“FE Analysis of Parabolic Leaf Spring with Military and

Reinforced Eye Ends using CAE Tools”

A Dissertation submitted to the

Department of Mechanical Engineering In the partial fulfillment of the requirement for the award of degree of

MASTER OF TECHNOLOGY

IN MECHANICAL ENGINEERING

(MACHINE DESIGN)

By

Ishan Aggarwal 3133624

Under the esteemed guidance of

Dr. Gian Bhushan Dr. Pankaj Chandna Professor Professor Mechanical Engineering Department Mechanical Engineering Department NIT Kurukshetra, India NIT Kurukshetra, India

National Institute of Technology Kurukshetra

CERTIFICATE

This is to certify that the work, which is being presented in the thesis, entitled “FE

Analysis of Parabolic Leaf Spring with Military and Reinforced Eye Ends using

CAE Tools” by “Mr. Ishan Aggarwal” in fulfillment of requirement for the award of

degree of Master of Technology in Mechanical Engineering (Machine Design)

submitted in the Department of Mechanical Engineering at National Institute of

Technology, Kurukshetra is an authentic record of original work carried out by him

under our supervision in conformity with the rules and regulations of the institute.

The matter presented in this thesis has not been submitted in any other

University/Institute for the award of any diploma and degree.

(Dr. Gian Bhushan)

Professor

Mechanical Engineering Department

NIT Kurukshetra, India

(Dr. Pankaj Chandna)

Professor

Mechanical Engineering Department

NIT Kurukshetra, India

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ABSTRACT

Continuously changing technologies, increased competition and development of

advanced materials has forced industries to bring new products to the market in least

possible time and with least cost involved in the preliminary design. The above factors

leads to increased design complexities and number of iterations in the design process

of mechanical systems and components. Increased design iterations leads to repeated

experiments which is economically not feasible and also time taking. This leads to

increased use of the computer aided engineering (CAE) tools such as computer aided

design (CAD), computational fluid dynamics (CFD) etc. Various software packages

like ANSYS, ABAQUS, and NASTRAN etc. have evolved on these basis and are

capable of solving structure, thermal, electromagnetic, flow, noise, various

multiphysics problems and design optimization.

The subject of this thesis analyses the static structure analysis of reinforced and military

eye ends of a four layer symmetrical parabolic leaf spring using CAE tools. Analysis

method has been provided for both eye ends using ANSYS. This ensures improvement

in design with minimum actual experimental validation for each design iteration. The

completion of the thesis is carried out in two major steps.

First stage involves the validation of CAE tools used. Assembly CAD model of the

reinforced and military eye ends are generated. The 3D CAD models are complex

assemblies of 11 parts each. CAD models are generated using SOLIDWORKS and

imported to ANSYS for preprocessing. Preprocessing includes material definition,

contact definition, meshing and boundary condition definition. After preprocessing the

structure analysis is carried out in static load conditions for four type of loading

conditions. The analysis results are then post processed for the maximum deformation

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and Von-Mises stress distribution. For validation, the results of the reinforced eye end

parabolic leaf spring using CAE tools are compared with the experimental results.

These are found in accordance with experimental results with a variation of 7.6 % in

load deflection rate. The result is a validated design and analysis procedure which forms

the base of mechanical model.

Once validated the second stage involves the comparison of the maximum deformation

and Von-Mises plot for the reinforced and military eye ends using CAE tools. In both

eye ends the post processing results are found to be almost. Deformation is slightly

lower in Military eye because of high stiffness and Von-Mises stresses are slightly more

but well below the material yield stress value.

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ACKNOWLEDGMENTS

I would like to express my sincere thanks and gratitude to Dr. Gian Bhushan and Dr.

Pankaj Chandna for their continued guidance and encouragement during this work.

Their contribution of time and technical expertise during this work has been of great

importance. I also thank them for all their patience and excellent supervision.

I would also like to give my special thanks to Mr. Vinkel Arora, Assistant Professor

(NIFTEM) for his valuable contribution and inspiring guidance for this dissertation. I

also extend my thanks to him for valuable feedbacks and necessary suggestions.

I express my gratitude to Dr. Dixit Garg for his support in providing various

departmental facilities which makes this work possible in smooth manner.

I would like to thank my colleague Ishan Aggarwal for his continuous support and

knowledge sharing during whole the time of this dissertation work. In end I extend my

gratitude to each and every person who directly or indirectly has been associated to this

work and during my stay here making it a learning experience of my life.

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DEDICATION

This work is dedicated to my mother and sister for all the encouragement, love, patience

and support in completion of this project. I also thank them for all the sacrifices they

made to enlighten my life.

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TABLE OF CONTENTS

Chapter Page

CERTIFICATE ............................................................................................................... i

ABSTRACT ................................................................................................................... ii

ACKNOWLEDGMENTS ............................................................................................ iv

DEDICATION ............................................................................................................... v

TABLE OF CONTENTS .............................................................................................. vi

LIST OF TABLES ..................................................................................................... viii

LIST OF FIGURES ...................................................................................................... ix

CHAPTER I: Introduction ............................................................................................. 1

1.1 Background .......................................................................................................... 2

1.1.1 Springs .......................................................................................................... 2

1.1.2 Leaf Springs .................................................................................................. 4

1.1.3 Classification of Leaf Springs ....................................................................... 6

1.1.4 CAE and Its Tools ......................................................................................... 8

1.1.5 Computer Aided Design (CAD) ................................................................. 10

1.1.6 Finite Element Analysis (FEA) and Its Tools ............................................. 12

1.2 Thesis Objectives ............................................................................................... 15

1.3 Organization of the thesis .................................................................................. 15

CHAPTER II: Background and Literature Review ..................................................... 18

2.1 Literature Review............................................................................................... 18

2.2 Gaps in Literature .............................................................................................. 25

2.3 Problem Formulation and Statement ................................................................. 27

CHAPTER III: METHODOLOGY ............................................................................. 28

3.1 Parametric CAD Modelling ............................................................................... 28

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3.1.1 Part Modelling ............................................................................................ 29

3.1.2 Assembly Modelling ................................................................................... 30

3.2 CAE Static Structure Analysis using ANSYS WB............................................ 31

3.2.1 Material Definition ...................................................................................... 34

3.2.2 Geometry..................................................................................................... 34

3.2.3 Contact Definition ....................................................................................... 35

3.2.4 Meshing....................................................................................................... 37

3.2.5 Boundary Conditions .................................................................................. 38

3.2.6 Solution ....................................................................................................... 40

CHAPTER IV: RESULTS AND DISCUSSIONS ...................................................... 41

4.1 FEA Results of Reinforced Eye End Parabolic Leaf Spring ............................. 41

4.1.1 Experimental Load Deflection Curve for Reinforced Eye End .................. 45

4.1.2 Comparison of FEA Load Deflection Curve and Experimental Load

Deflection Curve .................................................................................................. 46

4.2 FEA Results of Military Wrapper Eye Parabolic Leaf Spring .......................... 47

4.2.1 Comparison of FEA results for Reinforced and Military wrapper eye ....... 51

CHAPTER V: CONCLUSION.................................................................................... 52

CHAPTER VI: FUTURE SCOPE ............................................................................... 53

REFERENCES ............................................................................................................ 54

Appendix A .................................................................................................................. 56

List of Publications .................................................................................................. 56

vii

LIST OF TABLES

Table Page

Table 1: Material properties of SUP 11A .................................................................... 34

Table 2: Comparison of FEA results for Reinforced and Military wrapper eye ......... 51

viii

LIST OF FIGURES

Figure Page

Figure 1: Helical Springs Employed in Suspension ...................................................... 3

Figure 2: Elliptical leaf spring ....................................................................................... 3

Figure 3: Coil Spring ..................................................................................................... 3

Figure 4: Belleville Springs ........................................................................................... 3

Figure 5: Leaf Spring attached to automobile suspension ............................................. 5

Figure 6: Upturned eye .................................................................................................. 7

Figure 7: Military eye .................................................................................................... 7

Figure 8: Downturned eye ............................................................................................. 7

Figure 9: Berlin eye ....................................................................................................... 8

Figure 10: Welded eye ................................................................................................... 8

Figure 11: Oval eye ........................................................................................................ 8

Figure 12: 2D drawing of the parabolic leaf spring ..................................................... 29

Figure 13: Bill of Materials .......................................................................................... 29

Figure 14: Part modelling of main and second leaf of parabolic leaf spring ............... 30

Figure 15: Assembly model of parabolic leaf spring with reinforced eye end ............ 31

Figure 16: Assembly model of parabolic leaf spring with military wrapper eye end .. 32

Figure 17: CAD geometry imported to ANSYS for reinforced eye end ..................... 33

Figure 18: CAD geometry imported to ANSYS for military wrapper eye end ........... 33

Figure 19: Contact definition in reinforced eye end parabolic leaf spring .................. 36

Figure 20: Contact definition in military wrapper eye end parabolic leaf spring ........ 37

Figure 21: Meshed 3D model for reinforced eye end .................................................. 38

Figure 22: Meshed 3D model for military wrapper eye end ........................................ 38

Figure 23: Boundary conditions applied to reinforced eye end ................................... 39

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Figure 24: Boundary conditions applied to military wrapper eye end ......................... 39

Figure 25: Deflection at specified load for reinforced eye end ................................... 42

Figure 26: Equivalent stresses at specified load for reinforced eye end ...................... 42

Figure 27: Deflection at unladen load for reinforced eye end ..................................... 43

Figure 28: Equivalent stresses at unladen load for reinforced eye end ........................ 43

Figure 29: Deflection at laden load for reinforced eye end ......................................... 44

Figure 30: Equivalent stresses at laden load for reinforced eye end ............................ 44

Figure 31: Deflection at 2G load for reinforced eye end ............................................. 45

Figure 32: Equivalent stresses at 2G load for reinforced eye end ............................... 45

Figure 33: Experimental results of load vs deflection for reinforced eye end ............. 46

Figure 34: Comparison between CAE and experimental load deflection curve .......... 46

Figure 35: Deflection at specified load for military wrapper eye end ......................... 47

Figure 36: Equivalent stresses at specified load for military wrapper eye end ........... 48

Figure 37: Deflection at unladen load for military wrapper eye end ........................... 48

Figure 38: Equivalent stresses at unladen load for military wrapper eye end ............. 48

Figure 39: Deflection at laden load for military wrapper eye end ............................... 49

Figure 40: Equivalent stresses at laden load for military wrapper eye end ................. 49

Figure 41: Deflection at 2G load for military wrapper eye end ................................... 50

Figure 42: Equivalent stresses at 2G load for military wrapper eye end ..................... 50

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CHAPTER I: Introduction

Suspension in automobiles is the link between wheels and the automobile body. It

absorbs sudden and shock loading arising from the road conditions and isolates the

vibration, carries lateral loads, brake torque and driving torque by storing the elastic

energy and releasing that later on. Design criterions, though, for the suspension systems

are more or less based on the strength but comfort conditions are also increasingly

becoming a necessary factor.

For design based on rigidity criterion [19], best approximation is to assume negligible

deformation. Suspension systems however are designed on the basis of flexibility

conditions which is provided by metal bodies with controlled geometries. This

flexibility however can be of linear or nonlinear nature depending upon the nature of

loading.

Springs are the most basic type of suspension systems providing flexible design. One

of the special types of springs are leaf springs and are conventionally referred as mono

and multi leaf springs. Multi Leaf springs are being used in automobiles ranging from

heavy to light commercial vehicles and even the passenger vehicles. These springs

absorb the mechanical energy upon deflection and releases it slowly to reduce the

impact of sudden loads. Constant efforts has been made in order to improve the

efficiency of the springs in the current age of optimization and also the comfort

conditions in modern technological world.

Latest advances in the leaf spring technology are parabolic multi leaf springs. Parabolic

leaf spring are regarded as tapered beams or tapered leafs with thickness maximum at

center of certain length and parabolic at rear and front end with straight extremes. The

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advantages of using parabolic leaf spring are seen in weight reductions, have better

fatigue life, surface stresses are constant over the length, minimum interleaf friction and

contacts and ability to reduce the ride clearance providing more stability and comfort

conditions.

1.1 Background

1.1.1 Springs

Springs are essentially the flexible members. These bodies can exhibit flexibility to the

degrees as desired by the design engineer. This flexibility can be linear or nonlinear in

terms of load deflection rate. Flexibility allows temporary distortion for immediate

restoration of function. Springs allow controlled application of force, storing and

release of energy which could be due to shock or vibrations. Other functions include

the control of motion which could be seen in cams and followers to maintain contact,

creation of necessary pressure in friction surfaces such as clutches and brakes,

restoration of machine parts to their original position such as in governors or valves.

Springs are also employed in spring balances and gauges for measuring forces and

storage of energy in clocks. [20]. Because of advantages to designers, springs have been

extensively studied and mass production is carried out. Different configurations of the

design have led to their use in wide variety of mechanical applications.

Generally springs are classified as wire springs, flat springs, or special-shaped springs,

and each of these divisions is having its own classification also. Wire springs include

helical springs of round or square wire, made to resist and deflect under tensile,

compressive, or torsional loads. Flat springs mainly include cantilever and elliptical

types regarded as leaf spring, motor or clock type power springs, and flat spring

washers, usually referred as Belleville springs. General spring materials used are

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Chromium Vanadium, Chrome Silicon, Music wire, Stainless steel, Phosphorus

Bronze, Spring Brass etc.

Figure 1: Helical Springs Employed in Suspension

Figure 2: Elliptical leaf spring

Figure 3: Coil Spring

Figure 4: Belleville Springs

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1.1.2 Leaf Springs

Leaf springs are one of the important safety elements in the vehicle suspension system.

The primary purpose of the leaf spring is to isolate the vibrations by absorbing and then

releasing energy thereby providing the necessary comfort conditions. These are usually

of the shape of slender arcs and are referred as semi elliptical springs. Generally the

material used is spring steel and are of rectangular cross section. Axle is located at the

center of the arc and tie holes are provided at either ends for attaching the vehicle

chassis. Leaf springs have the advantage of being guided along a specified path. In order

to facilitate the movement along definite path one end of the leaf spring should be

connected to shackle regarded as short swinging arm and other end be fixed to the frame

of the vehicle or chassis. Leaf springs are commonly used in automobiles ranging from

medium commercial vehicles to heavy commercial vehicles.

Other commonly used materials for leaf springs are Plain carbon steel, Chromium

vanadium steel, Chromium- Nickel- Molybdenum steel, Silicon- manganese steel etc.

leaf springs for heavy load applications are made from several leaves stacked one above

the other in several layers and with progressively shorter leaves. Longest leaf is called

as main leaf and is rolled at both ends to form the eyes. Various leaves are connected

together by center bolt and these springs are regarded as multi leaf springs. They serve

the purpose of locating and to some extent damping with springing action. The damping

in these springs is facilitate by the interleaf friction which also has disadvantages as it

is difficult to control, causes noise and wear and affects the comfort riding also leading

to hard ride conditions. Leaf spring attached to the automobile suspension can be seen

in Fig. 5.

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Figure 5: Leaf Spring attached to automobile suspension

Leaf springs being cantilever beams, always desired to have uniform bending stresses,

which is achieved in parabolic leaf springs by tapered leaves with maximum thickness

at center and varying parabolically towards the ends. Parabolic leaf springs are the latest

advances in the leaf spring technology. This design is characterized by few number of

leaves in comparison to conventional multi leaf springs. The contact is present only at

the ends and at the center of the leaf usually regarded as seat length. Due to parabolic

shape at all other points there is no contact because of spaces. This leads to reduction

in interleaf friction the result of which is soft ride. Parabolic leaf springs are compared

with coil spring suspension in terms of comfort ride. Various advantages of using these

springs are listed as:

• Appreciable reduction in weight.

• Surface stresses are constant over the length.

• Minimum interleaf friction.

• Scope for reduction in ride clearance leading to more stability and comfort conditions.

• Better fatigue life.

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1.1.3 Classification of Leaf Springs

1. Leaf springs are generally classified as mono leaf springs, multi leaf springs and

parabolic leaf springs.

Mono leaf springs as the name suggests have only one leaf and is called as

main leaf. This leaf is heat treated plate of steel and can be of many

configurations such as constant thickness and constant width design, constant

thickness and varying width design or constant width and varying thickness

design. Varying thickness parabolically or varying width linearly is done in

order to achieve the uniform strength design. These are obsolete now as they

are having safety issues as there is no other leaf to back up the main leaf in case

of failure.

Multi leaf springs are having several leaves which are placed one over other

and are held together with center bolt. These are of flat steel bars of hardened

spring steel obtained after heat treatment and the first leaf is regarded as main

leaf and all other leaves are regarded as supporting leaves. They have edge over

the mono leaf springs in terms of safety as in this case supporting leaves can

support the main leaf in case of any failure condition.

Parabolic leaf spring are the one having tapered leaves having parabolically

varying thickness. The thickness is maximum at the center and varies towards

the end. Top leaf is regarded as main leaf in parabolic leaf springs also and other

leaves as supporting leaves. These are having certain advantages in terms of ride

height, comfort conditions, uniform bending stresses which enables them to be

used increasingly in the modern automobile applications.

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2. Classification based on the eye end designs. Based on this these are classified

as standard or upturned eye, military wrapper eye, downturned eye, berlin eye,

welded eye, oval eye etc.

Standard or upturned eye is the most commonly used leaf spring eye end

owing to its ease of manufacturing. Main leaf in this receives support from the

extension of second leaf in some cases.

Military wrapper eye is the design in which the second leaf also has an eye

and it comes in action during rebound operation and provides support to main

leaf. It also has an advantage of continued use in case of failure of main leaf and

its eye.

Downturned eye is used to improve the steering and axle control.

Berlin eye reduces the tendency of the eye to unwrap and load here is applied

through centerline of main plate.

Welded eye is preferable in applications where horizontal force is high. A word

of caution in this is to complete welding before the heat treatment.

Oval eye is preferable to use when different horizontal and vertical rates are

present.

Figure 6: Upturned eye

Figure 7: Military eye

Figure 8: Downturned eye

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Figure 9: Berlin eye

Figure 10: Welded eye

Figure 11: Oval eye

3. Other classifications are based on load, number of eyes, and leaf ends which are

of less particle importance as are rarely used.

1.1.4 CAE and Its Tools

Computer Aided Engineering covers the use of computers in all activities from the

design to the manufacture of a product. It is at the forefront of information technology

and of crucial importance to industries in terms of increase in the productivity, which

is estimated to be increased to double than earlier. Another advantages are seen in terms

of shortened project turnaround times and improved quality and accuracy of the work.

It is now regarded as vital part of many global industries including those of automotive,

aerospace, oil, defense and health etc. In broader terms CAE is the integration of more

than one computer tools which help in automating the design process. It is hence

defined as the use of computer softwares to simulate performance in order to improve

product designs or assist in the resolution of engineering problems. This includes 3D

model generation, simulation, validation, and optimization of products, processes, and

manufacturing tools. Some of the CAE tools commonly used are SolidWorks, CATIA,

I-DEAS, Pro Engineer, ANSYS, ABAQUS, and NX NASTRAN etc. [21, 22,23,24,25,

26, and 27].

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Typically CAE process comprises three major steps defined as preprocessing, solving,

and post processing. In the preprocessing phase, engineers model the geometry and the

physical properties of the design using CAD tools. Other details include the

environment in the form of applied loads or constraints. The model is then solved using

an appropriate mathematical formulation as per the physics of the problem. In the post-

processing phase, the results are presented to the engineer for review. Typically CAE

includes the following tools and analysis:

• Computer aided design (CAD) tools: Used for physical creation of the geometry. This may consist of 2-D or 3-D figures/shapes/curves/surfaces.

• Computer aided manufacturing (CAM) tools: It is a system of automatically producing finished products by using computer controlled production machines Used to generate the programs for the computer numeric controlled (CNC) machines for production and process scheduling.

• Finite element analysis (FEA) and its tools: Used for stress and dynamic analysis of components and assemblies.

• Computational fluid dynamics (CFD): Used for thermal and fluid interactions.

• Multi body dynamics (MBD): Used to understand the dynamics behavior of the Multibody systems under the application of forces. In other words it is the study of motion under forces. Multibody system mentioned is a system that consists of solid bodies, or links, that are connected to each other by joints that restrict their relative motion.

• Optimization tools: These are used for the optimization of the products and processes in simulation.

• Rapid Prototyping: Computer Aided Engineering systems also provide virtual product development environments by the rapid prototyping methods allowing 3D models to be created, analyzed, optimized and stored efficiently. Various operational and extreme physical conditions can also be evaluated. This leads to reducing the need for prototypes and actual testing.

The CAE tools used in the current study include the use of CAD tool software

Solidworks and FEA software tool ANSYS.

9

1.1.5 Computer Aided Design (CAD)

Since recent times the techniques for modelling and simulation are becoming mature.

This leads to increasing implementation by industries of CAD tools. Computer aided

design (CAD) is essentially the mathematical interpretation of shape for use in

computer graphics, manufacturing, or analysis applications. It draws upon the fields of

geometry, computer graphics, numerical analysis, approximation theory, data structures

and computer algebra. Computer Aided Design (CAD) involves the use of computer

hardware and graphics software to generate design drawings.

Modern CAD equipment enables the designer to quickly produce very accurate and

realistic images of products to be manufactured. Current mechanical systems are 3D

systems and have dominance to other application sectors as well. 3D modelling can be

Wire Frame, Surface or Solid Modelling. Wire frames being the first ones to represent

the 3D model are based on representation by edges in form of skeleton of the model.

Surface modeling develops the surface or skin instead of wireframe. In early times these

were based on Fergusson and Bezier curves although in modern times these are replaced

by non-uniform rational B-spline (NURBS) which are capable of modelling almost all

industrial parts. Solid modelling is the latest advances and offers complete

representation of the geometry of part. Solid modeling was in early times based on

constructive solid modeling system referred as CSG system but nowadays use B-Rep

modeling technique to model the topology of the part. Most of the CAD systems

nowadays are Parametric and Feature Based Solid Modelling systems. Parameters are

used to define dimensions, relations between various parameters and also the relations

between various parts of the model. These are defined in terms of positions and size.

Parameterization hence helps to define new part just by changing the values of the

parameters or can define a whole family of parts through the use tables of dimensions.

10

Various operations employed in the solid modelling systems are, 2-D and 3-D

wireframe models, swept, revolved solids, and Booleans as well as parametric editing.

With feature modelling the user can create a variety of holes, slots, pockets, pads,

bosses, cylinders, blocks, cones, spheres, tubes, rods, blends, chamfers and more.

Hollow and thin walled solid models can also be generated.

A beneficiary factor in this is the implementation of three-dimensional (3D) CAD

models into the design stages of product development creating a virtual prototype which

acts as base for further computational simulations. Presently, CAD is not particularly

effective in the initial synthesis of design or in the redesign portion of the design

procedure [28]; however, it is very useful in providing more efficient ways to help the

designer in the design iterations. CAD systems are usually not well integrated with

current simulation techniques although the simulation techniques are well developed.

However, integrated analysis is possible where CAD models can be used for creating

Finite Element Models (FEM) for structural analysis, the procedure employed in the

current study.

Another advantage of using CAD is seen in optimization of the design. Optimization

process can be carried forward with the help of parameterization. Wide changes can be

done quickly to a 3D model throughout if proper parameterization is done. The rapid

development and implementation of new tools allow CAD to be used in a greater part

of the development chain.

Current study uses CAD tool Solidworks. Solidworks is solid modeling CAD software

produced by Dassault Systems Solidworks Corp., a subsidiary of Dassault Systems, S.

A. (France). Building a model in Solidworks usually starts with a 2D sketch consists

of geometry such as points, lines etc. Relations are used to define attributes such as

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tangency, parallelism, perpendicularity, and concentricity. In an assembly, the analog

to sketch relations are mates. Just as sketch relations define conditions such as tangency,

parallelism, and concentricity with respect to sketch geometry, assembly mates define

equivalent relations with respect to the individual parts or components, allowing the

easy construction of assemblies. Finally, drawings can be created either from parts or

assemblies.

1.1.6 Finite Element Analysis (FEA) and Its Tools

Finite-element analysis is a powerful numerical analysis process widely used in the

analysis of engineering applications. Finite element method (FEM) is a numerical

method for solving a differential or integral equation specifically the partial differential

equations. These equations are converted to a large system of algebraic equations and

solved with the help of computers. Partial differential equations arise in the

mathematical modelling of many physical, chemical and biological phenomena. These

covers very wide areas of applications including aerospace, automobile, medical

devices, fluid and thermal interactions, electromagnetics etc. These equations are so

complicated that finding their exact solutions in closed form or by purely analytical

means (e.g. by Laplace and Fourier transform methods, or in the form of a power series)

is either impossible or impracticable, and one has to resort to seeking numerical

approximations to the unknown analytical solution.

FEA has its origins in structure mechanics. Analysis procedure using FEM involves

dividing it into a number of small building blocks, called finite elements [29]. For this,

the object is first divided into number of elements that forms a model of the real object.

These are interconnected at common points of two or more elements called as nodes.

Commonly used elements are of simple shape such as a square, triangle, or cube or

12

other standard shape for which the governing equations in the form of a stiffness matrix

could be written using algorithms. Finite-Element software assembles the stiffness

matrices for these simple elements to form the global stiffness matrix for the entire

model. This stiffness matrix is solved for the unknown displacements, given the known

forces and boundary conditions. From the displacement at the nodes, the stresses in

each element can then be calculated. The analysis procedure using FEA is divided in

three major steps i.e. Preprocessing, Solution and Post processing. The preprocessing

involves the following steps:

1. Selection of analysis type: Various analysis types which can be commonly

solved by FEA are as follows:

• Static Structural Analysis and Transient Structural Analysis.

• Modal Analysis

• Transient Dynamic Analysis

• Buckling Analysis

• Contact Analysis

• Steady-state Thermal Analysis and Transient Thermal Analysis

• Buckling Analysis

• Fatigue analysis (cyclic loading) etc.

2. Selection of the elements: In this selection is done from 1D, 2D or 3D elements

types depending upon the physics of the problem.

3. Material properties: The material properties are input in this step on the basis of

material used.

4. Connections definition: Contact or joint definitions are carried out in this step.

13

5. Meshing: Disintegrating the continuous object model into finite number of

elements in order to facilitate the solution to the problem.

6. Loading and boundary conditions: Loading and constraints to the problem are

applied in this step as per the actual environment of the problem.

Next step is the solution to the problem defined in preprocessing stage. During this

stage the element matrices are computed and results are stored in result files. These files

are generated for the next stage of post processing which enables viewing the results in

form of graphic and tabular displays.

Last step in the analysis is the post processing. It gives the detailed output of the analysis

carried out in numerical values and represents the various stress, displacement, thermal

etc. plots for better understanding through graphics. Detailed report of the analysis is

also generated by most of the FEA software packages which is finally followed by

interpretation of the result sad conclusions.

Although the FEA and its software capabilities are already developed to a great extent

but still there are sources of errors which leads to abrupt results. These mainly includes

errors in the 3D modeling of the parts or assemblies. Sketch cleanup is always

recommended in order to minimize these errors. Another major source of error is the

interpretation of the physics of the problem which ultimately leads to error caused by

inappropriate boundary conditions. Restrictions in terms of computer capabilities and

experience of the CAE analyst at industries adds to errors in simulations.

In the current study the FEA tool employed is ANSYS Workbench. ANSYS is an

engineering simulation software (computer-aided engineering, or CAE) developed by

Ansys, Inc., USA. ANSYS is a general purpose finite element modeling package for

14

numerically solving a wide variety of mechanical problems. These problems include

static and dynamic structural analysis (both linear and non-linear), heat transfer and

fluid problems, as well as acoustic and electro-magnetic problems.

1.2 Thesis Objectives

Main objectives are as follows:

1. To understand the static structural capability in terms of total deformation and

Von-Mises plots, of four layer symmetrical parabolic leaf spring having leaves

(with included z bending details in the CAD geometry). Static structure analysis

of both reinforced and military wrapper eye ends to be carried out and also the

validation of the design analysis procedure of reinforced eye end with the

experimental results.

2. To compare the FEA results of validated reinforced eye end and military

wrapper eye and comments on the recommended applications and flexibility of

designs.

1.3 Organization of the thesis

Chapter 1 gives the brief introduction about the springs, leaf springs including

parabolic leaf springs and their design criterion. Detailed background of springs and

leaf springs is discussed in this chapter. Leaf spring considered in this study is also

discussed in details with its advantages. Discussions on the classification of various leaf

springs and their applications is outlined. Following this detailed introduction on

computer aided design and computer aided engineering is carried out to understand the

need to use these techniques in modern design and their tools. This introduction is

15

followed by prime objectives of the current work. In end organization of the thesis is

outlined.

Chapter 2 primarily discusses the literature survey and gaps in literature. Detailed

literature study discussed which covers parabolic and conventional leaf springs. It

covers the various FEA modelling techniques used to understand the static, fatigue and

contact behaviors of leaf springs. The literature survey is followed by gaps in literature

and problem formulation of the current study.

Chapter 3 outlines the actual implementation and methodology to carry out the static

structure analysis in ANSYS for reinforced and military wrapper eye ends. It includes

the methods and procedures to carry out the 3D modeling in Solidworks. Ultimately a

3D CAD model is generated as per specifications. Next step is the analysis after

importing the CAD model. Step by step explanation of the analysis procedure is then

discussed. Preprocessing information explanation includes the details regarding contact

definitions, meshing information and applied boundary conditions. Details of solution

section are discussed in last.

Chapter 4 includes the post processing results of the static structure analysis carried

out in ANSYS for reinforced and military eye ends. Von-Mises plots and total

deformation plots for all sets of loading conditions is presented. Comparative study is

demonstrated with the help of tables and graphs showing various FEA and experimental

results.

Chapter 5 finally concludes the thesis listing the conclusion points.

16

Chapter 6 discusses the future scopes of the current study. It is followed by references

used. Lastly appendix is given which gives the details of publications associated with

the current study.

17

CHAPTER II: Background and Literature Review

Leaf springs are among few mechanical components, of which, design has been evolved

and standardized by the international community. Standard design procedure of a leaf

spring can be found in the SAE manual of leaf spring design [30]. The Bureau of Indian

Standards has also worked towards the standardization of the leaf spring in respect to

international standards [31]. This includes primarily the design and material selection

for the leaf springs. Ample amount of literature, research publications and journals are

present on conventional leaf springs. In this prospectus brief summary regarding spring,

leaf springs and CAE tools is presented in regard to current work.

2.1 Literature Review

W.J. Yu and H.C. Kim [1] worked on double tapered FRP leaf spring so as to replace

that with four leaf spring made of steel. Double tapered shape was achieved by linearly

varying thickness, hyperbolically varying width and constant cross section area along

the length of the spring or in simple words it was regarded as double cantilever beams.

Material chosen for the study is S2-glass/epoxy and E-glass/epoxy. Stress analysis

under static loading conditions of the GRP spring was carried out using FEM software

ANSYS 4.2B by employing quadrilateral shell elements. Tsai-Hill theory was used as

failure criterion and the results were found in accordance with the experimental results.

Additionally flexural fatigue testing was also performed for both the samples to 100000

cycles. S2-glass withstand the required cycles without any failure of operation or

damage reported but E-glass showed some damage on upper surface which was due to

presence of voids on the material surface. Despite damage no loss of spring action was

seen thus not regarded as fatigue failure. Also a prototype GRP leaf spring was also

prepared with concave width profile so that steel fitting could be easily mounted.

18

Andrea Corvi [2] presented a program on preliminary structural analysis of composite

beams based on composite mechanics and finite element method. The element used was

derived using Timoshenko beam theory which allows accounting for shear effects on

beam deflection. The inputs to the program included material properties covering fiber

and matrix properties, 2D meshed beam geometry, loading conditions and constraints.

Finite element analysis was used and nodal displacements and stress were evaluated to

determine failures and structure collapse load. Convergence tests of the solutions were

conducted firstly on structure behavior of isotropic materials with known behavior and

then on the composite beams whose data were already present in the literature. These

results were then compared with FEM results using ABAQUS and NASTRAN in order

to prove programs reliability on general structure. The program was then applied to

understand the structural behavior of a composite mono leaf spring under varying

design parameters. The parameters studied were change in the glass fiber volume

content, use of combined glass and carbon epoxy layers and variation in glass fiber

angle while maintaining other parameters as constant.

E. Zahavi [3] analyzed a conventional multi leaf spring for analysis of contact problem

using ANSYS. Loaded leaf spring was taken for the analysis and the deformation is

related to the contact. The contact problem in the leaf spring under load was found to

be of receding type. Contact was defined by use of one dimensional interface elements

which allows the tangential sliding. Friction was taken in account and because of this,

to converge to solution a new iterative process was developed based on new algorithm.

To stop iterations verification check based on Coulomb’s friction law was applied.

Deformation plots of loaded spring superimposed on unloaded was shown and also the

forces in interface elements between first and second leaves were plotted.

19

Peiyong et al. [4] carried out the CAE simulation to determine stresses and deformation

under different loading conditions, of a two stage multi leaf spring, a leaf spring

assembly and Hotchkiss suspension. The software used was ABAQUS and effect of

large deformations, interleaf friction and contact were included in the analysis leading

to non-linearity. Analysis was carried out for leaf spring vertical push, leaf spring

assembly vertical push, windup, suspension roll and suspension cornering. The results

of the analysis were found in agreement with the experimental results. The simulation

models presented could be used in development of leaf springs and suspension.

Predicted rates also could be used in full vehicle NVH (Noise, Vibration, and

Harshness) models such as in NASTRAN or MBD (Multi body dynamics) software

packages.

Mahmood M. Shokrieh and Davood Rezaei [5] analyzed a steel leaf spring using

analytical methods as per SAE, finite element methods and finally comparison is

made with experimental results for verification. The steel spring selected for study was

unsymmetrical and ANSYS 5.4 is used to carry out FEA. The element used is SOLID

45 and for contacts CONTA 49 to represent sliding and friction between leaves. Stress

analysis was carried out for static and bump condition. The results were found in close

accordance with experimental. The steel leaf spring was then optimized for weight

reduction and material is replaced with E-glass/epoxy which brings about 80 %

reduction in weight. The composite leaf spring was mono leaf spring thus its shape was

optimized by parameterizing width and thickness and objective function was fed as

input. First order method to optimize was selected in ANSYS. The optimized spring

was found to have width decreasing hyperbolically and thickness increasing linearly

form spring wye towards axle seat. The stresses in composite spring were much lower

than the steel spring, natural frequency was higher to avoid resonance.

20

J.P. Hou et al. [6] studied the evolution of the eye end designs of a composite leaf

spring used for the freight rail applications. The material used in the study was glass

fiber reinforced plastic (GRP). FEA study was carried out using MSC-Marc and static

and fatigue analysis was carried out to get stress and deflection results. Three main

designs were studied in which first two designs have integrated eye ends in which skin

tape layers went around the eye and along the leaf body. The problem with the first

design lies in the delamination failure at the interface of the fibers owing to the shear

stress concentration but the FEM results showed that it sustained the static load and

required fatigue cycles. In the second design additional transverse bandage were

provided in the delamination region. Results showed decrease in delamination but not

prevented. In the final design open eye end was used and the results of static and fatigue

analysis were found to be in good agreement and was selected as final design.

Vinkel Kumar Arora et al. [7] presented CAE analysis of a 65Si7 conventional leaf

spring. The CAD model was generated in Solidworks and analysis was carried out using

ANSYS. The CAE results in terms of Von-Mises stress and deformation were

compared with the analytical and experimental results to validate the CAE analysis and

found in acceptable ranges of variation. Load deflection curves were also plotted and

found experimental results show nonlinear relationship between load and deflection

values.

Manas Patnaik et al. [8] studied the mono parabolic leaf spring using FEA and DOE

(Design of Experiments) approach. CAD modeling and analysis was carried out using

CATIA. Effect of camber and eye diameter were selected for study from design of

experiments approach. FE results in terms of Von-Mises stresses and displacement are

evaluated from static structure analysis and were plotted. With the increase in camber

21

there was decrease in displacement and increase in the stresses. With the increase in

eye distance there was increase in displacement, however, the stresses were found to

decrease.

Karthik et al. [9] presented the comparison of CAE fatigue analysis of a parabolic leaf

spring using three materials. The loading used in fatigue analysis was non constant

amplitude proportional loading and CAE tool used in the analysis was ANSYS.

Goodman and Gerber approach for the mean stress correlation theory and life

comparisons were made. Additionally an attempt was made to understand the mean

stress correlations.

F.N. Refngah et al. [10] carried out fatigue life predictions using FEA and comparison

was made between a multi leaf and a parabolic leaf spring. The material of multi leaf

spring was SAE 5160H and that of parabolic leaf spring was SAE 6150. 20 noded hexa

elements were used in meshing and appropriate boundary conditions were applied in

the analysis. Fatigue life predictions using Morrow stress mean correlation model was

done for strain based life calculation under variable amplitude loading. Strain data for

correlation was collected using SoMat eDAQ data acquisition system on a public load.

The collected data was then used as input for FE based fatigue life calculations. No

damage was reported on eyes, however, multi leaf spring experienced high damage at

center owing to stress concentration. Parabolic spring however had distributed stresses.

Krishan Kumar and M.L. Aggarwal [11] worked on CAE analysis of a symmetrical

EN45 parabolic leaf spring consisting of three leaves. CAD model was generated using

CATIA V5 and analysis was carried out using ANSYS 11. The spring in study was a

three layer parabolic spring and meshing was carried out by using relevance, sizing

controls and refinements. Appropriate boundary conditions in terms of joint rotation

22

and vertically applied force at seat length were applied. A stress deflection curve was

plotted for the rated and maximum loading and comparison made with the experimental

results. The curve was linear and CAE results were found to be in accordance with the

experimental results.

J.P. Karthik et al. [12] predicted the fatigue life of parabolic leaf spring using three

different SAE standard materials using two Palmer-Miner rule and Morrows method

under predominantly tensile loading sequence. Study was carried out under non

constant amplitude proportional loading. FE based fatigue analysis was carried out for

both stress and strain life approach. An attempt was also made to understand the effect

of mean stress on fatigue life.

Ahmet Kanbolat et al. [13] presented hybrid method for the fatigue life evaluation

based on non-linear analysis. Evaluation of production parameters and geometric

tolerances were studied. Important parameters affecting fatigue were identified and

CAE study from 2D and 3D models completed. CAE results were in accordance with

the theoretical load deflection curve and effect of heat treatment, quenching etc. were

more than the effects of geometric tolerances.

Y.S. Kong et al. [14] presented the stress behavior using FEM under combination of

vertical and windup loads. CAD model was generated using NX 6 and imported to

Hyperworks for the analysis. 8 noded hexa elements were used to mesh the 3D model

and interleaf friction was assigned to the model. Material selected for the study was

carbon steel. Maximum windup load was assumed to be half of the vertical load and

acting in longitudinal direction. Critical stress regions were identified and stress values

calculated. Results were found to be well within the yield strength criterions. Newly

23

designed spring was having 30 % reduction in weight and 10 % less vertical stiffness

than the conventional multi leaf spring.

Murathan Soner et al. [15] studied non-linear finite element model of a five layer

parabolic spring using Abaqus 6.10 and results of analysis were verified with the

theoretical load deflection diagram. The same spring was then optimized to reduce

weight by converting a five layer parabolic spring to a four leaf spring by increasing

thickness of main leaf. Difference of only 13 MPa was found between the design

iterations with appreciable reduction in weight of the spring.

Vinkel Arora et al. [16] attempted to determine the effects of eye end design on a

conventional 65Si7 mono leaf spring using CAE analysis under similar loading

condition. The eyes used in the analysis were standard and casted eyes and results in

form of equivalent stresses and deformation plots were compared with experimental

results in order to propose a cost effective design. The equivalent stresses were

decreased in casted eye end design but deformation values found to be increased.

Decrease of 13% in factor of safety in casted eye end design lead to rejection of casted

eye end for the design used.

Jayanaidu et al. [17] presented the comparison of standard, inverted and centered eye

end designs of a mono leaf spring using 65Si7 and Titanium material under similar

loading conditions. The modelling of the study was done in Pro-E and analysis was

carried out using ANSYS and results were presented in the form of total deformation

and Von-Mises stress plots.

Y.S. Kong et al. [18] studied the fatigue life of a parabolic leaf spring under variable

amplitude loading (VAL). VAL includes the occasional severe events which occur

24

during actual driving conditions. VAL data was collected from three different road

conditions i.e. smooth highway, curvy road and rough road. Strain life approach using

Morrow and Smith Watson Topper (SWT) strain model was applied for fatigue life

estimation. Elastic plastic material, SAE 5160 was used in the study. FE analysis was

carried out at full load conditions with appropriate boundary conditions using

Hyperworks to obtain the stress and displacement plots. 8 noded hexa elements is used

to mesh the 3D model of the spring and nonlinear implicit quasi static time integration

scheme was used to perform analysis. Effects of large deformation and friction were

taken in account. VAL data was noted experimentally and also the load deflection rate

was determined which was having a variation of 4.7 % with the FE results. For Fe based

fatigue simulation n-Code Design Life was used and VAL data and FE analysis data at

fully loaded condition was input and results were evaluated. Based on these rough road

condition leads to highest damage and minimum fatigue life followed by curve road

and smooth highway road.

2.2 Gaps in Literature

It can be concluded from the study that leaf springs are one of the crucial members of

the automotive suspension systems and increasing need for comfort conditions, weight

reduction and increased performance have forced to optimize the design of

conventional multi leaf spring. Recent advances in leaf spring technology to cater the

above needs has led to development of parabolic leaf springs. These springs have

advantages in terms of low ride height and appreciable reduction in the mass owing to

reduced number of leaves and no to minimum interleaf friction.

Analytical design for parabolic leaf spring is cumbersome and has its limitations in

form of assumptions thereby deviating results from the actual results and thus one is

25

largely dependent on the experimental analysis. Repeated experiments thus need to be

carried out which is economically not feasible and also time taking. Recent

developments in the computer based tools in last two decades had put a great impact on

the product development and lead design time. Especially, the areas of computer aided

design (CAD) [32], led to change in the best practices followed by the design industry.

Development of computers, productivity, and design CAE tools like analysis and

simulation has led to development of new engineering disciplines.

Among the tools for design of mechanical systems, computer aided simulation

techniques for complex mechanical systems, structure analysis [33] have large say in

product development. Structure analysis simulations is used to reduce the need of

experimental validation for each design iterations and leads to tremendous saving in

development cost and lead design time. Hence CAE tools are used nowadays widely in

the automotive industries.

It also enables designers to carry out modifications, changing of material properties,

analyzing design in different environment etc. with minimum experimentation. CAE

techniques also leads to appreciable reduction in the design lead time which is of prime

importance in modern times to bring new products.

There have been many advances in the CAE tools but still they have their limitations in

determination of proper assumptions corresponding to the physics of the problem.

Other limitations lies in the software capabilities, user knowledge, and quality mesh

generation etc. Hence the validation of final result is to be carried out by the physical

testing.

26

Although every effort has been made to understand the static, contact and fatigue

behavior of multi leaf springs and three to four layer parabolic leaf spring still no work

has been reported till date on four layer parabolic leaf spring with included z bending

details in main leaf. Z-bending in leaf spring being a very new concept in leaf spring

technology is yet to be developed fully. Hence R&D efforts in this direction are being

carried out nowadays.

2.3 Problem Formulation and Statement

Leaf springs are oldest members of suspension and latest technology in these are

parabolic leaf spring which is the component of study in current work. It is having four

leaves including one leaf and three supporting leaves. All these leaves have

parabolically varying thickness from center to end and are regarded as uniform stress

leaves because of this profile. Z bending details are included in main leaf, third leaf and

fourth leaf.

3D CAD models are generated for reinforced and military wrapper eye and FE static

structure analysis is carried out on both type of eye ends in order to understand the static

capabilities of these springs under different sets of loading conditions. Four type of

loading is used and results in the form of total deflection and equivalent stresses is

calculated using ANSYS. The FEA results of reinforced eye end are compared with the

experimental results in order to validate the design and analysis procedure. Appropriate

design changes in the eye of reinforced eye end are carried out to generate military

wrapper eye and then FE analysis of that is carried out to understand its static behavior

under same loading conditions and boundary conditions.

27

CHAPTER III: METHODOLOGY

3.1 Parametric CAD Modelling

3D CAD modeling is the primary step of the CAE. It is regarded as one of the most

important step and is most time consuming also. Final result of CAD modelling is the

virtual prototype which is employed for further simulation analysis. The generated 3D

models are also suitable for visualization of the design and revision of design at later

stage in the design process.

The model of the parabolic leaf spring used in the current study is generated by using

CAD tool Solidworks. It is a complex assembly of total 11 parts including four leaves

of a four layer parabolic spring, interleaf liners, and fasteners. The 3D solid modelling

can be summarized in two major steps [34]:

1. Part modelling

2. Assembly modelling

The 3D solid models of each individual parts is generated as per the dimensions given

in 2D drawing as shown in Figure 12 and then each individual part is assembled to get

the complete assembly of the parabolic leaf spring with reinforced eye end as shown in

Figure 15. As per the drawing the bill of materials is given as in Figure 13. The 3D

solid model of leaf spring with military wrapper eye is also generated with appropriate

changes in the eye design of reinforced eye leaf spring. 3D model for military wrapper

eye can be seen in the Figure 16.

28

Figure 12: 2D drawing of the parabolic leaf spring

Figure 13: Bill of Materials

3.1.1 Part Modelling

Part modelling is the basic building block of any large scale design. Features are the

individual shapes which when combined leads to a part. 3D part section enables one to

edit features by editing the definition, sketch, or the properties of a feature, view the

parent and child relationship in the tree formed, can move or resize the features, control

to access of dimensions and changing the order in which features are constructed or roll

back the part to state it was before. One sketching is complete part modelling facilitates

feature preview in the features such as extrude, ribs, drafts etc. These are employed to

add thickness as per requirements and finally after previews are accepted to form 3D

29

solid models of parts. Defeature, dragging and copying of features is also possible

through various options in the software. Part modeling of main leaf and second leaf

used in assembly is shown as in Figure 14.

Figure 14: Part modelling of main and second leaf of parabolic leaf spring

3.1.2 Assembly Modelling

Complex assemblies consisting of many components, which can be parts or other

assemblies, called subassemblies can be created in the assembly module. Adding a

component to an assembly creates a link between the assembly and the component.

When SolidWorks opens the assembly, it finds the component file to show it in the

assembly. Changes in the component are automatically reflected in the assembly.

Important features of the assembly modeling includes

1. Feature manager design tree which shows top-level assembly (the first item),

various folders such as annotations and mates, assembly planes and origin,

components (subassemblies and individual parts), assembly features (cuts or

holes) and component patterns.

2. Basic component operations for adding, editing, deleting etc. operations for the

components in the assembly.

30

3. Design methods i.e. one can create assemblies using bottom-up design, top-

down design, or a combination of both methods.

4. Mates which create geometric relationships between assembly components. As

mates are added, one define the allowable directions of linear or rotational

motion of the components. Components can be moved within their degrees of

freedom to facilitate visualizing of the assembly's behavior.

5. Other features of subassemblies, detection of problem in assemblies and

exploded views are also present.

Assembly model of both eye ends can be seen in Figure 15 and Figure 16.

Figure 15: Assembly model of parabolic leaf spring with reinforced eye end

3.2 CAE Static Structure Analysis using ANSYS WB

Static structure analysis is used to determine the displacements, stresses, strains in a

part or assembly based on material, constraints and loads applied in the form of

boundary conditions. Static analysis doesn’t include the significant inertia loads and

damping loads and calculates the effects under static conditions. Static structure

31

analysis (in ANSYS WB) can be performed by using ANSYS, ABAQUS or Samcef

solvers depending upon the problem statement.

Figure 16: Assembly model of parabolic leaf spring with military wrapper eye end

A static analysis can be either linear or nonlinear. All types of nonlinearities are allowed

- large deformations, plasticity, creep, stress stiffening, contact (gap) elements,

hyperelastic elements, and so on. ANSYS utilizes basic finite element methods (FEM)

for static analysis given as

[k] {u} = {F}

Where k represents the global stiffness matrix, u represents deformation vector,

response to be determined and F represents load vector or external forces vector applied

to the structure. Certain assumptions which are followed in static structure analysis are:

1. Material behavior has to be linear elastic.

2. Small deformation theory used i.e. effects of large deformation are neglected.

3. Load applied statically. No damping or time varying forces.

32

Initial step to start analysis is the CAD model import. 3D model of assembly of

parabolic leaf spring is imported into ANSYS Workbench. Solid models for both eye

ends are as shown in Figure 17 and Figure 18 respectively. There are three basic stages

of the practical FEA i.e. Pre-Processing, Solution and Post processing [35, 36]. Pre-

Processing includes the material data definition, geometry, contact definition, meshing,

and application of boundary conditions (loads and constraints). After solution results

are displayed in Post-Processor which includes Equivalent Von Mises stresses and

Maximum Displacement. Various steps in FEA are described as below.

Figure 17: CAD geometry imported to ANSYS for reinforced eye end

Figure 18: CAD geometry imported to ANSYS for military wrapper eye end

33

3.2.1 Material Definition

The selection of material is one of the most important step in the spring design and is

based on the application of the spring and affects the quality and cost in large manner.

More precise selection is based on the conditions in which spring is going to be used,

load, deflection or fatigue life requirements, material grades and their availability and

hardenability requirements. The spring steel grade used in this study is JIS SUP 11A, a

spring steel grade which is Boron treated. Material used in the liners is Grey Cast Iron

and material used for Caster plate and Centre Bolt is Steel which can be seen from the

bill of materials also given in Figure 13. The material definition for both type of eye

ends is same and is defined as new material in the material library of ANSYS WB. The

various mechanical properties of SUP 11A are as shown in Table 1.

Table 1: Material properties of SUP 11A Property Value

Material selected JIS SUP11A Young’s Modulus, E 2e5 MPa Poisson’s Ratio 0.29 BHN 415-461 Tensile strength Ultimate 1272 MPa Tensile strength Yield 1145 MPa Density 7.7e-6 kg mm^-3 Behavior Isotropic

3.2.2 Geometry

CAD model imported in the ANSYS is displayed with details of the geometry in the

outline window on the extreme left side of the workbench window. All individual parts

of the assembly can be seen here. On selecting a part, details associated to it i.e. graphic

properties in which color visibility of individual part can be changed, definition details

to change the behavior to flexible or rigid, material assignment for each individual part.

It also shows the details of dimensions, various properties such as mass, volume,

34

centroids and moment of inertia. Material assignment of each part in assembly has to

be done individually by selecting appropriate materials from drop down menu or

material library. Meshing details i.e. number of nodes and elements are also displayed

however numeric values in these can be seen only once the model is meshed.

Geometry imported can be edited in ANSYS Design Modeler. In the current study a

feature of face split is used to define seat length region in the parabolic leaf spring. A

seat length region is regarded as no action region as if it acts as rigid. The inaction of

seat length region is due to the U clamp with which leaf spring is clamped to the axle

of the automobile. To define face split first a sketch is generated as per the required

dimensions on the required plane. Face split feature can be evoked by selecting the

newly created plane. The required dimensions depend upon the seat length which could

be of maximum value equal to 0.9 times the length of the interleaf liners [30].

3.2.3 Contact Definition

The contact definition is next step after geometry and material definitions and is very

vital in order to converge to a meaningful result. Without contact different parts in

assembly won’t interact when loaded i.e. load transfer will not take place. Contact

elements can be visualized as a skin covering the region where contact occurs. ANSYS

Workbench generates contacts automatically between two bodies upon importing the

CAD file, whenever there is a contact detected between them. Contacts can also be

defined manually in connections branch given in outline window. Automatic contact is

detected by very efficient contact algorithms which works on simple principle of

proximity. If two parts are in close proximity ranges, of defined range value, they are

assumed to be in contact.

35

ANSYS automatically detects a bonded type contact which has zero degree of freedom

and behaves as a welded joint or glued part. They have surfaces fixed to each other so

that no gap can open between them and no sliding takes place. In the current study

instead of bonded joint type of contact (between two leaves or between leaf and liner)

no separation type of contact is used. No separation contacts also leads to no gaps but

it allows tangential frictionless sliding between leafs and between leafs and liners. Both

bonded and no separation contact are regarded as linear contact as only one iteration is

used to converge to result unlike frictionless, rough and frictional contacts which are

highly nonlinear and requires multiple iterations.

All other automatically generated contacts are taken as bonded only and in bonded

contacts. The contact definitions applies to face segments and care must be taken in

selecting a specific region especially near the eye. Too large contact gap can lead to

divergence. The 3D elements at contact region defined here are CONTA 174 (to define

contact) and TARGE 170 (to define target). The contact definitions for reinforced and

military eye end remains same and can be seen in Figure 19 and Figure 20 respectively.

Figure 19: Contact definition in reinforced eye end parabolic leaf spring

36

Figure 20: Contact definition in military wrapper eye end parabolic leaf spring

3.2.4 Meshing

Any continuous object has infinite degree of freedom based on the basics of continuum

mechanics, which makes the analysis impossible to be carried out and hence meshing

is carried out. Meshing is a process of reducing the infinite degree of freedom to a finite

degree of freedom problem thereby leading to solution of the analysis. SOLID187

tetrahedron element, a 3D 10-node element having quadratic displacement behavior

with three degree of freedom at each node i.e. displacements in x, y and z directions

taken in the analysis. SOLID 187 has capabilities of irregular modelling meshes. Global

meshing controls are used in both models of parabolic leaf spring which applies to the

whole assembly instead of local meshing controls. Mesh sizing options include

advanced size function on curvature, relevance center as fine, smoothing as high and

transition as slow. Total number of elements generated is 28747 for reinforced eye end

and 19500 for military wrapper eye end. Meshed models for both eye ends are seen in

Figure 21 and Figure 22.

37

Figure 21: Meshed 3D model for reinforced eye end

Figure 22: Meshed 3D model for military wrapper eye end

3.2.5 Boundary Conditions

Boundary conditions include loading and constraints in the form of force, pressure,

supports and other conditions to carry out the analysis. Boundary condition application

is one of the most critical step in pre-processing stage in order to carry out CAE

analysis. In current study the spring is modelled in flat condition, which is the maximum

deflection position in actual loading and load applied such that spring deflects to initial

position. The total load is divided on front and rear eye pin of the master leaf and fixed

support is applied on seat length (on main leaf and caster plate at bottom) and center

bolt.

38

Force is the boundary condition which could be applied to nodes, vertices, edges or

surface. Care must be taken in applying the force boundary condition to scoped

geometry. Force is evenly distributed on all entities i.e. if multiple surfaces are scoped

force would be evenly distributed on all. In current study force boundary condition is

thus applied individually to each surface of eye end. Four different magnitude of forces

are applied in order to analyze the model in four design conditions.

Figure 23: Boundary conditions applied to reinforced eye end

Figure 24: Boundary conditions applied to military wrapper eye end

39

A fixed support boundary condition constraints all the degree of freedom on vertex,

edges or surface. In current study fixed support is applied to surface. The boundary

conditions applied to the model can be seen in Figure 23 and Figure 24 respectively.

3.2.6 Solution

Static structural analysis is a part of the solution stage of FEA and aims at getting the

output as numerical values of the Von-Mises stresses and the displacement under the

application of the boundary conditions. Steady state conditions are assumed for loading

with respect to time. Analysis is performed for the pre-processed information including

material properties, loading details, supports conditions and contact definitions.

40

CHAPTER IV: RESULTS AND DISCUSSIONS

The results as obtained from the analysis of reinforced and military wrapper eye ends

are analyzed in the detailed information. Von-Mises stresses and displacement contours

have been obtained under four sets of loading conditions i.e. specified load of 4905 N,

unladen load of 12645 N, laden load of 15696 N and 2G load of 31392 N which is the

maximum load for a loaded condition, g being the design load. Analysis results for both

eye ends is obtained by static structure analysis under similar conditions.

4.1 FEA Results of Reinforced Eye End Parabolic Leaf Spring

Detailed results and discussions for reinforced eye end parabolic leaf spring are

discussed here.

Deformation at specified load (4905 N) applied on the eye ends is shown in Figure 25.

Maximum deformation is found at the eye ends (as seen in red color) and minimum

deformation in the seat length region as expected. Figure 26 shows the Equivalent Von-

Mises contour for the specified loading. Maximum value is observed near the end of

leaf length (as seen in red color) and minimum at the seat length as expected. The

maximum deformation is found to be 22.41 mm with percentage deviation of 2.69 %

from actual results and maximum stress is found to be 174.2 MPa which is well below

the yield stress.

Figure 27 shows the deformation at unladen load (12645 N) applied on the eye end.

Maximum deformation is found at the spring eye ends (as seen in red color) and

minimum deformation in the seat length region as expected. Figure 28 shows the

Equivalent Von-Mises stresses for the unladen loading. Maximum value is observed

near the end of leaf length and minimum at the seat length. The maximum deformation

41

is found to be 55.19 mm having percentage deviation of 6.46 % from experimental

results and maximum stress is found to be 449.09 MPa much below yield stress value.

Figure 25: Deflection at specified load for reinforced eye end

Figure 26: Equivalent stresses at specified load for reinforced eye end

42

Figure 27: Deflection at unladen load for reinforced eye end

Figure 28: Equivalent stresses at unladen load for reinforced eye end

Figure 29 shows the deformation at laden load (15696 N) applied on the spring eye end.

Maximum deformation is found at the eye ends (as seen in red color) and minimum

deformation in the seat length region as expected. Figure 30 shows the Equivalent Von-

Mises contour for the laden loading. Maximum value is observed near the end of leaf

length and minimum at the seat length. The maximum deformation is found to be 68.5

mm having percentage deviation from experimental results of 7.42 % and maximum

stress is below the yield stress value and is having magnitude of 557.45 MPa.

43

Figure 29: Deflection at laden load for reinforced eye end

Figure 30: Equivalent stresses at laden load for reinforced eye end

Total deformation at 2G load (31392 N) applied on the eye end is shown in Figure 31.

Maximum deformation is found at the eye ends and minimum deformation in the seat

length region as expected. Equivalent Von-Mises contour for the 2G load is shown in

Figure 32. Maximum value is observed near the end of leaf length and minimum at the

seat length. The maximum deformation is found to be 137.03 mm with 6.78 %

percentage deviation from actual results and maximum stress is found to be 1115 MPa

which is much below the yield stress of the material.

44

Figure 31: Deflection at 2G load for reinforced eye end

Figure 32: Equivalent stresses at 2G load for reinforced eye end

4.1.1 Experimental Load Deflection Curve for Reinforced Eye End

Experimental results for reinforced eye end are considered to validate the design and

analysis procedure of CAE analysis using ANSYS. These results are obtained by

experiments under static loading conditions assuming linear steady sate behavior and

plotted as load vs deflection curve. In addition to this load deflection rate is also given

for stiffness comparisons. These results are as shown in Figure 33

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Figure 33: Experimental results of load vs deflection for reinforced eye end

4.1.2 Comparison of FEA Load Deflection Curve and Experimental Load Deflection Curve

Figure 34 shows load deflection curve for the CAE results and the experimental results.

In both cases a linear relation is seen between the load and deflection under given

loading condition. Both curves are straight hence validating the CAE results.

Figure 34: Comparison between CAE and experimental load deflection curve

46

4.2 FEA Results of Military Wrapper Eye Parabolic Leaf Spring

The results of design and analysis procedure Detailed results and discussions for

military wrapper eye end parabolic leaf spring are discussed here.

Figure 35 depicts the deformation at specified load of 4905 N for the military eye end

designs. Maximum value of deformation is found to be at the eye end and minimum

value is found at seat length as per the loading condition applied. Maximum total

deformation (shown in red color) in military wrapper is 21.15 mm. Figure 36 shows the

equivalent Von-Mises plots at specified load. Maximum value of stress in military end

design is 174.92 MPa. Maximum value is found near the leaf length ends and is below

material yield stress value.

Figure 35: Deflection at specified load for military wrapper eye end

Figure 37 shows deformation plot of military eye ends at unladen load of 12645 N.

Maximum deformation of 54.52 mm in case of military wrapper eye, is found at spring

ends and minimum total deformation is found in seat length region as predicted.

Equivalent Von-Mises contour plot is as shown in Figure 38. In military wrapper eye

this value is found to be 450.94 MPa present in same region as in reinforced eye.

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Figure 36: Equivalent stresses at specified load for military wrapper eye end

Figure 37: Deflection at unladen load for military wrapper eye end

Figure 38: Equivalent stresses at unladen load for military wrapper eye end

48

Total deformation plot for military wrapper eye under similar loading condition of

laden load having force value of 15696 N is shown in Figure 39. Maximum deformation

found at eye ends and is having value of 67.68 mm. The maximum total deformation is

found to be in accordance with the applied load and minimum deformation is found at

the seat length region. Stress contour plot of military wrapper eye is as shown in Figure

40. Maximum stress is much below the yield stress values and is found maximum near

the ends and minimum values at seat length region. Maximum stress in military eye is

having value of 559.74 MPa.

Figure 39: Deflection at laden load for military wrapper eye end

Figure 40: Equivalent stresses at laden load for military wrapper eye end

49

Maximum deformation in case of military wrapper eye at 2G load of 31392 N is shown

in Figure 41. Maximum deformation value of 135.36 mm as shown in red color at spring

eye ends is predicted by FEA analysis for military wrapper eye. Minimum value is

found at seat length region in accord with boundary conditions applied. Maximum

equivalent Von-Mises stresses is shown in Figure 42 and in military wrapper its

magnitude is 1119.5 MPa as shown in red color. Maximum stress value being less than

material yield stress thereby validates the designs and analysis. It is seen near ends and

minimum values at seat length regions as the result of constraints and loading.

Figure 41: Deflection at 2G load for military wrapper eye end

Figure 42: Equivalent stresses at 2G load for military wrapper eye end

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4.2.1 Comparison of FEA results for Reinforced and Military wrapper eye

Table 2 shown below gives the comparison of FEA results for the reinforced eye and

military wrapper eye for the four sets of loading applied. The Von-Mises stresses and

total deformation is almost same for reinforced and military eye. These results are in

line with the SAE manual for leaf spring [30]. Deformation is slightly lower in military

eye because of high stiffness and Von-Mises stresses are slightly more but well below

the material yield stress value. The military eye is mostly preferred in heavy duty

applications where high safety margins are required.

Table 2: Comparison of FEA results for Reinforced and Military wrapper eye

Load set

Load (N)

Reinforced Eye Military wrapper eye Deflection

(mm) Equivalent Von-Mises

Stress (MPa)

Deflection (mm)

Equivalent Von-Mises

Stress (MPa) Specified load

4905 21.41 174.2 21.15 174.92

Unladen load

12645 55.19 449.09 54.52 450.94

Laden load 15696 68.50 557.45 67.68 559.74 2G load 31392 137.03 1115 135.36 1119.5

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CHAPTER V: CONCLUSION

From the results obtained from the FEA analysis and on comparison with experimental

results following conclusion have been made in the current study:

1. The load deflection curve as calculated from finite element analysis for

Reinforced eye end is found to be linear and in accordance with the

experimental load deflection curve. The CAE load rate is 23.35 Kgf/mm, a

variation of 7.6 % is observed from actual rate value (21.58±7% Kgf/mm).

2. Maximum total deformation in Reinforced eye is found to be 137.03 mm under

2G load and maximum equivalent Von-Mises stress is 1115 MPa which is well

below the yield stress (1196 MPa) indicating safe design. Maximum stress

concentration is found near end of the leaf length probably developed because

of change in thickness and geometry.

3. Variation in total deformation under all type of loading in Reinforced eye is

found to be 2.7 to 7.4 % with respect to experimental load deflection curve

which is acceptable and hence the analysis stands validated.

4. Von-Mises stresses and total deformation for Reinforced and Military wrapper

eye are found to be almost the same.

5. Military wrapper eye results in stiffer and safer design and ability of the wrapper

on second leaf to be used as an eye in case of failure of main leaf eye. Military

wrapper eyes are hence recommended for use in heavy loading application.

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CHAPTER VI: FUTURE SCOPE

1. The design has to be optimized further in order to reduce the maximum

equivalent Von-Mises stresses as they are near to yield stresses in case of 2G

loading (maximum load conditions).

2. Fatigue analysis can also be carried out to validate the fatigue life cycles

requirements. This can be done by FE analysis by employing CAE tools and

validation of the same by experimental techniques.

53

REFERENCES

[1] Yu, W. J. & Kim, H. C., “Double tapered FRP beam for automotive suspension leaf spring”, Composite Structures, 9 (1988), pp. 279-300.

[2] Andrea Corvi, “A Preliminary Approach to Composite Beam Design Using FEM Analysis”, Composite Structures, 16 (1990), pp. 259-275.

[3] E. Zahavi, “Analysis of Contact Problem in Leaf Springs”, Mechanics Research Communications, 19 (1) (1992), pp. 21-27.

[4] Peiyong Qin, Glenn Dentel, and Mikhail Mesh, “Multi-Leaf Spring and Hotchkiss Suspension CAE Simulation”, ABAQUS Users’ Conference (2002).

[5] Mahmood M. Shokrieh, Davood Rezaei, “Analysis and optimization of a composite leaf spring”, Composite Structures, 60 (2003), pp. 317–325.

[6] J.P. Hou, J.Y. Cherruault, I. Nairne, G. Jeronimidis, R.M. Mayer, “Evolution of the eye-end design of a composite leaf spring for heavy axle loads”, Composite Structures, 78 (2007),pp. 351–358.

[7] Arora Vinkel Kumar, Bhushan Gian, Aggarwal M.L., “Static structural CAE analysis of symmetrical 65Si7 leaf springs in automotive vehicles”, Engineering Solid Mechanics, 3 (2014).

[8] M. Patnaik, N. Yadav, R. Dewangan, “Study of a Parabolic Leaf Spring by Finite Element Method & Design of Experiments”, International Journal of Modern Engineering Research, 2 (4) (2012), pp.1920-1922.

[9] J.P. Karthik, K.L. Chaitanya, C. Tara Sanaka, “Life Assessment of A Parabolic Spring Under Cyclic Stress & Cyclic Strain Loading Using Finite Element Method”, International Journal of Mechanical and Industrial Engineering, 2 (1) (2012), pp. 36-43.

[10] F. N. Ahmad Refngah, S. Abdullah, A. Jalar and L. B. Chua, “Fatigue Life Evaluation of two types of steel Leaf Springs”, International Journal of Mechanical and Materials Engineering, 4 (2009), pp. 135-140.

[11] Krishan Kumar and M.L. Aggarwal, “Computer aided FEA simulation of EN45A parabolic leaf spring”, International Journal of Industrial Engineering Computations, 4 (2013), pp. 297–304.

[12] J. P. Karthik, K. L. Chaitanya and C. Tara Sasanka, “Fatigue Life Prediction of a Parabolic Spring under Non-constant Amplitude Proportional Loading using Finite Element Method”, International Journal of Advanced Science and Technology, 46 (2012), pp. 143-156.

[13] Kanbolat A., Soner M., Erdogus T. and Karaagac M., "Parabolic Leaf Spring Optimization and Fatigue Strength Evaluation on the Base of Road Load Data, Endurance Rig Tests and Non Linear Finite Element Analysis," SAE Technical Paper (2011).

[14] Y. S. Kong, M. Z. Omar, L. B. Chua, S. Abdullah, “Stress Behavior of a Novel Parabolic Spring for Light Duty Vehicle”, International Review of Mechanical Engineering, 6 (2012), pp. 617-620.

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[15] Soner M., Guven N., Kanbolat A., Erdogus T., & Karaagac M., “Parabolic leaf spring design optimization considering FEA & rig test correlation”, Commercial Vehicle Engineering Congress, Chicago, SAE International (2011), Paper Number: 2011-01-2167.

[16] Arora Vinkel Kumar, Bhushan Gian, Aggarwal M.L., “Eye Design Analysis of Single Leaf Spring in Automotive Vehicles using CAE tools” International Journal of Applied Engineering and Technology, 1(1) (2011), pp. 88-97.

[17] Jayanaidu, Hibbatullah M., Baskar P., “Optimization of Eye End Design of a Single Leaf Spring”, International Journal of Engineering Trends and Technology, 11 (5) (2014), pp. 225-229.

[18] Y.S. Kong, M.Z. Omar, L.B. Chua, S. Abdullah, “Fatigue life prediction of parabolic leaf spring under various road conditions”, Engineering Failure Analysis, 46 (2014), pp. 92–103.

[19] Richard Gordon Budynas, J. Keith Nisbett, Joseph Edward Shigley, Shigley’s Mechanical Engineering Design, McGraw-Hill (2008).

[20] NPTEL web based series on Design of Machine elements, http://nptel.ac.in/syllabus/syllabus.php?subjectId=112105125

[21] SolidWorks, SolidWorks Corporation, http://www.solidworks.com

[22] CATIA, Dassault Systems, http://www.3ds.com/products-services/catia/

[23] I-DEAS, Structural Dynamics Research Corporation, http://www.sdrc.com

[24] Pro Engineer, PTC, http://www.ptc.com

[25] ANSYS, ANSYS Inc., http://www.ansys.com

[26] ABAQUS, Hibbitt, Karlsson & Sorensen, Inc., http://www.abaqus.com

[27] MSC NASTRAN, MSC Software, http://www.mscsoftware.com/product/msc-nastran

[28] Haug, E. J., Computer Aided Kinematics and Dynamics of Mechanical Systems, Volume I: Basic Methods, Allyn and Bacon, Boston (1989).

[29] Practical Aspects of Finite Element Simulation, A Study Guide, Academic program, Altair University (2014).

[30] Spring Design Manual, AE-11, SAE (1990).

[31] Springs – Leaf Springs Assembly for Automobiles-Specification, Bureau of Indian Standard, IS 1135, Indian Standard (1995).

[32] Taylor, D. L., Computer-Aided Design, Addison-Wesley Publishing Company (1992).

[33] T. Stolarski, Y. Nakasone, S. Yoshimoto, Engineering Analysis with ANSYS Software, Elsevier (2006).

[34] Matt Lombard, Solidworks 2009 Bible, Wiley Publishing (2009).

[35] ANSYS Mechanical User’s Guide, ANSYS Help.

[36] Workbench User's Guide, ANSYS Help.

55

Appendix A

List of Publications

1. Ishan Aggarwal, Gian Bhushan, Pankaj Chandna, “Static Structure Analysis

of SUP11A Multi Leaf Symmetrical Parabolic Leaf Spring”, International

Bulletin of Mathematical Research, ISSN: 2394-7802, Vol. 2 (1), 2015, pp. 229-

225.

2. Ishan Aggarwal, Gian Bhushan, Pankaj Chandna, “Linear Static Structure

Analysis of Military Eye and Reinforced Eye Ends of Parabolic Leaf

Spring”, Proceedings of the 5th National Conference on Recent Advances in

Manufacturing, 2015, ISBN: 978-93-5212-649-1, pp. 308-313

56