Design and Analysis of Helical Spring Used in Rail Wagon

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C.S.I. INSTITUTE OF TECHNOLOGY
THOVALAI
PROJECT REPORT
DESIGN AND ANALYSIS OF HELICALSPRING
USED IN RAIL WAGON
Guided by
MR.R. JOSELIN B.E

Submitted by
S.SAMRAJ
T.SELVARAJ
S.G.SUMATHI
DEPARTMENT OF MECHANICAL
ENGINEERING
2002 – 2003
C.S.I. INSTITUTE OF TECHNOLOGY
THOVALAI
DEPARTMENT OF MECHANICAL ENGINEERING
Project Report
On
DESIGN AND ANALYSIS OF HELICALSPRING
USED IN RAIL WAGON

CERTIFICATE
Certified that this is the bonafied record of project work on DESIGN done by
Selvan………………………………………..Reg No…………………… of VIII
Semester Mechanical Engineering branch during the academic year 2002 – 2003.
Project Guide Head of the Department
Submitted for the Board examination held on…………….
Internal Examiner External Examiner
ACKNOWLEDGEMENT
First of all we thank the most merciful, the most graceful and the most
beneficent almighty.
At the outset we thank everyone who was with us in thoughts and action
during our project.

We are graceful to our institution C.S.I INSTITUTE OF TECHNOLOGY , to
its correspondent and to our principal, who gave us the facilities to prove our
abilities.
We extremely thank Mr. ., head of the department of mechanical
engineering for his constant help in doing this project.
We owe our credence to our internal guide for his assistance in project
consultation, guidance and documentation. we also extend our thanks to all
lecturers in the department for their encouragement.
We extend our heartful gratitude to our parents who give us life, love and
education.
SYNOPSIS
Spring is an elastic body, which is used to absorb the sudden
shocks, mostly it is used in all mechanical components for example:
Shock absorbers.
In this project, various cross-sections of spring under identical
loading conditions are compared and best-suited spring is identified.
The present study is focussed on the structural analysis of the
spring.

The three-dimensional model is developed in PRO/E and is
analysed using ANSYS. While comparing Factor of Safety, Stress,
Displacement for various cross sections of spring use find out
circular spring is the best one for the suspension of Rail Wagon.
CONTENTS
Introduction
CAD/CAM/CAE
PRO/Engineer
ANSYS
Auto design
FINITE ELEMENT ANALYSIS
Introduction
General Procedure of the FEA

Modeling Capabilities of Finite Elements Soft wares
Common Elements used in finite Element Analysis
Advantages & Disadvantages of FEA
ABOUT SPRINGS
Introduction
Terms used in Springs
Stresses in Helical Springs of Circular wire
Deflection of helical Springs
Material Properties of the Spring
Properties
Specification
Comparison of Springs
Types of C/S area of the Springs
Design of Springs
Design of Rectangular C/S springs
Design of Square C/S Springs
Modelling of the Spring using Pro/E
Modelling of Rectangular C/S Springs
Modelling of Square C/S Springs

Modelling of Circular C/S Springs
Structural Analysis using ANSYS
Checking
Conclusion
Bibliography

LIST OF PHOTO COPIES
PRO-E MODEL :
1. Rectangular C/S Springs
2. Square C/S Springs
3. Circular C/S Springs
MESH MODEL :
ANALYSIS MODEL :
a. Stresses acting on the springs
b. Displacement of the springs
c. Stresses acting on the springs
a. Displacement of the springs
d. Stresses acting on the springs
a. Displacement of the springs

INTRODUCTION
CAD/CAM/CAE
Computer aided design or CAD has very broad meaning and can be
defined as the use of computers in creation, modification, analysis and
optimization of a design. CAM (Computer Aided Manufacturing) involves
computer in the areas of process planning and tool path generation. CAE
(Computer Aided Engineering) is referred to computers in engineering analysis
like stress/strain, heat transfer, flow analysis. CAD/CAM/CAE is said to have
more potential to radically increase productivity than any development since
electricity. CAD/CAM/CAE builds quality form concept to final product. Instead
of bringing in quality control during the final inspection it helps to develop a
process in which quality is there through the life cycle of the product.
CAD/CAM/CAE can eliminate the need for prototypes. But it required prototypes
can be used to confirm rather predict performance and other characteristics.
CAD/CAM/CAE is employed in numerous industries like manufacturing,
automotive, aerospace, casting, mold making, plastic, electronics and other
general purpose industries. CAD/CAM/CAE systems can be broadly divided into
low end, mid end and high-end systems.

Low-end systems are those systems which do only 2D modeling and with
only little 3D modeling capabilities. According to industry static’s 70-80% of all
mechanical designer still use 2D CAD applications. This may be mainly due to
the high cost of high-end systems and a lack of expertise etc.
Mid-end systems are actually similar t high-end systems with all their
design capabilities with the difference that they are offered at much lower prices.
3D sold modeling on the PC is burgeoning because of many reasons like
affordable and powerful hardware, strong sound software that offers windows
case of use shortened design and production cycles and smooth integration with
downstream application. More and more designers and engineers are shifting to
mid end system.
High end CAD/CAM/CAE soft wares are for the completer modeling,
analysis and manufacturing of products. High-end systems can be visualized as
the brain of concurrent engineering. Concurrent engineering plays an important
role in all the research and developments going throughout the world and these
are not possible without the high-end systems. The design and development of
products which took years in the passed to completer is now made in days with
the help of high end CAD/CAM/CAE systems and concurrent engineering.

In India CAD/CAM/CAE scenario is in the developing stage. As Indian
engineers generally accept technology only to service. The high-end
CAD/CAM/CAE software’s has taken tome to enter into the Indian industries, but
now it is in a booming stage.
Most of the India engineers and designers still use old 2D modelers.
Certainly some of the inertia holding them in the entry to the high-end cad world
is the reluctance on the part the drafters and engineers to give up methods drilled
into them over period of years. But just as competition demanded the
replacement of drafting boards by computers, they will surely switch over to high-
end CAD/CAM/CAE soft ware with the genera push. As the CAD/CAM/CAE
scenario is a very vast one, it is always impossible to dig into the details of all the
available soft ware in the market in a short time. Even then a sincere effort has
been made to get details of all the market leading software and they are
described below.
PRO-ENGINEER
To succeed in today’s competitive internet-driven marketplace, discrete
manufacturers need to introduce products faster than their competition, with built-
in differential advantages, higher levels of customer acceptance and all at a
lower cost to them. Pro/engineer is designed form the ground up to accomplish
this goal-with unmatched technical innovation productivity advantages that have

made it the de-facto standard for product development across all manufacturing
industries. It provides a Flexible Engineering infrastructure for product
development that can rapidly respond to changing market conditions to support
company business initiative.
Pro/ENGINEER-Foundation
The cornerstone of the Pro/ENGINEER family is Pro/ENGINEER-
Foundation. This single package provides best-in-class, integrated capabilities
for creating detailed sold and sheet metal components, building assemblies,
designing weldments producing fully documented production drawing and
creating photo realistic rendering. It is built on PTC’s industry leading
Pro/ENGINEER feature-based, associative parametric sold-modeling kernel. In
addition Pro/ENGINEER-Foundation . As your business grows and your needs
change, you can build on this powerful functionality with the following extension
and options for every phase of development and level of expertise.

Behavioral Modelling
best possible, fully engineered design. Simple design problems become less
tedious to solve. Complex design problems can be solved conclusively in a
fraction of time that it would take to find a “close enough” solution through
cumbersome manual techniques. Behavioral Modeling is a next-generation
general design tool that raises mechanical design automation beyond geometry
“documentation” to true design. It provides a process that allows informed
design exploration leading to an optimal design solution based on requirements.
Advanced Assembly
The Advanced Assembly Extension expands the power of
Pro/ENGINEER-Foundation to include the engineering and management of
medium to very large assemblies throughout an enterprise-wide product
development process. It offers rich capabilities for design criteria management,
top-down assembly design, large assembly management, associative shrink-
wrap, and process planning. these tools enhance the productivity of design
teams creating and managing, complex product designs-and help downstream
users produce accurate lifecycle documentation for assembly on the shop floor.
They also encourage distribution of engineering tasks and collaboration between
dispersed terms.

Advanced Surface
The Advanced Surface Extension, in conjunction wit Pro/ENGINEER
FoundationTM
caters to clients who require more control over the shape of their
designs. It’s capabilities allow designers to address a full range of products, form
prismatic engine components, to contoured gold clubs, to organic shapes like
human teeth. The Advanced Surface Extension offers high-powered tools for
design criteria management, parametric surface modeling and direct surface
modeling for reverse engineering.
Model CHECKTM
Model CHECK is a knowledge management and quality control add-on to
Pro/ENGINEER. It detects design deviations and inconsistencies in
Pro/ENGINEER models that can make it difficult to share or reuse models and
provides online design guidance. Model CHECK is used today in many
organizations to help uses create parts, drawing and assemblies according to
corporate standards and best practices. Through the regular use of Model
CHECK, users will increase their Pro/ENGINEER proficiency. The new Shape
IndexingTM
technology in Model CHECK is used to find similar models making it
easier to reuse existing designs.

Routed Systems
The Routed Systems Option for Pro/ENGINEER offers comprehensive
and associative capabilities for electrical, cabling, and piping design and
manufacturing. Pro/ENGINEER Routed System help designers, packing and
manufacturing engineers, to quickly and accurately design, route, document,
and produce complex harness and piping systems. This results in a significant in
quality and productivity for complex routed systems.
Plastic Advisor
The Pro/ENGINEER Plastic Advisor Option provides plastics part
designers with immediate and easy access to reliable and easy-to-understand
manufacturing feedback and advice. Designed to evaluate every design change
nor just every design-for injection moulding manufacturability, Plastic Advisor is
the ideal cost and time saving tool. Designers simply select the material type
and proposed gate locations and Plastic Advisor provides on-screen animations
for the mold filing, plots describing the “mouldability” of the design, and the
locations of potential problem areas such as wells lines and air traps.

Mechanism Design
The Pro/ENGINEER Mechanism Design Extension enables
designers to quickly and easily assemble pro/ENGINEER parts and
subassemblies using pre-defined connection (pin joints, ball joints, sliders, etc.)
to create a mechanism assembly . These connections are intelligent
pro/ENGINEER features and can be used in conjunction with the traditional
assembly constraints like mat, align and insert. The mechanism can then be
interactively dragged through its range of motion, or the designer can used
‘drivers’ to create animations f pre-defined motion that can then be stored and
replayed.
Design Animation
The pro/ENGINEER Design Animation option enables the creation of
animation sequences within pro/ENGINEER, using parts, assemblies, and
mechanisms. Using key frames, drivers and inherited mechanism joints,
animations can be created and manipulated with ease. As a simple yet powerful
way to convey complex information about a product or process, these animation
sequences can be used as concept communication tools fir sales and marketing,
managements, design reviews, and as a method for remote communication of
information.

APItoolkit
The Application Programming Toolkit allows customers to extend,
automate, and customize a wide range of pro/ENGINEER design-though-
manufacturing functionality. The Application programming Toolkit consist of a
library of function, often referred to an application-programming interface(API),
written in the co programming language. these functions are typically used by
MIS organizations to create applications that run in parallel with pro/ENGINEER
and to integrate product information with the customers corporate MRP/ERP
systems. The extensive Application Programming Toolkit API library provides
programmatic access for creating, interrogating, and manipulating almost every
aspect of the engineering model and its data management.
CADAM migration
The CADAM Migration option can maintain, modify, and revise mainframe
CADAM drawings in a desktop environment. It maintains familiar CADAM
structure so users can access, update, and plot legacy CADAM drawings with no
retraining. Using the CADAM Migration option, its easy to make simple drawing
changes. It a part changes, the drawing can be easily revised, and the part
quickly returned to production.

ANSYS
ANSYS can be used for all levels of analysis, from basic Stressing to full
non-linear dynamic analysis.
ANSYS, Inc., a leader in collaborative engineering, exemplifies its ongoing
commitment to engineering education through the ANSYS, Inc., Education
program. Currently the ANSYS, Inc., Educational Program aids over 2,000
colleges, universities, and educational institutions worldwide in teaching the
fundamentals of finite element analysis.
Today the focus of the Educational Program has been directed towards
recognizing the many technical and economic developments that the constant
changing the nature of manufacturing thus creating a demand for engineers who
understand advanced computational techniques. Thousands of engineers will be
needed to meet the demands of this ever-changing engineering community, and
ANSYS, Inc’s goal is to ensure institutions of higher education will be capable
preparing a new generation of engineers for the challenges that lie ahead.
ANSYS provide advanced engineering analysis and support in man
disciples, including:
o Stress-Analysis-Linear &Nonlinear, Elastic-Plastic, Fatigue.
o Dynamics-Vibration, Shock/Impact, Containment, Random,
Vibration, Rotor Dynamics.

o Mechanisms-Rigid and Flex Body Kinematics.
o Heat Transfer-Steady-state & Transient, Linear & Nonlinear,
Couple Thermal/Structural.
o Coupled/Field Analysis- Piezoelectric, acoustics and fluid-
structure interaction.
Auto Design 5.0
Auto Design 5.0 is the only Finite Element Analysis Product completely
integrated inside Mechanical Desktop. Any 3D solids, surfaces and wire-frames,
as well as Designer solids, can be automatically meshed. Static, Dynamic and
Thermal analysis, as well as design optimization, can be performed inside the
Mechanical Desktop/Auto CAD, New intuitive toolbars/icons and dialog boxes
make it even easier to rapidly evaluate and optimize designs and perform stress
analysis for design engineers. Auto Design 5.0, in conjunction with Mechanical
Desktop, provides a fully integrated and streamlined mechanical design solution
for the first time to AutoCAD users.

FINITE ELEMENT ANALYSIS
Introduction of FEA
It is not possible to obtain analytical solution for many engineering
problems. At the engineering solution is a mathematical model or expression
that gives the value of the field variable at any location in the body.
For problems involving complex shapes, material properties and
complicated boundary conditions it is difficult, so for many of the practical
problems, and engineer uses numerical methods to solve the problems and that
provides approximate solutions, which is also acceptable one. The three
methods are used.
a. Functional approximation
b. Functional difference method
c. Finite element method
Finite element method (FEM) and analysis (FEA) are tow of the very popular
engineering applications offered by existing CAD/CAM systems. This is
attributed to the fact that the finite element method is perhaps the most popular
numerical technique for solving engineering problems. The method is general
enough to handle any complex shape or geometry (problem domain), any

material properties, any boundary conditions and any loading conditions. The
generality of the finite element method analysis requirements to today’s complex
engineering systems and designs where closed form solutions of governing
equilibrium equations are generally not available. In addition, it is an efficient
design tool by which designers can perform parametric design studies by
considering various design cases (different shapes, materials, loads, etc)
analyzing them and choosing the optimum design.
The finite element method is numerical technique for obtaining
approximates solutions to engineering problems. This method is adopted in the
industry as a tool to study stresses in complex air frame structures. The method
has gained popularity amid of both researches and practitioners.
General Procedure of the FEA
The solution of a continuum problem by the finite element method usually
follows an orderly step-by-step process. the following steps show in general how
the finite element method works.

a. Discretize the given continuum
The importance of the finite element method is to divide a continuum that
is problem domain, into quasi-disjoint, non-overlapping elements. This is
achieved by replacing the continuum by the set of key points; called nodes when
connected properly, produce the elements. The collection of nodes and
elements form the finite element mesh. A variety of element shapes and types
are available. The analyst or designer can mix element types to solve one
problem. The number of nodes and elements that can be used in problem is a
matter of engineering judgment. As a general rule, the larger number of nodes
and elements, the more accurate the finite element solution, but also the more
expensive the solution, is more memory space is needed to obtain the solution.
b. Select the solution approximation:
The variation of the unknown (called field variable) in the problem is
approximated within each element by a polynomial. The field variable may be a
scalar (e.g., temperature) or a vector (e.g., horizontal and vertical
displacements). Polynomials are usually used to approximate the solution over
an element domain because they are easy to integrate and differentiate. the
degree of the polynomial depends on the number of nodes per element, the
number of unknown (components of field variable) at each node and certain
continuity requirements along element boundaries.

c. Develop element matrices and equations:
The finite element formulation involves transformation of the governing
equilibrium equations form the continuum domain to the element domain. Once
the nodes and material properties of a given element it’s be derived. Four
method are derive element matrices and equations; the direct method, the
variation method, the weighted residual method, and the energy method.
d. Assembling the element equations
The individual element matrices are added together by summing
equilibrium the equations of the elements to obtain the global matrices and
systems to algebraic equations. Before solving this system, it must be modified
by applying the boundary conditions. It boundary conditions are nor applied,
wrong results are obtained or a singular system of equations may result.
e. Solve for the unknown at the nodes
The global system of algebraic equations is solved via Gauss elimination
methods to prove the values of the fields variables at the nodes of the finite
element mesh. Values of field variables at their derivatives at the nodes from the
completer finite element solution of the original continuum other than nodes are
possible to obtain although it is not usually done.

f. Interpret the result
The final step is to analyze the solution and the results obtained from the
previous stop to make design decisions. the correct interpretation of these
results requires a sound background in both engineering and FEA.
In the context of the above step-by-step procedure, it is clear that there
are various critical decisions that practitioners of the finite element analysis have
to make, e.g. the type of analysis. the number of nodes, the degree of freedom
(components of the field variable) at each node, the element shape and type, the
material type and finally the interpretation of the results.
Modeling Capabilities of Finite Element Software
There are several such software packages available today which can run
on mainframe, mini-computers as 16 and 32 bit PC, I-DEAS, NASTRAN,
PATRAN, ANSYS, COSMOS, etc., are some of the well-known analysis
packages.

The following list give some of the capabilities of Finite Element Software
package.
Types of analysis Determination
Static Stresses and displacement
Dynamic Transient and steady state response
Modal Natural frequencies, mode shapes, random
Vibration and force vibration problems
Stability Buckling loads on a structure
Heat transfer Temperature distribution, heat flow under
steady state and transient conditions
Field Fields intensity, flux density of magnetic field,
field problems in acoustics and fluid
mechanics
Coupling Displacement forces, temperature, heat flows,
fluid pressure and velocity
Common elements used in Finite Element Analysis
Elements types used in FEA may be described in terms of their shape
(through relative position of its modes) and degree of freedom (possible direction

of movements of each node). Total number of degrees of freedom in the mesh
give s the stiffness matrix. For example a triangular element has three nodes
and tow degree of freedom at each node. Hence the size of the stiffness matrix is
3*2=6.
Common types of elements used in FEA. They are classified below:
1. Rod
2. Beam
3. 2D plane stress type
4. Plate Elements
5. Shell Elements
6. Solid Elements
Advantages and Disadvantages of Finite Elements Analysis
Advantages
Main advantage is that physical problems, which were so far intractable
and complex for any closed bound solutions, can be analyzed by this method.
1) It can be efficiently applied to cater irregular geometry.
2) It can take care of any type of boundary.
3) Material in homogeneity can be treated without much difficult.
4) Any type of loading can be handled.

Disadvantages
1) Cost involved in the solution of problem is more.
2) Approximations used in the development of the stiffness matrix.
3) Stress values may vary by 25% form fine mesh analysis to average
mesh analysis.
4) There are trouble sports such as “ Aspects ratio” (ratio of longer to
smaller dimension at the element) which may affect the final result.

ABOUT SPRINGS
(a) Definition:
A spring is defined as an elastic body, whose function is to distort when
loaded and to recover its original shape when load is removed . It is nothing but
a mechanical storage device.
(b) Types of springs:
 Helical springs
 Conical &volute springs
 Torsional springs
 Laminated & leaf springs
 Special purpose springs
(c) Common uses:
i) To cushion, absorb or control energy due to either shock or
vibration as in car spring, railway buffers, air-craft landing gears,
shock absorbers and vibration dampers.
ii) To apply force, as in brakes, clutches and sprint-located values.

iii) To measure forces, as in spring balances and engine indicators.
iv) To store energy, as in watches, toys etc.
In our project we have chosen compression helical springs used in Rail
Wagon for suspension.
(d) Terms used in compression springs:
The following terms used in connection with compression springs are
important form the subject point of view.
1. Solid length:
When the compression spring is compressed until the coils come in
contact with each other, then the spring is said to be solid. The solid length of a
spring is the product of total number of coils and the diameter of the wire.
Mathematically,
Solid length of the spring,
Ls = n’.d
Where n’ = Total number of coils and
d = Diameter of the wire.

2. Free length:
The free length of a compression spring is the length of the spring in the
free or unloaded condition. It is equal to the solid length plus the maximum
deflection or compression of the spring and the clearance between the adjacent
coils(when fully compressed). Mathematically,
Free length of the spring,
Lf = Solid length + Maximum compression + Clearance between
adjacent coils (or clash allowance)
= n’d + δmax + 0.15 δmax
The following relation may also used to find the free length of the
spring, i.e.,
LF = n’.d + δmax + (n’-1) * 1mm
In this expression, the clearance between the tow adjacent coils is
taken as 1 mm.
3. Spring index:
The spring index is defines as the ratio of the mean diameter of the wire.
Mathematically
Spring index, C = D/d
Where D = Mean diameter of the coil, and
d = Diameter of the wire.

4. Spring rate:
The spring rate (or stiffness of spring constant) is defined as the load
required per unit deflection of the spring. Mathematically:
Spring rate, k = W/δ
W = Load, and
δ = Deflection of the spring.
5. Pitch:
The pitch of the coil is defined as the axial distance between adjacent coils
in uncompressed state. Mathematically:
Pitch of the coil, p = Free length
n’-1
(e) End connections for compression helical springs:
 plain ends
 plain and ground ends
 squared ends
 squared and ground ends.
In this we have taken plain & ground end for the sake of simplicity.

(f) Stresses in Helical Springs of Circular Wire:
Consider a helical compression spring made of circular wire and subjected
to an axial load W.
Let D = Mean diameter of the spring coil
d = Diameter of the spring wire,
n = Number of active coils,
G = Modulus of rigidity for the spring material,
W = Axial load on the spring,
τ = Maximum shear stress induced in the wire,
C = Spring index = D/d
p = Pitch of the coils, and
δ = Deflection of the spring, as a result of an axial load W.
Now consider a part of the compression spring. The load W tends to
rotate the wire due to the twisting moment (T) set up in the wire. Thus torsional
shear stress in induced in the wire.
A little consideration will show that part of the spring, is in equilibrium
under the action of two forces W and the twisting moment T. We know that the
twisting moment,
T = W * D/2 = π/16 * τ1 * d3

= 8 W.D/πd3
In addition to the torsional shear stress (1) induced in the wire, the
following stress also act on the wire:
1. Direct shear stress due to the load W, and
2. Stress due to curvature of wire.
We know that direct shear stress due to the load W,
τ2 = Load
Cross- sectional area of the wire
= w = 4W
π/4 * d2
π d2
We know that the resultant shear stress induced in the wire,
τ = τ1 ± τ2 = 8W.D + 4W
πd3
π d2
The positive sign used for the inner edge of the wire and negative sign in
used for the other edge of the wire. Since, the stress is maximum at the inner
edge of the wire, therefore,
Maximum shear stress induced in the wire,
= Torsional shear stress + Direct shear stress
= 8W.D + 4W = 8W.D (1+ d/2D)

πd 3
π d 2
π d 3
= 8W.D (1+ d/2C) = Ks * 8W.D
π d 3
π d 3
Where Ks = Shear stress factor = 1+1/2C
From the above equation, it can be observed that the effect of direct shear
8W.D * 1
d 3
2C
is appreciable for springs of small spring index C. Also we have
neglected the effect of wire curvature in equation (iii). It may be noted that when
the springs are subjected to static loads, the effect of wire curvature may be
neglected, because yielding of the material will relieve the stresses. In order to
consider the effects of both direct shear as well as curvature of the wire. A.M
Wahl’s stress factor (K) introduced by A.M.. Wahl may be used. Maximum shear
stress induced in the wire.
τ = K* 8W.D = K* 8 W.C
π d 3
π d 2
Where
K = 4C – 1 + 0.615
4C – 4 C

(g) Deflection of helical springs of circular wire.
Total active length of the wire
l = Length of one coil x No. of active coils = D x n
Let = Angular deflection of the wire when acted upon by the torque T.
Axial deflection of the spring.
δ = θ * D/2
We also know that T/ J = τ / D / 2 = G * θ / 1
θ = T.L / J/ G considering T / J + G.θ / J
Where J = Polar moment of the spring wire
= 3.14 / 32 * d 4
;
d being the diameter of spring wire.
and G = Modulus of rigidity for the material of the spring wire.
Now substituting the value of L and J in the above equation, we have,
θ = T. 1 = W * D/2 π D . n = 16 W. D2. n
J. G π / 32 * d 4
G G. d4
Substituting this value of 0 in equation (i), we have,
τ = 16 W. D2
.n * D = 8 W. D3
.n = 8 W. C3
.n
G. d 4
2 G. d 4
G. d

and the stiffness of the spring rate,
W = G.d4
= G .d = constant
θ 8D3
.n 8C3
.n
Material Property of the spring used is Rail wagon:
The material of the spring should have high fatigue strength, high ductility,
high resilience and it should be creep resistance.
For satisfying these conditions we have chosen the material such as
50Cr1V23 (Chromium Vanadium Alloy steel)
Properties:
% Carbon - 0.45 – 0.55 %
% Si - 0.1 – 0.35 %
% Mn - 0.5 – 0.8 %
% Cr - 0.9 – 1.2 %
Tensile strength - 190 – 240 kgf / mm2
Yield strength - 180 kgf / mm2
Brinell hardness number - 500 – 580
Poisson’s ratio - 0.3
Young’s modulus - 21800 kgf / mm2

Density - 7850 kg /m3
Modulus of Rigidity G - 84*102
kg / mm2
COMPARISON OF SPRINGS
Specifications:
The values for the design of the spring used is Rail wagon are taken form
Railway Department. They are,
Mass of Rail wagon - 20 tonnes
Maximum Deflection of the spring - 250 mm
Maximum allowable shear stress - 600 mpa, = 600N / mm2
Pitch Dia D - 300mm
Velocity of Rail wagon - 2 m/s
Comparison of springs
In our project, by taking different cross sectional areas in the spring wire,
we have modeled using PRO / E and Analyzed by ANSYS. After this the
different cross, sectional wire are analyzed and found out which one is the best
suit for Rail wagon suspension.
So we have taken this project and compared its cross sections in order to
improve the life of the spring.
Types of cross sectional areas we have taken:
(i) Rectangular

(ii) Circular
(iii) Square
Design of springs:
(a) Design of Rectangular springs:
The helical spring may e made of non-circular wire such as rectangular of
square wire in order to provide greater resilience. Kinetic energy = ½ mv2
From the specification the values are taken and substituted, Kinetic
Energy = ½ (20,000) (2)^ 2 = 40,000 N-m.
Let W be equivalent load which applied gradually,
Since there is 2 springs
= ½ * W * δ * 2 = W * δ = W * 250 = 250W N-mm.
W = 40 * 106
/ 250 = 160 * 103
N
W = 160 * 103
N
D = 300 mm, δ = 250 mm τ = 600 N / mm2
From Data book,
C = D/d = C = D / (b+t) for Rectangular,
Take 2t = b, blt = 2
From data book,
c = Q 2.P.D / 2t. b^2

Where t = thickness
b = breath
Table from data book,
bit 1 1.5 2 3 4 6 8 10 2
Q1 7.09 5.1 4.36 3.8 3.56 3.36 3.26 3.21 3
Q3 4.79 4.35 4.05 3.7 3.52 3.35 3.25 3.2 3
Q1, Q2 – Factors for spring of rectangular section Q2 = 4.05
τ = 4.05 * 160 * 103
* 300 / 2 * t (2t)2
600 = 4.05 * 160 * 103
* 300/2 * t (2t)2
= t = 34.3
t = 34 mm
b = 2 * t = 68 mm =b = 68 mm
Deflection from data book,
δ = Q1 π PD3
n / 4Gt3
b
From table, Q1 = 4.36
250 = 4.36 * π * 160 * 103
* (300)3
* n / 4 * 84 * 103
* (34)3
*68
n = 4 turns

Free length:
Lf = n.b + δ + 0.158 δmax
= 4(68) + 250 + 0.15 * 250
Lf = 560 mm.
Pitch value:
P = Lf / n-1
= 560 / 4 = 140 mm
P = 140 mm
From design; values are
b = 68 mm
t = 34 mm
n = 4 turns
Lf = 560 mm
P = 140 mm
Design of Square c/s Section:
W = 160 * 103
N, δ = 250 mm
D = 300 mm τ = 600 N /mm2

by obtaining the W,
τ = Q2 PD / 2tb2
here t = b,
τ = Q2 PD / 2b3
= 4.79 * 160 * 103
* 300 / 2*b3
= 600
b = 57.52
δ = Q1 π PD3
n / 4Gt3
6 b
= 7.09 * π * 160 * 103
*(300)3
* n / 4*84* 103
* (57.52)4
here δ = 250 mm.
n = 8 turns
Free length:
Lf = nb + δ + .15* δmax
= 8* 57.52 + 250 + 0.15 * 250
Lf = 747.66 mm = 748 mm.
Pitch:
P = 748 /8-1 = 93.5
P = 93.5 mm.
Values, b = 57.52 mm

D = 300 mm
Lf = 748 mm
n = 8
P = 93.5 mm.
Design of Circular c/s Springs:
D = 300 mm
δ = 250 mm τ = 600 N / mm2
Torque,
T = W * D / 2 = 160* 103
* 300 / 2* 106
N-mm
We also know that, torque transmitted by spring (T),
24* 106
= π / 16* τ* d3
= τ / 16* 600* d3
= 117.8d3
d = 58.8 say 600 mm
d = 60 mm
No. of turns of the spring coil,
n = Number of active turns
We know deflection S = 250.
250 = 8.W.D3.n / G.d4

= 8* 160* 103
* (300)3
* n / 84* 103
* (60)4
= 31.7 n
n = 250 /31.7 = 8 n = 8
Free length of coil:
Lf = n.d + δ + 0.15 δmax
= 8* 60 + 250 + 0.15* 250
Lf = 767 mm
Pitch of the coil:
P = Free length / n-1 = 95.87
Values:
W = 160* 10 ^3 N
d = 60 mm
D = 300 mm
n = 8 turns
P = 95.87 mm
Lf = 767mm

Modeling of the spring using Pro / E:
For analyzing the springs, the spring should be designed and modeled.
For that we had used the soft ware PRO / E.
In Pro / E, for designing, the apt values should be known. That is taken
form theoretical design. From design, the values of different cross sections are
taken out and they are separately modeled.
(a)Modeling of Rectangular C/S springs
Values b = 68 mm
t = 34 mm
n = 4 turns
Lf = 560 mm
P = 140 mm
D = 300 mm
 In Pro/E first of all, we have created the datum place using Default
command.
 Then protrusion command is used, after that by going Advanced
Geometry and Helical sweep command, the spring has created. In
this the values from specifications were given as the input.

 then using plane, the two ends are cutted and it is considered as
grounded.
 In this for Rectangular cross section, the rectangular is directly
drawn and the dimensions are also checked.
 By this the Rectangular spring had modeled.
Modeling of square c/s springs:
b = 57.52 mm
D = 300 mm
Lf = 748 mm
n = 8 turns
P = 93.5 mm
 The procedure of this are same as like as the above explained in
rectangular C/S.
 For achieving square cross section, by giving the same values of b,
that has been obtained.
 then cutting at the tow ends we can get the end condition such as
plain and ground ends.
 Now the square c/s sections were also modeled.

Modeling of circular c/s springs:
Values:
d = 60 mm
D = 300 mm
n = 8 coils
Lf = 767
P = 95.87 mm
 The procedure for this also same as like as the above explained but the
cross section drawn is only varied.
 At the place of square the circle is drawn to get the circular section.
 By giving the suitable, radius, above given, we can get the circular spring.
 Then by cutting at the two ends the plain and ground end has been
obtained.
In Pro/E, analyzing the object (springs) is not possible. It is design
package. Therefore, for analyzing, we had switched over to the another package
such as ANSYS. To transform the file form Pro/E to ANSYS. Some
transformation file should be used for that purpose, IGES file has been used, in
our project.

STRUCTURAL ANALYSIS USIN ANSYS:
 In the ANSYS software, first of all we had selected the mode of the
analysis such as structural analysis.
 For analyzing the spring, the element should be chosen. For that, we
have been chosen the element such as Tet 92.
SOLID92 3-D 10-Node Tetrahedral Structural Solid
 Then the material property such as Young’s modulus, Density, Poisson’s
ratio etc are given as the input by selecting the isotropic material.
 Now the main part of analysis such as meshing has been done by
selecting mesh and also by giving the value of mesh the meshing process
for the spring has been carried out.
 Then arresting the degree of freedom at the bottom most coil of the spring.
 And also the load has applied on the top most portion of the coil of the
spring.
 Now, by using current LS command the solution of the analysis has been
done.
 This process is carried out separately for Rectangular, Circular and
Square cross sectional springs.

Analysis Result:
By analyzing this, the maximum and minimum deflection values and also
direct animated view has been displayed by the system using the command plot
Result and USUM.
Then the stress values are also displayed for different cross sectional
areas such as Rectangular, Square and Circular.
Checking:
After analyzed by ANSYS software, the valued are checked t find out the
answer for the question such as ‘Which one is the best suit for suspension?’.
(a) Rectangular:
The theoretical value of maximum allowable deflection of the spring at
max. Load is 250 mm. But maximum obtained value from ANSYS is 220 mm.
Now this value tells about the deflection is not very perfect one.
Now, by considering the value of stress, the three c/s springs are
analyzed. By using the factor of safety formula we had analyzed which one give
more factor of safety. The highest F.O.S value spring has withstander highest
loads for this, The formula such as,
F.O.S = Yield stress / Workings stress

Here the working stress obtained form the analysis is 325 N / mm^2. But
the yield stress for the alloy material 50 Cr IV 23 is 180 N / mm^2.
By applying the formula, the F.O.S value is .55. By this, it has proven that
Rectangular section is not a suitable one.
(b) Square c/s springs:
By the value obtained form analysis, the maximum deflection is 249 mm.
This is somewhat better than Rectangular.
But the stress value obtained from the analysis square sprints is 166 N /
mm^2. the factor of safety value is 1.08 and not having a very good value and
that is,
F.O.S = 180 / 166
Here, we can see form the figure, the stresses are acting at the end of the
coils. So that, chance for failure of the spring is easy manner.
(c)Circular C/S Spring:
For this, the value obtained for the Max. deflection is 220 – 230 mm. This
give s very good suspension for the wagon.
Considering the stress aspects also it gives the better result. That is, the
stress value obtained from analysis is around 140 – 150 N / mm2. It gives good
F.O.S value also.The Factor of Safty value is 1.2. Since it has not edges on its
coil, the stress acting is very very less. By this life of the spring is very good
compared to others.

CONCLUSION
By analyzing the three different Cross sectional springs such as
Rectangular, Circular & Square, the values re checked. Since Rectangular
springs performs very low deflection as well as at it is having high stress at its
edges. By this the F.O.S value also very less. So that life of this spring is also
less. Therefore it is not a suitable one for suspension in rail wagon.
The square spring also having somewhat low deflection. It is also having
more stress compare to Circular C/S springs. So the F.O.S value also less. By
comparing with circular it is also having low life time.
In this project, we had proven using analysis, and concluded that the
circular cross sectional spring is the best one for the suspension of Rail wagon’s
due to its high deflection & also high factor of safety.
So “The Circular Cross Section is the Best” for Rail wagon.

BIBLIOGRAPHY
Reference Books:
(i) Machine Design by
- R.S. Khurmi, J.K. Guptha
(ii) Mechanical Engineering Design by
- Joseph Edward Singley
(MC Graw – Hill)
(iii) Machine Design by
- T.V. Sunder Raja Moothty
(iv) Pro/CAD the concepts by
- Doux systems
(v) CAD/ CAM by
- Mikell P. Groover and Emory
- W.Zimmers
(vi) Machine Design by
- T. Prabhu
(vii) Design Data Book. PSG College of Technology.
(viii) Websites: www.ansys.com
www.proe.com
www.ptc.com

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