A
PROJECT REPORT
ON
STRUCTURAL ANALYSIS OF REAR DEAD AXLE USING FEA
Submitted in partial fulfillment of the award for the degree of
BACHELOR OF TECHNOLOGY
IN
MECHANICAL ENGINEERING
BY
G.K.S.RAMA KRISHNA 12K65A0306
P.SANDEEP 11K61A0384
S.K.SUMANTH VARMA 11K61A0397
K.KUMAR RAJA 12K65A0309
Under the esteemed guidance of
R. NARENDRA
DEPARTMENT OF MECHANICAL ENGINEERING
SASI INSTITUTE OF TECHNOLOGY & ENGINEERING
(Accredited by NAAC with ‘A’ Grade, Approved by A.I.C.T.E New Delhi and
Affiliated to JNTU, KAKINADA and SBTET, Hyderabad)
TADEPALLIGUDEM
2014-2015

SASI INSTITUTE OF TECHNOLOGY & ENGINEERING
(Accredited by NAAC with ‘A’ Grade, Approved by A.I.C.T.E New Delhi and
Affiliated to JNTU, KAKINADA and SBTET, Hyderabad)
TADEPALLIGUDEM
Department of mechanical engineering
CERTIFICATE
This is to certify that this titled STRUCTURAL ANALYSIS OF
REAR DEAD AXLE USING FEA, has been submitted by G.K.S.RAMA
KRISHNA (12K65A0306), P.SANDEEP (11K61A0384), S.K.SUMANTH
VARMA (11K61AO397), K.KUMAR RAJA (12K65A0309) to the Jawaharlal
Nehru Technological University, Kakinada during the academic year 2014-
2015In the partial fulfillment for the award of Degree of BACHELOR OF
TECHNOLOGY in MECHANICAL Engineering, is a record of bonafide work carried
out by him.
The results embodied in this report have not been submitted by the student to any
other University or Institution for the award of any degree or diploma.
Internal Project Guide Head of the Department
Mr. R. NARENDRA Dr. R.B.CHOUDARY
Assistant Professor Professor
Dept of Mech Engg. Dept of Mech Engg.
External Examiner

i
ACKNOWLEDGEMENT
We express our sincere thanks to The Management of “Sasi Institute of
Technology and Engineering” for the facilities made available for completion of
project.
We convey our deep sense of gratitude to Dr. K.BHANU PRASAD, Principle
under whose guidance and encouragement we have carried out this work successfully.
We would like to express our sincere thanks to Prof. R.B.CHOUDARY, Head of
the department of Mechanical Engineering.
We express our heart full thanks to our esteemed guidance R.NARENDRA, for
the grateful patience he has shown towards our work for this timely advices and
guidance.
We are also thankful to all Staff and Technicians of Mechanical Department for
their support during the course of the work.
We are also thankful to the Library (& Library Staff) of the college for the
reference books which helped us gathering some information about the project.
PROJECT ASSOCIATES
G.K.S.RAMA KRISHNA
P.SANDEEP
S.K.SUMANTHVARMA
K.KUMAR RAJA

ii
ABSTRACT
An axle is a central shaft for a rotating wheel. On wheeled vehicles, the axle may
be fixed to the wheels, rotating with them, or fixed to its surroundings, with the wheels
rotating around the axle, as well as to maintain the position of the wheels relative to each
other and to the vehicle body. The axles in a system must also bear the weight of the
vehicle plus any cargo, about 60 percent of the total vehicle weight is taken up by the
rear axle.
The component will be drafted in solid works. Applications resulting from the
advancement in computer technology made numerical methods to be employed in
analyzing various stresses acting on a component. One such technique is the “Finite
Element Analysis”, which is meant to analyze the design of rear dead axle under working
conditions by using ANSYS. Using Finite Element Method an effort is made to analyze
the load distribution within the rear axle, structural analysis is done on the axle to find out
the varying stresses, displacements and frequencies which occur by the forces developed
due to rotation
By considering present conditions the loads will be applied on the component by
using work bench. Finally the stresses, displacement and frequencies are varied for
different materials to suggest which is suitable for the vehicles.

iii
TABLE OF CONTENTS
PAGE.NO
ACKNOWLEDGEMENT i
ABSTRACT ii
LIST OF FIGURES vii
LIST OF TABLES ix
CHAPTER 1: INTRODUCTION TO AXLE
1.1 Introduction 1
1.1.1 Front Axle 1
1.1.2 Rear Axle 3
1.2 Structural Features of Axle 4
1.2.1 Straight Axle 5
1.2.2 Split Axle 5
1.2.3 Tandem axle 5
1.3 Axle Specifications 6
1.3.1 Dimensions of Axle 6
1.3.2 Design Restriction 6
1.3.3 Loads 7
CHAPTER2: LITERATURE SURVEY
2.1 Definition 8
2.2 History 8
2.3 Introduction 9
2.4 Description 10
2.4.1 Weight Reduction 11
2.4.2 Features 11
2.4.3 Benefits 11
2.4.4 Cross Section of Axle 12
2.4.4.1 I-Section Beam 12
CHAPTER3: MATERIAL SELECTION

iv
3.1 Introduction 14
3.2 Engineering Requirements 15
3.2.1 Mechanical Properties 15
3.2.2 Thermal Properties 16
3.2.3 Electrical Properties 17
3.2.4 Magnetic Properties 18
3.2.5 Chemical Properties 18
3.3 Classification of Engineering Materials 18
3.3.1 Metals 19
3.4 Selection of Materials 23
3.4.1 Ductile Cast Iron 23
3.4.1.1 Chemical Composition 23
3.4.1.2 Mechanical Properties 24
3.4.1.3 Thermal Properties 24
3.4.2 High Grade Steel 24
3.4.2.1 Chemical Composition 24
3.4.2.2 Mechanical Properties 25
3.4.2.3 Thermal Properties 25
CHAPTER 4: SOLIDWORKS
4.1 Introduction 26
4.2 Starting of SolidWorks 27
4.2.1 Checking the Option Setting 27
4.2.2 General Toolbox 28
4.3 Generating New Part 29
4.4 Sketching 30
CHAPTER 5: FINITE ELEMENT METHOD
5.1 Introduction 33
5.2 Boundary Conditions of FEM 34
5.3 Description of FEM 35
5.3.1 Type of Elements 36
5.3.2 Number of Elements 36

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5.3.3 Size of Elements 36
5.4 Finite Element Analysis 38
5.4.1 Type of Analysis 38
5.4.1.1 Structural Analysis 38
5.4.1.2 Vibration Analysis 38
5.5 Finite Element Process 38
5.6 Introduction to Ansys Software 39
5.6.1 Various Stages of Ansys 40
5.6.2 Pre processor 40
5.6.3 Meshing 40
5.6.3.1 Manual 40
5.6.3.2 Mesh Control 41
5.6.3.3 Smart Sizing of Elements 41
5.6.4 Solution 41
5.6.5 Post-Processor 41
5.7 Structural Analysis 42
5.7.1 Model Analysis 42
5.7.1.1 Definition 42
5.7.1.2 Uses of Model 42
5.7.2 Static Analysis 42
5.7.2.1 Definition 42
5.7.2.2 Loads in Static Analysis 43
5.8 Advantages of FEM 43
5.9 Disadvantages of FEM 44
CHAPTER 6: MODELLING & STRUCTURAL ANALYSIS OF
TANDEM AXLE
6.1Problem Definition 45
6.2 Analytical Method 45
6.2.1Moment of Inertia of I-Section 45
6.3 Calculation of Load 46
6.4 Modelling of Tandem Axle in 3D-Solid 46

vi
6.4.1 Creating Model 46
6.5 Structural Analysis of Rear Dead Axle 50
6.5.1 Static Analysis 50
6.5.2 Results 54
6.5.2 Modal Analysis 60
6.5.5 Results 62
CHAPTER 7: CONCLUSION 72
CHAPTER 8: REFERENCES 73

vii
LIST OF FIGURES
FIG. NO PAGE. NO
2.4.4.1 Rear Dead Axel 14
4.2.1 SolidWorks Windows 29
4.2.1.1 System Option Dialogue Box 30
4.2.2 Tool Bar Menu 31
4.3 New Document Window 32
6.2.1 I-Cross Section of Axle 47
6.4.1 2-D Line Diagram 50
6.4.1.1 Mirror Image of Solid 51
6.4.1.2 Extruded Image of Solid 51
6.4.1.3 Isometric View of Solid 52
6.5.1.1 Importing Of Geomentry 53
6.5.1.2 Ductile Cast Iron 54
6.5.1.3 High Grade Steel 54
6.5.1.4 Meshing 56
6.5.1.5 Applying Loads and Support 56
6.5.2.1 Total Deformation X-Direction 57
6.5.2.2 Total Deformation Y-Direction 57
6.5.2.3 Total Deformation Z-Direction 58
6.5.2.4 Von-Mises X-Direction 58
6.5.2.5 Von-Mises Y-Direction 59
6.5.2.6 Von-Mises Z-Direction 59

viii
6.5.3.1 Total Deformation X-Direction 60
6.5.3.2 Total Deformation Y-Direction 60
6.5.3.3 Total Deformation Z-Direction 61
6.5.3.4 Von-Mises X-Direction 61
6.5.3.5 Von-Mises Y-Direction 62
6.5.3.6 Von-Mises Z-Direction 62
6.5.4.1 Importing Geomentry 63
6.5.4.2 Ductile Cast Iron 64
6.5.4.3 High Grade Steels 64
6.5.4.4 Fixed Supports 65
6.5.5.1 Total Deformation 1 65
6.5.7.1 Ductile Cast Iron Graph 69
6.5.7.2 High Grade Steel Graph 70

ix
LIST OF TABLES
TABLE. NO PAGE. NO
1.3.1 Dimensions of Axle 7
1.3.2 Design Restriction 8
1.3.3 Load onAxle 8
3.1 Factor Effecting Selection of Materials 15
3.2.2 Thermal Conductivity of Materials 23
3.3.1 Important Grouping of Materials 23
3.3.2 Properties for Grouping of Materials 24
3.4.1.3 Mechanical Properties for DCI 26
3.4.1.4 Thermal Properties for DCI 26
3.4.2.3 Mechanical Properties for HGS 27
3.4.2.3 Thermal Properties for HGS 27
5.2 Various Applications of FEA 36
5.6.1 Various Stages of Ansys 42
6.5.1 Meshing Parameters 55
6.6.1 Static Analysis Results 73
6.6.2 Modal Analysis Results 73

Structural Analysis of Rear Dead Axle by Using FEA
1
1. INTRODUCTION OF AXLE
1.1 Introduction
An axle is a central shaft for a rotating wheel or gear. On wheeled vehicles, the
axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the
wheels rotating around the axle. In the former case, bearings or bushings are provided at
the mounting points where the axle is supported. In the latter case, a bearing or bushing
sits inside a central hole in the wheel to allow the wheel or gear to rotate around the axle.
Sometimes, especially on bicycles, the latter type axle is referred to as a spindle.
During the vehicle operation, road surface irregularity causes cyclic fluctuation of
stresses on the axle, which is the main load carrying member. Therefore it is important to
make sure whether the axle resists against the fatigue failure for a predicted service life.
Axle experiences different loads in different direction, primarily vertical beaming or
bending load due to curb weight and payload, torsion. Due to drive torque, cornering load
and braking load. In real life scenario all these loads vary with time. Vertical beaming is
one of the severe and frequent loads on an axle Due to their higher loading capacity; solid
axles are typically used in the heavy commercial vehicles. During the vehicle service life,
dynamic forces caused by the road surface roughness produce dynamic stresses and these
forces lead to fatigue failure of axle housing, which is the main load carrying part of the
assembly.
Axles are classified into 2 types, they are
1. Front Axle
2. Rear Axle
1.1.1 Front Axle:
Front axle wheels consist of wheel alignment and steering mechanism that gives
the vehicle directional stability promotes ease of steering and reduces tire wear to a
minimum.
A wheel is said to have directional stability or control if it can:
- run straight down a road,
- enter and leave a turn easily, and

2
- resist road shocks.
The front wheel alignment depends upon the following factors:
a. Camber
b. King pin inclination
c. Caster
a. Camber:
Camber is the tilting in or out of the front wheels from the vertical when viewed
from the front of the vehicle. If the top of the wheel tilts out, it has "positive" camber. If
the top of the wheel tilts in, it has "negative" camber. The amount of tilt measured in
degrees from the vertical, is called "camber angle". Any amount of camber, positive or
negative, tends to cause uneven or more tyrewear on one side than on the other side.
Camber should not exceed two degrees.
b. King-pin inclination:
The king-pin inclination (or steering axle inclination) is the angle between the
verticalline and centre of the kingpin or steering axle, when viewed from the front of the
vehicle. The king-pin inclination is absolutely necessary due to the following reasons:
i. It helps the car to have steering stability.
ii. It makes the operation of the steering quite easy particularly when the vehicle
is stationary.
iii. It helps in reducing the wear on the tyre.
c. Included angle:
The combined camber and king-pin inclination is called the "included angle".
This angle is important because it determines the point of intersection of the wheel and
king pin center lines.
This in turn determines whether the wheel will tend to toe-out or toe-in.
i. If the point of intersection is above the ground, the wheel tends to toe-in.
ii. If it is below the ground, the wheel tends to toe-out.

3
iii. If it is at the ground, the wheel keeps its straight position without any
tendency to toe-in or toe-out.
In this position the steering is called center point steering.
d. Caster:
The angle between the king-pin center line (or steering axis) and the vertical, in
the plane of the wheel is called Caster angle. If the King-pin center line meets the ground
at a point ahead of the vertical center line, it is called positive caster while if it is behind
the vertical, wheel center Front line it is called negative caster. The caster angle in
modern vehicles ranges from 2° to 8°.
1.1.2 Rear Axle:
Rear axle is used to support the whole weight of the vehicle and transmits power
to the rear wheels. It bears the load up to 50% to 80% weight of the vehicle. Rear axle
transmits the power and supports the vehicle. Based on the transmission system and the
weight supporting of the vehicle rear axle is divided into two types.
They are:
a. Live axle
b. Dead axle
a. Live axle:The rear drive axles transfer power from the differential assembly to the
rear wheels. There are two major kinds of drive axle designs. One is the solid drive
axle and the other is the independently suspended drive axle
A solid drive axle or live axle is a hardened-steel shaft. Each rear axle assembly in
solid axle rear suspension systems has two. External splines on the inboard (inner)
end of each axle mate with internal splines on the differential side gear to which it is
connected. An axle flange at the outboard (outer) end of each axle acts as a wheel
hub. It provides the mounting surface for the brake drum or rotor and the wheel. The
brake assembly and wheel are installed directly on the flange wheel studs.
Each shaft is supported on the outboard end by an axle bearing, also called a
wheel bearing. The axle bearing can be installed on the shaft or in the axle tube.

4
Axle bearings that are installed on the shaft are usually packed with grease. An axle
seal is pressed into the housing behind, or on the inboard side of, the bearing. The lip
of the seal seats against a machined area of the shaft. This seal keeps rear end
lubricant from reaching the bearing. An outer seal prevents water and dirt from
leaking through the outer ends of the rear axle housing and entering the bearing.
Axle bearings that are installed in the housing are lubricated by rear end lubricant
(gear oil). When the vehicle makes a turn, lubricant is thrown outward from the
carrier, reaching the axle bearing. An axle seal is installed in front of, or on the
outboard side of, the bearing to keep lubricant from leaking out from the outer ends
of the rear axle housing. The shaft is held in place by a clip as explained in the next
section.
An axle bearing installed on the shaft is held in place by an axle collar. The axle
collar is tightly pressed on the shaft. In addition, some will have a spacer to keep the
bearing at the proper distance from the end of the axle. The axle retainer plate holds
the axle and axle bearing to the axle tube.
b. Dead Axle (Lazy Axle):A dead axle, also called lazy axle, is not part of the drive
train but is instead free-rotating. The rear axle of a front-wheel drive car is usually a
dead axle. Many trucks and trailers use dead axles for strictly load-bearing purposes.
A dead axle located immediately in front of a drive axle is called a pusher axle. A
tag axle is a dead axle situated behind a drive axle. Dead axles are also found on
semi-trailers, farm equipment, and certain heavy construction machinery serving the
same function. On some vehicles (such as motor coaches), the tag axle may be
steerable. In some designs the wheels on a lazy axle only come into contact with
ground when the load is significant, thus saving unnecessary tire wear
1.2 Structural Features of Axles
Based on the structural features axle is divided into 3 types, they are
1. Straight axle
2. Split-axle
3. Tandem axle

5
1.2.1 Straight Axle:
A straight axle is a single rigid shaft connecting a wheel on the left side of the
vehicle to a wheel on the right side. The axis of rotation fixed by the axle is common to
both wheels. Such a design can keep the wheel positions steady under heavy stress, and
can therefore support heavy loads. Straight axles are used on trains (that is locomotives
and railway wagons), for the rear axles of commercial trucks, and on heavy duty off-road
vehicles. The axle can optionally be protected and further reinforced by enclosing the
length of the axle in housing
1.2.2 Split-Axle:
In split-axle designs, the wheel on each side is attached to a separate shaft.
Modern passenger cars have split drive axles. In some designs, this allows independent
suspension of the left and right wheels, and therefore a smoother ride. Even when the
suspension is not independent, split axles permit the use of a differential, allowing the left
and right drive wheels to be driven at different speeds as the automobile turns, improving
traction and extending tire life.
1.2.3 Tandem Axle:
A tandem axle is a group of two or more axles situated close together. Truck
designs will use such a configuration to provide a greater weight capacity than a single
axle. Semi-trailers usually have a tandem axle at the rear.
In heavy trucks tandem refers to two closely spaced axles. Legally defined by the
distance between the axles (up to 2.5m or 40 to 96inches), mechanically there are many
configurations. Either or both axles may be powered, and often interact with each other.
In some vehicles both axles are typically powered and equalized, in the other vehicles
one axle is typically unpowered, and can often be adjusted to load, and even raised off the
ground, turning a tandem into a single axle.

6
1.3 Axle Specifications
1.3.1 Dimensions of Axle:
Table1.3.1 Dimensions of axle
Wheel Base 4330 mm
Overall Length 7766 mm
Overall Width 2425 mm
Front Track 1915 mm
Rear Track 1816 mm
Min. Ground Clearance 253 mm
Min. Turning Circle Diameter 17500 mm
Loading Body Length 5640 mm
Max. Speed In Top Gear 74.5 kmph
Maximum Grade ability 12%
1.3.2 Design Restriction:
Table1.3.2 Design Restriction
Maximum track 2160.5 mm
Spring mounting centre 810-910 mm
Bearing shoulder to bearing shoulder 2040.5 mm
Overall width 2590.99 mm
Max tire static load radius 540.6 mm
Beam drop “S” 90.4mm
Beam drop “C” 30.81mm

7
1.3.3 Loads:
Table1.3.3 Load on axle
Unloaded Loaded
Front Axle 2420 6000
Rear Axle 1820 10200
Total 4240 16200

8
2. LITERRATURE SURVEY
2.1 Definition
A tandem axle is a group of two or more axles situated close together. Truck
designs will use such a configuration to provide a greater weight capacity than a single
axle. Semi-trailers usually have a tandem axle at the rear.
2.2 History
The Hendrickson story began in 1913 with the founding of The Hendrickson
Motor Truck Company by inventor and businessman Magnus Hendrickson. This small
Chicago-based manufacturing company built trucks often equipped with cranes, which
were used to haul stone and other building materials.
In 1926, Hendrickson introduced the first tandem truck suspension, which
mounted the axles on each end of an equalizing beam. This unique "walking beam"
design distributed the truck's load evenly between the two rear axles, which improved
traction and greatly reduced the effects of bumps and potholes in the road. The walking
beam soon gained widespread acceptance among the industry's new 6x4 "six wheeler"
trucks, which allowed more payload.
In 1978, The Boler Company, whose holdings included manufacturers of leaf
springs and metal bumpers, purchased Hendrickson. In the years that followed,
Hendrickson would expand into or acquire additional businesses in related areas—trailer
suspension systems, auxiliary axle systems, springs, metal bumpers, and other heavy-duty
components.
Eventually Hendrickson sold the truck manufacturing operation to focus solely on
suspension systems and related components. Today, Hendrickson is comprised of state-
of-the-art facilities, technical centers and manufacturing centers,in the United States,
Canada, Mexico, the United Kingdom, France, Austria, Romania, Turkey, India, China
and Australia.

9
At Hendrickson, we commit to serving the transportation industry with innovative
products that help improve productivity and profitability. Across the globe, our dedicated
employees champion Hendrickson’s proud heritage through creativity, integrity and
superior service. Our legacy embodies 100 years as the leading innovator and
manufacturer of suspension systems and components for the global heavy-duty vehicle
industry.
2.3 Introduction
The auto industry is one of the key sectors of the Indian economy. The Industry
comprises of automobile and the auto components sectors and encompasses commercial
vehicles, multi-utility vehicles, passenger cars, two wheelers, three wheelers and related
auto components. During last few decades due to global economic scenario optimum
vehicle design is major concern. To accomplish the need to design a moderate car, the
structural engineer will need to use imaginative concepts. The demands on the
automobile designer increased and changed rapidly, first to meet new safety requirements
and later to reduce weight in order to satisfy fuel economy requirements. Experience
could not be extended to new vehicle sizes, and performance data was not available on
the new criteria. Mathematical modeling was therefore a logical avenue to explore. Most
recently, the finite element method, a computer dependent numerical technique, has
opened up a new approach to vehicle design. During the vehicle operation, road surface
irregularity causes cyclic fluctuation of stresses on the axle, which is the main load
carrying member. Therefore it is important to make sure whether the axle resists against
the fatigue failure for a predicted service life. Axle experiences different loads in
different direction, primarily vertical beaming or bending load due to curb weight and
payload, torsion. There had been exhaustive efforts to develop thefront axle design by
studying the noise and vibration analysis atstatic and dynamic loading conditions. The
model selected is thatof a light commercial vehicle (LCV) which has a gross vehicle load
of around 5-10 tons. The front basically is of drop forged steel type depending upon the
extent of total load the LCVexperiences. The collapse of LCV axle (front) while dynamic
and static loading conditions is of huge apprehension to both goods and human lives,
hence it becomes essential to scrutinize the structural integrity of the axle to endure
characteristic such loading which can build up stresses in the same being consequential to
fracture and finally failure. Stressed regions dueto vehicle static load, braking torque, and
during turning is established and the front axle beam is investigated to find out its factor
of safety and maximum deformation under the mentioned conditions. The present work
aims to determine the load capacity of the front rigid axle of a LCV and determine its
behaviour at static and dynamic conditions.This paper analysis the static, transient and
modal analysis of the front axle beam. The geometry of axle is created in Pro-E
WildFire5.0 software which is imported to ANSYS14.5. A fine congregate finite element
model (meshed) is generated using the software to assess thestrength and capability of the
product to survive against all forces and vibrations.

10
The front dead axle supports the weight of front part of the vehicle, facilitates steering,
absorbs shocks which are transmitted due to road surface irregularities and also absorbs
torque applied on it due to braking of vehicle. Front axle is made of I-section in the
middle portion and circular or elliptical section or I section at the ends. The special x-
section of the axle makes it able to withstand bending loads due to weight of the vehicle
and torque applied due to braking. A typical LCV front axle consists of main beam, stub
axle, and swivel pin or kingpin. The wheels are mounted on stub axles. The front axle
beam is subjected to bending loads due to vertical forces due to mass present above in
static condition of the vehicle, while driving a truck around a corner results in multiple
forces such as twisting forces on kingpin or steering knuckle, axial forces between Pad
and spring interface along the length of the beam and unsymmetrical vertical loads due to
centrifugal action. Worst situation arises while a cornering truck is braked to stop giving
rise to turning moment on Pad and a retarding force acting on the surface of the Pad in
the sense of vehicle motion. Current article carries on the numerical simulation towards
the front axle to understand comprehensively the automobile front axle’s stress, the
strain distribution and the vibration frequency under different varieties of conditions, and
provides the scientific theoretical base for the designer, thus improves design quality,
shortens design cycle and reduces design cost.
Various experiments and numerical methods were adopted by Leon et al. to obtain the
stress analysis of a frontal truck axle beam. The results obtained by finite element method
were verified experimentally using photo stress. [1]
Based on an experimental and numerical analysis of a tractor’s front axle carried out by
Mahanty et al, redesign was carried out for the front axle for weight optimization and
easy manufacturability. Five different models were proposed based on ease of
manufacturing and weight reduction. The results obtained by finite element method were
analyzed by thirteen different certification test load conditions. [2]
Another survey done by Topac et al. 9 deals with a premature failure that occurs prior to
the expected load cycles during the vertical fatigue tests of a truck rear axle housing
prototype. In these tests, crack mainly originated from the same region on test samples
[3]
2.4 Description
In heavy trucks tandem refers to two closely spaced axles. Legally defined by the
distance between the axles (up to 2.5m or 40 to 96inches), mechanically there are many
configurations. Either or both axles may be powered, and often interact with each other.
In some vehicles both axles are typically powered and equalized, in the other vehicles
one axle is typically unpowered, and can often be adjusted to load, and even raised off the
ground, turning a tandem into a single axle.

11
The tandem axle is specifically engineered to dramatically decrease weight and
increase your bottom line. Approximately 100 pounds lighter than the nearest competitive
product, is designed for 80,000 lb GCW applications with engines of up to 475 HP and
1,750 lb. ft. torque with overdrive transmissions. This lightweight axle offers improved
inter-axle driveline angles and is available in a popular range of ratios (3.25 – 3.91) for
the professional line haul, regional haul, and city delivery fleets
2.4.1 Weight Reduction
 Offers improved fuel economy
 Increases your bottom line with a significant increase in payload ability
2.4.2 Features
 Maintains full load rating for hubs, with 0 – 0.56" outset wheels
 Diff Lock option on forward axle
 Optional lube pump
 Maintains overall tire width limits for both single wide-based tires
 and traditional dual-tire applications
 Keeps vertical load inboard to lower stress on hub, outer wheel
 bearings, and spindle
 Available in 11 mm or 9.5 mm wall thickness
2.4.3 Benefits
 Increased longevity and service intervals for wheel ends
 Flexibility of tire and wheel configurations for different applications and resale
 Allows for maximum hub ratings to promote aluminium hubs in lightweight
applications
 Improved lube flow and efficiency
 Standard without inter-axle shift system

12
2.4.4 Cross Section of Axle
The tandem axle consists of several cross sectional beams they are rectangular
section, circular section, triangular section, I-beam section, H-beam section etc., In this
project we are using I-section beam.
2.4.4.1 I-Section Beam:
All standard axles have an I-cross section in the middle (spring seat to spring seat)
and circular or elliptical cross sections at the ends. The axle beam will have I cross
section in the middle and circular cross sections at the ends. An axle is usually a forged
component for which a higher strength to weight ratio is desirable.
The I-cross section has lower section modulus and hence gives better performance
with lower weight. This type of construction produces an axle that is lightweight and yet
has great strength. The I-beam axle is shaped so that the centre part is several inches
below the ends. This permits the body of the vehicle to be mounted lower than it could be
if the axle were straight.
A vehicle body that is closer to the road has a lower centre of gravity and holds
the road better. On the top of the axle, the springs are mounted on flat, smooth surfaces or
pads. The mounting surfaces are called spring seats and usually have five holes. The four
holes on the outer edge of the mounting surface are for the U-bolts which hold the spring
and axle together. The centre hole provides an anchor point for the centre bolt of the
spring. The head of the centre bolt, seated in the centre hole in the mounting surface,
ensures proper alignment of the axle with the vehicle frame.

13
Fig.2.4.4.1 Rear Dead Axle

14
3. MATERIAL SELECTION
3.1 Introduction
Materials science and engineering plays a vital role in this modern age of science
and technology. Various kinds of materials are used in industry, housing, agriculture,
transportation, etc. to meet the plant and individual requirements. The rapid
developments in the field of quantum theory of solids have opened vastopportunities for
better understanding and utilization of various materials. The spectacular success in the
field of space is primarily due to the rapid advances in high-temperature and high-
strength materials. The selection of a specific material for a particular use is a very
complex process. However, one can simplify the choice if the details about (i) operating
parameters, (ii) manufacturing processes, (iii) functional requirements and (iv) cost
considerations are known. Factors affecting the selection of materials are summarized
Table3.1 Factors effecting the selection of materials
Manufacturing
processes
Functional
requirements
Cost
considerations
Operating
parameters
Plasticity Strength Raw material Pressure
Malleability Hardness Processing Temperature
Ductility Rigidity Storage Flow
Machinability Toughness Manpower Type of material
Casting properties Thermal conductivity Special treatment
Corrosion
requirements
Weldability Fatigue Inspection Environment
Heat Electrical treatment
Packaging
properties
Protection from fire
Tooling Creep Inventory Weathering
Surface finish Aesthetic look
Taxes and custom
duty
Biological effects
There are thousands and thousands of materials available and it is very difficult
for an engineer to possess a detailed knowledge of all the materials. However, a good
grasp of the fundamental principles which control the properties of various materials help
one to make the optimum selection of material. In this respect, materials science and
engineering draw heavily from the engineering branches, e.g. metallurgy, ceramics and
polymer science.
The subject of material science is very vast and unlimited. Broadly speaking, one
can sub-divide the fieldof study into following four branches:

15
(i) Science of metals,
(ii) Mechanical behaviour of metals
(iii) Engineering metallurgy
(iv) Engineering materials
3.2 Engineering Requirements
While selecting materials for engineering purposes, properties such as impact
strength, tensile strength,and hardness indicate the suitability for selection but the design
engineer will have to make sure that the radiography and other properties of the material
are as per the specifications. One can dictate the method of production of the component,
service life, cost etc. However, due to the varied demands made metallic materials, one
may require special surface treatment, e.g. hardening, normalizing to cope with the
service requires. Besides, chemical properties of materials, e.g. structure, bonding energy,
resistance to environmental degradation also effect the selection of materials for
engineering purposes.
In recent years polymeric materials or plastics have gained considerable
popularity as engineeringmaterials. Though inferior to most metallic materials in strength
and temperature resistance, these are being used not only in corrosive environment but
also in the places where minimum wear is required, e.g. small gear wheels, originally
produced from hardened steels, now manufactured from nylon or Teflon. These materials
perform satisfactorily, are quiet and do not require lubrication. Thus, before selecting a
material or designing a component, it is essential for one to understand the requirements
of the process thoroughly, operating limitations like hazardous or non-hazardous
conditions, continuous or non-continuous operation, availability of raw materials as well
as spares, availability of alternate materials life span of the instrument/equipment, cost
etc. Different materials possess different properties to meet the various requirements for
engineering purposes. The properties of materials which dictate the selection are as
follows
3.2.1 Mechanical Properties:
The important mechanical properties affecting the selection of a material are:
a. Tensile Strength: This enables the material to resist the application of a tensile
force. To withstandthe tensile force, the internal structure of the material provides
the internal resistance.
b. Hardness: It is the degree of resistance to indentation or scratching, abrasion and
wear. Alloyingtechniques and heat treatment help to achieve the same.
c. Ductility: This is the property of a metal by virtue of which it can be drawn into
wires or elongatedbefore rupture takes place. It depends upon the grain size of the
metal crystals.

16
d. Impact Strength: It is the energy required per unit cross-sectional area to fracture
a specimen, i.e., a measure of the response of a material to shock loading.
e. Wear Resistance: The ability of a material to resist friction wear under particular
conditions, i.e. tomaintain its physical dimensions when in sliding or rolling
contact with a second member.
f. Corrosion Resistance: Those metals and alloys which can withstand the
corrosive action of a medium i.e. corrosion processes proceed in them at a
relatively low rate are termed corrosion-resistant.
g. Density: This is an important factor of a material where weight and thus the mass
is critical, i.e.aircraft components.
3.2.2 Thermal Properties:
The characteristics of a material, which are functions of the temperature, are
termed its thermal properties. One can predict the performance of machine components
during normal operation, if he has the knowledge of thermal properties. Specific heat,
latent heat, thermal conductivity, thermal expansion, thermal stresses, thermal fatigue,
etc. are few important thermal properties of materials.
These properties play a vital role in selection of material for engineering
applications, e.g. when materialsure considered for high temperature service. Now, we
briefly discuss few of these properties:
a. Specific Heat (c): It is the heat capacity of a unit mass of a homogeneous
substance. For a homogeneous body, c = C/M, where C is the heat capacity and M
is the mass of the body. One can also define it as the quantity of heat required to
raise the temperature of a unit mass of the substance through 1°C. Its units are
Cal/g/°C.
b. Thermal Conductivity (K): This represents the amount of heat conducted per unit
time through a unit area perpendicular to the direction of heat conduction when the
temperature gradient across the heat conducting element is one unit. Truly
speaking the capability of the material to transmit heat through it is termed as the
thermal conductivity. Higher the value of thermal conductivity, the greater is the
rate at which heat will be transferred through a piece of given size. Copper and
Aluminium are good conductors of heat and therefore extensively used whenever
transfer of heat is desired. Bakelite is a poor conductor of heat and hence used as
heat insulator.

17
Table 3.2.2 Thermal Conductivity for Materials
Type of the material Material
Thermal conductivity (K)
(W/m/k)
Metals
Copper
Aluminium
Cast iron
Mild steel
Stainless steel
380
230
52
54
16
Ceramics Alumina 2.0
Titanium
Carbide
Glass
2.0
3.0
1.0
Polymers Bakelite 0.23
Composites
Wood
Concrete
1.4
0.14
c. Thermal Expansion: All solids expand on heating and contract on cooling.
Thermal expansion may takeplace as linear, circumferential or cubical. A solid
which expands equally in three mutually orthogonaldirections is termed as
thermally isotropic. The increase in any linear dimension of a solid, e.g.
length,width, height on heating is termed as linear expansion.
The coefficient of linear expansionis the increasein length per unit length per
degree rise in temperature. The increase in volume of a solid on heating
iscalledcubical expansion. The thermal expansion of solids has its origin in the
lattice vibration and lattice vibrations increases with the rise in temperature.
d. Thermal Resistance (RT): It is the resistance offered by the conductor when heat
flow due to temperature difference between two points of a conductor.
e. Thermal Diffusivity (h): A material having high heat requirement per unit volume
possesses a low thermal diffusivity becausemore heat must be added to or
removed from the material for effecting a temperature change.
f. Thermal Fatigue: This is the mechanical effect of repeated thermal stresses caused
by repeated heatingandcooling.The thermal stresses can be very large, involving
considerable plastic flow. We can see that fatiguefailures can occur after relatively
few cycles. The effect of the high part of the temperature cycle on thestrength of
material plays an important factor in reducing its life under thermal fatigue.
3.2.3 Electrical Properties:
Conductivity, resistivity and dielectric strength are few important electrical
properties of a material. A material which offers little resistance to the passage of an

18
electric current is said to be a good conductor of electricity. The electrical resistance of a
material depends on its dimensions. Usually resistivity of a material is quoted in the
literature. Unit of resistivity is Ohm-meter.
On the basis of electrical resistivity materials are divided as Conductors,
Semiconductors and Insulators. In general metals are good conductors. Insulators have
very high resistivity. Ceramic insulators are most common examples and are used on
automobile spark plugs, Bakelite handles for electric iron, and plastic coverings on cables
in domestic wiring.
When a large number of metals and alloys are sufficiently cooled below transition
temperature, Tcenterthe state of superconductivity in which the dc resistivity goes to
zero. The highest value of Tcup to 133 K has been reached for mercury curate.
3.2.4 Magnetic Properties:
Materials in which a state of magnetism can be induced are termed
magneticmaterials. There are five classes into which magnetic materials may be grouped:
(i) Diamagnetic (ii) Paramagnetic (iii) Ferromagnetic and (iv)Anti ferromagnetic
Iron, Cobalt, Nickel and some of their alloys and compounds possess spontaneous
magnetization. Magnetic oxides like ferrites and garnets could be used at high
frequencies. Because of their excellent magnetic properties along with their high
electrical resistivity these materials today find use in a variety of applications like
magnetic recording tapes, inductors and transformers, memory elements, microwave
devices, bubble domain devices, recording hardcore’s, etc. Hysteresis, permeability and
coercive forces are some of the magnetic properties of magnetic substances which are to
be considered for the manufacture of transformers and other electronic components.
3.2.5 Chemical Properties:
This property includes atomic weight, molecular weight, atomic number,valence,
chemical composition, acidity, alkalinity, etc. These properties govern the selection of
materials particularly in Chemical plant.
3.3 Structure of Materials
The properties of engineering materials mainly depend on the internal
arrangement of the atoms on molecules. We must note that in the selection of materials,
the awareness regarding differences and similarities between materials is extremely
important.

19
Metals of a single type atom are named pure metals. Metals in actual commercial
use are almost exclusively alloys, and not pure metals, since it is possible for the designer
to realize an infinite variety of physical properties in the product by varying the metallic
composition of the alloy. Alloys are prepared from mixed types of atoms. Alloys are
classified as binary alloys, composed of two components, as ternary alloys, composed of
three components or as multi component alloys. Most commercial alloys are multi
component.
The composition of an alloy is described by giving the percentage (either by
weight or by atoms) of each element in it. The basic atomic arrangement or pattern is not
apparent in the final component, e.g. a shaft or a pulley but the properties of the
individual crystals within the metallic component, which are controlled by the atomic
arrangement, are mainly responsible for their application in industry.
One can determine the strength of a piece of metal by its ability to withstand
external loading. The structure of metal or alloy responds internally to the applied load by
trying to counteract the magnitude of the applied load and thus tries to keep the
constituent atoms in their ordered positions if however the load is higher than the force
which holds the atoms in place, the metallic bond becomes ineffective and atomsin the
metal are then forced into new displaced positions. The movement of atoms from their
original positions in the metal is termed as slip.The ease with which atoms move or slip
in a metal is an indication of hardness. We must note that the relative movement of atoms
or slip within a material has a direct bearing on the mechanical properties of the material.
3.4 Classification of Engineering Materials
The factors which form the basis of various systems of classifications of materials
in material science and engineering are (i)the chemical composition of the material,
(ii)the mode of the occurrence of the material in the nature, (iii) the refining and the
manufacturing process to which the material is subjected prior it acquires the required
properties, (iv) the atomic and crystalline structure of material and (v)the industrial and
technical use of the material.
Common engineering materials that fall within the scope of material science and
engineering may beclassified into one of the following six groups:
a. Metals (ferrous and non-ferrous) and alloys
b. Ceramics
c. Organic Polymers
d. Composites
e. Semi-conductors

20
f. Biomaterials
g. Advanced Material
3.4.1 Metals:
All the elements are broadly divided into metals and non-metals according to their
properties.Metals are element substances which readily give up electrons to form metallic
bonds and conduct electricity.Some of the important basic properties of metals are: (a)
metals are usually good electrical andthermal conductors, (b) at ordinary temperature
metals are usually solid, (c) to some extent metals aremalleable and ductile, (d) the
freshly cut surfaces of metals are lustrous, (e) when struck metal producetypical sound,
and (f) most of the metals form alloys. When two or more pure metals are melted
together to form a new metal whose properties are quite different from those of original
metals, it is called an alloy.
Metallic materials possess specific properties like plasticity and strength. Few
favorable characteristicsof metallic materials are high luster, hardness, resistance to
corrosion, good thermal and electrical conductivity, malleability, stiffness, the property of
magnetism, etc. Metals may be magnetic, non-magnetic innature. These properties of
metallic materials are due to: (i) the atoms of which these metallic materials arecomposed
and (ii) the way in which these atoms are arranged in the space lattice.
Metallic materials are typically classified according to their use in engineering as under:
(i) Pure Metals: Generally it is very difficult to obtain pure metal. Usually, they are
obtained by refiningthe ore. Mostly, pure metals are not of any use to the engineers.
However, by specialized and very expensivetechniques, one can obtain pure metals
(purity ~ 99.99%), e.g. aluminum, copper etc.
(ii) Alloyed Metals:Alloys can be formed by blending two or more metals or at least one
being metal. Theproperties of an alloy can be totally different from its constituent
substances, e.g. 18-8 stainless steel, whichcontains 18%, chromium and 8% nickel,
in low carbon steel, carbon is less than 0.15% and this is extremelytough,
exceedingly ductile and highly resistant to corrosion. We must note that these
properties are quitedifferent from the behavior of original carbon steel.
(iii)Ferrous Metals:Iron is the principal constituent of these ferrous metals. Ferrous
alloys contain significantamount of non-ferrous metals. Ferrous alloys are
extremely important for engineering purposes. On thebasis of the percentage of
carbon and their alloying elements present, these can be classified into
followinggroups:

21
(a) Mild Steels:The percentage of carbon in these materials range from 0.15% to
0.25%. These are moderately strong and have good weld ability. The
production cost of these materials is also low.
(b) Medium Carbon Steels:These contains carbon between 0.3% to 0.6%. The
strength of these materials is high but their weld ability is comparatively less.
(c) High Carbon Steels:These contains carbon varying from 0.65% to 1.5%.
These materials get hardened tough by heat treatment and their weld ability is
poor.The steel formed in which carbon content is up to 1.5%, silica up to
0.5%, and manganese up to 1.5%alongwith traces of other elements is called
plain carbon steel.
(d) Cast Irons:The carbon content in these substances varies between 2% to 4%.
The cost of productionofthese substances is quite low and these are used as
ferrous casting alloys.
(iv) Non-Ferrous Metals:These substances are composed of metals other than iron.
However, thesemaycontain iron in small proportion. Out of several non-ferrous
metals only seven are available in sufficientquantity reasonably at low cost and
used as common engineering metals. These are aluminum, tin, copper, nickel, zinc
and magnesium. Some other non-ferrous metals, about fourteen in number, are
produced inrelatively small quantities but these are of vital importance in modern
industry. These include chromium,mercury, cobalt, tungsten, vanadium,
molybdenum, antimony, cadmium, zirconium, beryllium, niobium,titanium,
tantalum and manganese.
(v) Sintered Metals:These materials possess very different properties and structures as
compared to themetals from which these substances have been cast. Powder
metallurgy technique is used to produces interred metals. The metals to be sintered
are first obtained in powered form and then mixed in rightcalculated proportions.
After mixing properly, they are put in the die of desired shape and then
processedwith certain pressure. Finally, one gets them sintered in the furnace. We
must note that the mixture soproduced is not the true alloy but it possesses some of
the properties of typical alloys.
(vi) Clad Metals:A sandwich of two materials is prepared in order to avail the advantage
of the propertiesof both the materials. This technique is termed as cladding. Using
this technique stainless steel is mostlyembedded with a thick layer of mild steel, by
rolling the two metals together while they are red hot. Thistechnique will not allow
corrosion of one surface. Another example of the use of this technique is claddingof
duralumin with thin sheets of pure aluminum. The surface layers, i.e. outside layers

22
of aluminum resistcorrosion, whereas inner layer of duralumin imparts high
strength. This technique is relatively cheap tomanufacture.
Table3.4.1 Important grouping of Materials
Material group Important characteristics
Typical examples of
engineering use
1. Metals and Alloys
Lustre, hardness, thermal
and electrical conductivity,
resistance to corrosion,
malleability,
stiffness and the property of
magnetism
Iron and steels, aluminium,
copper, silver, gold, zinc,
magnesium, brasses,
bronzes,
Manganin, invar, super
alloy, boron, rare-earth
alloys, conductors, etc.
2. Ceramics and Glasses
Thermal resistance,
hardness, brittleness,
opaqueness to light,
electrical insulation
abrasiveness, high
temperature strength and
resistance to corrosion
Silica, soda-lime-glass,
concrete, cement,
refractory’s, Ferrites and
garnets, ceramic
superconductors, MgO,
CdS, Al2O3, SiC, BaTiO3,
etc
3. Organic Polymers
Soft, light in weight, poor
conductors of electricity and
heat, dimensionally
unstable,
ductile, combustible, low
thermal resistance
Plastics:PVC, PTFE,
polyethylene, polycarbonate
Fibres:terylene, nylon,
cotton, natural and
synthetic rubbers, leather
Other uses:refrigerants,
explosives, insulators,
lubricants, detergents, fuels,
vitamins, medicines for
surface treatment,
adhesives,
fibre-reinforced plastics, etc.
Composites
(i) Metals and alloys
and ceramics
(ii) Metals and alloys
and organic polymers
(iii) Ceramics and
organic polymers
They are better than any of
the individual
components as regards to
their properties
like strength, stiffness, heat
resistance,
etc.
Steel-reinforced concrete,
dispersion hardened alloys.
Vinyl coated steel, whisker
reinforced Plastics.
Fibre-reinforced plastics,
Carbon-reinforced rubber.

23
Table3.4.1.2 Properties for Grouping of Materials
Property Metals Ceramics Polymers
Composites
(wood)
1.Tensilestrength
(N/mm2
)
200–2000 10–400 30–100 20–110
2.Density (10N/mm2
) 2–8 *10e3 2–17 * 10e3 1–2 * 10e3 0.5 * 10e3
3. Hardness Medium High low low
4.Tensilemodulus
(103N/mm2
)
100–200 150–450 0.7–3.5
4–20
5. Melting point (°C) 200–3500 2000–4000 70–200 —
6. Thermal expansion Medium Low High Low
7.Thermal conductivity High Medium Low Low
8.Electrical conductivity Good
conductor
Insulator Insulator Insulator
3.4.2 Engineering Metallurgy:
This includes the study of metallurgy, which is of special interest to an engineer. At the
time of taking final decision regarding the selection of suitable material for a particular
job, it is essential for an engineer to have a thorough knowledge of engineering
metallurgy. This helps him in deciding the treatment processes and their sequence, which
are to be carried out on the finished components and structures. This includes the
following processes:
(i) Iron-carbon alloy system: This deals with the structure of iron and steel as well as
iron-carbon equilibrium diagrams. This also deals with the transformation of alloys
and steels under various sets of condition. A detailed and thorough study of this
process helps an engineer to decide the suitability of process and the selection of iron
alloy for various types of his jobs.
(ii) Heat Treatment: A thorough knowledge of this helps an engineer in deciding the
type of process to be undertaken for the smooth and efficient working of the
components and structures.
(iii) Corrosion of Metals:This deals with the colossal problem of corrosion of metals
and its prevention. It also deals with the processes which help engineers in
improving the life and outward appearance of themetal components and structures.

24
3.5 Selection of Materials
One of the most challenging task of an engineer is the proper selection of the
material for a particular job,e.g., a particular component of a machine or structure. An
engineer must be in a position to choose the optimum combination of properties in a
material at the lowest possible cost without compromising the quality. The properties and
behavior of a material depends upon the several factors, e.g., composition, crystal
structure, conditions during service and the interaction among them. The performance of
materials may be found satisfactory within certain limitations or conditions. However,
beyond these conditions, the performance of materials may not be found satisfactory.
One can list the major factors affecting the selection of materials as
i. Component shape
ii. Dimensional tolerance
iii. Mechanical properties
iv. Fabrication requirements
v. Service requirements
vi. Cost of the material
vii. Cost of processing, and
viii. Availability of the material.
All these major factors have a complex effect on the selection of materials. The
shape and size of a component has great effect on the choice of the processing unit which
ultimately affects the choice of themat serial even the efficient utilization of materials.
In this project we are using the two materials from the ferrous alloys
(i) Ductile cast iron
(ii) High grade
3.5.1 Ductile Cast Iron:
3.5.1.2Chemical Composition:
Nodular cast iron of high strength.
GGG-70: Ferro (Fe) rest,
Carbon (C) 3.0,
Silicon (Si) 2.40,
Manganese (Mn) 0.50,
Chromium (Cr) 0.50 (wt%)

25
3.5.1.3Mechanical properties:
Table3.5.1.3Mechanical properties for DCI
3.5.1.4 Thermal properties:
Table3.5.1.4Thermal properties for DCI
Minimum value Maximum value Units
Melting temperature 1150 1250 °C
Service temperature -100 350 °C
Thermal conductivity 25 42 W/mK
Thermal expansion 10 13 K
3.5.2 High Grade Steel:
3.5.2.1 Chemical Composition:
14NiCr14: Ferro (Fe) rest,
Carbon (C) 0.11-0.17,
Nickel (Ni) 3.25-3.75,
Chromium (Cr) 1.25-1.75,
Silicon (Si) 0.17-0.37,
Manganese (Mn) 0.30-0.60.
Minimum
value
Maximum value Unit
Density 7100 7300 kg/m³
Elongation 1 2 %
Tensile strength 650 700 MPa
Yield strength 380 400 MPa
Young's modulus 177000 185000 MPa

26
3.5.2.2 Mechanical properties:
Table3.5.2.2 Mechanical properties for HGS
Density 7860 7860 kg/m³
Elongation 1 2 %
Tensile strength 1100 1400 MPa
Yield strength 300 400 MPa
Young’s modulus 203000 203000 MPa
3.5.2.3 Thermal properties:
Table3.5.2.3Thermal properties for HGS
Melting temperature 1540 1540 °C
Specific heat 500 500 J/kgK
Thermal conductivity 40 40 W/mK
Thermal expansion 12 12 K

27
4. SOLID WORKS
4.1 Introduction
SolidWorks is the state of the art in computer-aided design(CAD).
SolidWorksrepresents an object in a virtual environment just as it exists in reality, i.e.,
having volume as well as surfaces and edges. Complex three-dimensional parts with
contoured surfaces and detailed features can be modeled quickly and easily with
SolidWorks. Then, many parts can be assemblingdin virtual environment to create a
computer model of the finished product. In addition, traditional engineering drawings can
be easily extracted from the solidmodels of both the parts and the final assembly. This
approach opens the door to innovative design concepts, speeds product development, and
minimizes design errors. The result is the ability to bring high-quality products to market
very quickly. Solid modeling represents objects in a computer as volumes, rather than just
as collections of edges and surfaces. Features are three-dimensional geometries with
direct analogies to shapes that can be machined or manufactured, such as holes or rounds.
Feature-based solid modeling creates and modifies the geometric shapes of an object in a
way that represents common manufacturing processes. This makes SolidWorksa very
powerful and effective tool for engineering design. As with other computer programs,
SolidWorks organize and stores data in files. Each file has a name followed by a
period(dot) and an extension. There are several file types used in SolidWorks, but the
most common file types and their extension sore
Part files .prt or ldprt
Assembly files .asmor.sldasm
Drawing files .drw or .slddrw
a. Part files:The files are the individual parts that are modeled. Part files contain all of
the pertinent information about the part. Because SolidWorks is a solids-modeling
program, the virtual part on the screen will look very similar to the actual
manufacture part.
b. Assembly files:These files created from several individual part files that are
virtually assembled(in the computer) to create the finished product.
c. Drawing files:Thetwo dimensional engineering drawing representations of both the
part and assembly file. The drawings should contain all of the necessary
information for the manufacture of the part, including dimensions, part tolerances,
and so on. The part file is the driving file for all other file types. The modeling
procedure begins with Part files. Subsequent assemblies and drawings are based on
the original part files. One advantage of SolidWorksfiles is the feature of dynamic
links. Any change to apartfile will automatically be updated in any corresponding

28
assembly or drawing file.Therefore, both drawing and assembly files must be able
to find and access their corresponding partfiles in order to be opened. SolidWorks
uses information embedded within the file and the filename to maintain these links
automatically.
4.2 Starting Solid Works
SolidWorks runs on computers running the Microsoft Windows operating
system.You open Solid Works in the same way that you would start any other program.
4.2.1 CheckingtheOptionsSettings:
TheSolidWorkswindow that appears on the computer screen looks similar to the
standard Microsoft Windows interface. The top line of the window is the Menu bar from
which menus for various operations can be opened. Below the Menu bar are the toolbars
which provide access to a variety of commonly used operations, ortools, with a single
click of the mouse button. Toolbars can also extend down the right and left sides of the
window. They may or may not be shown on your screen. At this point, most items within
the toolbars are grayed out. This indicates that they are not presently available for use.
The main part of the window is the Graphics Window. This is where the model is
displayed. Just below the Graphics Window is the Status bar, which displays information
about the current operation. The Status bar should now indicate “Ready”, since
SolidWorks is ready to proceed.
Fig.4.2.1SolidWorks window
Before you begin a sketch you need to setup some appropriate options. These setting
may be changed according to your needs.

29
1. If the Welcome to SOLIDWORKSdialogue box is open, close it by clicking on
the Xin it super right corner.
2. Click Tools in the Menu bar. Next, select Options(that is, Tools⇒Options).
3. The System Options dialogue box appears with the System Options tab visible.
4. Reset all of the preferences to the factory default by clicking Reset All followed
by Yesin the confirmation dialog box.
5. Click on the check mark next to input dimension value to remove the check
mark. This changes the way that dimensions are added to sketches. Click OK to
close the dialogbox.
Fig.4.2.1.1 System Option dialog box
4.2.2 General Toolbars:
To specify which toolbars are displayed on the screen, select View Tool-
bars(i.e.,selectToolbars from the View menu). Be sure that the Features, Sketch,
SketchRelations, SketchTools, Standard, StandardViewsand View toolbars are checked.
If they are not, click on each of these items until all are checked. If other toolbars are
checked, click on them to uncheck them. It may be necessary to select View, then
Toolbars again to display them after checking(run-checking) an item to confirm that the
desired change was made. The Standard Views toolbar may appear as a dialogboxin the
Graphics Window instead of as a toolbar. If so, click the blue bar at the top of the
dialogbox with the left mouse button and drag it to the toolbar at the upper right of the
Graphics Window. Release the mouse button. The dialogbox should change to a toolbar.

30
Fig.4.2.2 Toolbar Menu
 The Sketch toolbar contains tools to set up and manipulate a sketch.
 The Sketch Tools toolbar contains tools to draw lines, circles, rectangles, arcs,
and so on.
 The Sketch Relations toolbar contains tools for constraining element sofa
sketch by using dimensions or relations.
 The Features toolbar contains tools that modify sketches and existing features
of a part.
 The Standard tool bar contains the usual commands available for manipulating
files, editing documentsand accessing Help.
 The Standard Views toolbar contains common orientations for a model.
 TheViewtoolbar contains tools to orient and rescale the view of a part.
You can find these toolbars around the Graphics Window by checking and un-checking in
the View⇒Toolbarsmenu. The toolbars will appear as you check them and disappear you
uncheck them. Currently, most of the items in the tool-bars are grayed out, since they are
unusable. They will become active when they are available for use.Be sure that the
Toolbars menu looks like the one before continuing. Click any open spot in the Graphics
Window to close all menus.
4.3 Creating a New Part
 With the SOLID WORKS window open, select File⇒Newin the Menubar, or
click the New button(a blank-sheet icon) in the Standard toolbar.

31
 The New SOLID WORKS Document dialogboxappears. You will be modelling a
new part. If Part is already highlighted, clickOK. If it is not highlighted, click
Part,thenOK.
Fig.4.3 New document window
4.4 Sketching
Every part begins as a cross section sketched on a two-dimensional plane. Once a
sketch is made, it is extruded or revolved into the thirddimension to create a three-
dimensional object.This is the base feature of the part.
The Sketch toolbar has tools to setup and manipulate a sketch of a cross section. Find
the Sketch toolbar. Move the cursor over each of the tools, but donotclick on any of the
tools. The Tool Tips should appear, displaying the name of each tool.
 Select highlights sketch entities drags sketch entities and endpoints and
Modifies dimension values.
 Grid activates the Grid/Snap field of the Document Properties dialogue box to
change the sketching environment.
 Dimension adds dimensions to sketch entities.
 Sketch opens and closes sketches as a part is created.
To set the units and grid size to be used, click the Grid toolbar button with the left
mouse button. Document properties dialogue box will appear. Click Units on the left side
of the dialogue box to set the units. Setup appropriate units(inches or mm) with the
desired number of decimal places or fraction denominator.

32
Click Grid/Snap on the left side of the dialogue box to control the grid that will
appear on the screen when a cross-section is sketched. Be sure that all three of the boxes
under Gridare checked. Adjust the grid spacing to desiredvalues.
Snap controls the way in which sketched lines are related to the grid. The points that
are sketched should “snap” to the nearest intersection of gridlines when they are close. Be
sure the Snap to point’s box is checked. If not, click the box to check it.
Click Detailing on the left side of tile dialogue box. If necessary, change
Dimensioning standard to ANSI for inch units and ISO in case of mm units. Then, click
OK at the bottom of the dialogue box to accept the values.
Open a new sketch by selecting Insert Sketch, or by clicking the Sketch button(a
pencil drawing a line) in the Sketch tool bar. A grid should appear on the screen,
indicating that the sketch mode is active. The window’s name changes to Sketch of Part1.
In the bottom right corner of the screen, the Status bar reads Editing Sketch. You are now
ready to sketch in the Front plane.
The Sketch Tools toolbar contains tools to create and modify two- dimensional
features, called Sketch Entities. Sketch Entities are items that can be drawn on the sketch.
The following Sketch Entities and Sketch Tools are available
 Line creates a straight line.
 Center point Arc creates a circular arc from a center point, a start point,
and an end point.
 Tangent Arc creates a circular arc tangent to an existing sketch entity.
 3 Pt Arc creates a circular arc through three points.
 Circle creates a circle.
 Spline creates a curved line that is not a circular arc.
 Polygon creates a regular polygon.
 Rectangle creates a rectangle.
 Point creates a reference point that is used for constructing other
sketch entities.
 Centerline creates a reference line that is used for constructing other sketch
entities.
 Convert Entities creates a sketch entity by projecting an edge, curve, or
contour onto the sketch plane.
 Mirror reflects entities about a center line.
• Fillet creates a tangent arc between two sketch entities by rounding
an inside or an outside corner.
• Offset Entities creates a sketch curve that is offset from a selected sketch
entity by a specified distance.
• Trim removes a portion of a line or curve.

33
• Construction Geometry creates entities that aid in sketching.
• Linear Sketch Step and Repeat creates a line and pattern of sketch entities.
• Circular Sketch Step and Repeat creates a circular pattern of sketch entities.
Move and hold the cursor over each of the tools to display its function but
donotclick on the tool. Note the description of each tool in the Status bar at the bottom of
the SolidWorks window. Some of these tools may not include in the toolbar or other
tools may be available, depending on the way in which it was previously setup. All tools
are available in the Tools Menu.

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5. FINITE ELEMENTANALYSIS
5.1 Introduction
The finite element method represents an extension of the matrix method for the
analysis of framed structures to the analysis of the continuum structures. The basic
philosophy of the method is to replace the structure of the continuum having an unlimited
or infinite number of unknowns at certain chosen discrete points. The method is
extremely powerful as it helps to accurately analyze structures with complex geometrical
properties and loading conditions. In the infinite method, a structure or continuum is
discretized and idealized by using a mathematical model which is an assembly of
subdivisions or discrete elements, known as finite element, are assumed to be
interconnected only at the joint called nodes. Simple functions such as polynomials are
chosen in terms of unknown displacements at the nodes to approximate the vibrations of
the actual displacement over each finite element. The external loading is also transformed
into equivalent forces applied at the nodes. Next, the behavior of each element
independently and later as an assembly of these elements is obtained by relating their
response to that of the nodes in such a way that the following basic conditions are
satisfied at each nodes:
 Equations of equilibrium
 The compatibility of displacements
 The material constitutive relationship
The equations, which are obtained using the above conditions, are in the form of
force-displacement relationship. Finally, the force-displacement equations are solved to
obtain displacement at the nodes, which are the basic unknown in the finite element
method.
The basic idea in the finite element method is to find solution of a complicated
problem by replacing it by simpler one. Since a simpler one in finding the solution
replaced the actual problem, we will be able to find only an approximate solution rather
than exact solution. In finite element method, it will often be possible to improve or
refine the approximate solution by sending more computational effort.
This is a numerical solution for obtaining solutions to many of the problems
encountered in engineering analysis. In this method, the body or the structure may be
divided into small element of finite dimensions called finite element. The original body
or continuum is then considered as assemblage of these elements connected at a finite
number of joint called nodes.

35
5.2 Boundary Conditions of Fem
The general nature of its theory makes it applicable to a wide variety of boundary
value problems in engineering. A boundary values problems is one of which a solution is
sought in domain (region) of a body subject to the satisfaction of the prescribed boundary
(edge) condition of the dependent variable of their derivatives. Mostly all engineering
problems which are illustrated in the table 5.2 of the finite element method comes under
three categories of boundary problems, namely
1. Equilibrium or steady state or time independent problem,
2. Eigen value problem,
3. Transient or propagation problem.
Table 5.2 various applications of finite element analysis
Area of study Equilibrium
problems
Eigen value
problems
Propagation
problems
1.Civil engineering
structures
Static analysis of
the trusses,
frames, folded
plates, roofs,
shear walls
Natural
frequencies and
nodes structures
Propagation of
stress waves
2.Aircraft structures
Static analysis of
wings, rockets,
fuselages, fins
and missile
structures
Natural
frequencies
flutter and
stability of
aircraft, rocket.
Response of
aircraft structures
to random loads,
dynamic
response of
aircraft.
3.Hydraulic and water
resources engineering
Analysis of
potential flows,
free surface
flows, viscous
flows.
Natural periods
and modes of
shallow basins,
lakes and
harbours
Analysis of
unsteady state
fluid flow and
wave propagation
problems
4.Nuclear engineering Analysis of
nuclear pressures
vessel and
containment
structures
Natural
frequencies and
stability of
containment
structures
Response of
reactor
containment
structures to
dynamic loads.
5.Mechanical design Stress
concentration
problems, stress
analysis of
pressure vessel,
pistons, gears.
Natural
frequencies and
stability of
linkages, gears
and machine
tools.
Crack and
fracture problems
under dynamic
loads.

36
5.3 General Description of Fem
The step by step procedure for static problem can be stated as follows:
Step 1: Discretization of continuum
The first step in the finite element is to divide the structure of solution region into
sub division of element. The sub division or discretization process of the continuum is
essentially an exercise of engineering judgment. These subdivisions are called elements,
and are connected to the adjacent of the elements in such a way that the original body is
represented by it as closely as possible. Hence, the general objective of such an
idealization is to discretize the body into finite number of elements sufficiently small so
that the simple displacement models can adequately approximate the true solution.
Step 2: Selection of proper interpolation model
Since the displacement (field variable) solution of the complex structure under
any specific load condition cannot be predicted exactly, we assume some suitable with in
an element to approximate the unknown solution. The assumed solution must be from
computational point of view and it should satisfy certain convergence requirements.
Step 3: Derivative of element stiffness matrices (Characteristics matrices) and load2
vectors
From the assumed displacement model the stiffness matrix {K(e)} and load P(e)
of the element ‘e’ are to be divided by using either equilibrium conditions or a suitable
variation principle.
Step 4: Assemblage of element equation to obtain the overall equilibrium equation
Since the structure is compared of several finite elements, the individual element
stiffness matrices and load vectors are to be assembled in a variable manner and the
overall equilibrium equations have to be formulated as:
[K] {d}=[P]
Where [K] is called assemblage stiffness matrix,
{d} is called nodal displacement vector and
P is called nodal vector for the complete structure

37
Step 5: Solution of system equation to find nodal values of the displacement (fixed
variable):
The overall equation have to be modified, account for the boundary conditions of
the problem, after the incorporation of the boundary conditions, the equilibrium equation
are solved.
5.3.1 Type of Elements:
Often the type of element to be used is evident from the problem itself. For
example, if the problem involves the analysis of the truss structure under a given set of
load conditions, the type of element to be used idealization of obviously the “the bar or
line element”. However, in some cases the type of the elements to be used for idealization
may not be appropriate and in such cases one has to choose the type of elements
judicially. In certain problem, the given body cannot be represented as an assemblage of
only one type of elements. In such cases we may have to use two or more types of
element idealization.
5.3.2 Number of Elements:
The number of elements to be chosen for idealization is related to the accuracy
desired, size of element and the number of degrees of freedom involved. Although an
increase in number of elements generally gives more accurate results, for any given
problem, there will be certain number of elements reaching the point, where no
significant improvement will be found. Moreover, since the use of large number of
elements involves large number of degrees of freedom, we may not be able to store the
resulting matrices in the available computer memory.
5.3.3 Size of Elements:
The size of elements influences the convergence of the solution directly and it has
to be chosen with a care. If the size of elements is small, the final solution is expected to
the more accurate. However, we have to remember that the use of element of smaller size
will also mean more complicated time. Sometimes, we may have to use the elements of
different sizes in the same body. Another characteristic related to the size of element,
which affects the finite element solution is the “aspect ratio” of the element. The aspect
ratio is taken as the ratio of the element largest dimension to the smallest dimension of
the element. Element with aspect ratio of nearly unity generally yield better results.
a. Convergence Requirements: Since the finite element method is a numerical
technique, we obtain a sequence of approximate solution as the element size is
reduced successively. The sequence will converge to the exact solution if the
interpolation polynomial satisfies the following requirements.

38
1. The displacement function must be continuous with in elements.
2. The displacement function must be capable of representing rigid body
displacement of the element.
3. The displacement function must be capable of representing strain states within
the element.
b. Nodal Degrees of Freedom:The basic idea of FEM is to consider a body as
composed to several elements, which is connected at a specific node points. The
unknown solution or the field variables (like displacement, pressures or
temperatures) any finite element is assumed to be given by a simple function in
terms of nodal values of the elements. The nodal displacement, rotations,
necessary to specify completely the deformation of the finite elements is the
degree of freedom of the element. The nodal values of the solution, also known as
nodal degree of freedom, are treated as unknowns in formulating the system of
overall equations. The solutions of the system equation (like force equilibrium
equations) gives the value of unknown nodal degrees of freedom. Once, the nodal
degrees of freedom are known, the solution within any elements will also be
known to us. For having the results in terms of nodal degrees of freedom of
interpolation of function must be derived in terms of nodal degrees of freedom
c. Assembly Of Element Equations:Once the elements characteristics, namely the
element matrices and element vectors are found in a global co-ordinate system,
the next step is to construct the overall or system equations. The procedure of
assembling the elements matrices and vectors is based on the requirement of
“Compatibility” at the element nodes. This means that at the nodes where
elements are connected, the values of unknown degrees of freedom of the
variables are same for all the elements at the nodes.
d. Incorporation of the boundary conductions:After assembling the characteristic
matrices [K(e)] and elements characteristic vectors P(e) the overall system
equation of the entire domain of the body can be written (for any equilibrium
problems) as,
[K] {∅ ] = {P}
These equations cannot be solved for {∅} since the matrix [K] will
be singular and hence its inverse does not exist. The physical significance of this,
in case of solid mechanics problems, is that the loaded body or structure is free to
undergo unlimited rigid body motion unless some support constraints are imposed
to keep the body or structure under equilibrium under the loads. Hence some
boundary or support conditions have to be applied before solving for {∅}. In non
structural problems we have to specify one or some times more than one nodal
degree of freedom. The number of degrees of freedom is dictated by the physics
of the problem.

39
5.4 Finite Element Analysis
Finite element analysis was first developed for the use of aerospace and
nuclear industries where the safety of structure is critical. Today growth in the usage of
method is directly attributable to the rapid advances in computer technology. As a result
commercial finite element packages exist that are capable of solving the most
sophisticated problems, not just in structural analysis, but for a wide range of phenomena
such as steady state and dynamic temperature distributions, fluid flow and manufacturing
processes such as injection molding and metal forming.
FEM is used in a new product design, and existing product refinement.
Modifying an existing product or structure is utilized to qualify the product or structure
for a new service condition. In case of structure failure, finite element analysis may be
used to help in determining the design modifications to meet the new conditions.
5.4.1 Types of Analysis:
There are different types of analysis that are used in a industry are
Structural, Model, Harmonic, Transient and Spectrum
5.4.1.1 Structural Analysis:
It consists of linear and non-linear models. Linear models are simple parameters
and assume that material is not plastically deformed. Non-linear models consist of
stressing the material past its elastic capabilities. The stresses in the material then vary
with the amount of deformation.
5.4.1.2 Vibration Analysis:
Itis used to test the material against random vibrations, shock and impact. Each of
these incidents may act on the natural vibration frequency of the material, which in turn,
may cause resonance and subsequent failure. So analysis is done on the material to
predict the life of the material. Heat-Transfer analysis models the thermal conductivity or
thermal fluid dynamics of the material or structure. This may consists of steady state or
transient transfer. Steady-State transfer refers to constant thermo properties in material
that yield linear heat diffusion.
5.5 Finite Element Analysis Process
The structure analyzed is subdivided into mesh of finite sized elements of a
simple shape. Within each element, the variation of displacement is assumed to be
determined by simple polynomial shape functions and nodal displacements. Equations for
strain and stresses are developed in terms of unknown nodal displacements. From this,
the equations of equilibrium are assembling in a matrix form, which can be easily

40
programmed and solved, on a computer. After applying appropriate boundary conditions,
the nodal displacements are found by solving the matrix stiffness equation. Once the
nodal displacements are known element stresses and strains can be calculated
5.6 Introduction to Ansys Software
The purpose of a finite element analysis is to model the behavior of a structure
under a system of loads. In order to do so, all influencing factors must be considered and
determined whether their effects are considerable or negligible on the final result.
Muchsoftware’s are used for this purpose. ANSYS, Pro-E, Uni Graphics, NISA, MSC,
NASTRAN etc,
The ANSYS program this self-contained general purpose finite element program
developed and maintained by Swanson Analysis System Inc. The program contains many
routines, all interrelated and all for many purpose of achieving a solution to an
engineering problem by Finite Element Method.
ANASYS provides a complete solution to design problems. It consists of
powerful design capabilities like full parametric solid modeling, design optimization and
auto meshing, which gives engineers full control over their analysis.
The following are the special features of ANSYS software:
 It includes bilinear elements.
 Heat flow analysis, fluid flow and element flow analysis can be done.
 Graphic package and extensive pre-processing and post processing.
The following shows the brief description of steps followed in each phase.

41
5.6.1 Various Stages of Ansys:
Table5.6.1 Stages of Ansys
5.6.2 Pre-Processor:
The pre-processor stage in ANSYS package involves the following:
 Specify the title, which is the name of the problem.
 Set the type of the analysis to be used, i.e., structural, thermal, fluid, or electro-
magnetic, etc.,
 Create the model - The model is drawn in 1-D, 2-D, or 3-D space in the
appropriate units (m, mm, in, etc). The model may be created in pre-processor, or
it can be imported from another CAD drafting package through a neutral file
format9 like IGES, STEP, ACIS, Para solid, DFX, etc.,. The same units should be
applied in all directions, otherwise results will be difficult to interpret, or in
extreme cases the result will not show up mistakes made during loading and
restraining of the model.
 Define the element type, this may be 1D, 2D or 3D, and specify the analysis type
being carried out.
 Apply mesh - Mesh generation is the process of dividing the analysis continuum
in to a number of discrete parts or finite elements. The finer mesh, the better
result, but the longer the analysis time. Therefore, the compromise between
accuracy and solution speed is usually made.
Pre-Processor Phase Solution Phase Post Processor Phase
Geometry definitions Element matrix formation Post solution operation
Mesh generation
Overall matrix
triangulation
Post data print out
Materials definition Wave front Post data display
Constraint definition Displacement, Stress, etc.,
Load definition Calculations

42
 Assign the properties - Material properties (Young's Modulus, Poisson's ratio,
density, and if applicable coefficient of expansion, friction, thermal conductivity,
damping effect, specific heat, etc.,) have to be defined.
5.6.3 Meshing:
5.6.3.1 Manual Meshing:
In manual meshing the elements are smaller at joint. This known as mesh
refinement, and it enables the stress to be captured at the geometric discontinuity. Manual
meshing is long and tedious process for models with any degree of geometric
complication, but with useful tool emerging in preprocesses, the task is becoming easier
 Free and Mapped Mesh:A free mesh is one that has no restrictions in terms of
element shapes, and no specific pattern applied to it. Compared to a free mesh, a
mapped mesh is restricted in terms of the element shape it contains and the pattern
of the mesh. A mapped mesh contains only quadrilateral (area) or only
hexahedron (volume) elements. If this type of mesh is desired, the user must build
the geometry as series of fairly a regular volumes and/or areas that can accept a
mapped mesh.
5.6.3.2 Meshing controls:
The default meshing controls that the program uses may produce a mesh that is
adequate for the model we are analyzing. In this case, we need not specify any meshing
controls. However if we do use meshing controls we must set them before meshing the
solved model
Meshing controls allow us to establish the element shape, midsize node placement
and element size to be used in meshing the solid model, this step is one of the most
important of the entire analysis for the decisions we make at this stage in the model
development will profoundly affect the accuracy and economy of the analysis.
 Smart Sizing Of Element:Smart element sizing (Smart sizing) is a meshing
feature that creates initial element sizes for free meshing operations. Smart sizing
gives the mesher a better chance of creating reasonably shaped elements during
automatic mesh generation.
5.6.4 Solution:
 Apply the loads. Some type of load is actually applied to the analysis of the
model. The loading may be in the form of point load, pressure a displacement in
a stress analysis, a temperature or heat flux in thermal analysis and a fluid

43
pressure or velocity in a fluid analysis. The loads may be applied to a point, an
edge, a surface or even to a complete body
 Applying boundary conditions. After applying load to the model in order to stop
it accelerating infinitely through the computer virtually either at least one
boundary conditions must be applied.
 FE solver can be logically divided into three main parts, the pre-solver, the
mathematical-engine and the post-solver. The pre-solver reads the model created
by the pre-processor and formulates the mathematical representation of the
model and calls the mathematical-engine, which calculates the results. The result
returned to the solver and the post -solver is used to calculate the strains,
stresses, etc., for each node within the component or continuum.
5.6.5 Post-Processor:
In this module, the results of the analysis are read and interpret. All post-
processor include the calculation of stress and strain in the entire X, Y, Z directions or
indeed in the direction at an angle to the co-ordinate axes. The principle stress and strain
may also be plotted.
5.7 Structural Analysis
Structural analysis is probably the most common-application of FEM.
The term structural implies not only civil engineering structures such as bridges and
buildings, but also naval, aeronautical, mechanical components such as axles, pistons,
machine parts and tools. The primary unknowns (nodal degree of freedom) calculated in
a structural analysis are displacements other qualities such as strains, stresses and
reaction forces are derived from the nodal displacements.
5.7.1 Modal Analysis:
5.7.1.1 Definition:
We use Modal Analysis to determine the vibrations characteristics (Natural
frequencies and mode shapes) of a structure of machine component while it is be
designed. It also can be a starting point for another, more detailed, Dynamics Analysis,
such as a transient dynamics, a harmonic response analysis, or a spectrum analysis.
5.7.1.2 Uses for Modal Analysis:
The natural frequencies and mode shapes are important parameters in the design
of structure for dynamic loading conditions. They are also required if you want to do a
spectrum analysis or a mode superposition harmonic or transient analysis.
We can do modal analysis on a pre stressed structure, such as a spinning turbine
blade. Another useful feature is modal cyclic symmetry, which allows you to review the
mode shapes of a cyclically symmetry structure by modelling just a sector of it.

44
Modal analysis in the ANSYS family of the products is a linear analysis. Any
nonlinearity, such as plasticity and contact (gap) elements, are ignored even if they are
defined. You can choose from several mode extraction methods: sub spaces, block
lanczos, power dynamics, reduced, unsymmetrical, and damped. The damped method
allows you to include damping in the structure. Details about mode extraction methods
are covered later in this section.
5.7.2 Structural Static Analysis:
5.7.2.1 Definition:
A static analysis calculates the effects of steady loading conditions on a structure,
while ignoring inertia and damping effects, such those caused by time varying loads. A
static analysis can, however, include steady inertia loads (such as gravity and rotational
velocity), and time varying loads that can be approximated as static equivalent loads
(such as the static equivalent wind and seismic loads commonly defined in many building
codes).
5.7.2.2 Loads in a Static Analysis:
Staticanalysis is used to determine displacements, stress, strains and forces in
structures or components caused by loads that do not induced significant inertia and
damping effects. Steady loading and response conditions are assumed; i.e., the loads and
the structure's response are assumed to vary slowly with time. The kinds of loadings that
can be applied in a static analysis include:
 Externally applied forces and pressures
 Steady-State inertia forces (such as gravity or rational velocity)
 Imposed ( non-zero ) displacements
 Temperatures (for thermal strain)
 fluencies (for nuclear swelling)
A static analysis calculates the effects of steady loading conditions on a
structure, while ignoring inertia and damping effects, such as those caused by time
varying loads. A static analysis can, however, include steady inertia loads (such as
gravity and rotational velocity), and time varying loads that can be approximated as static
equivalent loads (such as static equivalent wind and seismic loads commonly defined in
many building codes).
5.8 Advantages of FEM
1. Its ability to use various size and shape and to model a structure of
arbitrary geometry.
2. Its ability to accommodate arbitrary boundary conditions, loading,
including thermal loading

45
3. Its ability to modal composite structures involving different structural
components such as stiffening members on a shell and combination of
plates , bars and solid etc.,
4. The finite element structure closely reassembles the actual structural
instead of being quite different obstruction that is hard to visualize.
5. The FEM is proven successfully in representing various types of
complicated material properties and material behaviour (nonlinear,
anisotropic, time dependent or temperature dependent material behaviour).
6. It readily account for non-homogeneity of the material by assigning
different properties to different elements or event it is possible to vary the
properties within an element according to a pre-determined polynomial
pattern
5.9 Disadvantages of FEM
Specific numerical results obtained for a specific problem.
1. Experience and judgment are required in order to construct a good finite
element model.
2. A big computer and a reliable computer program (software) are essential.
Input and output data are tedious to prepare and interpret.

46
6. MODELING AND STRUCTURAL ANALYSIS OF REAR DEAD AXLE
6.1 Problem Definition
The component which we are modeling and analyzing is rear dead axle, which
plays an important role in supporting the wheels for rotation and as well as to bear the
total weight of the vehicle.
By considering laden weight on 3g condition, the rear dead axle having the force
of total load acting is 300kN in y-direction. On the both sides, beyond the axle there will
be leaf springs fixed or attached. On the leaf springs the load was equally distributed i.e.,
150kN at each side and the rear dead axle end is fixed with the wheels.
The rear dead axle is drafted in solid works in 3D,this 3D solid is imported to the
work bench to analyze and find the stresses and deformation of the component for two
different materials and finally states which is preferable.
6.2 Analytical Method:
6.2.1 Moment of Inertia of I-Cross Section:
Fig6.2.1 I-Cross Section of Axle

47
Assumption
H=1.2*B
h= (H/2)
b= (B/2)
We will design the axle beam by taking consideration of yield stress of both
material i.e. Ductile Cast Iron and High grade steel.
The value of yield stress of both materials is 370 MPa.
6.3 Calculation of Weight:
For Truck,
Loaded Weight = 10200 kg.
Actual weight coming on axle is,
Considering 3g condition (bump load) = 3 * 10200
= 30600 kg
Total Weight on axle is given by = 30600* 9.81
= 300.186 kN
Weight on each spring seat = 300.186/ 2
= 150.093 kN
6.4 Modeling of Rear Dead Axle in 3D Solid
6.4.1Creation of the model:
Modeling is the art of abstracting or representing a phenomenon and
geometric modeling is no exception. A geometric model is defined as the complete
representation of an object that includes both its graphical and non graphical information.
Geometric model is complete in all aspects and contains geometric well as topological
information. Objects can be classified into three types from geometric construction point
of view. These are two and a half dimensional, three dimensional or a combination of
both. The geometric model of the rear dead axle has been created using SOLID
WORKS2014. The main steps involved in the creation of the model are as follows.
Step1. Create a new file

48
To create a New File - click file > new A dialog box will be opened with Part, Assembly
and Drawing. Select the Part and click ok.
Step2.Set the units
To set the Units select, Options>Document Options and set the required units. For our
requirement select MMGS (millimeters, gram, second) or change the necessary
dimensions by selecting the option given in bottom command bar.
Step3. Select the plane
To start sketching firstly the working plane has to be selected. For this select the front
plane and enter into sketcher. Press Cntrl+8 to get normal view.
Step4. Select the line command.
To draw the diagram select the origin point and draw the required 2D figure.
Step5. Dimension the line
Select the smart dimensions for the 2D figure.
Step6. Select the arc
Select the three point arc and join the two lines.
Step7.Dimension the arc
Select the smart dimension and dimensions are given.
Fig6.4.1 2D Line diagram

49
Step8. Extrude the 2D diagram
Select the extrude command, and extrude the diagram with necessary dimensions.
Step9. Select the circle
Draw the circle on side of the 3D solid and smart dimensions are given.
Step10. Select the line
Select the ctrl+8 for normal view. Draw the lines that necessary on 3D solid for creating
I-section.
Step11. Mirror the extruded diagram
Select the reference plane and create the plane at the end of diagram. Select the mirror
command, mirror the extruded figure.
Fig.6.4.1.1 Mirror Image of Solid

Fig.6.4.1.2 Extruded Image of Solid
Fig.6.4.1.3 Isometric view of solid
50

51
6.5 Structural Analysis of Rear Dead Axle
 Analysis in Work Bench:
The modeling of rear dead axle created in solid works is converted into the
IGES format and imported to work bench. In work bench there are different analysis
systems. In that analysis system static structural and modal are used for determining the
stresses and deformations in the component.
6.5.1 Static Analysis:
 Geometry:
The 3D solid component is imported to geometry.
Fig.6.5.1.1 importing of geometry
 Engineering Data:
Select the engineering data source and add the required materials to the
library, In library select the required properties.

52
 Applying Material:
Edit the model select the geometry and apply the ductile cast iron, high
grade steel materials for all components of the rear dead axle.
Fig.6.5.1.2 Ductile Cast Iron
Fig.6.5.1.3 High Grade Steel

53
 Meshing:
In the meshing select all components of rear dead axle by selecting the
fine meshing option and give the minimum edge length of 5.e-003m.
Table6.5.1 Meshing Parameters
Object Name Mesh
State Solved
Defaults
Physics Preference Mechanical
Relevance 0
Sizing
Use Advanced Size Function On Proximity and Curvature
Relevance Center Fine
Element Size 5×10-3
m
Initial Size Seed Fully Assembly
Smoothing High
Transition Fast
Span Angle Center Fine
Curvature Normal Angle 18 degrees
No of cells Across Gap 3
Min Size 3.2449×10-4
m
Proximity Min Size 3.2449×10-4
Max Phase Size 3.2449×10-2
m
Max Size 6.4898×10-4
m
Minimum Edge Length 5×10-3
m
Inflation
Use Automatic Inflation All Faces in chosen named section
Inflation Option Total Thickness
Transition Ratio 0.272
Maximum Layers 5
Growth Rate 1.2
Inflation Algorithm Pre
View Advanced Options No
Patch Conforming Options
Triangle Surface Mesher Program Controlled
Patch Independent Options
Topology Checking Yes
Advanced
Number of CPUs for Parallel Part
Meshing
Program Controlled
Shape Checking Standard Mechanical
Element Midside Nodes Program Controlled
Straight Sided Elements Yes
Number of Retries 4

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Extra Retries For Assembly Yes
Rigid Body Behavior Dimensionally Reduced
Mesh Morphing Enabled
Defeaturing
Pinch Tolerance 2×10-3
m
Generate Pinch on Refresh Yes
Automatic Mesh Based Defeaturing On
Defeaturing Tolerance 1.6224×10-4
m
Statistics
Nodes 54608
Elements 29360
Mesh Metric None
Fig.6.5.1.4 Meshing
 Applying Loads and Supports:
The rear dead axle component two ends are fixed and two loads are
applied at the centre of leaf springs arranged

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Fig.6.5.1.5 Applied loads and Fixed Supports
 Solution:
Solution is done,Stresses and Deformation are obtained.
6.5.2 Results
6.5.2.1 Total Deformation for Ductile Cast Iron Material:
Fig.6.5.2.1 Total Deformation in X-Direction

56
Fig.6.5.2.2 Total Deformation in Y-Direction
Fig.6.5.2.3 Total Deformation in Z-Direction

Here are the key points about axles:1.1.1 Front Axle- Connects the front wheels to the vehicle and allows them to rotate freely. - Supports part of the vehicle weight and transmits steering forces.- Usually independent suspension with coil or leaf springs. Allows wheels to move up/down independently.- May have solid beam or I-beam design.1.1.2 Rear Axle- Connects the rear wheels to the vehicle and allows them to rotate freely.- Supports around 60% of the total vehicle weight. Heavier duty than front axle. - Can have solid beam, banjo, or live axle design. Live

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