DESIGN AND ANALYSIS OF COMPOSITE LEAF SPRING

Transcription

1 DESIGN AND ANALYSIS OF COMPOSITE LEAF SPRING JIGNESH R. PATEL (M10CAD09) DEPARTMENT OF MECHANICAL ENGINEERING U. V. PATEL COLLEGE OF ENGINEERING GANPAT UNIVERSITY KHERVA, MEHSANA

2 DESIGN AND ANALYSIS OF COMPOSITE LEAF SPRING A DISSERTATION SUBMITTED TO U.V. PATEL COLLEGE OF ENGINEERING GANPAT UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF TECHNOLOGY IN MECHANICAL ENGINEERING WITH SPECIALIZATION IN COMPUTER AIDED DESIGN / COMPUTER AIDED MANUFACTURING SUBMITTED BY JIGNESH R. PATEL (ENROLLMENT NO ) (ROLL NO. M10CAD09) UNDER THE GUIDANCE OF PROF U. J. PATEL FEBRUARY DEPARTMENT OF MECHANICAL ENGINEERING U. V. PATEL COLLEGE OF ENGINEERING GANPAT UNIVERSITY KHERVA, MEHSANA i

3 Department of Mechanical Engineering U.V. Patel College of Engineering Ganpat University Kherva, Mehsana Certificate This is to certify that the work presented in the Dissertation Entitled DESIGN AND ANALYSIS OF COMPOSITE LEAF SPRING Has been carried out by JIGNESH R. PATEL (Enrollment No ) In a manner sufficiently satisfactory to warrant its acceptance as a partial fulfillment of the requirement for the award of the Degree of MASTER OF TECHNOLOGY IN MECHANICAL ENGINEERING WITH SPECIALIZATION IN COMPUTER AIDED DESIGN / COMPUTER AIDED MANUFACTURING This is a bonafide work done by the student and has not been submitted to any other university / Institute for the award of any other Degree. Prof. U. J. Patel Guide, Assistant Professor, U. V. Patel College of Engineering Prof. V. B. Patel Dr. P. H. SHAH Associate Professor and Head, Principal, Mechanical Engg. Department, U. V. Patel College of Engg, U. V. Patel College of Engg. Ganpat University, Kherva. ii

4 Department of Mechanical Engineering U.V. Patel College of Engineering Ganpat University Kherva, Mehsana Certificate of Examination This is to certify that we have examined the thesis entitled DESIGN AND ANALYSIS OF COMPOSITE LEAF SPRING submitted by Mr. JIGNESH R. PATEL (M10CAD09), a postgraduate student of Mechanical Engineering with specialization in COMPUTER AIDED DESIGN / COMPUTER AIDED MANUFACTURING. We hereby accord our approval of it as a study carried out and presented in manner required for its acceptance in partial fulfillment for the Post Graduate Degree for which it has been submitted. This approval does not necessarily endorse or accept every statement made, opinion expressed or conclusion drawn as recorded in this thesis. It only signifies the acceptance of the thesis for the purpose for which it is submitted. External Examiner Internal Examiner iii

5 ACNOWLEDGEMENT Successful completion of work will never be one man s task. It requires hard work in right direction. There are many who have helped to make my experience as a student a rewarding one. In particular, I express my gratitude and deep regards to my guide Prof. U.J. PATEL for kindly providing me to work under his supervision and guidance. I extend my deep sense of indebtedness and gratitude to him first for his valuable guidance, constant encouragement & kind co-operation throughout period of work which has been instrumental in the success of thesis. I also express my sincere gratitude to Prof. V.B. PATEL, Head of the Department, Mechanical Engineering, for providing valuable departmental facilities. In the end, I wish to express my deep sense of gratitude to my family, for supporting and encouraging me at every step of my work. It is power of their blessings, which has given me the courage, confidence and zeal for hard work. Last but not the least, my sincere thanks to all my friends for their patronage. JIGNESH R. PATEL (M10CAD09) iv

6 ABSTRACT In now a day the fuel efficiency and emission gas regulation of automobiles are two important issues. To fulfill this problem the automobile industries are trying to make new vehicle which can provide high efficiency with low cost. The best way to increase the fuel efficiency is to reduce the weight of the automobile. The weight reduction can be achieved primarily by the introduction of better material, design optimization and better manufacturing processes. The achievement of weight reduction with adequate improvement of mechanical properties has made composite a very good replacement material for conventional steel. The automobile vehicles have number of parts which can be able to replace by composite material, but due to the improvement of mechanical properties of composite material. It has more elastic strength and high strength to weight ratio has compared with those of steel material. So, out of many components one of the components of automobile, the leaf spring which use for carried out the whole weight of the vehicle is best option for replacement of steel material by composite material. For reduce the weight of leaf spring the analysis was carried out on the model of Force Motors Trax Cruiser s leaf spring with same dimensional geometry. The material select for leaf spring are E-glass/epoxy, Carbon epoxy and Graphite epoxy composite material which is more economical with similar mechanical and geometrical properties to the steel leaf spring. The analysis was carried out on ANSYS 12.1 with same loading condition for deflection and bending stress of steel as well as E-glass/epoxy, Carbon epoxy and Graphite epoxy composite material. From the static analysis results it is found that there is a maximum displacement of mm in the steel leaf spring and the corresponding displacements in E-glass/epoxy, Carbon epoxy and Graphite epoxy are mm, mm and mm, also the vonmises stress in the steel leaf spring is found MPa and in E-glass/epoxy, Carbon epoxy and Graphite epoxy are MPa, MPa and MPa respectively. All three composite leaf springs have lower displacements and stresses than that of existing steel leaf spring. A comparative study has been made between steel and composite leaf spring with respect to strength and weight. Composite leaf spring reduces the weight by 74.54% for E-glass/epoxy, 79.66% for Carbon epoxy and 79.77% for Graphite epoxy over steel leaf spring. The size optimization has been carried out for further mass reduction of composite leaf spring. Composite leaf spring reduces the weight by 78.21% for E-glass/epoxy, 82.56% for Carbon epoxy and 82.67% for Graphite epoxy compared to steel leaf spring. v

7 CONTENTS Title Title page Certificate Acknowledgement Abstract Contents List of table List of figure Nomenclature 1. INTRODUCTION Introduction Types of spring Leaf spring Construction of leaf spring Standard sizes of suspension leaf spring Applications of leaf spring Characteristics of leaf spring Material for leaf spring Manufacturing of leaf spring Why a composite? LITERATURE REVIEW DESIGN CALCULATION OF LEAF SPRING MODELING AND ANALYSIS OF STEEL LEAF SPRING Introduction of solid works Modeling of leaf spring Introduction of ANSYS Static analysis of steel leaf spring 34 Page No. 4.5 Result analysis of steel leaf spring ANALYSIS OF COMPOSITE LEAF SPRING 41 i ii iv v vi viii ix xi vi

8 5.1 Static analysis of composite leaf spring Result analysis of composite leaf spring Comparison of steel and composite leaf spring analysis data SIZE OPTIMIZATION Continues optimization problem Procedure for size optimization Before optimization After optimization Comparison of result before and after optimization CONCLUSION FUTURE SCOPE 63 REFERENCES 65 vii

9 LIST OF TABLE Table No. Description Page No. 4.1 Properties of steel material Comparison of analytical and analysis result for steel leaf spring Properties of composite material Comparison of analysis results for steel and composite leaf spring Comparison of before and after optimization result 60 viii

10 LIST OF FIGURE Figure No. Description Page No. 1.1 Flat spring cantilever type (a) Cross-section of plate, (b) Bending stress diagram, 4 (c) Shear stress diagram 1.3 Flat spring simply supported beam type Flat spring simply supported beam type Laminated leaf spring Semi-elliptical leaf spring Sketch of master leaf D model of master leaf D model of leaf spring Define materials in ANSYS Workbench Assign materials to leaf spring Define contact between leaves of leaf spring Meshed model of leaf spring Define force Define displacements constrain at one end Define displacements constrain at another end Von mises stress contour Maximum deflection contours Define materials in ANSYS Workbench Apply materials at each leaf of leaf spring Define contact between each leaf of leaf spring Meshed model of leaf spring Define force Define displacements constrain at one end Define displacements constrain at another end Von mises stress of E-glass/epoxy leaf spring Von mises stress of Carbon epoxy leaf spring 47 ix

11 5.10 Von mises stress of Graphite epoxy leaf spring Maximum deflection of E-glass/epoxy leaf spring Maximum deflection of Carbon epoxy leaf spring Maximum deflection of Graphite epoxy leaf spring Before optimization von mises stress of E-glass/epoxy leaf spring Before optimization von mises stress of Carbon epoxy leaf spring Before optimization von mises stress of Graphite epoxy leaf spring Before optimization maximum deflection of E-glass/epoxy 55 leaf spring 6.5 Before optimization maximum deflection of Carbon epoxy 56 leaf spring 6.6 Before optimization maximum deflection of Graphite epoxy 56 leaf spring 6.7 After optimization von mises stress of E-glass/epoxy leaf spring After optimization von misses stress of Carbon epoxy leaf spring After optimization von mises stress of Graphite epoxy leaf spring After optimization maximum deflection of E-glass/epoxy 58 leaf spring 6.11 After optimization maximum deflection of Carbon epoxy 59 leaf spring 6.12 After optimization maximum deflection of Graphite epoxy 59 leaf spring x

12 NOMENCLATURE U : Strain energy : Stress : Density : Young s modulus n f : No. of full length leaves n g : No. of graduated leaves t : Thickness of leaf b : Width of the leaf spring : Tensile strength t : Yield strength y W : Load on the spring b : Bending stress y : Deflection of the spring p b : Bearing pressure of the eye l : Length of the pin p M : Bending moment on the pin Z : Modulus of section of the pin d : Internal diameter of the eye : Shear stress l : Ineffective length of the leaf spring L : Effective length of the leaf spring R : Radius to which the leaves should be initially bent y : Camber of the spring mm : Millimeter N : Newton Kg : Kilogram xi

13 Kgf : Kilogram force MPa : Mega Pascal BHN : Brinell hardness number Ex : Tensile modulus along X-direction Ey : Tensile modulus along Y-direction Ez : Tensile modulus along Z-direction Gxy : Shear modulus along XY-direction Gyz : Shear modulus along YZ-direction Gzx : Shear modulus along ZX-direction PR XY : Poisson ratio along XY-direction PR YZ : Poisson ratio along YZ-direction PR ZX : Poisson ratio along ZX-direction xii

14 CHAPTER: 1 INTRODUCTION 1

15 1.1 INTRODUCTION CHAPTER: 1 INTRODUCTION In now a day the fuel efficiency and emission gas regulation of automobiles are two important issues. To fulfill this problem the automobile industries are trying to make new vehicle which can provide high efficiency with low cost. The best way to increase the fuel efficiency is to reduce the weight of the automobile. The weight reduction can be achieved primarily by the introduction of better material, design optimization and better manufacturing processes. The achievement of weight reduction with adequate improvement of mechanical properties has made composite a very good replacement material for conventional steel. In automobile car out of many components one of the components of automobile which can be easily replaced is leaf spring. A leaf spring is a simple form of spring, commonly used for the suspension in wheeled vehicles. The suspension of leaf spring is the area which needs to focus to improve the suspensions of the vehicle for comfort ride. The suspension leaf spring is one of the potential items for weight reduction in automobile as it accounts for 10 to 20% of unsprung weight. It is well known that springs are designed to absorb shocks. So the strain energy of the material becomes a major factor in designing the springs. The introduction of composite material will make it possible to reduce the weight of the leaf spring without reduction in load carrying capacity and stiffness. Since the composite material have high strength to weight ratio and have more elastic strain energy storage capacity as compared with steel. The relationship of specific strain energy can be expressed as 2 1 U 2 (1.1) It can be easily observed that material having lower density and modulus will have a greater specific strain energy capacity. Thus composite material offer high strength and light weight. In this work, leaf springs of automobile vehicle are force India cruiser passenger car is considers for further investigation. The suspension quality can be improved by minimizing the vertical vibrations, impacts and bumps due to road irregularities which create the comfortable ride. 2

16 The automobile sector is introducing a number of cars which are newly designed, modified with replacing new parts with advanced and composite material for better comfort ride, low weight and having better mechanical properties. India is a country with more than one billion people, require vehicle to move anywhere around the country for their personal and transportation purpose. We have personally seen and observed that vehicle having no smoothed suspension or comfort ride create the tiredness to the people and more especially to drivers of car who is the life of passenger. Also, now days so many passenger cars available in the state of Gujarat which can especially used in local transport around 200 to 300 km, a day with overloading of passengers which increase the total weight of the vehicle and also increase the fuel consumption which leads to noise and breakage problem in the suspension of leaf springs and create the pollution in the environment. So for further analysis to increase fuel efficiency and to reduce the pollution the commercial vehicle Force Motors Trax Cruiser is consider. 1.2 TYPES OF SPRING 1) Helical springs 2) Conical and volute springs 3) Torsion springs 4) Disc or bellevile springs 5) Special purpose springs 6) Laminated or leaf springs 1.3 LEAF SPRING A spring is defined as an elastic body, whose function is to distort when loaded and to recover its original shape when the load is removed. Springs are elastic bodies that can be twisted, pulled or stretched by some force. They can return to their original shape when the force is released. Leaf spring (also known as flat springs) is made out of flat plate. The advantage in leaf spring over helical spring is that the ends of the spring may be guided along a definite path as it deflects to act as a structural member in addition the energy absorbing device. Thus the leaf springs may carry lateral loads, brake torque, driving torque etc., in addition to shocks. Single plate fixed at one end and loaded at the other end as shown in figure 1.1. This plate may be used as a flat spring. 3

17 Figure 1.1 Flat spring cantilever type The bending stress & deflection of this flat plate is calculated using following equation. Bending stress in spring : Deflection of spring : b y 6W L 2 b t WL (1.2) 3 3 b t (1.3) In the bending moment, top fiber will be in tension and bottom fibers in compression, but the shear stress is zero at the extreme fibers and maximum at the center. Bending stress zero at the centre where shear stress maximum at the center as shown in figure 1.2. Figure 1.2 (a) Cross-section of plate (b) Bending stress (c) Shear stress diagram 4

18 If the spring is consider as simply supported beam the length is 2L and load 2W as shown in figure 1.3. The bending stress & deflection of this at plate is calculated using following equation. Bending stress in spring : Deflection of spring : Figure 1.3 Flat spring simply supported beam type b y 6W L 2 b t WL (1.4) 3 3 b t (1.5) If the spring having n-strips and it is consider as cantilever beam having width b and thickness t as shown in figure 1.4. The bending stress & deflection of this type of spring is calculated using following equation. Figure 1.4 Flat spring simply supported beam type 5

19 Bending stress in spring : Deflection of spring : b 6W L 2 n bt 3 WL y n b t 3 (1.6) (1.7) The above relations give the stress and deflection of a spring of uniform cross section. The stress at such a spring is maximum at the support. If the spring having triangular plate as shown in figure 1.5 (a), the stress will be uniform throughout. If this triangle plate is cut into strips of uniform width and placed one below the other as shown figure 1.5 (b) to form a graduated or laminated leaf spring, then The bending stress & deflection of this at plate is calculated using following equation. Bending stress of leaf spring : Deflection of spring : Figure 1.5 Laminated leaf spring b 6W L 2 n bt (1.8) (1.9) 3 WL y n b t 3 6

20 1.4 CONSTRUCTION OF LEAF SPRING A leaf spring commonly used in automobiles is of semi-elliptical form as shown in figure 1.6. It is built up of a number of plates (known as leaves). The leaves are usually given an initial curvature or cambered so that they will tend to straighten under the load. The leaves are held together by means of a band shrunk around them at the centre or by a bolt passing through the centre. Since the band exerts stiffening and strengthening effect, therefore the effective length of the spring for bending will be overall length of the spring minus width of band. In case of a centre bolt, two-third distance between centers of U-bolt should be subtracted from the overall length of the spring in order to find effective length. The spring is clamped to the axle housing by means of U-bolts. Figure 1.6 Semi elliptical leaf spring 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 hanger or shackle, are provided with bushings of some antifriction material such as bronze or rubber. The other leaves of the spring are known as graduated leaves. In order to prevent digging in the adjacent leaves, the ends of the 7

21 graduated leaves are trimmed in various forms as shown in figure 1.6. 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 to provide two full length leaves and the rest graduated leaves as shown in figure 1.6. 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. 1.5 STANDARD SIZES OF SUSPENSION LEAF SPRING Standard nominal widths are: 32,40,45,55,60,65,70,75,80,90,100 and 125 mm. Standard nominal thickness are: 3.2,4.5,5,6,6.5,7,7.5,8,9,10,11,12,14 and 16 mm. At the eye, the following bore diameter are recommended: 19,20,22,23,25,27,28, 30,32,35,38,50,55 mm. 1.6 APPLICATIONS OF LEAF SPRING To cushion, absorb or control energy due to either shock or vibration as in car springs, railway buffers, air-craft landing gears, shock absorbers and vibration dampers. To apply forces, as in brakes, clutches and spring loaded valves. To control motion by maintaining contact between two elements as in cams and followers. To measure forces, as in spring balances and engine indicators. To store energy, as in watches, toys, etc. 1.7 CHARACTERISTICS OF LEAF SPRING The leaf spring acts as a linkage for holding the axle in position and thus separate linkage are not necessary. It makes the construction of the suspension simple and strong. The positioning of the axle is carried out by the leaf springs so it makes it disadvantageous to use soft springs i.e. a spring with low spring constant. This type of suspension does not provide good riding comfort. The inter-leaf friction between the leaf springs affects the riding comfort. Acceleration and braking torque cause wind-up and vibration. Also wind-up causes rear-end squat and nose-diving. 8

22 1.8 MATERIAL FOR LEAF SPRING The material used for leaf springs is usually a plain carbon steel having 0.90 to 1.0% carbon. The leaves are heat treated after the forming process. The heat treatment of spring steel produces greater strength and therefore greater load capacity, greater range of deflection and better fatigue properties. Materials constitute nearly 60%-70% of the vehicle cost and contribute to the quality and the performance of the vehicle. 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 connection with weight reduction of the vehicle. Hence, the composite materials have been selected for leaf spring design. The material of the spring should have high fatigue strength, high ductility, high resilience and it should be creep resistant. It largely depends upon the service for which they are used i.e. severe service, average service or light service. Severe service means rapid continuous loading where the ratio of minimum to maximum load (or stress) is one-half or less, as in automotive valve springs. Average service includes the same stress range as in severe service but with only intermittent operation, as in engine governor springs and automobile suspension springs. Light service includes springs subjected to loads that are static or very infrequently varied, as in safety valve springs. 1.9 MANUFACTURING OF LEAF SPRING Multi-leaf springs are made as follows: Shearing of flat bar Center hole punching / Drilling End Heating process forming (hot and cold process) 1. Eye Forming / Wrapper Forming 2. Diamond cutting / end trimming / width cutting / end tapering 3. End punching / end grooving / end bending / end forging / eye grinding 4. Center hole punching / Drilling / nibbing Heat Treatment 1. Heating 2. Camber forming 3. Quenching 4. Tempering 9

23 Surface preparation 1. Shot peening / stress peening 2. Painting Eye bush preparation process 1. Eye reaming / eye boring 2. Bush insertion 3. Bush reaming Assemble 1. Presetting and load testing 2. Paint touch-up 3. Marking and packing 1.10 WHY A COMPOSITE? Over the last thirty years composite materials, plastics and ceramics have been the dominant emerging materials. The volume and number of applications of composite materials have grown steadily, penetrating and conquering new markets relentlessly. Modern composite materials constitute a significant proportion of the engineered materials market ranging from everyday products to sophisticated niche applications. While composites have already proven their worth as weight-saving materials, the current challenge is to make them cost effective. The efforts to produce economically attractive composite components have resulted in several innovative manufacturing techniques currently being used in the composites industry. It is obvious, especially for composites, that the improvement in manufacturing technology alone is not enough to overcome the cost hurdle. It is essential that there be an integrated effort in design, material, process, tooling quality assurance, manufacturing, and even program management for composites to become competitive with metals. Further, the need of composite for lighter construction materials and more seismic resistant structures has placed high emphasis on the use of new and advanced materials that not only decreases dead weight but also absorbs the shock & vibration. Composites are now extensively being used for rehabilitation/ strengthening of pre-existing structures that have to be retrofitted to make them seismic resistant, or to repair damage caused by seismic activity. 10

24 Unlike conventional materials (e.g. steel), the properties of the composite material can be designed considering the structural aspects. The design of a structural component using composites involves both material and structural design. Composite properties (e.g. stiffness,) can be varied continuously over a broad range of values under the control of the designer. Careful selection of reinforcement type enables finished product characteristics to be tailored to almost any specific engineering requirement. Whilst the use of composites will be a clear choice in many instances, material selection in others will depend on factors such as working lifetime requirements, number of items to be produced (run length), complexity of product shape, possible savings in assembly costs and on the experience & skills the designer in tapping the optimum potential of composites. In some instances, best results may be achieved through the use of composites in conjunction with traditional materials. 11

25 CHAPTER: 2 LITERATURE REVIEW 12

26 CHAPTER: 2 LITERATURE REVIEW Before starting any dissertation work, the literature review of the topic is must, because it helps us in knowing the amount of work that has been done in that topic by the different researchers. It also helps us in doing the further work by taking the reference of the previous work done in the best possible way. Pankaj Saini, Ashish Goel and Dushyant Kumar have worked on design and analysis of composite leaf spring for light vehicles. In this paper, they consider passenger vehicle with ten-leaf steel spring for analysis of stress and deflection by using ANSYS 9 software. The objective is to compare the stresses and weight savings of composite leaf spring with that of steel leaf spring. The material selected was E-glass/epoxy, carbon epoxy and graphite epoxy which is use against conventional steel. The dimensions and the number of leaves for both steel leaf spring and composite leaf springs are considered to be the same. They consider design constraints were stresses and deflections. From the static analysis results it was found that there is a maximum displacement of 10.16mm in the steel leaf spring and the corresponding displacements in E-glass/epoxy, Graphite epoxy, and Carbon epoxy are 15 mm, mm and mm. From the static analysis results, the von-mises stress in the steel is MPa and the von-mises stress in E- glass epoxy, Graphite epoxy and Carbon epoxy is MPa, MPa and MPa was exiting respectively. A comparative study has been made between steel and composite leaf spring with respect to strength and weight. Composite mono leaf spring reduces the weight by 81.22% for E-Glass/epoxy, 91.95% for Graphite epoxy, and % for Carbon epoxy over conventional leaf spring [1]. Mahmood M. Shokrieh and Davood Rezaei have worked on analysis and optimization of a composite leaf spring. In this work, they consider light vehicle rear suspension system with four-steel leaf spring for analysis of stress and deflection by using ANSYS V 5.4 software. Also they have compared the finite element result of stresses and deflection with existing analytical and experimental solution. After that using this result they have replace steel leaf spring by composite material of fiberglass with epoxy resin and analyze it with same loading condition for stresses and deflection. Also from the analysis result they optimized spring geometry and found that spring width is decrease with hyperbolically and thickness is 13

27 increase linearly from spring eyes towards the axle seat. Also they concluded that the optimize composite leaf spring has much lower stress as compared to steel spring and the spring weight without eye units which having in steel is 9.2 kg is decrease by 80 % of its value. The natural frequency of composite leaf spring is higher than that of the steel leaf spring [2]. M.Venkatesan and D.Helmen have worked on design and analysis of composite leaf spring in light vehicle. In this paper, they consider passenger cars with seven-leaf steel spring for analysis of stress and deflection by using ANSYS 10 software. The objective is to compare the load carrying capacity, stiffness and weight savings of composite leaf spring with that of steel leaf spring. Also they have compared the finite element result of stresses and deflection with existing analytical and experimental result. After using that result they have replace steel leaf spring by composite material of E-glass/Epoxy and analyze it with same loading condition for stresses and deflection. The dimensions and the number of leaves for both steel leaf spring and composite leaf springs are considered to be the same. They consider design constraints were stresses and deflections. They concluded that, the composite leaf spring having 67.35% less stress, 64.95% higher stiffness and % higher natural frequency than that of existing steel leaf spring. A weight reduction of 76.4% is achieved by using optimized composite leaf spring [3]. Gulur Siddaramanna Shiva Shankar and Sambagam Vijayarangan have worked on mono composite leaf spring for light weight vehicle Design, end joint analysis and testing. In this paper, they consider light weight vehicle leaf spring for analysis of stress and deflection by using ANSYS software. The design constraints were stresses and deflection for both materials. The 3-D modeling of both steel and composite leaf spring was done and analysis was carried out using ANSYS software with same loading condition and dimension for both materials steel and composite. The ANSYS software results were verified with analytical and experimental results and they concluded that optimize composite spring having much lower stress, weight is reduce nearly 85 % and the natural frequency is higher as compared to steel leaf spring [4]. Mouleeswaran Senthil Kumar and Sabapathy Vijayarangan have done work on analytical and experimental studies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysis. The analysis was carried out by using ANSYS 7.1 software for finding stress and deflection in steel leaf spring. The objective is to 14

28 compare the load carrying capacity, stiffness, and fatigue life and weight savings of composite leaf spring with that of steel leaf spring. The dimensions of an existing conventional steel leaf spring of a light commercial vehicle are taken and are verified by design calculations. Also they have compared the finite element result of stresses and deflection with existing analytical and experimental result. The same dimensions of conventional leaf spring are used to fabricate a composite leaf spring using glass fibre reinforced polymer unidirectional laminates and analyze it with same loading condition for stresses and deflection. The load carrying capacity, stiffness and weight of composite leaf spring are compared with that of steel leaf spring analytically and experimentally. They analyze that, the composite leaf spring has % lesser stress, % higher stiffness and % higher natural frequency compare to existing steel leaf spring. A weight reduction of % is also achieved by using composite leaf spring. Also they concluded that, the composite leaf spring fatigue life is more than that of conventional steel leaf spring [5]. K. K. Jadhao and DR. R. S. Dalu have worked on experimental investigation & numerical analysis of composite leaf spring. They describe static analysis of steel leaf spring and composite multi leaf spring by using ANSYS software. Primary objective is to compare the load carrying capacity, stiffness and weight savings of composite leaf spring with that of steel leaf spring. The material selected was glass fiber reinforced plastic (GFRP) and the polyester resin can be used which was more economical this will reduce total cost of composite leaf spring. They have compared the analysis results with experimental results. They concluded that, Composite leaf spring have much lower stress and higher stiffness than that of existing steel leaf spring. Also they concluded that weight of composite leaf spring was nearly reduced up to 85% compare to steel leaf spring [6]. Kumar Krisha and Aggarwal M.L have worked on Computer aided FEA comparison of mono steel and mono GRP leaf spring. In this paper, they consider material of the mono steel leaf spring is SUP9 for analysis of stress and deflection by using ANSYS software. The objective is to compare the load carrying capacity, stiffness and weight savings of composite leaf spring with that of steel leaf spring. Also they have compared the finite element result of stresses and deflection with existing analytical and experimental result. After that using this result they have replace steel leaf spring by composite material of GRP (Glass Reinforced Plastic) and analyze it with same loading condition for stresses and deflection. The dimensions and the number of leaves for both steel leaf spring and composite leaf springs are considered to be the same. They consider design constraints were stresses and deflections. 15

29 From the results they concluded that, When steel leaf spring is replaced by composite material (GRP), the deflection is reduced by 6.51%. The bending stress in GRP leaf spring is decreased by 83.64% that of steel leaf spring. The material saving 71.85% is obtained by weight [7]. Joo-teck Jeffrey and Tarlochan Faris have worked on Finite element analysis on the static and fatigue characteristics of composite multi-leaf spring. In this paper, they investigated the static and fatigue behaviors of steel and composite leaf spring using the ANSYS V12 software. The dimensions of an existing conventional leaf spring of a light commercial vehicle were used. The same dimensions were used to design composite leaf spring for the two materials, E-glass fiber/epoxy and E-glass fiber/vinyl ester, which are of great interest to the transportation industry. The design constraints were bending stresses, deflection and fatigue life. They concluded that, the maximum bending stresses and deflection in composite leaf spring are much lower than that of steel spring. The fatigue life of E-glass/epoxy or E- glass/vinyl ester composite leaf spring was proven to be 2 and 4 times higher than that of steel leaf spring [8]. N. P. Dhoshi, Prof. N. K. Ingole and Prof. U. D. Gulhane have worked on analysis and modification of composite leaf spring of tractor trailer using analytical and finite element method. In this paper, they consider tractor trailer with seventeen-leaf steel spring for analysis of stress and deflection by using ANSYS 11.0 software. The objective is to compare the load carrying capacity, stiffness and weight savings of composite leaf spring with that of steel leaf spring. Also they have compared the finite element result of stresses and deflection with existing analytical and experimental result and using this result they replace steel leaf spring by composite material of E-glass/epoxy and analyze it with same loading condition for stresses and deflection. The dimensions and the number of leaves for both steel leaf spring and composite leaf springs are considered to be the same. They consider design constraints were stresses and deflections. They concluded that, the composite leaf spring have much lower stress and deflection than that of existing steel leaf spring. Also they concluded that weight of composite leaf spring was nearly reduced up to 80% compare to steel leaf spring [9]. M. M. Patunkar and D. R. Dolas have worked on modelling and analysis of composite leaf spring under the static load condition by using FEA. In this paper, they consider commercial 16

30 vehicle suspension system with leaf spring for modeling and analysis of stress, deflection and weight reduction ratio by using ANSYS 10.0 software for better understanding. They have compared the analysis results of stresses, deflection and weight reduction ratio with existing analytical and experimental solution. After that using this result they have replace steel leaf spring by composite material of glass fiber rain forced plastic and analyze it with same loading condition. Under the same static load conditions for deflection and stresses of steel leaf spring and composite leaf spring are found with the great difference. Deflection of composite leaf spring is less as compared to steel leaf spring with the same loading condition. They concluded that optimize conventional steel leaf spring have weight 23 Kg. whereas composite leaf spring weight is only 3.59 Kg. So it is indicating the reduction in weight by 84.40% at same level of performance. Composite leaf spring can be used on smooth road with very high performance expectations. However on rough road conditions due to lower chipping resistance failure from chipping of composite leaf spring [10]. M Senthil Kumar and S Vijayarangan have worked on static analysis and fatigue life prediction of steel and composite leaf spring for light passenger vehicles. They describe static and fatigue analysis of steel leaf spring and composite multi leaf spring by using ANSYS 7.1 software. Primary objective is to compare the load carrying capacity, stiffness and weight savings of composite leaf spring with that of steel leaf spring. They have compared the analysis results with experimental results. They concluded that, Composite leaf spring have 67.35% lesser stress, 64.95% higher stiffness and % higher natural frequency than that of existing steel leaf spring. Also they concluded that optimize steel leaf spring weight about 13.5 kg whereas the E-glass/Epoxy multi leaf spring weight only 4.3 kg, thereby weight reduction (68.15%) is achieved and fatigue life of composite leaf spring (10, 00,000 cycles) has more than that of conventional steel leaf spring (2, 00,000 cycles) [11]. H.A. Al-Qureshi has worked on automobile leaf springs from composite materials. The aim of this paper is to present a general study on the analysis, design and fabrication of composite springs. From this viewpoint, the suspension spring of a compact car, ``a jeep'' was selected as a prototype. A single leaf, variable thickness spring of glass fiber reinforced plastic (GFRP) with similar mechanical and geometrical properties to the multi leaf steel spring, was designed, fabricated and tested. The testing was performed experimentally in the laboratory and was followed by the road test. He concluded that, composite leaf spring have better fatigue behavior than steel spring. Also he found the hybridization technique can be used effectively to improve weight saving and performance in the automotive industry [12]. 17

31 J.P. Hou, J.Y. Cherruault, I. Nairne, G. Jeronimidis and R.M. Mayer have worked on Evolution of the eye-end design of a composite leaf spring for heavy axle loads. In this paper, they consider freight rail applications with two leaf steel spring for analysis of stress and deflection by using FEA. Also they have compared the finite element result of stresses and deflection with existing analytical and experimental solution. After that using this result they have replace steel leaf spring by composite material of glass reinforced polyester (GRP) and analyze it with same loading condition for stresses and deflection. They concluded that, composite leaf spring have lesser stress, higher stiffness compared to steel leaf spring. Also they concluded that, composite leaf spring have very good fatigue life than that of existing steel leaf spring and reduction of shear stresses in eye-end design [13]. Vinkel Arora, Dr. M. L. Aggarwal and Dr. Gian Bhushan have worked on a comparative study of CAE and experimental results of leaf springs in automotive vehicles. In this paper, they consider commercial vehicle suspension system with front end leaf spring for modeling by using CATIA and analysis of bending stress, deflection and maximum equivalent stress by using ANSYS 11 software. This conventional leaf spring model consists of 37 parts. The material of the leaf spring is 65Si7. The objective of this work is to carry out computer aided design and analysis of a conventional leaf spring, with experimental design considerations and loading conditions. The experimental and CAE results are compared for validation. From the results obtained from ANSYS, they concluded that the leaf spring is fully/half loaded, a variation of 1.17% in deflection is observed among the experimental & CAE value, which proves the validation of our CAD model and analysis. Also they found that maximum equivalent stress is MPa & MPa for fully and half loaded leaf spring respectively, which is below the yield stress i.e. 250MPa, therefore the design, is safe [14]. Mr. Anandkumar A. Satpute and Prof. S. S. Chavan worked on mono composite leaf spring design and testing. In this work, they consider light vehicle of Maruti Omni s rear suspension system with steel leaf spring for analysis of strength and weight reduction ratio by using ANSYS software. The objective is to compare strength and weight savings of composite leaf spring with that of steel leaf spring. Also they have compared the finite element result of strength and weight reduction ratio with existing analytical and experimental result. After that using this result they have replace steel leaf spring by composite material of Glass fiber-7781 and epoxy resin and analyze it with same loading condition. After they concluded that the results of the analytical and experimental analysis are almost same and they use the composite material instead of steel, they have to change dimensions. Here they have changed 18

32 the thickness from 5 mm to 12 mm. The weight reduction is achieved 88%. The composite material is having chipping resistance problem, but it may avoid by using carbon fibers [15]. I. Rajendran and S. Vijayarangan had studied about optimal design of a composite leaf spring using genetic algorithms. In this paper, they consider automobile steel leaf spring for solution of fatigue failure and weight reduction ratio by using genetic algorithms. After that using this result they have replace steel leaf spring by composite material and analyze it with same loading condition. The dimensions and the number of leaves for both steel leaf spring and composite leaf springs are considered to be the same. Also from the result, they concluded that the composite leaf spring have very good fatigue life than that of existing steel leaf spring and weight reduction is achieved 75.6% [16]. Abdul Rahim Abu Talib, Aidy Ali, G. Goudah, Nur Azida Che Lah and A.F. Golestaneh have worked on developing a composite based elliptic spring for automotive applications. They consider light and heavy trucks with steel elliptic spring for analysis of fatigue behavior and weight reduction by using ANSYS software. The objective is to compare the load carrying capacity, fatigue behavior and weight savings of composite leaf spring with that of steel leaf spring. Also they have compared the finite element result of fatigue life and weight reduction with existing analytical and experimental result. After that using this result they have replace steel leaf spring by composite material and analyze it with same loading condition. They concluded that composite elliptical springs have better fatigue behavior than the conventional steel leaf spring and weight reduction ratio is achieved [17]. Malaga. Anilkumar, T. N. Charyulu and Ch. Ramesh studied on design optimization of leaf spring. The objective of this paper is to replace the multi-leaf steel spring by three types composite leaf spring for the same load carrying capacity and stiffness. Since the composite materials have more elastic strain energy storage capacity and high strength-to-weight ratio as compared to those of steel. It is possible to reduce the weight of the leaf spring without any reduction on load carrying capacity and stiffness. The design constraints were limiting stresses and displacement. Modeling and analysis of both the steel and composite leaf springs have been done using ANSYS 9.0 software. From the static analysis results, they saw that the von-mises stress in the steel is MPa and the von-mises stress in E-glass/epoxy, Graphite/epoxy and Carbon/epoxy is MPa, 1556 MPa and 1061 MPa respectively. And they was found that the maximum displacement of mm in the steel leaf spring and the corresponding displacements in E-glass/epoxy, graphite/epoxy and carbon/epoxy are 19

33 mm, mm and mm in composite leaf spring. Composite leaf spring reduces the weight by 85% for E-Glass/Epoxy, 94.18% for Graphite/Epoxy and % for Carbon/Epoxy over conventional leaf spring [18]. Makarand B. Shirke and Prof. V. D. Wakchaure studied on performance association of static and fatigue behavior of steel and glass epoxy composite leaf spring of light motor vehicle. They consider light motor vehicle steel leaf spring for analysis of stress and deflection by using ANSYS workbench 14.0 software. The objective is to reduce cost, weight that is capable of carrying given static external forces without failure. They have replaced steel leaf spring by composite material of Glass Epoxy and analyze it with same loading condition for stresses and deflection. From the analysis they concluded that, the composite leaf spring have % lesser stress and lesser deflection compared to steel leaf spring. The predicted fatigue life of the steel leaf spring is 10 6 cycles and composite leaf spring is 10 9 cycles which are higher than that of exiting steel leaf spring. Composite leaf spring weight is reduced by % as compare to steel leaf spring [19]. SUMMARY From the literature survey of the past researchers it can see that the weight reduction is very common issues to increase the fuel efficiency and reduce the air pollution in automobile industries in now a day. The reduction of the weight is achieved by replacing composite material in place of steel leaf spring. Also the composite materials have much lower stresses and deflection and higher fatigue life. 20

34 CHAPTER: 3 DESIGN CALCULATION OF LEAF SPRING 21

35 CHAPTER: 3 DESIGN CALCULATION OF LEAF SPRING Conventional design methods of leaf springs are largely based on the application of empirical and semi-empirical rules along with the use of available information in the existing literature. The functions of springs are absorbing energy and release this energy according to the desired functions to be performed. So leaf springs design depends on load carrying capacity and deflection. Hence the Force Motors Trax Cruiser is consider for design of leaf spring. Step (1): Material of leaf spring : Material selected steel : 50 Cr 1 V 23 Composition of material : 0.45% C, % Si, % Mn, % Cr Step (2): Basic data of Force Motors Trax Cruiser leaf spring : Total length of the spring (Eye to Eye) = 1250 mm No. of full length leaves (n f ) = 02 No. of graduated leaves (n g ) = 04 Thickness of leaf ( t ) = 7 mm Width of the leaf spring ( b ) = 60 mm Young s modulus ( E )= 2x10 5 N/ mm 2 Central band 110 mm wide (Ineffective length) Tensile strength ( t ) = N/ mm 2 Yield strength ( y ) = 1800 N/ mm 2 Total load = 2850 Kg BHN = HB with hardened and tempered 22

36 Step (3): Basic requirement of load : Maximum capacity = 2850 Kg = 2850 x 10 = N Force Motors Trax Cruiser is equipped with 4 nos. of semi elliptical leaf spring, So load acting on the leaf spring assembly = = 7125 N Step (4): Calculation of the load and effective length of leaf spring : Consider the leaf spring is cantilever beam. So the load acting on the each assembly of the leaf spring is acted on the two ends of the leaf spring. Load acted on the leaf spring is divided by the two because of consideration of the cantilever beam. 2 W = 7125 N W = W = N For support and clamping of the leaf spring the U bolt is use and the distance between the U bolt is 110 mm. This is considered as an unbent portion of the leaf spring. Ineffective length of the leaf spring is as under : l = mm Effective Length of the spring, L = 2L l 1 L = (110) L =

37 L = L = mm Step (5): Calculations of the stress generated in the leaf spring are as under : Material of the leaf spring is 50 Cr 1 V 23 Property of the material are as under: Tensile strength ( ) = Kgf/ mm 2 t = N/ mm 2 Yield strength ( ) = 180 Kgf/ mm 2 y = 1800 N/ mm 2 Modulus of elasticity (E) = N/ mm 2 BHN = HB with hardened and tempered By considering the factor of safety for the safety purpose of the leaf spring is 1.5 for automobile leaf spring [20]. So the allowable stress for the leaf spring is as under : Tensile strength ( t ) = Yield strength ( y ) = = N/ mm 2 = 1200 N/ mm 2 Bending stress generated in the leaf spring is as under : b b 6W L 2 n bt

38 b = N/ mm 2 So, the stress generated in the leaf spring is lower than the allowable design stress. So design is safe. Deflection generated in the assembly of leaf spring is as under : 3 6W L y n b t 3 6 y y = mm 3 Step (6): Calculation of the pin of the leaf spring is as under : 3 Allowable bearing pressure of the eye [20] ( p ) = 8 N/ mm 2 Take length of the eye ( l 1 ) = 60 mm. Load acting on the eye are as under: W d l1 pb W d l p 1 b d d mm d mm Considering factor of safety is 2. Calculation of the bending moment of the pin is as under : b Length of the pin = Length of the eye + (2 Clearance) (Take the clearance 2.50 mm per side [20]) 25

39 l p = 60 + (2 x 2.50) l = 65 mm p Maximum bending moment acting on the pin is as under : W l M p 4 M 4 M N mm Modulus of the section of the pin is as under : d Z 32 3 Z d mm 3 3 Bending stress generated on the pin is as under : b Z b d d d = mm d mm 3 3 So, internal diameter of eye is d mm Shear stress generated in the pin is as under : (Considering bending stress N/mm 2 [20]) In assembly of the leaf spring pin acting under the double shear action due to assembly structure of the leaf spring. 26

40 W 4 2 d W 2 d 2 N/mm Both the stresses; Tensile stress and shear stress are lower than the allowable stress. So design is safe. Step (7): Calculations of the length of leaves are as under : Ineffective length of the leaf spring (l) = 110 mm Length of the leaf spring is as under: Effectivelength Length of the smallest leaf n 1 Length of the 2 nd leaf 2L 1] n ] 1 mm 2L ] n 1 2 ] 1 mm 2 (Ineffective length) 3 (Ineffective length) 2 (Ineffective length) 3 Length of the 3 rd leaf 2L ] n 1 2 (Ineffective length) 3 27

41 Length of the 4 th leaf Length of the 5 th leaf 2 ] 1 mm 2L ] n 1 2 ] 1 mm 2L ] n 1 2 ] 1 mm 2 (Ineffective length) 3 2 (Ineffective length) 3 But 5 th and 6 th leaves are full length leaves and 6 th leaf is known as a master leaf. Length of the master leaf calculated is as under: Length of master leaf 2L1 d t) 2 ) 2 mm Step (8): Calculation of radius is as under : R = Radius to which the leaves should be initially bent y = Camber of the spring y R y) L ) R ) ) R = mm 28

42 CHAPTER: 4 MODELING AND ANALYSIS OF STEEL LEAF SPRING 29

43 CHAPTER: 4 MODELING AND ANALYSIS OF STEEL LEAF SPRING 4.1 INTRODUCTION OF SOLIDWORKS Based on the dimensions obtained from the conventional design of leaf spring, the model of the leaf spring was created with the help of the 3-D modeling CAD software Solidworks Solid works is modeling software for modeling various mechanical designs for performing related design and manufacturing operations. The system uses a 3D solid modeling system as the core, and applies the feature base parametric modeling method. What this means that if a change is made anywhere in the product structure, such as the drawing or assembly, the changes are reflected everywhere. The solid model is the master file and all of the deliverables are merely windows looking in at the part file. This single database allows the user to make changes very easily without having to go back and update all the drawings and assemblies. In short Solidworks is a feature based parametric solid modeling system with many extended design and manufacturing applications. Some of the features of solid works are as below: Ease of use Parametric & feature based modeling Robustness 4.2 MODELING OF LEAF SPRING Modeling of leaf spring is performed in Solidworks Procedure of modeling leaf spring is as follows: There are different procedures available for modeling of leaf spring. Here we utilize divisional method of generation of parabolic leaf spring. 1) Create below sketch with the help of leaf spring length and camber. Divide leaf spring length and camber into equal division and draw a spline which passes through intersection of camber and length division. 30

44 Figure 4.1 Sketch of master leaf 2) Extrude above sketch to leaf spring width to create one leaf. Figure 4.2 3D model of master leaf 31

45 3) Same way create six leaves for generating leaf spring. 4.3 INTRODOCTION OF ANSYS Figure 4.3 3D model of leaf spring ANSYS is a finite element analysis (FEA) software package. It uses a preprocessor software engine to create geometry. Then it uses a solution routine to apply loads to the meshed geometry. Finally it outputs desired results in post-processing. FEA is used throughout almost all engineering design including mechanical systems and civil engineering structures. In most structural analysis applications it is necessary to compute displacements and stresses at various points of interest. The finite element method is a very valuable tool for studying the behavior of structures. In the finite element method, the finite element model is created by dividing the structure in to a number of finite elements. Each element is interconnected by nodes. The selection of elements for modeling the structure depends upon the behavior and geometry of the structure being analyzed. The modeling pattern, which is generally called mesh for the finite element method, is a very important part of the modeling process. The results obtained from the analysis depend upon the selection of the finite elements and the mesh size. Although the finite element model does not behave exactly like the actual structure, it is possible to obtain sufficiently accurate results for most practical applications. 32

46 The goal of meshing in ANSYS Workbench is to provide robust, easy to use meshing tools that will simplify the mesh generation process. These tools have the benefit of being highly automated along with having a moderate to high degree of user control. Advantages of FEA: Visualization increases Design cycle time reduces No. of prototypes reduces Testing reduces Optimum design The process of performing ANSYS can be broken down into three main steps. 1) Pre-processing 2) Solver 3) Post-processing Pre-processing: This step is most important in analysis of leaf spring. Any modeling software can be used for modeling of geometry and can be shifted to other simulation software for analysis purpose. After mesh generation (grid generation) is the process of subdividing a region to be modeled into a set of small elements. Meshing is the method to define and breaking up the model into small elements. In general a finite element model is defined by a mesh network, which is made up of the geometric arrangement of elements and nodes. Nodes represent points at which features such as displacements are calculated. Elements are bounded by set of nodes, and define localized mass and stiffness properties of the model. Elements are also defined by the number of mesh, which allowed reference to be made to corresponding deflections, stresses at specific model location. The common type of mesh element used in ANSYS solver is hexahedral, tetrahedral and brick. Solver: During preprocessing user has to work hard while solution step is the turn of computer to do the job. User has to just click on solve icon & enjoy a cup of tea! 33

47 Internally software carries out matrix formations, inversion, multiplication & solution for unknown. e.g. displacement & then find strain & stress for static analysis. Post-procesiing: The final step in ANSYS is Post-processing, during which the ANSYS results are analyzed. However, the real value of ANSYS simulation is frequently found in its ability to provide accurate predictions of integrated quantities such as find displacement and stresses. Post processing is viewing results, verifications, conclusions & thinking about what steps could be taken to improve the design. Assumptions : Software to be used for ANSYS 12.1 Model simplification for FEA. Meshing size is limited to computer compatibilities. Static analysis is considered. Material used for steel leaf spring analysis is isotropic. Properties of steel material : Parameter Material selected Young s modulus Passion s ratio Cr1V23 2*10 5 MPa BHN Tensile strength ultimate Tensile strength yield 2000 MPa 1800 MPa Density 7850 Kg/m 3 Values Table 4.1 Properties of steel material 4.4 STATIC ANALYSIS OF STEEL LEAF SPRING 1) After creating solid model of steel leaf spring in Solidworks Save that model in STEP format. 2) Import above 3D model in ANSYS Workbench static structural module for static analysis. 34

48 3) Create leaf spring material 50Cr1V23. Provide material properties as per table 4.1 in the ANSYS Workbench. Figure 4.4 Define materials in ANSYS Workbench 4) Assign material to six leaves of leaf spring. Figure 4.5 Assign materials to leaf spring 35

49 5) Define contact between leaves of leaf spring Contact type: No separation Figure 4.6 Define contact between leaves of leaf spring 6) Create meshing of leaf spring. Meshing is the process in which your geometry is spatially discredited into elements and nodes. This mesh along with material properties is used to mathematically represent the stiffness and mass distribution of the structure. The mesh has been generated automatically. The default element size is determined based on a number of factors including the overall model size, the proximity of other topologies, body curvature, and the complexity of the feature. As shown in figure 4.7 Number of elements used are 2352 & and number of nodes used are Type of meshing: 3D Type of elements: Automatic 36

50 7) Apply boundary condition Figure 4.7 Meshed model of leaf spring Boundary condition one end remote displacement for component X free, Y and Z fixed and rotation Z free, X and Y fixed and other end remote displacement for component X, Y and Z fixed and rotation Z free, X and Y fixed. Loading conditions involves applying a load upper side at the centre of the bottom leaf spring. Define force. Figure 4.8 Define force 37

51 Define displacement constrain. 8) Run the analysis. Figure 4.9 Define displacements constrain at one end Figure 4.10 Define displacements constrain at another end 9) Get the results. 38

52 4.5 RESULT ANALTSIS OF STEEL LEAF SPRING Static structural analysis for bending stress and deflection as shown in figure 4.11 and 4.12 respectively. Von-mises stress contour Maximum deflection contour Figure 4.11 Von mises stress contour Figure 4.12 Maximum deflection contours 39

53 Result table for analytical and analysis of steel leaf spring Below table shows that static analysis fairly matches with the analytical results but it also shows that static analytical results underestimate the results. For the optimization of leaf spring, accurate prediction of stress and deflection is necessary for that reason we have to perform model and transient analysis of leaf spring. Parameters Von-mises stress Analytical results Static analysis results Percentage variation (MPa) % Maximum deflection (mm) % Table 4.2 Comparison of analytical and analysis result for steel leaf spring 40

54 CHAPTER: 5 ANALYSIS OF COMPOSITE LEAF SPRING 41

55 CHAPTER: 5 ANALYSIS OF COMPOSITE LEAF SPRING As mentioned earlier, the ability to absorb and store more amount of energy ensures the comfortable operation of a suspension system. However, the problem of heavy weight of spring is still persistent. This can be remedied by introducing composite material, in place of steel in the conventional leaf spring. Research has indicated that the results of E-glass/epoxy, Carbon epoxy and Graphite epoxy were found with good characteristics for storing strain energy. So, a virtual model of leaf spring was created in Solidwork. Model is imported in ANSYS and then material is assigned to the model. These results can be used for comparison with the steel leaf spring. Assumptions : Software to be used for ANSYS 12.1 Model simplification for FEA. Meshing size is limited to computer compatibilities. Static analysis is considered. Material used for steel leaf spring analysis is isotropic. Properties of composite material : Sr No. Properties E-glass/epoxy Carbon epoxy Graphite epoxy 1 E X (MPa) E Y (MPa) E Z (MPa) PR XY PR YZ PR ZX G XY (MPa) G YZ (MPa) G ZX (MPa) ρ (kg/mm³) Table 5.1 Properties of composite material 42

56 5.1 STATIC ANALYSIS OF COMPOSITE LEAF SPRING 1) After creating solid model of steel leaf spring in Solidworks Save that model in *.IGES format. 2) Import above 3D model in ANSYS Workbench static structural module for static analysis. 3) Create leaf spring material E-glass/epoxy. Provide material properties as per table 5.1 in the ANSYS Workbench. Figure 5.1 Define materials in ANSYS Workbench 4) Assign material to six leaves of leaf spring. Figure 5.2 Apply materials at each leaf of leaf spring 43

57 5) Define contact between leaves of leaf spring. Contact type: Bonded Figure 5.3 Define contact between each leaf of leaf spring 6) Create meshing of leaf spring. This mesh along with material properties is used to mathematically represent the stiffness and mass distribution of the structure. The mesh has been generated automatically. As shown in figure 5.4 Number of elements used are 2352 & and number of nodes used are Figure 5.4 Meshed model of leaf spring 44

58 7) Apply boundary condition Boundary condition one end remote displacement for component X free, Y and Z fixed and rotation Z free, X and Y fixed and other end remote displacement for component X, Y and Z fixed and rotation Z free, X and Y fixed. Loading conditions involves applying a load upper side at the centre of the bottom leaf spring. Define force. Define displacement constrain. Figure 5.5 Define force Figure 5.6 Define displacements constrain at one end 45

59 8) Run analysis. 9) Get results. Figure 5.7 Define displacements constrain at another end 5.2 RESULT ANALYSIS OF COMPOSITE LEAF SPRING Von-mises stress contour Figure 5.8 Von mises stress contour of E-glass/epoxy leaf spring 46

60 Figure 5.9 Von mises stress contour of Carbon epoxy leaf spring Figure 5.10 Von mises stress contour of Graphite epoxy leaf spring 47

61 Maximum deflection contour Figure 5.11 Maximum deflection contours of E-glass/epoxy leaf spring Figure 5.12 Maximum deflection contours of Carbon epoxy leaf spring 48

62 Figure 5.13 Maximum deflection contours of Graphite epoxy leaf spring 5.3 COMPARISON OF STEEL AND COMPOSITE LEAF SPRING ANALYSIS DATA Materials Displacements (mm) Stress (MPa) Weight (Kg) Steel E-glass/epoxy Carbon epoxy Graphite epoxy Table 5.2 Comparison of analysis result for steel and composite leaf spring Here, from comparison of steel leaf spring with composite leaf spring as shown in table 5.2, it can be see that the maximum deflection mm on steel leaf spring and corresponding deflection in E-glass/epoxy, Carbon epoxy and Graphite epoxy are mm, mm and mm. Also the von-misses stress in the steel leaf spring MPa while in E- glass/epoxy, Carbon epoxy and Graphite epoxy the von-misses stress are MPa, MPa and MPa respectively. A comparative study has been made between steel and 49

63 composite leaf spring with respect to strength and weight. Composite leaf spring reduces the weight by 74.54% for E-glass/epoxy, 79.66% for Carbon epoxy and 79.77% for Graphite epoxy over steel leaf spring. 50

64 CHAPTER: 6 SIZE OPTIMIZATION 51

65 CHAPTER: 6 SIZE OPTIMIZATION Size optimization is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being solved depends on the solution of a given partial differential equation defined on the variable domain. Shape optimization problems are usually solved numerically, by using iterative methods. That is, one starts with an initial guess for a shape, and then gradually evolves it, until it morphs into the optimal shape. In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories depending on whether the variables are continuous or discrete. An optimization problem with discrete variables is known as a combinatorial optimization problem. In a combinatorial optimization problem, we are looking for an object such as an integer, permutation or graph of a finite (or possibly countable infinite) set. 6.1 CONTINUES OPTIMIZATION PROBLEM The standard form of optimization problem is g ( x) 0 i = 1...m i h( x) 0 i =1...n i Minimization f( x ) subjected to where f( x ) : R n R is the objective function to be minimized over the variable, g ( x) 0 are called inequality constraints, and i h( x) 0 are called equality constraints. i By convention, the standard form defines a minimization problem. A maximization problem can be treated by negating the objective function. 52

66 6.2 PROCEDURE FOR SIZE OPTIMIZATION The procedure for optimization is described as follows. Creating solid model of leaf spring in Solidwork Save that model in STEP format. Import above 3D model in ANSYS Workbench static structural module for static analysis. Provide material properties as per table 5.1 in the ANSYS Workbench. Assign material to six leaves of leaf spring. Define contact between leaves of leaf spring. Create meshing of leaf spring. Apply boundary condition. Create in analysis page optimization. In optimization constraints considered is stress and objective function minimization mass. Solving the model for size optimization and obtain reduction thickness. Get results BEFORE OPTIMIZATION The analysis results for von-mises stress and deflection on E-glass/epoxy, Carbon epoxy and Graphite epoxy before optimization are shown in figure 6.1 to figure 6.6 respectively. The weight of the springs is 4.57 kg for E-glass/epoxy material, 3.65 kg for Carbon epoxy material and 3.63 kg for Graphite epoxy material. Also the thickness of all leaf spring is 7 mm. 53

67 Figure 6.1 Before optimization von mises stress of E-glass/epoxy leaf spring Figure 6.2 Before optimization von mises stress of Carbon epoxy leaf spring 54

68 Figure 6.3 Before optimization von mises stress of Graphite epoxy leaf spring Figure 6.4 Before optimization maximum deflection of E-glass/epoxy leaf spring 55

69 Figure 6.5 Before optimization maximum deflection of Carbon epoxy leaf spring Figure 6.6 Before optimization maximum deflection of Graphite epoxy leaf spring 56