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ADAMA SCIENCE AND TECHNOLOGY UNIVERSITY 

School of Mechanical, Chemical and Materials Engineering 

 

 

 

Design and analysis of mono composite leaf spring for light weight vehicle 

Thesis  

Submitted to school of mechanical and chemical engineering in partial fulfillment of the 

requirement for the award of the degree of Master of Science in automotive engineering 

 

By 

Beresaw Belestie 

 

Major Advisor: 

N.Ramesh Babu (Associate Professor) 

 

Co- Advisor: 

K. Sririvasa Reddy (associate professor) 

 

May 2015 

Adama 



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ACKNOWLEDGEMENT 

I am grateful to the God for the good health and well being that were necessary to accomplish 

this work. 

I would like to express my special thanks to my advisor, N. Ramesh Babu (Associate Professor), 

for his comments, continuous support, guidance and suggestions throughout the entire thesis 

work.  

I also gratefully acknowledge the help, valuable comments and suggestions offered by my co-

advisor K. Sririvasa Reddy (Associate professor) which contribute much in enhancing the quality 

of my work. 

I wish to express my sincere thanks to Bishoftu Automotive Industry specifically design section 

workers, Ethio plastic corporation, ethio- leaf spring (balestira) factory workers for providing me 

the necessary facilities for the thesis work. 

Finally, my sincere thanks go to all my friends and members of the staff of Mechanical 

Engineering department, who helped me in many ways. 

 

 

 

 

 

 

 

 

 

 

 

 

 



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TABLE OF CONTENTS 

           Contents                                                                                                 pages 

ACKNOWLEDGEMENT ............................................................................................................... i 

ACRONYMS AND ABBREVIATIONS ...................................................................................... vi 

LIST OF FIGURES ..................................................................................................................... viii 

LIST OF TABLES .......................................................................................................................... x 

1.INTRODUCTION ....................................................................................................................... 1 

1.1. Background of the study ...................................................................................................... 2 

1.2. Statement of the problem ..................................................................................................... 2 

1.3. Significance of the study ...................................................................................................... 3 

1.4. Objectives of the study ......................................................................................................... 4 

1.4.1 General objective ............................................................................................................ 4 

1.4.2 Specific objective ........................................................................................................... 4 

1.5. Scope of the study ................................................................................................................ 4 

1.6. Limitations of the study........................................................................................................ 5 

2. LITERATURE REVIEW ........................................................................................................... 6 

2.1. Suspension system................................................................................................................ 9 

2.1.1 Suspension springs ....................................................................................................... 10 

2.1.2 Classification of spring ................................................................................................. 11 

2.1.2.1 Leaf spring ............................................................................................................ 11 

2.1.2.2 Cylindrical helical spring ...................................................................................... 11 

2.1.4 Spring materials ............................................................................................................ 12 

2.1.4.1Commonly used steel alloys for leaf spring ........................................................... 16 

2.2 Theories of Failure .............................................................................................................. 16 

2.2.1 Maximum Principal or Normal Stress Theory ............................................................. 17 

2.3 Composite............................................................................................................................ 17 

2.3.1 Contributing factors to the mechanical performance of composite fiber ..................... 18 

2.3.2 Classes and Characteristics of Composite Materials .................................................... 19 

2.4.3 Comparative Properties of Composite Materials.......................................................... 20 

2.3.4 Advantages of composite materials .............................................................................. 21 

2.3.5 Limitations of composite materials .............................................................................. 22 



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2.4 REINFORCEMENTS AND MATRIX MATERIALS ....................................................... 22 

2.4.1 Reinforcements ............................................................................................................. 22 

2.4.1.1 Fibers..................................................................................................................... 23 

2.4.1.1.1 Glass Fibers .................................................................................................... 23 

2.4.1.1.2 Carbon Fibers ................................................................................................. 24 

2.4.1.1.3 Boron Fibers................................................................................................... 25 

2.4.1.1.4 Fibers Based on Silicon Carbide .................................................................... 25 

2.4.1.1.5 Alumina based fibers ..................................................................................... 26 

2.4.1.1.6 Aramid Fibers ................................................................................................ 26 

2.4.1.1.7 High Density Polyethylene Fibers ................................................................. 26 

2.4.2 Matrix Materials ........................................................................................................... 26 

2.4.2.1 Polymer Matrix Materials ..................................................................................... 27 

2.4.2.1.1 Thermosetting Resins..................................................................................... 28 

2.4.2.1.2 Thermoplastic Resins ..................................................................................... 28 

2.5 Material selections............................................................................................................... 28 

2.7 Resin selection..................................................................................................................... 30 

2.8 Manufacturing Process Selection ........................................................................................ 31 

2.8.1 Hand Lay-up Technique ............................................................................................... 31 

2.9 Manufacturing composite leaf spring .................................................................................. 33 

3. BETTER MATERIALS AND METHODS ............................................................................. 34 

3.1 Methodology and software used ......................................................................................... 34 

3.1.1 CATIA .......................................................................................................................... 34 

3.1.2 ANSYS ......................................................................................................................... 34 

3.2 Huanghai pickup DD1022T model specification ................................................................ 34 

3.3 Construction of existing steel Leaf spring........................................................................... 36 

3.3.1 Modeling existing steel leaf spring (CAD Modeling) .................................................. 36 

3.3.2 Existing steel leaf spring dimensions ........................................................................... 37 

3.3.3 Existing steel leaf spring material specification ........................................................... 38 

3.4 STATIC ANALYSIS OF EXISTING STEEL LEAF SPRING ......................................... 38 

3.4.1 Analytical calculation ................................................................................................... 38 

3.5 DYNAMIC ANALYSIS ..................................................................................................... 44 



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3.5.1 Accelerating on level road ............................................................................................ 44 

3.5.2 Accelerating on an inclined road .................................................................................. 47 

3.6 Designing mono composite leaf spring ............................................................................... 53 

3.7 Finite element analysis of existing leaf spring .................................................................... 58 

3.7.1 Boundary conditions ..................................................................................................... 59 

3.7.2 Meshing ........................................................................................................................ 59 

3.7.3 Applying load ............................................................................................................... 60 

4. ANALYSIS RESULTS AND DISCUSSION .......................................................................... 61 

4.1 Finite element analysis results of existing leaf spring......................................................... 61 

4.1.1 Stress and deformation results ...................................................................................... 61 

4.1.2 Mode shape and natural frequency Analysis ................................................................ 63 

4.1.3 Fatigue analysis results ................................................................................................. 65 

4.1.4 Harmonic analysis ........................................................................................................ 67 

4.2 Finite element analysis of mono composite lea f spring results .......................................... 69 

4.2.1 Stress and deformation ................................................................................................. 70 

4.2.2 Mode shape and frequency analysis of composite leaf spring ..................................... 72 

4.2.3 Fatigue analysis of mono composite leaf spring results ............................................... 74 

4.2.4 Harmonic analysis of composite leaf spring ................................................................. 75 

4.3 Existing and mono composite leaf spring analysis results comparison .............................. 77 

5. CONCLUSIONS, SUMMARYAND RECOMMENDATION ................................................ 81 

6. REFERENCES ......................................................................................................................... 84 

 

 

 

 

 

 

 

 



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ACRONYMS AND ABBREVIATIONS 

FEA – Finite Element Analysis 

3D – Three Dimensional 

BIS – Bureau of Indian Standard 

FS – Factor of Safety 

BC – Before Jesus Chris 

PMCs – Polymer Matrix Composites 

MMCs – Metal Matrix Composites 

CMCs – Ceramic Matrix Composites 

CCCs – Carbon/Carbon Matrixes 

CTE – Coefficient of Thermal Expansion 

SMC – Sheet Molding Compound  

SRIM – Structural Reinforcement Injection Molding 

HS – High Strength 

PAN – Polyacryonitride 

FRP – Fiber Reinforced Polymer 

CAD – Computer Aided Design 

CATIA – Computer Aided Three Dimensional Interactive Applications 

CAM – Computer Aided Modeling 

CAE – Computer Aided Engineering 

FEM – Finite Element Method 



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GVM – Gross Vehicle Mass 

SN – Stress Vs Number of Cycle 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



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                              LIST OF FIGURES                                                pages 

Figure 1 leaf spring ....................................................................................................................... 11 

Figure 2 cylindrical helical spring ................................................................................................ 12 

Figure 3:-Reinforcement forms of composite ............................................................................... 20 

Figure 4:- Fabrication procedure of composite ............................................................................. 32 

Figure 5:- Huanghai pick up ......................................................................................................... 35 

Figure 6:- existing steel leaf spring CATIA model ...................................................................... 37 

Figure 7:- free body diagram for cantilever beam with load at the free end ................................ 39 

Figure 8:- accelerating vehicle on level road ................................................................................ 45 

Figure 9:-accelerating vehicle on inclined road (pavement)......................................................... 47 

Figure 10:- stress versus deflection graph .................................................................................... 50 

Figure 11:- Schematic illustration of a constant life or Goodman diagram .................................. 53 

Figure 12:-designed composite leaf spring model ........................................................................ 56 

Figure 13:- boundary conditions of existing leaf spring ............................................................... 59 

Figure 14:-meshed model of existing leaf spring ......................................................................... 60 

Figure 15:- loading constraint ....................................................................................................... 60 

Figure 16:- total deformation ........................................................................................................ 61 

Figure 17:- un-deformed and deformed shape .............................................................................. 61 

Figure 18:- equivalent von- mises stress ....................................................................................... 62 

Figure 19:- equivalent von- mises elastic strain ........................................................................... 62 

Figure 20:- First natural frequency and mode shape .................................................................... 63 

Figure 21:-Second mode and natural frequency ........................................................................... 63 

Figure 22:- third natural frequency and deformation mode .......................................................... 64 

Figure 23:- fourth natural frequency and deformation mode ........................................................ 64 

Figure 24:- fifth natural frequency and deformation mode .......................................................... 64 

Figure 25:- sixth natural frequency and mode shape .................................................................... 65 

Figure 26:- fatigue life .................................................................................................................. 66 

Figure 27:- factor of safety ........................................................................................................... 66 

Figure 28:-deflection due to fatigue stress .................................................................................... 67 

Figure 29:-equivalent fatigue stress amplitude ............................................................................. 67 

Figure 30:- equivalent (von – mises) stress .................................................................................. 68 

Figure 31:- deformation ................................................................................................................ 68 

Figure 32:-harmonic response of existing leaf spring ................................................................... 69 

Figure 33:- designed mono composite leaf model ........................................................................ 69 

Figure 34:- total deformation of composite leaf ........................................................................... 70 

Figure 35:-un-deformed and deformed shape of composite leaf .................................................. 70 

Figure 36:- Equivalent stress (von-mises ) of composite leaf....................................................... 71 

Figure 37:- Elastic Strain (von mises ) of composite leaf ............................................................. 71 

Figure 38:-shear stress on composite leaf ..................................................................................... 71 

Figure 39:- first natural frequency of composite leaf ................................................................... 72 



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Figure 40:- second natural frequency of composite leaf ............................................................... 72 

Figure 41:- the third natural frequency of composite leaf ............................................................ 73 

Figure 42:- fourth natural frequency and mode shape .................................................................. 73 

Figure 43:- fifth natural frequency and mode shape of composite leaf spring ............................. 73 

Figure 44:-sixth natural frequency and its mode shape of composite leaf spring ........................ 74 

Figure 45:- alternating stress amplitude ........................................................................................ 74 

Figure 46:- number of cycles to fatigue failure of mono composite leaf spring ........................... 75 

Figure 47:- safety factor ................................................................................................................ 75 

Figure 48:-equivalent (von- mises) stress ..................................................................................... 75 

Figure 49:- deformation ................................................................................................................ 76 

Figure 50:- amplitude versus frequency graph of composite leaf spring...................................... 76 

Figure 51:- stress and deflection of leaf springs ........................................................................... 77 

Figure 52:-weight of steel and composite leaf spring ................................................................... 78 

Figure 53:- natural frequency comparison .................................................................................... 79 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



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                                          LIST OF TABLES                                       pages 

Table 1 physical properties of common spring materials ............................................................. 14 

Table 2:- types of composite materials [41] ................................................................................. 20 

Table 3:- properties of matrix materials
 
[41] ................................................................................ 28 

Table 4;-Mechanical propreties of epoxy resin ............................................................................ 30 

Table 5:- Huanghai pickup DD1022T model specification .......................................................... 35 

Table 6:- existing steel leaf spring measured dimensions ............................................................ 37 

Table 7:- Mechanical properties of 55SiMn90 ............................................................................. 38 

Table 8:- Composition of 55si2Mn90 [24] ................................................................................... 38 

Table 9:-stress and deflection values of leaf at different load conditions ..................................... 49 

Table 10:-Dimensions of mono composite leaf spring ................................................................. 56 

Table 11:-mechanical properties of E-glass Epoxy [21, 40] ......................................................... 57 

Table 12:- Natural frequency analysis results of multi leaf spring ............................................... 65 

Table 13: Stress and deflection analysis of mono composite leaf using FEA .............................. 72 

Table 14:-stress and deflection comparison between steel and composite leaf spring ................. 77 

Table 15:-frequency comparison of existing steel leaf spring and composite leaf spring results 78 

Table 16:- Fatigue analysis results ................................................................................................ 79 

Table 17:-harmonic response amplitude results ........................................................................... 80 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



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ABSTRACT 

This thesis focuses on the replacement of steel or conventional leaf spring of a suspension 

system with composite material. Design and analysis of composite material leaf spring has 

become essential in showing the comparative results with conventional leaf spring. The 

Automobile industry has shown the interest for replacement of steel leaf spring with that of glass 

fiber composite leaf spring, since the composite has high strength to weight ratio, good corrosion 

resistance and tailor-able properties.  The suspension system in automobile significantly affects 

the behavior of vehicle, i.e. vibration characteristics including ride comfort, directional stability, 

etc. leaf spring used in the suspension system of automobile are subjected to millions of varying 

stress cycles leading to fatigue failure. If the unsprung weight (the weight, which is not 

supported by the suspension system) is reduced, then the fatigue stress induced in the leaf spring 

is also reduced. Even a small amount of weight reduction in the leaf spring will lead to 

improvements in passenger comfort as well as reduction in vehicle cost. In this context, the 

replacement of steel leaf spring by composite material reduces the weight of leaf springs. In this 

work, the existing steel leaf (multi-leaf) spring of Huanghai pick up is taken for modeling and 

analysis. The design constraints are stress and displacement. A composite mono leaf spring of E- 

glass Epoxy composite material is modeled and subjected to the same load as that of steel leaf 

spring. Composite mono leaf spring is modeled with constant cross section in CATIA and stress, 

deflection, modal (natural frequency) safety factor and fatigue analysis of this model is 

performed using ANSYS 12.0 and results were compared.  Analysis results of stress, weight, 

deflection and fatigue life of existing and mono composite leaf spring is found with a great 

difference. Mono composite leaf spring has 73.24% lesser stress, 5.3% lesser deflection, 92.9% 

weight reduction and longer fatigue life than existing leaf spring thereby increased safety factor 

is observed. Natural frequency of composite leaf is less than existing but which is greater than 

road frequency (12Hz), so that it is comfortable and resonance is also very much reduced. 

Keywords: composite leaf spring, carbon/Epoxy composite material, conventional leaf spring, 

design and analysis 



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1. INTRODUCTION 

 Leaf springs are crucial suspension element used on the vehicle to minimize the vertical 

vibrations impacts and bumps due to road irregularities and to create a comfortable ride. Leaf 

springs are widely used for automobile and rail road suspensions. The leaf spring should absorb 

or minimize the vertical vibrations and impacts due to road irregularities by means of variations 

in the spring deflection. 

To meet the needs of natural resources conservation and economize energy, weight reduction has 

been the main focus of automobile manufacturer in the present scenario. Weight reduction can be 

achieved primarily by the introduction of better material, design optimization and better 

manufacturing processes. The introduction of composite materials was made it possible to reduce 

the weight of leaf spring without any reduction on load carrying capacity and stiffness. Since ,the 

composite materials have more elastic strain energy storage capacity and high strength to weight 

ratio as compared with those of steel, multi- leaf steel spring are being replaced by mono 

composite leaf spring. The composite material offer opportunities for substantial weight saving 

but not always are cost- effective over their steel counter parts. The leaf spring should absorb the 

vertical vibrations and impacts due to road irregularities by means of variations in the spring 

deflection so that potential energy stored in spring as strain energy and then released slowly. So, 

increasing the energy storage capability of a leaf spring ensures a more compliant suspension 

system. According to the studies made, a material with maximum strength and minimum 

modulus of elasticity in the longitudinal direction is the most suitable material for a leaf spring. 

Fortunately, composite have these characteristics.  

Increasing competition and innovations in automobile sector tends to modify the existing 

products or replacing old products by new and advanced materials products. To improve the 

suspension system many modification have taken place over the time. Inventions of parabolic 

leaf spring, use of composite material for this spring are some of the latest modification in 

suspension systems. This paper is mainly focused on the implementation of composite materials 

by replacing steel in conventional leaf spring of a suspension system and analysis of composite 

material leaf spring has become essential in showing the comparative results with conventional 

leaf spring. 



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In this analysis the conventional steel leaf spring is tested for different load conditions and 

results will be compared with a virtual model of mono composite leaf spring. Leaf spring is 

modeled in CATIA V5 and imported in to ANSYS for better results. Results are compared on 

the basis of analysis reports produced by ANSYS software. 

The suspension leaf spring is one of the potential items for weight reduction in automobile as it 

accounts for ten to twenty percent of the unsprung weight. This helps in achieving the vehicle 

with improved riding qualities. Springs are designed to absorb and store energy and release it. 

Hence, the strain energy of the material becomes a major factor in designing the springs.  

 

1.1. Background of the study 

As it is known that our country is in the stage of developing automotive industry, and believed 

that the industry is playing crucial role in the development of the country. However, most of the 

existing automotive industries except some import the components of the car and assemble it. 

This will increase the initial the cost of the car and intelligence dependency will not be 

eradicated unless the company starts analyzing and designing the existing material or produce 

new alternative from other different material which is available nearby.    

Therefore, in order to improve the development of industry it is important to give emphasis 

towards replacing components which can easily produced locally having the same or more 

strength and stiffness. One of the methods to reduce the weight and cost of the car can be done 

by thoroughly analyzing and designing the existing component. This research focuses on 

replacing the conventional multi steel leaf spring with mono composite leaf spring.   

1.2. Statement of the problem  

 The ever growing of interest of problem finding and solving will bring many changes in the 

future that we think it would be impossible to improve the present technologies we are using 

every day in our life. In automotive industries also many improvements have been done so far 

and will in the future. In this study multi leaf steel leaf spring will be replaced with single 

composite leaf spring. Since multi- leaf structure creates problem such as producing squeaking 

sound, fretting corrosion thereby decreasing the fatigue life. The conventional leaf spring has 

low strength to weight ratio, this intern increases the overall weight of the car. It is well known 

that as the weight of the car increases more power is required to propel the car. This can be done 



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by burning more fuel; on the other hand it will lead to air pollution and low fuel economy. 

Therefore, the problem can be reduced a little bit by replacing steel leaf with composite material, 

since composite materials have high strength to weight ratio (light in weight and high strength) 

which makes them preferable than steel in the present days because of the counter problems 

related to increasing weight and low strength such as low fatigue life, low fuel economy and high 

emission. As long as the above problems are concerned steel has to be changed with another 

material which can reduce those problems even though it seems that steel leaf spring performs 

well. 

This work considers an existing multi steel leaf spring of pick up and mono composite leaf 

spring with upturned eye and analyzing it. This is done to replace conventional steel leaf spring 

with glass fiber/epoxy composite leaf spring and to achieve substantial weight reduction and 

increased fatigue life in the suspension system by replacing steel leaf spring with composite leaf 

spring. On this thesis, designing single composite leaf spring of pick up will be done. As we can 

see on the literature review all researchers have done their research on other different type of 

vehicle other than pick up and this will make this work unique (new) and dynamic loads will be 

done, this will add some different work load since all the parameter that will be taken will be 

different.   A virtual model of both steel and mono composite leaf spring will be created in 

CATIA Vs.  ANSYS is used for analysis by applying loads. 

This research will pave the way for automotive industries to look for composite material and 

other material that can be produced in their work shop.    

1.3. Significance of the study 

Since sufficient studies have not been done to mitigate running cost of the vehicle throughout its 

life span and environmental pollution caused by automobile emissions, intern these emission 

highly dependent on the type of the vehicle we are running, type of fuel we are using, age of the 

vehicle, and the weight of the vehicle. This study attempts new approach to reduce the weight of 

the car thereby there will be high fuel economy, low emissions and reduce cost savings due to 

importing. The study will help the company (automotive industry) at large and the public in 

particular, if the outcome of this study is implemented. The industry will maximize its profit due 

to the absence of importing steel leaf spring and customers will get an advantage on the 



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reduction of sales cost and good fuel economy. Introducing use of composite material for 

Ethiopian automotive industries for different parts of the car as it will help them save costs. 

- Economical benefit 

 Saving costs of importing steel leaf spring 

 Optimize Automotive industry usage 

 Due to weight reduction there will be low fuel consumption 

 Job opportunity  

- Environmental benefits 

 Reduce pollution  

1.4. Objectives of the study 

1.4.1 General objective 

 The general objective of this thesis work is to analyze mono composite leaf spring designed for 

light weight vehicle.   

1.4.2 Specific objective 

 To study the conventional leaf spring of Huanghai pick up 

 To develop model of leaf spring using CATIA  

 To analyze conventional leaf spring and mono composite leaf spring with ANSYS 

 To study the manufacturing processes of composite material 

1.5. Scope of the study  

This research work covers design and static and dynamic analysis of mono composite leaf 

spring for light weight vehicle and composite leaf spring having constant cross-section 

throughout its length. Variable thickness with variable width and constant thickness with 

variable width leaf spring are not considered. The data related to type of material and 

dimension of existing pick-up multi leaf spring will be modeled and analyzed subjected to 

loads as if it is on real road condition and results will be compared with that of analysis 

results of mono composite leaf spring subjected to the same load as that of  multi leaf spring. 

 



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1.6. Limitations of the study  

Problems encountered while doing this thesis work are the following: 

 In order to cope with shortage of time and resources, the study did not include transient 

analysis  

 Finding the exact dimensions of the existing leaf spring was challenging because, the 

right measuring tools by which measurements can be done is not available. 

 Getting existing leaf spring material composition was also the real problem using the 

standard instruments because the manufacturer hides from being seen and this helps them 

to keep their technology away from illegal duplication. 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 



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2. LITERATURE REVIEW 

The literature review mainly focuses on the replacement of steel spring with composite leaf 

spring made of glass fiber reinforced polymer. 

Leaf springs are used for absorbing vehicle vibrations, shocks and bump loads (induced due to 

road irregularities) by means of deflection. For the same load and shock absorbing performance, 

steel leaf spring uses excess material which makes them considerably heavy. This can be 

improved by introducing composite material in place of steel leaf spring. Studies and researches 

were carried out on the application of composite material in leaf spring. 

Amol Bhanage [1] has described design and simulation comparison of mono leaf spring using 

SAE1045-450-QT and E-Glass/Epoxy materials for automotive performance. This study 

presented comparative simulation results of E-glass epoxy mono composite leaf spring  for 

different layup as well as for different thickness conditions  and simulation results of SAE 1045- 

450- QT steel material. ANSYS software was used for simulation results. Variation in thickness 

and layup thought to have effect on stress and deflection parameter; therefore, this will be helpful 

for the researchers for selecting the proper layup and thickness of leaf spring. 

M. Raghavedra et al. [2] described modeling and analysis of laminated composite leaf spring 

under static load condition by using FEA. The dimensions of an existing mono steel leaf spring 

of a Maruti 800 passenger vehicle is taken for modeling and analysis of laminated composite 

mono leaf spring with three different composite materials namely, E-glass/Epoxy, S-lass/Epoxy 

and carbon/Epoxy. Analysis of a 3-D model has been done using ANSYS 10.0 and laminated 

composite mono leaf spring is found to have 47% lesser stress, 25%- 65% higher stiffness, 73%- 

80% weight reduction. 

Achamyeleh et al. [3] described design of single composite leaf spring for light weight vehicle. 

Reducing weight of the vehicle and increasing or maintaining the strength of their spare parts are 

considered by replacing steel leaf spring with fiber glass composite leaf spring. Dimensions of 

steel leaf spring of TATA-Ace light weight vehicle were taken and 68.14% weight reduction was 

observed for the same dimension of fiber glass composite leaf spring as that of steel leaf spring. 

V. Pozhilarasu et al. [4] performed performance comparison of conventional and composite leaf 

spring. The conventional steel leaf spring and composite leaf spring were analyzed under similar 



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conditions using ANSYS software. Leaf spring is modeled in unigraphics NX4 software and 

imported in ANSYS 11.0 to be analyzed. The result has shown that deflection and stress of steel 

leaf spring and composite leaf spring are found with great difference under the same static load 

condition. Deflection of composite leaf spring is less as compared to steel leaf spring. 

J.P. Hou et al. [5] presented the design evolution process of a composite leaf spring for freight 

rail applications. Three designs of eye end attachment for composite leaf spring are described. 

The material used is glass fiber reinforced polyester. Static testing and finite element analysis 

have been carried out to obtain the characteristics of the spring. Load deflection curves and strain 

measurement as a function of load for the three designs tested have been plotted for comparison 

with FEA predicted values. The main concern associated with the first design is the delamination 

failure at the interface of the fiber that have passed around the eye and the spring body, even 

though the design can withstand 150KN static proof load and one million cycles fatigue load. 

FEA results confirmed that there is a high inter laminar shear stress concentration in the region. 

The second design feature is an additional transverse bandage around the region prone to 

delamination. Delamination was contained but not completely prevented. The third design 

overcomes the problem by ending the fibers at the end of the eye section.   

Mouleeswaaran Senthil Kumar et al. [6] in this paper composite leaf is designed on the basis of 

fatigue failure. Theoretical equation for prediction of fatigue life is formulated using fatigue 

modulus and its degrading rate. The dimensions and numbers of leaves for both steel leaf spring 

and composite leaf spring are considered to be the same. The stress analysis is performed using 

finite element method. The element selected for analysis is solid 45 which behave like spring. 

For the fabrication of each leave the filament winding machine is used and assembled. This 

leaves together with the help of center bolt and four side clamps. The testing of steel multi leaf 

spring and composite multi leaf spring are carried out with the help of an electro hydraulic leaf 

spring test rig. Design and fatigue analysis of composite multi leaf spring are carried out using 

data analysis. It is found that composite leaf spring has 67.35% lesser stress, 64.95% higher 

stiffness and 126.98% higher natural frequency and also 68.15% weight reduction is achieved. 

Kumar Y. N. V. Santosh et. al. [36], this study focused on many advantages of composite 

structures for conventional structures because of higher specific stiffness and strength of 

composite materials. The aim of this work was to compare the conventional leaf spring with the 



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composite one in several aspects such as weight, cost, and strength and load carrying capacity. 

The objective of this work was to consider an existing automobile leaf spring model TATA sumo 

ezrr parabolic rear and to design and analyze a composite leaf spring with upturned eye without 

changing stiffness in order to replace the existing steel leaf spring with a composite leaf spring. 

In this work a leaf spring modeled in Pro/E was imported to ANSYS in IGS format and where it 

was analyzed in metaphysics using steel material (55Si2Mn90) and than by changing the 

material as composite one (E-glass/ epoxy) again analyzed. The comparison was done after 

analyzing. On comparing it was found that the deflection in the composite leaf spring almost 

equal to the conventional leaf spring and hence stiffness of both same. It was also concluded that, 

the weight reduction was achieved by using composite material and reduced by 60.48% with 

good strength and load carrying capacity of the leaf spring. 

Patunkar M. M. et. al. [37], the objective of their work was to present modeling and analysis of 

composite mono leaf spring and compares its results. In this work conventional leaf spring was 

tested for the static load conditions and the material of the conventional leaf spring was 60Si7 

(BIS). According to the same design data a virtual model was created of a composite material 

leaf spring the material E-glass/Epoxy was selected as for composite one. Leaf spring was 

modeled in Pro/E 5.0 and analyzed in ANSYS 10.0. The tested results of the conventional leaf 

spring were compared with the virtual model of the composite material leaf spring. For analyzing 

the leaf spring finite element method was used. From the comparison it was found that the 

deflection of the composite leaf spring lesser than that of the conventional leaf spring. This work 

considered leaf spring because of it contributes considerable amount of weight to the vehicle and 

needs to be strong enough. This work considered for light weight three wheeler vehicles and a 

single E-glass/epoxy leaf spring designed, simulated by following design rules of the composite 

materials and fabricated by hand lay-up method. The leaf spring was tested and analyzed for 

static load only. It was concluded that E-glass/epoxy leaf spring designed and simulated in this 

work having stresses much below the strength properties of the material satisfying the maximum 

stress failure criterion.  

Manjunath H.N checked the suitability of composite materials like E-glass/epoxy, 

graphite/epoxy, boron/aluminum, carbon/Epoxy and kevlar/epoxy for light commercial vehicle 

leaf spring. The results are compared with theoretical values and concluded that they have good 

agreement with each other. They calculated the fatigue life of various composite leaf springs 



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using Hwang and Han relation. They found that boron/aluminum and graphite/epoxy are best 

suitable composite material for leaf spring. 

2.1. Suspension system 

Suspension systems have been widely applied to vehicles, from the horse drawn carriage with 

flexible leaf springs fixed in the four corners, to the modern automobile with complex control 

algorithms. The suspension of a road vehicle is usually designed with two objectives; to isolate 

the vehicle body from road irregularities and to maintain contact of the wheels with the roadway. 

Isolation is achieved by the use of springs and dampers and by rubber mountings at the 

connections of the individual suspension components. From a system design point of view, there 

are two main categories of disturbances on a vehicle, namely road and load disturbances. Road 

disturbances have the characteristics of large magnitude in low frequency such as hills and small 

magnitude in high frequency such as road roughness. Load disturbances include the variation of 

loads induced by accelerating, braking and cornering. Therefore, a good suspension design is 

concerned with disturbance rejection from these disturbances to the outputs. Roughly speaking, a 

conventional suspension needs to be soft to insulate against road disturbances and hard to 

insulate against load disturbances. Therefore, suspension design is an art of compromise between 

these two goals. The main functions of a vehicle‟s suspension systems are to isolate the structure 

and the occupants from shocks and vibrations generated by the road surface. The suspension 

systems basically consist of all the elements that provide the connection between the tires and the 

vehicle body. The suspension system requires an elastic resistance to absorb the road shocks and 

this job is fulfilled by the suspension springs. According to Gillepsie (1992), the primary 

functions for suspension systems are; 

 Provide vertical compliance so the wheels can follow the uneven road, isolating the 

chassis   from roughness in the road. 

 Maintain the wheels in the proper steer and camber attitudes to the road surface. 

  React to the control forces produced by the tires longitudinal (acceleration and braking) 

forces lateral (cornering) forces, and braking and driving torques. 

  Resist roll of the chassis. 

 Keep the tires in contact with the road with minimal load variations 

 



10 

 

To accomplish all functions, the suspension system requires an elastic resistance to absorb the 

road shocks and this job is fulfilled by the suspension springs.  

2.1.1 Suspension springs 

 Spring is defined as an elastic machine element, which deflects under the action of the load and 

returns to its original shape when the load is removed. Mechanical springs are used in machine 

designs to exert force, provide flexibility, and to store or absorb energy. Springs are 

manufactured for many different applications such as compression, extension, torsion, power, 

and constant force. Depending on the application, spring may be in a static, cyclic or dynamic 

operating mode. A spring is usually considered to be static if a change in deflection or load 

occurs only a few times, such as less than 10,000 cycles during the expected life of the spring. A 

static spring may remain loaded for very long periods of time. The failure modes of interest for 

static springs include spring relaxation, set and creep. 

The main objectives of spring are the following: 

 To apply force: A majority industrial, e.g. To provide the operating force in brakes and 

clutches, to provide a clamping force, to provide a return load, to keep rotational 

mechanisms in contact, make electrical contacts, counterbalance loading, etc. 

 To control motion: Typically storing energy, e.g. wind up springs for motor, constant 

torque applications, torsion control, position control, etc. 

 To control vibration: used in essence for noise and vibration control, e.g. flexible 

couplings, isolation mounts, spring and dampers, etc. 

 To reduce impact: Used to reduce the magnitude of the transmitted force due to impact or 

shock loading, e.g. buffers, end stops, bump stops etc. In practical situations, springs are 

used to provide more than one of the above functions at the same time. Because of 

superior strength and endurance characteristics under load, most springs are metallic 

However, other resilient materials, e.g. polymers, where special properties such as a low 

modulus and high internal damping capacity are required.  

 



11 

 

2.1.2 Classification of spring 

 2.1.2.1 Leaf spring 

Leaf springs can serve both damping as well as springing functions. The leaf spring can either be 

attached directly to the frame at both ends or attached at one end usually the front with the other 

end attached through a shackle, a short swinging arm. The shackle takes up the tendency of the 

leaf spring to elongate when compressed and thus makes softer springiness. Failure prediction in 

large scaled structures that are subjected to extreme loading conditions has been of utmost 

interest in the scientific and engineering community over the past century [15]. Failure of 

mechanical assembly component is a common phenomenon due to fracture that occurs almost 

everywhere in mechanical structures. The main cause of failure of leaf spring is due to large 

bending behavior [16, 17]. The plate spring or leaf spring is used in which the major stresses are 

tensile and compressive. Leaf springs may be of cantilever type or semi elliptical or elliptical. A 

leaf spring consists of flat leaves or plates of varying lengths clamped together so as to obtain 

greater efficiency and resilience. The figure shows leaf spring  

 

Figure 1 leaf spring 

2.1.2.2 Cylindrical helical spring 

Fig.2 shows cylindrical helical spring which may be in compression or tension. The major 

stresses produced in this are shear due to twisting. The load applied is parallel to the axis of 

spring. The cross section of the wire may be round, square or rectangular. These springs are 

wound in the form of a helix of a wire [32]. 



12 

 

 

Figure 2 cylindrical helical spring 

 

2.1.3 Concept of spring design 

The design of a new spring involves the following considerations: 

 Space into which the spring must fit and operate 

 Values of working forces and deflections 

 Accuracy and reliability needed 

 Tolerances and permissible variations in specifications 

 Environmental conditions such as temperature, presence of a corrosive atmosphere 

 Cost and qualities needed 

The designers use these factors to select a material and specify suitable values for the width, 

thickness, the number of leaves, the eye diameter and the free length, type of ends and the spring 

rate needed to satisfy working force deflection requirements. The primary design constraints are 

that the material with selected size should be commercially available and that the stress at the 

solid length be not greater than the tensional yield strength [33, 35]. 

2.1.4 Spring materials 

One of the important considerations in spring design is the choice of the spring material. Springs 

are usually made from alloys of steel. The most common spring steels are music wire, oil 

tempered wire, chrome silicon, chrome vanadium and stainless. Other materials can also be 

formed into springs, depending on the characteristics needed. Some of the more common of 

these exotic metals include beryllium copper, phosphor bronze, Monel, and titanium. Titanium is 

the strongest material, but it is very expensive. Next come chrome vanadium and chrome silicon, 

then music wire, and then oil tempered wire.  



13 

 

Some of the common spring materials are given below. 

 Hard-drawn wire: This is cold drawn, cheapest spring steel. Normally used for low stress 

and static load. The material is not suitable at subzero temperatures or at temperatures 

above 1200 . 

 Oil-tempered wire: It is a cold drawn, quenched, tempered, and general purpose spring 

steel. It is not suitable for fatigue or sudden loads, at subzero temperatures and at 

temperatures above 1800 . 

 Chrome Vanadium: This alloy spring steel is used for high stress conditions and at high 

temperature up to 2200 . It is good for fatigue resistance and long endurance for shock 

and impact loads. 

 Chrome Silicon: This material can be used for highly stressed springs. It offers excellent 

service for long life, shock loading and for temperature up to 2500 . 

  Music wire: - This spring material is most widely used for small springs. It is the 

toughest and has highest tensile strength and can withstand repeated loading at high 

stresses. It cannot be used at subzero temperatures or at temperatures above 1200 . 

  Stainless steel: Widely used alloy spring materials. 

 Phosphor Bronze/Spring Brass: It has good corrosion resistance and electrical 

conductivity. It is commonly used for contacts in electrical switches. Spring brass can be 

used at subzero temperatures [6]. 

 

 

 

 

 

 

 

 

 

 

 

 



14 

 

The following table shows the physical properties of spring materials [35]  

Table 1 physical properties of common spring materials 

 



15 

 

 

 



16 

 

2.1.4.1Commonly used steel alloys for leaf spring 

Steel is an alloy of iron and be the major component and small amounts of carbon as the major 

alloying element. The carbon contents in steel ranges from 0.02% to 2.0% by weight. Small 

amounts generally on the order of few percent of other alloying elements such as manganese, 

silicon chromium, nickel and molybdenum may also be present, but it is the carbon content that 

turns iron into steel. Toughness and ductility are obtained by the addition of elements like 

manganese, chromium, nickel, molybdenum, tungsten, vanadium, silicon etc. Generally leaf 

springs are made of various fine grade alloy steel. The most commonly used grades of steel are: 

55si2Mn90,  55 Si 7, 60 Si Cr7, 50 Cr V4. En 45 A,65 Si 7, 55 Si Cr 7, 65 Si cr7, En 42 60 s 87 

[26].  

2.2 Theories of Failure  

Strength of machine members is based upon the mechanical properties of the materials used. 

Since these properties are usually determined from simple tension or compression tests, 

therefore, predicting failure in members subjected to uni-axial stress is both simple and straight 

forward. But the problem of predicting the failure stresses for members subjected to bi-axial or 

tri-axial stresses is much more complicated. In fact, the problem is so complicated that a large 

number of different theories have been formulated. The principal theories of failure for a 

member subjected to bi-axial stress are as follows: 

i. Maximum principal (or normal) stress theory (also known as Rankine‟s theory). 

ii. Maximum shear stress theory (also known as Guest‟s or Tresca‟s theory). 

iii.  Maximum principal (or normal) strain theory (also known as Saint Venant theory). 

iv.  Maximum strain energy theory (also known as Haigh‟s theory). 

v. Maximum distortion energy theory (also known as Hencky and Von Mises theory). 

Since ductile materials usually fail by yielding i.e. when permanent deformations occur in the 

material and brittle materials fail by fracture, therefore the limiting strength for these two classes 

of materials is normally measured by different mechanical properties. For ductile materials, the 

limiting strength is the stress at yield point as determined from simple tension test and it is, 

assumed to be equal in tension or compression. For brittle materials, the limiting strength is the 

ultimate stress in tension or compression. 

 

 



17 

 

2.2.1 Maximum Principal or Normal Stress Theory  

According to this theory, the failure or yielding occurs at a point in a member when the 

maximum principal or normal stress in a bi-axial stress system reaches the limiting strength of 

the material in a simple tension test. Since the limiting strength for ductile materials is yield 

point stress and for brittle materials (which do not have well defined yield point) the limiting 

strength is ultimate stress, therefore according to the above theory, taking factor of safety (F.S) 

into consideration, the maximum principal or normal Stress (σt1) in a bi-axial stress system is 

given by: 

   =             for ductile materials  

 Where                    = yield point stress in tension  

                            F.s = factor of safety [11] 

2.3 Composite 

 

 Composite is a structural material that consists of two or more combined constituents that are 

combined at a macroscopic level and are not soluble in each other. One constituent is called the 

reinforcing phase and the one in which it is embedded is called the matrix. The reinforcing phase 

material may be in the form of fibers, particles, or flakes. The matrix phase materials are 

generally continuous. Examples of composite include concrete reinforced with steel and epoxy 

reinforced with graphite fibers, and naturally occurring composite like wood, where the lignin 

matrix is reinforced with cellulose fibers and bones in which the bone salt plates made of 

calcium and phosphate ions reinforce soft collagen, etc.  Composites are important materials that 

are now used widely, not only in the aerospace industry, but also in a large and increasing 

number of commercial mechanical engineering applications, such as internal combustion engines 

machine components; thermal control and electronic packaging; automobile, train, and aircraft 

structures and mechanical components, such as brakes, drive shafts, flywheels, tanks, and 

pressure vessels; dimensionally stable components; process industries equipment requiring 

resistance to high temperature corrosion, oxidation, and wear. 

Israelites using bricks made of clay and reinforced with straw are an early example of application 

of composites. The individual constituents, clay and straw, could not serve the function by 

themselves but did when put together. Historical examples of composites are abundant in the 



18 

 

literature. Significant examples include the use of reinforcing mud walls in houses with bamboo 

shoots, glued laminated wood by Egyptians (1500B.C.), and laminated metals in forging swords  

(A.D. 1800). In the 20
th

 century, modern composites were used in the 1930s when glass fibers 

reinforced resins. Boats and aircraft were built out of these glass composites, commonly called 

fiberglass. Since the 1970s, application of composites has widely increased due to development 

of new fibers such as carbon, boron, and aramids, and new composite systems with matrices 

made of metals and ceramics [11, 13]  

2.3.1 Contributing factors to the mechanical performance of composite fiber 

Four fiber factors contribute to the mechanical performance of a composite are: 

 Length: - fibers can be made long or short. Long, continuous fibers are easy to orient and 

process, but short fibers cannot be controlled fully for proper orientation. Long fibers 

provide many benefits over short fibers; these include impact resistance, low shrinkage, 

improved surface finish, and dimensional stability. However, short fibers provide low 

cost, are easy to work with, and have fast cycle time fabrication procedures. Short fibers 

also have fewer flaws and therefore have higher strength. 

 Orientation: fibers oriented in one direction give very high stiffness and strength in that 

direction. If the fibers are oriented in more than one direction, such as in a mat, there will 

be high stiffness and strength in the directions of the fiber orientations. However, for the 

same volume of fibers per unit volume of the composite, it cannot match the stiffness and 

strength of unidirectional composites. 

 Shape: the most common shape of fibers is circular because handling and manufacturing 

easiness. Hexagon and square shaped fibers are possible, but their advantages of strength 

and high packing factors do not outweigh the difficulty in handling and processing. 

 Material: The material of the fiber directly influences the mechanical performance of a 

composite. Fibers are generally expected to have high elastic modules and strengths. This 

expectation and cost have been key factors in the graphite, aramids, and glass dominating 

the fiber market for composites [13] 

 

 

 

 

 



19 

 

2.3.2 Classes and Characteristics of Composite Materials 

Solid materials can be divided into four categories: polymers, metals, ceramics, and carbon, 

which we consider as a separate class because of its unique characteristics.  Both reinforcements 

and matrix materials are found in all four categories. Composites are usually classified by the 

type of material used for the matrix. The four primary categories of composites are polymer 

matrix composites (PMCs), metal matrix composites (MMCs), ceramic matrix composites 

(CMCs), and carbon/carbon composites (CCCs). 

The main types of reinforcements used in composite materials are, aligned continuous fibers, 

discontinuous fibers, whiskers (elongated single crystals), particles, and numerous forms of 

fibrous architectures produced by textile technology, such as fabrics and braids. Increasingly, 

designers are using hybrid composites that combine different types of reinforcements to achieve 

more efficiency and to reduce cost. A common way to represent fiber reinforced composites is to 

show the fiber and matrix separated by a slash. For example, carbon fiber-reinforced epoxy is 

typically written "carbon/epoxy," or, "C/Ep." Composites are strongly heterogeneous materials; 

that is, the properties of a composite vary considerably from point to point in the material, 

depending on which material phase the point is located in. Many artificial composites, especially 

those reinforced with fibers, are anisotropic which means their properties vary with direction (the 

properties of isotropic materials are the same in every direction). Many fiber-reinforced 

composites, especially PMCs, MMCs, and CCCs, do not display plastic behavior as metals do, 

which makes them more sensitive to stress concentrations. However, the absence of plastic 

deformation does not mean that composites are brittle materials like monolithic ceramics. The 

heterogeneous nature of composites results in complex failure mechanisms that impart 

toughness. Fiber reinforced materials have been found to produce durable, reliable structural 

components in countless applications. 

 

 

 

 

 

 

 



20 

 

Table 2:- types of composite materials [41] 

 

 

 

 
Figure 3:-Reinforcement forms of composite 

 

2.4.3 Comparative Properties of Composite Materials 

 

There are a large and increasing number of materials that fall in each of the four types of 

composites, making generalization difficult. However, as a class of materials, composites tend to 

have the following characteristics: 

- High strength 

- High modulus 

-  Low density 

- Excellent resistance to fatigue, creep, creep rupture, corrosion, and wear; and low 

coefficient of thermal expansion (CTE). For applications in which both mechanical 

properties and low weight are important, useful figures of merit are specific 

strength (strength divided by specific gravity or density) and specific stiffness 

(stiffness divided by specific gravity or density).  



21 

 

2.3.4 Advantages of composite materials 

 Metals and their alloys cannot always meet the demands of today‟s advanced technologies. Only 

by combining several materials one can meet the performance requirements.  Trusses and 

benches used in satellites need to be dimensionally stable in space during temperature changes 

between –256  (–160 ) and 200  (93.3 ). Metal materials cannot meet these requirements; 

this leaves composites, such as graphite/epoxy, as the only materials to satisfy them. In many 

cases, using composites is more efficient. For example, in the highly competitive airline market, 

one is continuously looking for ways to lower the overall mass of the aircraft without decreasing 

the stiffness and strength of its components. This is possible by replacing conventional metal 

alloys with composite materials. Even if the composite material costs may be higher, the 

reduction in the number of parts in an assembly and the savings in fuel costs make them more 

profitable. Reducing 0.453 kg of mass in a commercial aircraft can save up to 360 gal (1360 L) 

of fuel per year. It is known that fuel expenses accounts 25% of the total operating costs of a 

commercial airline. Composites also offer a number of significant manufacturing advantages 

over metals and ceramics. Fiber reinforced polymers and ceramics can be fabricated in large, 

complex shapes that would be difficult or impossible to make with other materials. The ability to 

fabricate complex shapes allows consolidation of parts, which reduces machining and assembly 

costs. Some processes allow fabrication of parts to their final shape (net shape) or close to their 

final shape which also produces manufacturing cost savings. The relative ease with which 

smooth shapes can be made is a significant factor in the use of composites in aircraft and other 

applications for which aerodynamic considerations are important. Generally, composites offer 

several other advantages over conventional materials. These may include improved:  

 strength 

 stiffness 

 fatigue resistance  

  impact resistance 

 thermal conductivity 

 Corrosion resistance, etc. 

 



22 

 

2.3.5 Limitations of composite materials 

 

 High cost of fabrication of composites is a critical issue. For example, a part made of 

graphite/epoxy composite may cost up to 10 to 15 times as that of conventional steel 

material costs if fact this is not true for all, there are composites which have lower cost. A 

finished graphite/epoxy composite part may cost as much as ($650 to $900 per kilogram). 

Improvements in processing and manufacturing techniques will lower these costs in the 

future. Already, manufacturing techniques such as SMC (sheet molding compound) and 

SRIM (structural reinforcement injection molding) are lowering the cost and production 

time in manufacturing automobile parts. 

 Mechanical characterization of a composite structure is more complex than that of a 

metal structure. Unlike metals, composite materials are not isotropic, that is, their 

properties are not the same in all directions. Therefore, they require more material 

parameters. For example, a single layer of a graphite/epoxy composite requires nine 

stiffness and strength constants for conducting mechanical analysis. In the case of metal 

materials such as steel, one requires only four stiffness and strength constants. Such 

complexity makes structural analysis computationally and experimentally more 

complicated and intensive. In addition, evaluation and measuring techniques of some 

composite properties, such as compressive strengths are still being debated. 

 Repair of composites is not a simple process compared to that of metals. Sometimes 

critical flaws and cracks in composite structures may go undetected. 

 Composites do not have a high combination of strength and fracture toughness compared 

to metals [13] 

2.4 REINFORCEMENTS AND MATRIX MATERIALS 

2.4.1 Reinforcements 

The four key types of reinforcements used in composites are continuous fibers, discontinuous 

fibers, whiskers (elongated single crystals) and particles continuous aligned fibers are the most 

efficient reinforcement form and are widely used, especially in high performance applications. 

However, for ease of fabrication and to achieve specific properties, such as improved through 

thickness strength, continuous fibers are converted into a wide variety of reinforcement forms 

using textile technology.  



23 

 

2.4.1.1 Fibers 

The development of fibers with unprecedented properties has been largely responsible for the 

great importance of composites and the revolutionary improvements in properties compared to 

conventional materials that they offer. The key fibers for mechanical engineering applications 

are glasses, carbons (also called graphite), several types of ceramics, and high modulus organics. 

Most fibers are produced in the form of multifilament bundles called strands or end in their 

untwisted forms, and yarns when twisted. Some fibers are produced as monofilaments, which 

generally have much larger diameters than strand filaments. Most of the key fibrous 

reinforcements are made of brittle ceramics or carbon. It is well known that the strengths of 

monolithic ceramics decrease with increasing material volume because of the increasing 

probability of finding strength limiting flaws. This is called size effect. As a result of size effect, 

fiber strength typically decreases monotonically with increasing gage length (and diameter). 

Flaw sensitivity also results in considerable strength scatter at a fixed test length. Consequently, 

there is no single value that characterizes fiber strength. 

The main functions of the fibers in a composite are: 

 To carry the load, in a structural composite 70 to 90% of the load is carried by fibers. 

 To provide stiffness, strength, thermal stability, and other structural properties in the 

composites. 

 To provide electrical conductivity or insulation, depending on the type of fiber used. 

    2.4.1.1.1 Glass Fibers 

 

Glass fibers are prepared by mixing ingredients such as silica sand, limestone, folic acid and 

other compounds. The mixture is heated to melting temperature of about 1260°C and the molten 

glass is made to pass through fine holes of platinum plate. The glass strands thus formed are 

gathered, cooled and wound. The fibers are drawn and woven into various forms to increase the 

directional strength of composite materials. Glass fibers are predominantly used fibers in 

reinforced polymers as they are economical, easy to produce, have high strength, stiffness and 

easily moldable with plastics. Different types of glass fibers like E, S, C and D, can be 

manufactured by adding varied chemicals to silica sand. Their high strength, durability, low 

dielectric constant and relatively low cost have made them very useful in automotive, submarine 

and motorboat applications [22]. 



24 

 

Glass fibers are widely used as the reinforcing material for the following reasons: 

 Inexpensive and easily available 

 Manufacturing using simple and economical method 

 Possess high tensile strength and high resistance to corrosion 

The leading types of glass fibers for mechanical engineering applications are E-glass and high 

strength (HS) glass. E-glass fibers, the first major composite reinforcement, were originally 

developed for electrical insulation application. E-glass is the most widely used of all fibrous 

reinforcements. The primary reasons for this are its low cost and early development compared to 

other fibers. The thermal and electrical conductivities of glass fibers are low, and glass fiber 

reinforced PMCs are often used as thermal and electrical insulators [13]. 

      2.4.1.1.2 Carbon Fibers 

Carbon fibers, commonly called graphite fibers in the United States, are used as reinforcements 

for polymers, metals, ceramics, and carbon. There are dozens of commercial carbon fibers, with 

a wide range of strengths and modules. As a class of reinforcements, carbon fibers are 

characterized by high stiffness, strength, low density and CTE. Fibers with tensile modules as 

high as 895 GPa (130 Msi) and with tensile strengths of 7000 MPa (1000 Ksi) are commercially 

available. Carbon fibers have excellent resistance to creep, stress rupture, fatigue and corrosive 

environments, although they oxidize at high-temperatures. Some carbon fibers also have 

extremely high thermal conductivities many times greater than that of copper. This characteristic 

is of considerable interest in electronic packaging and other applications where thermal control is 

important. Carbon fibers are the workhorse reinforcements in high performance aerospace and 

commercial PMCs and some CMCs. Of course, as the name suggests, carbon fibers are also the 

reinforcements in carbon/carbon composites. 

Most carbon fibers are highly anisotropic. Axial stiffness, tension and compression strength, and 

thermal conductivity are typically much greater than the corresponding properties in the radial 

direction. Carbon fibers generally have small, negative axial CTEs (which means, that they get 

shorter when heated) and positive radial CTEs. Diameters of common reinforcing fibers, which 

are produced in the form of multifilament bundles, range from 4-10 micrometers (160-390 

micro-inches). Carbon fiber stress-strain curves tend to be nonlinear. Modulus increases under 

increasing tensile stress and decreases under increasing compressive stress. Carbon fibers are 

made primarily from three key precursor materials: polyacrylonitrile (PAN), petroleum pitch, 



25 

 

and coal tar pitch. Rayon based fibers, once the primary CCC reinforcement, are far less 

common in new applications. Experimental fibers also have been made by chemical vapor 

deposition. Carbon fibered composites are ideally suited for applications where strength, 

chemical inertness, stiffness, weightlessness, high damping and fatigue characteristics are the 

inevitable requirements. They can also be used at elevated temperatures without many 

consequences. Their properties make it an ideal choice of reinforcing materials used in 

aerospace, automobiles, civil engineering, military and various competitive sport applications. 

Carbon fibers are used as a reinforcing material due to: 

 Good physical strength, toughness and impact resistance. 

 Good vibration damping strength, lightweight, dimensional stability 

 Low abrasion rate, low coefficient of thermal expansion. 

    2.4.1.1.3 Boron Fibers  

Boron fibers are primarily used to reinforce polymers and metals. Boron fibers are produced as 

monofilaments (single filaments) by chemical vapor deposition of boron on a tungsten wire or 

carbon filament, the former being the most widely used. They have relatively large diameters, 

100-140 micrometers (4000-5600 micro-inches), and compared to most other reinforcements.  

The properties of boron fibers are influenced by the ratio of overall fiber diameter to that of the 

tungsten core. For example, fiber specific gravity is 2.57 for 100 micrometer fibers and 2.49 for 

140 micrometer fibers. 

    2.4.1.1.4 Fibers Based on Silicon Carbide 

 Silicon carbide based fibers are primarily used to reinforce metals and ceramics. There are a 

number of commercial fibers based on silicon carbide. One type, a monofilament, is produced by 

chemical vapor deposition of high purity silicon carbide on a carbon monofilament core. Some 

versions use a carbon rich surface layer that serves as a reaction barrier. There are a number of 

multifilament silicon carbide based fibers which are made by pyrolysis of polymers. Some of 

these contain varying amounts of silicon, carbon and oxygen, titanium, nitrogen, zirconium, and 

hydrogen. 



26 

 

  2.4.1.1.5 Alumina based fibers 

 Alumina based fibers are primarily used to reinforce metals and ceramics. Like silicon carbide 

based fibers, they have a number of different chemical formulations. The primary constituents, in 

addition to alumina, are boron, silica, and zirconia. 

  2.4.1.1.6 Aramid Fibers 

Aramid, or aromatic, poly amide fibers are high-modulus organic reinforcements primarily used 

to reinforce polymers and for ballistic protection. There are a number of commercial aramid 

fibers produced by several manufacturers. Like other reinforcements, they are proprietary 

materials with different properties. 

  2.4.1.1.7 High Density Polyethylene Fibers 

High density polyethylene fibers are primarily used to reinforce polymers and for ballistic 

protection. The properties of high density polyethylene tend to decrease significantly with 

increasing temperature and they tend to creep significantly under load even at low temperatures. 

  2.4.2 Matrix Materials 

The four classes of matrix materials are polymers, metals, ceramics, and carbon. A matrix 

material fulfills several functions in a composite structure, most of which are vital to the 

satisfactory performance of the structure.  

The important functions of a matrix material include the following: 

 The matrix material binds the fibers together and transfers the load to the fibers. It 

provides rigidity and shape to the structure. 

 The matrix isolates the fibers so that individual fibers can act separately. This stops or 

slows the propagation of a crack. 

 The matrix provides good surface finish quality and aids in the production of net-shape or 

near net- shape parts. 

 Through the quality of its grip on the fibers (the interfacial bond strength), the matrix can 

also be an important means of increasing the toughness of the composite [28]. 

 The matrix provides protection to reinforcing fibers against chemical attack and 

mechanical damage [13, 22]. 

 



27 

 

2.4.2.1 Polymer Matrix Materials 

Polymer matrix composites are the most commonly used, advanced composite materials 

comprising of a fibrous material of thin diameter (e.g., fiberglass, graphite, carbon, Kevlar, boron 

etc.) reinforced into polymerized resin (e.g., epoxy, polyester etc.) to enhance the required 

properties of composites to desired levels for specific applications. Polymer matrix composites 

have widespread usage due to their low cost, high strength and simple fabrication methods. 

Polymer matrix composites are advantageous, mainly due to the following properties. 

 Possess high tensile strength, stiffness and fracture toughness 

 Possess good abrasive resistance 

The major disadvantages are: 

 Thermal resistance is low 

 Coefficient of thermal expansion is high 

Properties of polymer matrix composites are determined by properties of the fibers, orientation 

of the fibers, concentration of the fibers, stacking sequence of fibers, aspect- ratio of fibers and 

properties of the matrix [18].There are two major classes of polymers used as matrix materials: 

thermosets and thermoplastics. Thermosets are materials that undergo a curing process during 

part fabrication, after which they are rigid and cannot be reformed. Thermoplastics, on the other 

hand, can be repeatedly softened and reformed by application of heat. Thermoplastics are often 

subdivided into several types: 

- Amorphous 

- Crystalline 

-  Liquid crystal  

There are numerous types of polymers in both classes. Thermo-sets tend to be more resistant to 

solvents and corrosive environments than thermoplastics, but there are exceptions to this rule. 

Resin selection is based on design requirements, as well as manufacturing and cost 

considerations. 

 

 

 

 

 



28 

 

2.4.2.1.1 Thermosetting Resins 

The key types of thermosetting resins used in composites are epoxies, bismaleimides, 

thermosetting polyimides, cyanate esters, thermosetting polyesters, vinyl esters, and phenolics. 

Epoxies are the workhorse materials for airframe structures and other aerospace applications, 

with decades of successful flight experience to their credit. They produce composites with 

excellent structural properties. Epoxies tend to be rather brittle materials, but toughened 

formulations with greatly improved impact resistance are available. The maximum service 

temperature is affected by reduced elevated temperature structural properties resulting from 

water absorption. A typical airframe limit is about 1200  (2500 ) [13, 41]. 

 

Table 3:- properties of matrix materials
 
[41] 

 

2.4.2.1.2 Thermoplastic Resins 

Thermoplastics are divided into three main classes: amorphous, crystalline, and liquid crystal. 

Polycarbonate, acrylonitrile-butadiene-styrene (ABS), polystyrene, polysulfone, and 

polyetherimide are amorphous materials. Crystalline thermoplastics include nylon, polyethylene, 

polyphenylene sulfide, polypropylene, acetal, polyethersulfone, and polyether etherketone. 

Amorphous thermoplastics tend to have poor solvent resistance. Crystalline materials tend to be 

better in this respect. Relatively inexpensive thermoplastics such as nylon are extensively used 

with chopped E-glass fiber reinforcements in countless injection molded parts. There are many 

numbers of applications using continuous fiber reinforced thermoplastics. 

2.5 Material selections 

Selection of the suitable material is a key aspect. Materials of the leaf spring consist of nearly 

60%-70% of the unsprung weight. Even a small amount in weight reduction of the vehicle, may 

have a wider economic impact. Composite materials are proved as suitable substitutes for steel in 



29 

 

connection with weight reduction of the vehicle. The material which is capable of storing more 

energy in the form of elastic strain would be preferred for leaf spring. 

Specific elastic energy is given by: 

                                                                                                                                   (2.5) 

                            Where   is the allowable stress,                  E is elastic modulus  

Composite materials have higher strain energy (energy storing capacity) as compared with 

metals because of their lower elastic modulus and low density. Hence, the composite materials 

can be selected for leaf spring design. Fiber reinforced polymer (FRP) composite materials 

consisting of fibers of high strength and modulus embedded in or bonded to resins with distinct 

interfaces between them. In general, fibers are the principal load carrying members, while the 

surrounding resins keep them in preferred location and orientation. [23] The commonly used 

fibers are carbon, glass, keviar, etc. Among these, glass fiber has been selected based on the cost 

factor and strength. The types of glass fibers are C-glass, D-glass, S-glass and E-glass. The C-

glass fiber is designed to give improved surface finish. D-glass is used when permeability to 

electromagnet wave is required. S-glass fiber is design to give very high modular, which is used 

particularly in aeronautic industries [19]. The material composition selected for mono composite 

leaf spring are E-glass, Epoxy resin, in which E-glass as fiber material because of which is used 

as standard reinforcement fiber for almost all the present systems well complying with 

mechanical property requirements and low cost. Thus, E-glass fiber is suitable for this 

application and the selected glass fiber is unidirectional with diameter of fiber is 0.0074mm, 204 

filaments per strand and average thickness of 2.1mm. A mono leaf E-glass epoxy has been used 

to replace a five leaf steel spring. In the selection of matrix material epoxy which is used to 

control the interleaf shear strength of laminate. Epoxy is in combination with hardener which 

cures, faster into hard resin at room temperature and is characterized by good mechanical 

properties and good chemical resistance properties. 

2.6 Layup selection 

 The stored energy in a leaf spring varies directly with the square of maximum allowable stress 

and inversely with the modulus of elasticity both in the longitudinal direction. Composite 

materials like the E-glass/epoxy in the direction of fibers have good characteristics for storing 



30 

 

strain energy. So, the layup is selected to be unidirectional along the longitudinal direction of the 

spring. The unidirectional layup may weaken the spring at the mechanical joint area and require 

strengthening the spring in this region [23]. 

 2.7 Resin selection  

In a fiber reinforced plastics (FRP) leaf spring, the Inter laminar shear strengths are controlled by 

the matrix system used; since these are reinforcement fibers in the thickness direction fiber do 

not influences inter laminar shear strength.  Therefore, the matrix should have good inter laminar 

shear strength characteristics compatibility to the selected reinforcement fiber. Many thermo-set 

resins such as polyester, vinyl ester, and Epoxy resins are being used for fiber reinforcement 

fabrication. Among these resin systems, epoxies show better inter laminar shear strength and 

good mechanical properties as shown in table 4 bellow. Hence, epoxide is found to be the best 

resins that would suit this application. Different grades of epoxy resins and hardener 

combinations are classified, based on the mechanical properties [19]. 

 

Table 4:-Mechanical propreties of epoxy resin 

Properties Values 

Tensile modulus(GPa) 3.53 

Poisson‟s ratio 0.347 

Compressive modulus (GPa) 2.98 

Shear modulus (GPa) 0.99 

0.2% offset tensile yield stress (MPa) 41.0 

Ultimate tensile strength (MPa) 76.3 

Ultimate tensile strain (%) 4.2 

0.2% offset compressive yield stress (MPa) -64.7 

Ultimate compressive strength (MPa) -91.0 

Ultimate compressive strain (%) -5.38 

0.2% offset shear stress (MPa) 26.1 

Shear stress at 5% strain (MPa) 37.7 

 

 

 



31 

 

2.8 Manufacturing Process Selection 

Apart from the selection of material and design procedure, the selection of manufacturing 

process also determines the quality and cost of the product. Hence, the composite leaf spring 

manufacturing process should fulfill the following criteria. 

 The process should be amenable to mass production. 

 The process should be capable of producing continuous reinforcement fiber 

A number of processes have been developed to produce and shape the fiber reinforced 

composites. Variations are based primarily on the orientation of the fibers, the length of 

continuous filaments and the property of the final product. Each seeks to embed the fibers in a 

selected matrix with the proper alignment is necessary to produce the desired properties. 

Discontinuous fibers can be combined with a matrix to produce either a random or preferred 

orientation. Continuous fibers are normally aligned in a unidirectional fashion in rods or tapes, 

woven into fabric layers. 

There are different types of manufacturing processes: 

 Hand Layup 

 Prepreg forming 

 Pressure molding 

 Vacuum bagging 

 Filament winding 

 Pultrusion  

 Spray method 

 Sheet molding 

 Bulk molding 

 Resin transfer molding 

2.8.1 Hand Lay-up Technique 

 

The hand layup is one of the oldest and most commonly used methods to manufacture the 

composite. The work is carried out in a female mold polished with gel coat on the inside surface. 

Having the required materials and setting up the mold at a convenient working height in the 

workshop, the following procedure is adopted: 



32 

 

 Wash the mould carefully with warm water and soft soap to remove dust, grease, finger 

marks, etc. 

 Dry the mould thoroughly. 

 Check the mould surface for chips or blemishes. These should be repaired by filling with 

polyester filler and cutting back with wet/dry paper. The odd small chip can be 

temporarily repaired by filling with filler material. 

 If the mold surface is in good condition the mold release wax is now applied, using a 

small piece of cloth. Three coats of wax are sufficient for a mould surface which has been 

previously used but a new mold surface will require at least six applications. Care must 

be taken to remove all streaks of wax. Make sure that the wax is polished and not 

removed by aggressive buffing. Failure to take care at this stage can result in stick up.  

 Cut the glass fiber to the desired length, so that they can be deposited on mold layer by 

layer during fabrication. 

 Prepare the solution of resin and place the first layer of glass fiber chopped mat on mould 

followed by epoxy resin solution over material. 

 Wait for 5-10 minutes; repeat the procedure till the desired thickness is obtained. Finally 

remove the composite material from the mould. 

 

Figu  re 4:- Fabrication procedure of composite 

Advantages:  

 low cost tools (low production cost) 

 versatile wide range of products 

 

 



33 

 

Disadvantages:  

 time consuming 

 easy to form air bubbles and disorientation of fibers 

 inconsistency 

2.9 Manufacturing composite leaf spring 

 Hand layup process mostly used in the case of continuous fiber reinforced composite. Layers of 

unidirectional or woven composite are combined to result in a material exhibiting desirable 

properties in one or more directions. Each layers oriented to achieve the maximum utilization of 

its properties. Layers of different material (different fiber in different directions) can be 

combined to further enhance the overall performance of the laminated composite material. 

Plywood mold is prepared with required dimensions of leaf spring. Wax polish (Manson) is 

applied on to the mold surface with the help of cloth for better surface finish and for easy 

removal of leaf spring after curing.  Resins are impregnated by hand into fibers, which are in the 

form of woven, knitted, stitched or bonded fabrics. This is usually accomplished by rollers or 

brushes, with an increase use of nip roller type impregnators for forcing resin into fabrics by 

means of rotating rollers and a bath of resin. Number of layers of E-glass, and epoxy are 

laminated simultaneously for required thickness of leaf spring. Finally, laminates are left to cure 

under standard atmospheric conditions for 24 hours before removal [29]. 

 

 

 

 

 

 

 



34 

 

 3. BETTER MATERIALS AND METHODS  

3.1 Methodology and software used 

 3D Modeling using CATIA V5 

 Analytical Calculations    

  3D Finite Element Meshing 

  Structural finite element analysis in ANSYS 12 (static and dynamic)  

  Comparing results and discussion  

3.1.1 CATIA 

CATIA (Computer Aided Three Dimensional Interactive Application) is multi- platform 

CAD/CAM/CAE commercial software, written in the C++ programming language which is used 

to model different structures [25]. 

3.1.2 ANSYS 

 ANSYS is being used by designers across a broad spectrum of industries such as aerospace, 

automotive, manufacturing, nuclear, electronics, biomedical, and many more. ANSYS provides 

simulation solutions that enable designers to simulate design performance directly on desktop. In this 

way, it provides fast, efficient and cost effective product development from design concept stage to 

performance validation stage of the product development cycle.  ANSYS package help to accelerate 

and streamline the product development process by helping designers to resolve issues related to 

structural deformation, heat transfer, fluid flow, electromagnetic effects, a combination of these 

phenomena acting together, and so on [25,26]. 

3.2 Huanghai pickup DD1022T model specification 

Figure 5 shows huanghai pick up on which this study is carried out. The rear leaf spring is taken 

to be analyzed, which have five leaves made of 55siMn90 (steel alloy). All the necessary 

parameters required for design and analysis is taken from its manual and also by measuring 

directly. It has two full length leaves and three graduated leaves connected with center bolt and 

with clips. 



35 

 

 

Figure 5:- Huanghai pick up 

Table 5:- Huanghai pickup DD1022T model specification 

Parameter Value (mm) 

length 5350 

width 1725 

wheelbase 3380 

Height 1690 

Height of c.g 300 

Total mass of the 

vehicle (kg) 

2495 

 

 Total or curb weight of the car  

                                                                                taking gravity (            

            Total weight (     

                    

                   =                   =           the total force experienced by four springs 

Force on one of the rear leaf spring is  
       

 
           this is the maximum force exerted at 

static condition at the center of the leaf spring. Force at the two ends of leaf spring is half of the 

force at the center   
 

 
 

    

 
          



36 

 

3.3 Construction of existing steel Leaf spring 

Leaf springs are built with a number of leaves or plates, having initial curvature or cambered 

which is the amount of bend that is given to the spring from the center line passing through the 

eyes, so that they will tend to straighten under the load and even at maximum load the deflected 

spring should not touch other vehicle part to which it is attached. The leaves are held together by 

means of a band shrunk around them at the center or by a bolt passing through the center. The 

longest leaf known as main leaf or master leaf has its ends formed in the shape of an eye through 

which the bolts are passed to secure the spring to its supports. Usually the eyes, through which 

the spring is attached to the shackle is provided with bushings of some antifriction material such 

as bronze or rubber. The other leaves of the spring are known as graduated leaves. Since the 

master leaf has to with stand vertical bending loads as well as loads due to sideways of the 

vehicle and twisting, therefore due to the presence of stresses caused by these loads, it is usual 

provided two full length leaves. Rebound clips are located at intermediate positions in the length 

of the spring so that the graduated leaves also share the stresses induced in the full length leaves 

when the spring rebounds. The value of width of leaf spring sometimes is too large to 

accommodate in the space provided in the vehicle. One practice is that instead of keeping this 

large width one can make several slices and put the pieces together as a laminate [24].  

3.3.1 Modeling existing steel leaf spring (CAD Modeling) 

Development of a leaf spring is a long process which requires number of tests to validate the 

design and manufacturing variable.  Computer aided engineering (CAE) is used to shorten this 

development thereby reducing the tests. CAE tools are widely used in the automotive industries; 

because of it enable them to reduce product development cost and time while improving safety, 

comfort and durability of the vehicles. Computer model of parabolic leaf spring of existing multi 

leaf spring is produced as exact replica of the physical specimen. Existing multi leaf spring and 

designed mono parabolic leaf spring is modeled in CATIA V5 in part design. The computer 

model is shown in figure 6 below based on the measured values. 



37 

 

 

 

Figure 6:- existing steel leaf spring CATIA model 

3.3.2 Existing steel leaf spring dimensions 

Table 6:- existing steel leaf spring measured dimensions 

No. Length Radius of 

curvature(mm) 

Width(mm) Thickness

(mm) 

First leaf  115cm 160  62 8.5 

Second leaf 115cm 168.5 62 8.5 

Third leaf 89cm 177 mm 62 8.5 

Forth leaf 75cm 185.5 mm 62 8.5 

Fifth leaf 39cm 194 mm 62 8.5 

camber 160mm 

 Graduated leaves 3 

 Full length leaves 2 

 



38 

 

3.3.3 Existing steel leaf spring material specification 

The basic requirements of a leaf spring steel is that the selected grade of steel must have 

sufficient harden- ability for the size involved to ensure a full reliable structure throughout the 

entire leaf section. In general terms higher alloy content is mandatory to ensure adequate harden-

ability when the thick leaf sections are used. The material used for the conventional steel leaf 

spring is 55Si2Mn90 and its property is shown in the table 7. 

 

Table 7:- Mechanical properties of 55SiMn90 

Parameter Value 

Material selected - steel 55si2Mn90 

Tensile yield strength 1500 MPa 

Tensile strength ultimate  1962 MPa 

Young‟s modulus(E) 210 GPa 

Poisson‟s ratio 0.3 

Density  7850 Kg/m
3
 

Thermal Expansion  11 10
-6   

 

Table 8:- Composition of 55si2Mn90 [24] 

Grade C Si Mn Cr Mo P S 

55Si2Mn90 0.55 1.74 0.87 0.1 0.02 0.05 0.05 

 

3.4 STATIC ANALYSIS OF EXISTING STEEL LEAF SPRING 

3.4.1 Analytical calculation  

The analytical formulation for a problem involves reference to the empirical and pure 

Engineering practices for arriving at a solution. Typically, empirical formulae that are 

historically developed for the application can offer a solution for the given problem. Considering 

the leaf spring as double cantilever beam, load is applied on free end as shown in the figure 7 

below.  

 



39 

 

                                                              

                                                                                                  = 
 

 
 

    

 
          

                      A                                                                B 

Figure 7:- free body diagram for cantilever beam with load at the free end 

Maximum bending moment at A is: 

                              M =                                                                                                          (3.4.1) 

Moment of inertia of rectangular section is given by: 

                              
   

  
                                                                                                         (3.4.2) 

Using equation 
 

 
 

 

 
 and substituting the values of bending moment and moment of inertia [11] 

                         
  

   

  

 
    

 

 

                                           where,       is the distance from center 

                          (
   

 

(
   

  
)
) = 

   

    

The stress in   number of leaves is given by [11]: 

             Maximum Stress (σmax) = 
     

                                                                                      (3.4.3)
 

The maximum stress (σmax) for the leaf spring having the following length, width and thickness 

can be calculated by substituting its values in equation (3.4.3) above.
 

                                 
            

 
       

    

 
        ,     ,                  

                                     
   

          

                                        
              

                       
 

                             σmax  = 4.7 10
8      



40 

 

 Moment of inertia 

                           I = bt
3
/12 

                             
       (        )

  

 

                             = 3,172.9 mm
4
 

     Elastic strain  

                                                                                                                                        (3.4.4) 

                            =     
   

   
      

                            = 0.00223 

Deflection of steel leaf spring during static load condition  

 Maximum deflection for a cantilever beam of concentrated load at the free end is given by [11]: 

                           for a leaf spring which have „n‟ number of leaves  which 

                                     have graduated leaves (                          would be [11]: 

                 = 12 pl
3 Ebt

3
 (       )                                                                                   (3.4.5) 

Taking the values of length, width, thickness, number of graduate and number of full length 

leaves from table 3.3.2 and substituting it in to equation 3.4.5 will give: 

                =                                               

                 = 72.7mm 

Mass of the existing steel leaf spring 

The mass of bolt, spring clip with bolt, mass of two leaf spring eyes are not included and the leaf 

spring is considered as straight beam even though it has parabolic shape [12]. 

                          



41 

 

                          m =  v                                                                                                           (3.4.6)                          

                                  where v is volume and   is density of the material 

                              = 7800 Kg/m
3
 

                           V =           = 5 62 1150 8.5 10
-9

/2 = 0.0015 m
3
 

                           m = 7800 Kg/ m
3 0.0015 m

3
 

                               = 11.8 Kg 

The following can be also used to find the total mass of leaf spring. 

First leaf volume =                       

                                       = 606,050 mm
3
 = 0.00060605 m

3
 

Second leaf volume =                        

                                           = 0.00060605    

Third leaf volume =                      

                                       =               

Forth leaf volume                      

                                                   

Fifth leaf volume                      

                                   = 0.00020555    

   Total volume of leaves