSIS OF SPUR GEAR
Submitted in partial fulfillment of the requirements
For the award of the degree
BACHELOR OF TECHNOLOGY
IN
MECHANICAL ENGINEERING
Submitted By
MOHD SHAROOQ JAFFER (14401A0392)
M. SRIKANTH (14401A0380)
P. ROHIT (14401A03B2)
K. SHASHIDHAR REDDY (14401A0364)
K. KRISHNA (14401A0367)
Under the esteemed guidance of
Mr. CH. SANDEEP
(Associate Professor)
DEPARTMENT OF MECHANICAL ENGINEERING
DVR COLLEGE OF ENGINEERING & TECHNOLOGY
(Affiliated to JNTUH, Approved by AICTE, New Delhi) KASHIPUR
KANDI, SANGAREDDY.
2017-2018

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DEPARTMENT OF MECHANICAL ENGINEERING
DVR COLLEGE OF ENGINEERING & TECHNOLOGY
(Affiliated to JNTUH, Approved by AICTE, New Delhi)
KASHIPUR, KANDI, SANGAREDDY
This is to certify that the project report entitled “MODELLING AND ANALYSIS OF
SPUR GEAR” is being certified by, bearing
MOHD SHAROOQ JAFFER (14401A0392)
M. SRIKANTH (14401A0380)
P. ROHIT (14401A03B2)
K. SHASHIDHAR REDDY (14401A0364)
K. KRISHNA (14401A0367)
In partial fulfillment for the award of degree of bachelor of technology in mechanical
engineering. The results embodied in this report have not been submitted to any other university
or institute for the award of any degree.
Internal Guide Head of the Department
External Examiner

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ACKNOWLEDGEMENT
The satisfaction and euphoria that accompany the successful completion of any task would be
incomplete without the mentioning of the people whose constant guidance and encouragement
made it possible. We take pleasure in presenting before you, our project, which is a result of
studies of both research and knowledge.
We express our earnest gratitude to our internal guide, Mr. CH. SANDEEP, (Associate
professor, Department of Mechanical Engineering) our project guide for his constant support,
encouragement and guidance. We are grateful for her cooperation and her valuable suggestions.
We express our sincere thanks and regards to Dr. M.J. PRAKASH (Principal),
Mr. A. RADHA KRISHNA, (Professor and Head of Department) and college management for
all their support and encouragement.
Finally, I express my gratitude to all other members who are involved either directly or
indirectly for the completion of this project.

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Abstract
Gear drive plays vital role in power transmission industries. Gears are usually subjected to
fluctuating loads. Due to these loads bending and compressive stresses will be developed in the
gears. While designing the gear it is very important to analyze the stresses for safety operation,
and weight reduction of gear is also one of the design criteria. In this project, the spur gear is
modelled in “CATIA V5” and imported to “ANSYS” for static structural analysis and modal
analysis. Static analysis is performed to determine the deformation and Von-misses stresses.
Modal analysis is performed to determine the natural frequencies and mode shapes. The results
were validated with theoretical calculations by Lewis equation. Analysis is done by considering
different materials for gears like Cast iron, carbon steel, brass, copper. and results are compared.

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INDEX
CONTENTS Page No
CHAPTER-1
INTRODUCTION
1.1 Introduction to Spur Gears 1
1.2 Traction Gear 2
1.2.1 Dimension Specifications 3
1.2.2 Design For Space Constrains 5
1.2.3 Determination Of Number Of Teeth–Interference 7
1.2.4 Design For Mechanical Strength – Lewis Equation 8
1.2.5 A More Realistic Approach – AGMA Strength Equation 9
1.2.6 Design For Surface Resistance 10
CHAPTER-2
REVIEW
2.1 Literature Review 11
2.1.1 Polymer gears in sugarcane juice machine 11
2.1.2 Stress Analysis of Mating Teeth in Spur Gears 11
2.1.3 Material Investigation 12
2.1.4 Free Vibration Behaviour Of Composite Gear 12
2.1.5 Parametric Model of Differential Gear Box 12
2.1.6 Comparative Performance of Materials 13
2.1.7 Computer Aided Analysis of Spur Gears 13
2.1.8 Stress Calculations at Various States 13
2.1.9 Wearing of Spur Gears 14
2.1.10 Contact Stresses Developed in Mating Spur Gears 15
CHAPTER-3
CATIA
3.1 Introduction to CATIA 16
3.2 Details of CATIA 16

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3.3 History of CATIA 16
3.4 Release History 17
3.5 Scope of Applications 18
3.6 Surfacing & Shape Design 18
3.7 Mechanical Engineering 18
3.8 Equipment Design 18
3.9 Starting CATIA 18
3.10 Sketch of the Model 19
3.11 Options Used to Create Solids 20
3.12 Reference Elements 22
3.12.1 Reference Planes 22
3.12.2 Reference Lines 22
3.12.3 Reference Points 22
3.13 Model of Traction Gear 23
3.14 Generative Drafting 24
3.14.1 Views 25
3.14.2 Dimensioning 25
3.14.3 Bill of Material (BOM) 26
3.14.4 Views of Traction Gear 26
CHAPTER-4
ANSYS
4.1 Introduction 28
4.2 Generic Steps to Taking Care of Any Problem in ANSYS 28
4.2.1 Build Geometry 29
4.2.2 Define Material Properties 29
4.2.3 Generative Mesh 29
4.2.4 Apply Loads 29
4.2.5 Obtain Solution 29
4.2.6 Present the Results 29
4.3 Specific Capabilities of ANSYS 30

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4.3.1 Thermal Analysis 30
4.3.2 Fluid Stream Analysis 30
4.4 Computational Fluid Dynamics 32
4.5 Methodology 32
CHAPTER-5
Conclusion 50
REFERENCE 51
List of figures Page No.
1.2 Spur Gear 3
1.2.1 Dimension Specifications 4
1.2.2 Space Constrain of Gear Design 6
1.2.3 A Pair of Gear Teeth Under Interference 7
1.2.4 Gear Tooth Under Load 9
1.2.6 Surface Deformation and Development 12
3.9 Starting CATIA 19
3.10 Sketch of the Model 19
3.13 Model of Traction Gear 23
3.14.3 Views of Traction Gear 24
4.5 Methodology of ANSYS 32
Transient (A5) 35
Total Deformation 41
Directional Deformation 42
Total Velocity 42
Equivalent Elastic Strain 43
Shear Elastic Strain 43
Equivalent Stress 44
Shear Stress 44
Shear Energy 45

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Maximum Principal Elastic Strain 45
Equivalent Total Strain 46
Maximum Principal Stress 46
Structural Error 46
List of tables Page No.
3.2 Details of CATIA 16
3.4 Release History 17
4.5 Table 1 (units) 32
Table 2 (geometry) 33
Table 8 (mesh) 33
Table 9 (mesh controls) 34
Table 10 (transient) 35
Table 11 (initial conditions) 35
Table 12 (initial conditions 2) 35
Table 13 (analysis setting) 36
Table 14 (rotations) 36
Table 15 (model transient loads) 37
Table 16 (model solutions) 39
Table 17 (solutions information) 39
Table 18 (results) 40
Table 19 (total deformation) 41
Table 20 (directional deformation) 41
Table 21 (total velocity) 42

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Table 22 (equivalent elastic strain) 42
Table 23 (shear elastic strain) 43
Table 24 (equivalent stress) 44
Table 25 (shear stress) 45
Table 26 (strain energy) 45
Table 27 (maximum principle strain) 45
Table 28 (equivalent total strain) 46
Table 29 (maximum principle stress) 46
Table 30 (results) 47
Table 31 (structural error) 47
Table 32 (grey cast iron constants) 48
Table 33 (compressive ultimate strength) 48
Table 34 (compressive yield strength) 48
Table 35 (tensile yield strength) 48
Table 36 (tensile ultimate strength) 48
Table 37 (isentropic secant coefficient of TE) 48
Table 38 (isentropic elasticity) 49
Table 39 (isentropic relative permeability) 49

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CHAPTER-1
1. INTRODUCTION:
Gear is an essential component in many machine parts; its application varies from small geared
motor to and complicated aerospace accessories. Human has been familiar about the idea that the
repeated bending of wood or metal back and forth with high amplitude could rupture it. He found
that the repeated stress can produce fracture with stress within elastic limit of material. The
fatigue analysis for structure designing relies on approach which has been progressed over the
last 100 years or so. The very first fatigue analysis has been done by German mining engineer,
W.A.S. Albert who performed number of repeated loading test on iron chain. Fatigue is the most
important failure mode to be considered in a mechanical design. Fatigue is the process of
continuous localized permanent structural change appearing in a material subjected to fluctuating
stress conditions. If the loading limit does not exceed the elastic limit, the body will regain its
original state. Designer should have a good knowledge of analytical and empirical techniques to
get effective results in averting failure. Mechanical failure is observed mainly due to fatigue
design therefore fatigue becomes an obvious design, consideration for many structure such as
aircraft, rail cars, automotive suspension, Vehicle frame and bridgesIn normal conditions,
contact fatigue is one of the most common failure modes for gear tooth surfaces. Gear tooth
interaction causes adhesive wear throughout the life of gear drive.
Under periodic loads, most materials will fracture when submitted to periodic loads over a large
number of cycles. There are two prominent modes of fatigue damage that is root bending stress
and contact stress. The tooth damage is mostly because of maximum bending stress. Mining
machine uses traction gear boxes in transmission system. It consists of single pinion and gear
setup and these gears are also known as speed reducer, gear head, gear reducer etc. which
consists of bearings and set of gear shafts. Gear analysis was performed using analytical methods
approach but nowadays computers have become more developed and use for numerical models
to predict fatigue behavior. Gear is an essential component in many machines. They are used in
many high speed applications.

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As gears transmit motion and power through surface contact, their performance depends on reliability
of their teeth surface. There are some wear modes such as contact fatigue, adhesion, abrasive,
corrosion. In case of gears, bending stress and contact stress are prominent modes of fatigue failure.
The contact fatigue process can be divided into two main stages: initiation of micro-cracks and crack
propagation. Initiation of fatigue cracks represents one of the most important stages in which cracks can
be initiated either on the surface or at some distance under the surface depending on the contact
conditions.
The main aim of this study is to predict contact fatigue crack initiation resulting from high
stresses or strains during the meshing process. These contact stresses are generally at their
highest at some distance under the surface, where initial cracks are most likely to appear. In
order to increase the bending fatigue strength at the tooth root fillet of gears, gears with high
pressure angle and positive addendum modification factor are generally adopted. Bharat Gupta
et. al. has considered contact stress, the deciding factor to determine the required dimension of
gears. Thorough studies of contact stress developed between the different mating gears are
mostly important for gear design. Analytic methods of calculating gear contact stresses use
Hertz’s equations, which were originally derived for contact between two cylinders
Gears are commonly made from metal, plastic, and wood. Although gear cutting is a substantial
industry, many metal and plastic gears are made without cutting, by processes such as die
casting or injection molding. Some metal gears made with powder metallurgy require subsequent
machining, whereas others are complete after sintering. Likewise, metal or plastic gears made
with additive manufacturing may or may not require finishing by cutting, depending on
application.
1.2 TRACTION GEAR:
Traction gear or straight-cut gears are the simplest type of gear. They consist of a cylinder or
disk with teeth projecting radially. Though the teeth are not straight-sided (but usually of special
form to achieve a constant drive ratio, mainly involute but less commonly cycloidal), the edge of
each tooth is straight and aligned parallel to the axis of rotation. These gears mesh together

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correctly only if fitted to parallel shafts. No axial thrust is created by the tooth loads. Spur gears
are excellent at moderate speeds but tend to be noisy at high speeds.
The spur gear is simplest type of gear manufactured and is generally used for transmission of
rotary motion between parallel shafts. The spur gear is the first choice option for gears except
when high speeds, loads, and ratios direct towards other options. Other gear types may also be
preferred to provide more silent low vibration operation. A single spur gear is generally selected
to have a ratio range of between 1:1 and 1:6 with a pitch line velocity up to 25 m/s. The spur gear
has an operating efficiency of 98-99%. The pinion is made from a harder material than the
wheel. A gear pair should be selected to have the highest number of teeth consistent with a
suitable safety margin in strength and wear. The minimum number of teeth on a gear with a
normal pressure angle of 20 degrees is 18.This is a cylindrical shaped gear in which the teeth are
parallel to the axis. It has the largest applications and, also, it is the easiest to manufacture. They
are simple in construction, easy to manufacture and cost less. They have highest efficiency and
excellent precision rating. They are used in high speed and high load application in all types of
trains and a wide range of velocity ratios. Hence, they find wide applications right from clocks,
household gadgets, motor cycles, automobiles, and railways to aircrafts.
Spur gears are regularly used for speed reduction or increase, torque multiplication, resolution
and accuracy enhancement for positioning systems. The teeth run parallel to the gear axis and
can only transfer motion between parallel-axis gear sets. Spur gears mate only one tooth at a
time, resulting in high stress on the mating teeth and noisy operation.

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1.2.1 Dimension Specifications:
Gears mate via teeth with very specific geometry. Pitch is a measure of tooth spacing and is
expressed in several ways.
Diametral pitch (DP) is the ratio of the number of teeth to the pitch diameter of a gear; a higher
DP therefore indicates finer tooth spacing. It is easily calculated by the formula DP= (N+2) ÷
OD, where N is the number of teeth, and OD represents the circumferential measurement.
Circular pitch (CP) is a direct measurement of the distance from one tooth center to the adjacent
tooth center. It can be measured by the formula CP= Π ÷ DP.
Module (M) is a typical gear discipline and is a measurement of the size and teeth number of the
gear. Gears measured in inches earn 'English module' distinction to prevent confusion. M = OD
÷ N
Pressure angle is the angle of tooth drive action, or the angle between the line of force between
meshing teeth and the tangent to the pitch circle at the point of mesh. Typical pressure angles are
14.5° or 20°.

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1.2.2 Design For Space Constrains
The designed gear system should fit within a space limit. So the designer could say if he sums
pitch diameters of the mating gears, it should be less than or equal to allowable space limit as
shown in figure below.

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The blue rectangle represents space on which gear should get fit. One can take 80% of width of
this space as allowable width for gear design. So following is the relation obtained by this
condition.
fig .3 Space constrain of gear design
We also know speed ratio of gears, this will lead to one more relation in terms of pitch circle
diameters.
By solving above 2 equations simultaneously we can obtain pitch circle diameters of both the
gears.
1.2.3 Determination of Number of Teeth – Interference
Here we will understand how to determine number of teeth on both the gears. To do this we have
to assume number of teeth on one gear(T1), say the smaller gear. Now using the relation given
below we can determine number of teeth on other gear,T2.

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So we got number of teeth on both the gears, but one should also check for a phenomenon called
interference if gear system has to have a smooth operation. Interference happens when gear teeth
has got profile below base circle. This will result high noise and material removal problem. This
phenomenon is shown in following figure.
If one has to remove interference , the pinion should have a minimum number of teeth specified
by following relation.
Fig.4 A pair of gear teeth under interference
Where aw represents addendum of tooth. For 20 degree pressure angle(which is normally taken
by designers) aw = 1 m and bw = 1.2 m. Module m, and pitch circle diameter Pd are defined as
follows.

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1.2.4 Design for Mechanical Strength - Lewis Equation
Now the major parameter remaining in gear design is width of the gear teeth, b. This is
determined by checking whether maximum bending stress induced by tangential component of
transmitted load, Ft at the root of gear is greater than allowable stress. As we know power
transmitted, P and pitch line velocity V of the gear Ft can be determined using following relation.
Here we consider gear tooth like a cantilever which is under static equilibrium. Gear forces and
detailed geometry of the tooth is shown in figure below.
One can easily find out maximum value of bending stress induced if all geometrical parameters
shown in above figure are known. But the quantities t and l are not easy to determine, so we use
an alternate approach to find out maximum bending stress value using Lewis approach.
Maximum bending stress induced is given by Lewis bending equation as follows.
Where Y is Lewis form factor, which is a function of pressure angle, number of teeth and
addendum and dedendum. Value of Y is available as in form of table or graph. Using above
relation one can determine value of b, by substituting maximum allowable stress value of

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material in LHS of equation. But a gear design obtained so will be so unrealistic, because in this
design we are considering gear tooth like a cantilever which is under static equilibrium. But
that's not the actual case. In next session we will incorporate many other parameters which will
affect mechanical strength of the gear in order to get more realistic design.
1.2.5 A More Realistic Approach - AGMA Strength Equation:
When a pair of gear rotates we often hear noise from this, this is due to collision happening
between gear teeth due to small clearance in between them. Such collisions will raise load on the
gear more than the previously calculated value. This effect is incorporated in dynamic loading
loading factor, Kv value of which is a function of pitch line velocity.
At root of the gear there could be fatigue failure due to stress concentration effect. Effect of
which is incorporated in a factor called Kf value of which is more than 1.
There will be factors to check for overload (Ko) and load distribution on gear tooth (Km). While
incorporating all these factors Lewis stregth equation will be modified like this
The above equation can also be represented in an alternating form (AGMA Strength equation)
like shown below
Where J is
Using above equation we can solve for value of b, so we have obtained all the output parameters
required for gear design. But such a gear does not guarantee a peacefull operation unless it does
not a have enough surface resistance.

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1.2.6 Design for surface resistance:
Usually failure happens in gears due to lack of surface resistance, this is also known as pitting
failure. Here when 2 mating surfaces come in contact under a specified load a contact stress is
developed at contact area and surfaces get deformed. A simple case of contact stress
development is depicted below, where 2 cylinders come in contact under a load F.
Fig.7 Surface deformation and development of surface stress due to load applied
For a gear tooth problem one can determine contact stress as function of following parameters
If contact stress developed in a gear interface is more than a critical value(specified by AGMA
standard), then pitting failure occurs. So designer has to make sure that this condition does not
arise.

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CHAPTER- 2
2.1 LITERATURE REVIEW:
The purpose of the paper is to examine the load capacity of PC/ABS spur gears and investigation
of gear damage. Further in this study usability of PC/ABS composite plastic material as spur gear
was investigated and was defined that PC/ABS gears were tested by applying three different
loading at two different numbers of revolutions on the FZG experiment set. The experiment
result summarized that the usage of PC/ABS materials brings an advantage in many industrial
area because such materials are durable against flame, air, ultraviolet lights and holding lower
moister than PA66 GFR 30 materials. The another result of this study was that good operating
condition are comprised at low numbers of revolution and the tooth loads. Further the suitable
environmental condition must be revolutions and the tooth load for gears. PC/ ABS gear should
be preferred at low tooth and unwanted high power transmission.
2.1.1 Polymer gears in sugarcane juice machine This paper describes design and analysis of
spur gear and it is proposed to substitute the metallic gears of sugarcane juice machine with
polymer gears to reduce the weight and noise. A virtual model of spur gear was created in PRO-
E, Model is imported in ANSYS 10.0 for analysis by applying normal load condition. The main
purpose of this paper to analysis the different polymer gears namely nylon, polycarbonate and
their viability checked with counterpart metallic gear like as cast iron. Concluding the study
using the FEA methodology, it can be proved that the composite gears, if well designed and
analysed, will give the useful properties like as a low cost, noise, Weight, vibration and perform
its operation similar to the metallic gears. Based on the static analysis Nylon gear are suitable for
the application of sugarcane juice machine under limited load condition in comparison with cast
iron spur gears.
2.1.2 Stress Analysis of Mating Teeth in Spur Gears This paper presents the stress analysis of
mating teeth of the spur gear to find maximum contact stress in the gear tooth. The results
obtained from finite element analysis are compared with theoretical Hertz equation values. The
spur gear are modelled and assembled in ANSYS DESIGN MODELER and stress analysis of
Spur gear tooth is done by the ANSYS 14.5 software. It was found that the results from both
Hertz equation and Finite Element Analysis are comparable. From the deformation pattern of

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steel and grey cast iron, it could be concluded that difference between the maximum values of
steel and grey CI gear deformation is very less.
2.1.3 Material Investigation In this paper, Metallic material Cast iron and Non Metallic
material Nylon are investigated. The stress analysis of the lathe machine headstock gear box are
analyzed by finite element analysis. Analytical bending stress is calculate by two formula Lewis
formula and AGMA formula. Analytical results is compared with the finite element method
result for validation. Concluding the study, we observed that finite element method software
ANSYS have values of stress distribution were in good agreement with the theoretical results.
Besides non metallic material can be used instead of metallic material because non metallic
material provide extra benefits like as less cost, self lubricating, low noise, low vibration and
easy manufacturing.
2.1.4 Free Vibration Behaviour of Composite Spur Gear The objective of this paper is to
study the free vibration behaviour of composite spur gear using finite element method which is
also known as first order shear deformation plate theory (FSDT). The finite element analysis has
been carried out for composite gear as a 4 nodded and 8 nodded quadrilateral element with each
nodes has five degree of freedom. Finite element formulation of composite gear is modelled and
coded using MATLAB. Based on the numerical analysis which is carried out for of spur gear the
following important conclusion can be drawn. The developed MATLAB code is validated with
the available result and it can be concluded that the present FE code result are in good agreement
with those of reference. Fundamental frequencies obtained for composite spur gear using
MATLAB are presented. It is found that natural frequency increases with increase in fibre
orientation.
2.1.5 Parametric model of Differential Gear Box In this paper the parametric model of
differential gear box is developed using some parameters i.e. ( number of teeth, Pressure angle,
helix angle, tooth thickness, module) in CATIA-V5 and weight analysis of differential gear box
for different material ( Aluminium alloy, alloy steel, cast iron, Glass filled Polyamide) under
static loading condition using FEA. The case study shows that the composite material can be
used effectively in place of metallic material because the weight of Glass filled Polyamide
composite material of differential is reduced by 60% Comparing with the traditional materials

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(Aluminium alloy, Alloy Steel, Cast iron). So, we conclude that Glass filled Polyamide
Composite material is selected as a best material for differential gear box.
2.1.6 Comparative Peformance of Materials In this study the comparative performance spur
gear of 30% Glass filled PA66 and 30% Glass filled PEEK was investigated at different torque
and speed. Wear test of the spur gear pairs and the experiment spur gear tooth were performed on
a FZG test machine. A weight loss is measured by 0.0001g sensitive weighing machine and the
tooth temperature of gear is measured by Impact infrared thermometer. After summarized the
experimental result of PA66 GF30 gears and PEEK GF30 gears are at different torque and
speeds. The tooth temperature increases with increase in torque and increased temperature
resulted into thermal softening of gear tooth which further increases specific wear rate. The
comparative results of PA66 GF30 and PEEK GF30 gears show that the specific wear rate of
PA66 GF30 is much higher than PEEK GF30 at all torque and speeds. Therefore the torque
transmission capacity of PEEK GF30 is higher than PA66 GF30.
2.1.7 Computer Aided Analysis of Spur Gears In this paper using ANSYS workbench
software, bending stress, contact stress and static load on the tooth of spur gear drive is found.
The Hertz theory and Lewis formula also are used for theoretical calculation of contact stress and
bending stress of spur gear. We observed that Theoretically results obtained by Lewis formula
and Hertz equation are comparable with finite element analysis of spur gear, keeping in mind the
comparison we can conclude that the finite element analytical result can be better as a problem
solving software and used for other analyzing purpose.
2.1.8 Stress Calculations at Various States The objective of paper is to study the various stress
state of spur gear. They calculated the tangential and radial forces which acts on various point
upon that basis we can analyze by applying the forces. By using Ansys software bending stress
and contact stress on the tooth of spur gear drive is found Gears are machine elements used to
transmit power between rotating shafts by means of engagement of projection called teeth. Gears
are most common means of transmitting power in the wooden mechanical world. They vary from
a tiny size used in watches to larger gears used in massive speed reducers, bridge lifting
mechanism and rail road turn table drive. The gears are vital elements of main and auxiliary
mechanism in many machines such as automobiles, tractors, metal cutting machine tools rolling
mills hosting and transmitting and transporting machinery, massive engines etc.

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2.1.9 Wearing of Spur gears Says that Spur gear wears either due to rubbing action between the
meshed gears or by the occurrence of unwanted elements like dust particles, metal fragments,
etc. which reduces its efficiency and service life. It is always a challenging task to determine the
remaining life of a component or the strength of a component once wear has occurred on teeth
surface. This paper presents an application of reverse engineering approach for reconstruct the

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spur gear 3D CAD model using scanned data. A gear has been scanned using PICZA 3D laser
scanner (RolandLPX60).
2.1.10 Contact Stresses Devloped in Mating Spur Gear Made an attempt to summarize about
contact stresses developed in a mating spur gear which has involute teeth. A pair of spur gears
are taken from a lathe gear box and proceeded forward to calculate contact stresses on their teeth.
Contact failure in gears is currently predicted by comparing the calculated Hertz contact stress to
experimentally determined allowable values for the given material. The method of calculating
gear contact stress by Hertz‟s equation originally derived for contact between two cylinders.
Analytically these contact stresses are calculated for different module, and these results are
compared with the results obtained in modeling analysis in ANSYS.

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CHAPTER- 3
3.1 INTRODUCTION TO CATIA:
CATIA (Computer Aided Three-dimensional Interactive Application) is a multi-platform
CAD/CAM/CAE commercial software suite developed by the French company Assault
Systems. Written in the C++ programming language, CATIA is the cornerstone of the Assault
Systems product lifecycle management software suite.
CATIA competes in the CAD/CAM/CAE market with Siemens NX, Pro/E, Autodesk Inventor,
and Solid Edge as well as many others.
3.2 DETAILS OF CATIA:
3.3 HISTORY OF CATIA:
CATIA started as an in-house development in 1977 by French aircraft manufacturer
Avions Marcel Dassault, at that time customer of the CADAM CAD software to develop
Dassault's Mirage fighter jet, then was adopted in the aerospace, automotive, shipbuilding, and
other industries.
Initially named CATI (Conception Assisted Tridimensional Interactive - French for Interactive
Aided Three-dimensional Design) - it was renamed CATIA in 1981, when Dassault created a
subsidiary to develop and sell the software, and signed a non-exclusive distribution agreement
with IBM.
Developer(s) Dassault`s Systems
Stable release V6R2011x / November 23, 2010
Operating system Unix / Windows
Type CAD software
License Proprietary
Website WWW.3ds.com

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In 1984, the Boeing Company chose CATIA as its main 3D CAD tool, becoming its largest
customer. In 1988, CATIA version 3 was ported from mainframe computers to UNIX. In 1990,
General Dynamics Electric Boat Corp chose CATIA as its main 3D CAD tool, to design the U.S.
Navy's Virginia class submarine.
In 1992, CADAM was purchased from IBM and the next year CATIA CADAM V4 was
published. In 1996, it was ported from one to four UNIX operating systems, including IBM AIX,
Silicon Graphics IRIX, Sun Microsystems SunOS and Hewlett-Packard HP-UX.
In 1998, an entirely rewritten version of CATIA, CATIA V5 was released, with support for
UNIX, Windows NT and Windows XP since 2001.
In 2008, Dassault announced and released CATIA V6. While the server can run on Microsoft
Windows, Linux or AIX, client support for any operating system other than Microsoft Windows
is dropped.
3.4 RELEASE HISTORY:
Name/Version Latest Build Number Original Release Date Latest Release Date
CATIA v4 R25 1993 January 2007
CATIA v5 R20 1998 February 2010
CATIA v6 R2012 29/05/2008 May 2011
SUPPORTED OPERATING SYSTEMS AND PLATFORMS
CATIA V6 runs only on Microsoft Windows and Mac OS with limited products.
CATIA V5 runs on Microsoft Windows (both 32-bit and 64-bit), and as of Release 18Service
Pack4 on Windows Vista 64.IBM AIX, Hewlett Packard HP-UX and Sun Microsystems Solaris
are supported.
CATIA V4 is supported for those Unixes and IBM MVS and VM/CMS mainframe platforms up
to release 1.7.
CATIA V3 and earlier run on the mainframe platforms.

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3.5 SCOPE OF APPLICATION:
Commonly referred to as 3D Product Lifecycle Management software suite, CATIA supports
multiple stages of product development (CAx), from conceptualization, design (CAD),
manufacturing (CAM), and engineering (CAE). CATIA facilitates collaborative engineering
across disciplines, including surfacing & shape design, mechanical engineering, equipment and
systems engineering.
3.6 SURFACING & SHAPE DESIGN:
CATIA provides a suite of surfacing, reverse engineering, and visualization solutions
to create, modify, and validate complex innovative shapes. From subdivision, styling, and Class
A surfaces to mechanical functional surfaces.
3.7 MECHANICAL ENGINEERING:
CATIA enables the creation of 3D parts, from 3D sketches, sheet metal, composites,
and molded, forged or tooling parts up to the definition of mechanical assemblies. It provides
tools to complete product definition, including functional tolerances, as well as kinematics
definition.
3.8 EQUIPMENT DESIGN:
CATIA facilitates the design of electronic, electrical as well as distributed
systems such as fluid and HVAC systems, all the way to the production of documentation for
manufacturing.
3.9 STARTING CATIA
To start CATIA there may be icon on the desktop or you may have to look in start
menu at the bottom of leaf of the screen windows taskbar .The program takes a while to load, so
be patient the start-up is complete when your screen looks like the following figure ,which is a
default CATIA screen.
There are different modules in CATIA using which different tasks can be performed. The main
window and modules of CATIA shown in figure:

29
Model of traction gear
Views of traction gear

30
3.11 OPTIONS USED TO CREATE SOLIDS
Pad - Pad is a method of defining three-dimensional geometry by projecting a two-dimensional
section at a specified distance normal to the sketching plane.
Pocket - Pocket is a method of extruding a profile or a surface and removing the material resulting
from the extrusion
Shaft - The Shaft tool creates a feature by revolving a sketched section around a centerline.
Fillet - A fillet is a curved face of a constant or variable radius that is tangent to, and that joins, two
surfaces. Together, these three surfaces form either an inside corner or an outside corner.
Chamfer - Chamfering consists in removing or adding a flat section from a selected edge to
create a beveled surface between the two original faces common to that edge.
Draft - Drafts are defined on molded parts to make them easier to remove from molds.
Thickness – Adds or removes to the faces.
Translation– Moving a body.
Mirror - Mirroring a body or a list of features consists in duplicating these elements using
symmetry by selecting a face or plane as reference.
Pattern - To duplicate the whole geometry of one or more features and to position this
geometry on a part.
3.12 REFERENCE ELEMENTS:
Reference elements are used as references for constructing the model. They are not geometry
features, but they aid in geometry construction by acting as references for sketching a feature,
orienting the model, assembles, components, and so on. Because of their versatility references
are frequently used.

31
1. Reference plane
2. Reference line
3. Reference points
3.12.1 REFERENCE PLANES:
Datum planes are used as reference to construct feature. Datum planes are considered feature, but
they are not considered model geometry. Datum planes can be created and used as a sketch plane
where no suitable exists.
Reference plane options used are: Thru plane, Offset plane, 9ffset coordinate system, Blend
section, thru axis, Thru Point/Vertex, Normal to axis, Tangent to cylinder, Angle to the plane etc.
3.12.2 REFERENCE LINES:
Reference lines are used to create surfaces and other features, or as a sweep trajectories. User
sketch reference line in the same manner as any other features. Sketched curves can consist of
one or more sketched segment and of one or more open or closed loop.
Reference lines option used are: Sketch, Intersection surface, thru point, Form files,
Composite, Projected, Formed, Split, Offset from surface, from curve, from curve, from
boundary, Offset curve, Form equation etc.
3.12.3 REFERENCE POINTS: points are used to specify point loads for mesh generation,
attach datum targets and notes in drawings, and create coordinate systems and pipe feature
trajectories. User can also place axis, planes, holes and shafts at a point.
Point options used are: On surface, Offset surface, Curve coordinate surface, on vertex, Offset
coordinate system, three surfaces, at center, on curve, on surface, Offset point etc.

32
3.13 MODEL OF TRACTION GEAR:
Circular pattern definition

33
Assembly the gears:
3.14 GENERATIVE DRAFTING:
Generative Drafting is a new generation product that provides users with powerful functionalities
to generate drawings from 3D parts and assembly definitions.

34
The Generative Drafting has been designed to show you how to generate drawings of varying
levels of complexity, as well as apply dimensions, annotations and dress-up elements to these
drawing.
Start – Mechanical Design – Drafting
3.14.1 Views
Front View - A front view is a projection view obtained by drawing perpendiculars from all
points on the edges of the part to the plane of projection. The plane of projection upon which the
front view is projected is called the frontal plane.
Projection View – Projection views are views conceived to be drawn or projected onto planes
known as projection planes. A transparent plane or pane of glass representing a projection plane
is located parallel to the front surfaces of the part.
Isometric View – The Isometric View command enables to create a 2D view with any
orientation, this orientation being the same as the one in the 3D viewer. Among other results, and
depending on how the 3D viewer is oriented when created the view, can obtain a regular X-Y-Z
isometric view.
3.14.2 Dimensioning
Generate Dimensions - To generate dimensions in one shot from the constraints of a 3D
part. Only the following constraints can be generated: distance, length, angle, radius and
diameter.
Dimensions- To create and modify dimensions. These dimensions will be associative to the
elements created from a part or an assembly. When created, these elements are associated with a
view.
Generate Balloons – To generate balloons automatically to the components of an assembly
which are previously generated in assembly.

35
Text - To create a text, with possible line wrapping.
3.14.3 Bill of Material [BOM]
The Bill of Material, or parts list, corresponds to information on the product from which the
views were generated. It consists of an itemized list of the parts of a structure shown on a
drawing or on an assembly.
3.14.3 Views of traction gear:

36
Drafting Views
CHAPTER- 4
ANSYS
4.1 INTRODUCTION
ANSYS is universally useful limited component investigation (FEA) programming
bundle. Limited Element Analysis is a numerical technique for deconstructing a mind boggling
framework into little pieces (of client assigned size) called components. The product executes
conditions that administer the conduct of these components and illuminates them all; making an
extensive clarification of how the framework goes about overall. These outcomes at that point
can be introduced in arranged or graphical structures. This sort of investigation is regularly
utilized for the outline and advancement of a framework extremely complex to break down by
hand. Frameworks that may fit into this class are excessively mind boggling due, making it
impossible to their geometry, scale, or representing conditions.
ANSYS is the standard FEA showing instrument inside the Mechanical Engineering
Department at numerous schools. ANSYS is likewise utilized as a part of Civil and Electrical
Engineering, and additionally the Physics and Chemistry divisions.
ANSYS gives a financially savvy approach to investigate the execution of items or
procedures in a virtual domain. This kind of item advancement is named virtual prototyping.
With virtual prototyping procedures, clients can repeat different situations to streamline
the item well before the assembling is begun. This empowers a lessening in the level of hazard,
and in the cost of inadequate plans. The multifaceted idea of ANSYS additionally gives a way to
guarantee that clients can see the impact of a plan in general conduct of the item, be it
electromagnetic, warm, mechanical and so on.
4.2 GENERIC STEPS TO TAKING CARE OF ANY PROBLEM IN ANSYS:
Like taking care of any issue diagnostically, you have to characterize (1) your answer
space, (2) the physical model, (3) limit conditions and (4) the physical properties. You at that
point take care of the issue and present the outcomes. In numerical techniques, the fundamental

37
distinction is an additional progression called work era. This is the progression that partitions the
unpredictable model into little components that wind up plainly feasible in a generally
excessively complex circumstance. Beneath portrays the procedures in phrasing marginally more
adjust to the product.
4.2.1 BUILD GEOMETRY :
Build an a few dimensional portrayal of the protest be demonstrated and tried utilizing
the work plane directions framework inside ANSYS.
4.2.2 DEFINE MATERIAL PROPERTIES:
Since the part exists, characterize a library of the fundamental materials that make the
question (or venture) being displayed. This incorporates warm and mechanical properties.
4.2.3GENERATE MESH:
Now ANSYS comprehends the cosmetics of the part. Presently characterize how the
displayed framework ought to be separated into limited pieces.
4.2.4 APPLY LOADS:
Once the framework is completely composed, the last assignment is to trouble the
framework with imperatives, for example, physical loadings or limit conditions.
4.2.5 OBTAIN SOLUTION:
This is really a stage, in light of the fact that ANSYS needs to comprehend inside what
state (enduring state, transient… and so on.) the issue must be illuminated.
4.2.6 PRESENT THE RESULTS:
After the arrangement has been gotten, there are numerous approaches to display
ANSYS' comes about, browse numerous choices, for example, tables, charts, and shape plots.

38
4.3 SPECIFIC CAPABALITIES OF ANSYS:
4.3.1 THERMAL ANALYSIS:
ANSYS is equipped for both consistent state and transient examination of any strong
with warm limit conditions.
Unfaltering state warm examinations ascertain the impacts of relentless warm loads on a
framework or part. Clients regularly play out a relentless state examination before doing a
transient warm investigation, to help build up introductory conditions. An enduring state
investigation likewise can be the last stride of a transient warm examination; performed after
every single transient impact have reduced. ANSYS can be utilized to decide temperatures,
warm angles, warm stream rates, and warmth fluxes in a protest that are caused by warm loads
that don't shift after some time. Such loads incorporate the accompanying:
• Convection
• Radiation
• Heat stream rates
• Heat fluxes (warm stream per unit territory)
• Heat era rates (warm stream per unit volume)
• Constant temperature limits
An enduring state warm examination might be either straight, with steady material
properties; or nonlinear, with material properties that rely upon temperature. The warm
properties of most material change with temperature. This temperature reliance being calculable,
the examination ends up plainly nonlinear. Radiation limit conditions additionally make the
investigation nonlinear. Transient counts are time ward and ANSYS can both explain
appropriations and in addition make video for time incremental presentations of models.
4.3.2 FLUID STREAM ANALYSIS
The ANSYS/FLOTRAN CFD (Computational Fluid Dynamics) offers extensive instruments for
dissecting two-dimensional and three-dimensional liquid stream fields. ANSYS is equipped for

39
Demonstrating a tremendous scope of investigation sorts, for example, airfoils for weight
examination of plane wings (lift and drag), stream in supersonic spouts, and mind boggling,
three-dimensional stream designs in a pipe twist. What's more, ANSYS/FLOTRAN could be
utilized to perform errands including:
• Calculating the gas weight and temperature dispersions in a motor ventilation system
• Studying the warm stratification and separation in funneling frameworks
• Using stream blending concentrates to assess potential for warm stun
• Doing normal convection examinations to assess the warm execution of chips in
electronic nooks
• Conducting heat exchanger ponders including distinctive liquids isolated by strong
locales
FLOTRAN investigation gives a precise approach to compute the impacts of liquid streams in
complex solids without using the run of the mill warm exchange similarity of warmth flux as
liquid stream. Sorts of FLOTRAN investigation that ANSYS can perform include:
• Laminar or Turbulent Flows
• Thermal Fluid Analysis
• Adiabatic Conditions
• Free surface Flow
• Compressible or incompressible Flows
• Newtonian or Non-Newtonian Fluids
• Multiple species transport
*NOTE: These sorts of investigations are not totally unrelated. For instance, a laminar
investigation can be warm or adiabatic. A turbulent examination can be compressible or
incompressible.

40
4.4 COMPUTATIONAL FLUID DYNAMICS:
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis
and data structures to solve and analyze problems that involve fluid flows. Computers are used to
perform the calculations required to simulate the interaction of liquids and gases with surfaces
defined by boundary conditions. With high-speed supercomputers, better solutions can be
achieved. Ongoing research yields software that improves the accuracy and speed of complex
simulation scenarios such as transonic or turbulent flows. Initial experimental validation of such
software is performed using a wind tunnel with the final validation coming in full-scale testing
4.5 METHODOLOGY:
In all of these approaches the same basic procedure is followed.
 During preprocessing
 The geometry and physical bounds of the problem can be defined using computer aided
design (CAD). From there, data can be suitably processed (cleaned-up) and the fluid
volume (or fluid domain) is extracted.
 The volume occupied by the fluid is divided into discrete cells (the mesh). The mesh may
be uniform or non-uniform, structured or unstructured, consisting of a combination of
hexahedral, tetrahedral, prismatic, pyramidal or polyhedral elements.
 The physical modeling is defined – for example, the equations of fluid motion + enthalpy
+ radiation + species conservation
 Boundary conditions are defined. This involves specifying the fluid behaviour and
properties at all bounding surfaces of the fluid domain. For transient problems, the initial
conditions are also defined.
 The simulation is started and the equations are solved iteratively as a steady-state or
transient.
 Finally, a postprocessor is used for the analysis and visualization of the resulting solution.

41
methodology
 Material Data
o Gray Cast Iron
Units
TABLE 1
Unit System Metric (cm, g, dyne, s, V, A) Degrees rad/s Celsius
Angle Degrees
Rotational Velocity rad/s

42
Temperature Celsius
Geometry
TABLE 2
Model (A4) > Geometry
Object Name Geometry
State Fully Defined
Bounding Box
Length X 6. cm
Length Y 47.958 cm
Length Z 26.542 cm
Properties
Volume 4515.4 cm³
Mass 32511 g
Scale Factor Value 1.
Statistics
Bodies 2
Active Bodies 2
Nodes 81836
Elements 48728
Mesh Metric None
Mesh
TABLE 8
Model (A4) > Mesh
Object Name Mesh
State Solved
Display
Display Style Body Color
Defaults

43
Physics Preference Mechanical
Solver Preference Mechanical APDL
Relevance 0
Sizing
Use Advanced Size Function Off
Relevance Center Fine
Element Size Default
Initial Size Seed Active Assembly
Smoothing Medium
Transition Fast
Span Angle Center Coarse
Minimum Edge Length 8.8929e-004 cm
Inflation
Use Automatic Inflation None
Inflation Option Smooth Transition
Transition Ratio 0.272
Maximum Layers 5
Growth Rate 1.2
Inflation Algorithm Pre
View Advanced Options No
Statistics
Nodes 81836
Elements 48728
Mesh Metric None
TABLE 9
Model (A4) > Mesh > Mesh Controls
Object Name Body Sizing
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 2 Bodies
Definition
Suppressed No

44
Type Element Size
Element Size Default
Behavior Soft
Transient (A5)
TABLE 10
Model (A4) > Analysis
Object Name Transient (A5)
State Solved
Definition
Physics Type Structural
Analysis Type Transient
Solver Target Mechanical APDL
Options
Environment Temperature 22. °C
Generate Input Only No
TABLE 11
Model (A4) > Transient (A5) > Initial Conditions
Object Name Initial Conditions
State Fully Defined

45
TABLE 12
Model (A4) > Transient (A5) > Initial Conditions > Initial Condition
Object Name Modal (None)
State Fully Defined
Definition
Pre-Stress Environment None
TABLE 13
Model (A4) > Transient (A5) > Analysis Settings
Object Name Analysis Settings
State Fully Defined
TABLE 14
Model (A4) > Transient (A5) > Rotations
Object Name Rotational Velocity
State Fully Defined
Scope
Geometry 2 Bodies
Definition
Define By Vector
Magnitude 261.8 rad/s (step applied)
Axis Defined
Suppressed No
FIGURE 1
Model (A4) > Transient (A5) > Rotational Velocity

46
TABLE 15
Model (A4) > Transient (A5) > Loads
Object Name Frictionless Support Force Force 2
State Fully Defined
Scope
Geometry 4 Faces 8 Faces 10 Faces
Definition
Type Frictionless Support Force
Suppressed No
Define By Vector
Magnitude 1.5333e+008 dyne (step applied)
Direction Defined
FIGURE 2
Model (A4) > Transient (A5) > Force

47
FIGURE 3
Model (A4) > Transient (A5) > Force 2

48
Solution (A6)
TABLE 16
Model (A4) > Transient (A5) > Solution
Object Name Solution (A6)
State Solved
Adaptive Mesh Refinement
Max Refinement Loops 1.
Refinement Depth 2.
Information
Status Done
Post Processing
Calculate Beam Section Results No
TABLE 17
Model (A4) > Transient (A5) > Solution (A6) > Solution Information
Object Name Solution Information

49
State Solved
Solution Information
Solution Output Solver Output
Newton-Raphson Residuals 0
Update Interval 2.5 s
Display Points All
FE Connection Visibility
Activate Visibility Yes
Display All FE Connectors
Draw Connections Attached To All Nodes
Line Color Connection Type
Visible on Results No
Line Thickness Single
Display Type Lines
TABLE 18
Model (A4) > Transient (A5) > Solution (A6) > Results
Object
Name
Total
Deforma
tion
Directio
nal
Deforma
tion
Total
Veloci
ty
Equival
ent
Elastic
Strain
Shear
Elasti
c
Strain
Equivale
nt Stress
Shear
Stress
Strain
Energ
y
Maxim
um
Princip
al
Elastic
Strain
Equival
ent
Total
Strain
Maximu
m
Principal
Stress
Results
Minim
um
1.9389e
-006 cm
-
2.1588e
-004 cm
3.845
7e-
006
cm/s
2.2434
e-007
cm/cm
-
1.055
9e-
004
cm/c
m
2.0203e
+005
dyne/cm²
-
4.5372e
+007
dyne/cm²
2.820
1e-
003
erg
-
4.3175
e-006
cm/cm
2.2434
e-007
cm/cm
-
3.1094e
+007
dyne/cm²
Maxim
um
5.1941e
-003 cm
2.1574e
-004 cm
1.030
2e-
002
cm/s
6.1114
e-004
cm/cm
1.129
8e-
004
cm/c
m
6.7215e
+008
dyne/cm²
4.8545e
+007
dyne/cm²
16586
erg
5.5413
e-004
cm/cm
6.1114
e-004
cm/cm
5.6564e
+008
dyne/cm²

50
Minim
um
Occur
s On
Part 2 Part 1 Part 2 Part 1 Part 2 Part 1 Part 2 Part 1 Part 2
Maxim
um
Occur
s On
Part 2
Information
Time 1. s
Load
Step
1
TABLE 19
Model (A4) > Transient (A5) > Solution (A6) > Total Deformation
Time [s] Minimum [cm] Maximum [cm]
1. 1.9389e-006 5.1941e-003
Total deformation
TABLE 20
Model (A4) > Transient (A5) > Solution (A6) > Directional Deformation
Time [s] Minimum [cm] Maximum [cm]

51
1. -2.1588e-004 2.1574e-004
Directional deformation
TABLE 21
Model (A4) > Transient (A5) > Solution (A6) > Total Velocity
Time [s] Minimum [cm/s] Maximum [cm/s]
1. 3.8457e-006 1.0302e-002
Total velcity
TABLE 22
Model (A4) > Transient (A5) > Solution (A6) > Equivalent Elastic Strain

52
Time [s] Minimum [cm/cm] Maximum [cm/cm]
1. 2.2434e-007 6.1114e-004
Equivalent elastic strain
TABLE 23
Model (A4) > Transient (A5) > Solution (A6) > Shear Elastic Strain
1. -1.0559e-004 1.1298e-004
Shear elastic strain
TABLE 24
Model (A4) > Transient (A5) > Solution (A6) > Equivalent Stress

53
Time [s] Minimum [dyne/cm²] Maximum [dyne/cm²]
1. 2.0203e+005 6.7215e+008
FIGURE 10
Model (A4) > Transient (A5) > Solution (A6) > Shear Stress
Equivalent stress
TABLE 25
Model (A4) > Transient (A5) > Solution (A6) > Shear Stress
1. -4.5372e+007 4.8545e+007
FIGURE 11
Model (A4) > Transient (A5) > Solution (A6) > Strain Energy
Shear stress

54
TABLE 26
Model (A4) > Transient (A5) > Solution (A6) > Strain Energy
Time [s] Minimum [erg] Maximum [erg]
1. 2.8201e-003 16586
FIGURE 12
Model (A4) > Transient (A5) > Solution (A6) > Maximum Principal Elastic Strain
Shear energy
TABLE 27
Model (A4) > Transient (A5) > Solution (A6) > Maximum Principal Elastic Strain
1. -4.3175e-006 5.5413e-004
FIGURE 13
Model (A4) > Transient (A5) > Solution (A6) > Equivalent Total Strain

55
TABLE 28
Model (A4) > Transient (A5) > Solution (A6) > Equivalent Total Strain
1. 2.2434e-007 6.1114e-004
FIGURE 14
Model (A4) > Transient (A5) > Solution (A6) > Maximum Principal Stress
Equivalent total strain
TABLE 29
Model (A4) > Transient (A5) > Solution (A6) > Maximum Principal Stress
1. -3.1094e+007 5.6564e+008

56
TABLE 30
Model (A4) > Transient (A5) > Solution (A6) > Results
Object Name Structural Error
State Solved
Scope
Geometry All Bodies
Definition
Type Structural Error
By Time
Display Time Last
Calculate Time History Yes
Identifier
Suppressed No
Results
Minimum 5.1822e-006 erg
Maximum 339.15 erg
Minimum Occurs On Part 1
Maximum Occurs On Part 2
Information
Time 1. s
Load Step 1
Substep 1
Iteration Number 4
FIGURE 15
Model (A4) > Transient (A5) > Solution (A6) > Structural Error
TABLE 31
Model (A4) > Transient (A5) > Solution (A6) > Structural Error
Time [s] Minimum [erg] Maximum [erg]
1. 5.1822e-006 339.15

57
Material Data
Gray Cast Iron
TABLE 32
Gray Cast Iron > Constants
Density 7.2 g cm^-3
Coefficient of Thermal Expansion 1.1e-005 C^-1
Specific Heat 4.47e+006 erg g^-1 C^-1
Thermal Conductivity 0.52 W cm^-1 C^-1
Resistivity 9.6e-006 ohm cm
TABLE 33
Gray Cast Iron > Compressive Ultimate Strength
Compressive Ultimate Strength dyne cm^-2
8.2e+009
TABLE 34
Gray Cast Iron > Compressive Yield Strength
Compressive Yield Strength dyne cm^-2
0
TABLE 35
Gray Cast Iron > Tensile Yield Strength
Tensile Yield Strength dyne cm^-2
0
TABLE 36
Gray Cast Iron > Tensile Ultimate Strength
Tensile Ultimate Strength dyne cm^-2
2.4e+009
TABLE 37
Gray Cast Iron > Isotropic Secant Coefficient of Thermal Expansion
Reference Temperature C
22

58
TABLE 38
Gray Cast Iron > Isotropic Elasticity
Temperature
C
Young's Modulus dyne
cm^-2
Poisson's
Ratio
Bulk Modulus dyne
cm^-2
Shear Modulus dyne
cm^-2
1.1e+012 0.28 8.3333e+011 4.2969e+011
TABLE 39
Gray Cast Iron > Isotropic Relative Permeability
Relative Permeability
10000

59
Conclusion
When the man-kind started using wheels they found the requirement of a typical wheel which
can reduce or increase the rotational speed so the gear was invented. Most of the power
transmission equipments consist of gear assemblies; many times gears play an important role. In
this study, to understand the behaviour of gear materials with respect to stresses Finite Element
Analyses were carried out.
 On the basis of that study, the analysis of aluminium silicon carbide, Carbone epoxy, cast
iron are analyzed in the application of gear box which is used in automobile vehicles.
 It was found that Carbone epoxy have got good resistance characteristics as compared to
other materials,
 So from these analysis results, we conclude that, the stress induced, cast iron deformation
of traction gear is less as compared to the other material gear.
 In model analysis carbon epoxy materials are give good vibration resistance comparing to
other two materials.

60
REFERENCES:
1. Darle W Dudley (1954), Practical Gear Design, McGraw-Hill Book Company.
2. Khurmi Gupta R S (2000), “Machine Design”, Khanna Publication.
3. Khurmi R S (1997), “Theory of Machine”, Khanna Publication.
4. Machine Design Data Book (2003), PSG Publication.
5. . Rattan S S (1998), “Theory of Machines”, Dhanpat Rai Publication.
6. Romlay F R M (2008), “Modeling of a Surface Contact Stress for Spur Gear Mechanism
Using Static and Transient Finite Element Method”, Journal of Structural Durability &
Health Monitoring (SDHM), Vol. 4, No. 1, Tech Science Press.
7. Shanavas S (2013), “Stress Analysis of Composite Spur Gear”, International Journal of
Engineering Research & Technology (IJERT), ISSN: 2278-0181
8. Shinde S P, Nikam A and Mulla T S (2012), “Static Analysis of Spur Gear Using Finite
Element Analysis”, IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE),
pp. 26-31, ISSN: 2278-1684.

Design & Analysis of Spur Gears

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