Design and Numerical Investigation of Static Loading characters of Hetrogeneous Model Leaf Spring

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Design and Numerical Investigation of Static Loading characters of Hetrogeneous Model Leaf Spring

Mr. M. Muthu Manikka Vinoth Kumar Department of Mechanical Engineering Sri Krishna College of Technology Coimbatore, India

Mr.G. Mohamed Khazzali, M.E., Department of Mechanical Engineering Sri Krishna College of Technology Coimbatore, India

Abstract Suspension system is a major unit in automotive design, especially leaf spring design. It absorbs payload and road loads to give comfort to vehicle. Leaf spring system is an assembly, contains arched leafs put together by U bolts. Loads travel through each leaf and produce contact stress with each contact members, this effectively reduces the life time of the spring system. Spring steels are majorly preferred as leaf spring material, but in practical nature vehicle caries loads that are much higher than designed limit and causes earlier failure to leaf spring, which is a catastrophic in a driving condition and should be avoided. Preferring composite materials is very costly even though they are far better than metals, so, it is evident to develop an economical, maintenance friendly design for the leaf spring system. In this project work, a heterogeneous model leaf spring system is developed and numerically tested for a better suitability for the existing model. This model will introduce synthetic rubber sleeves between spring leafs, which is a hyperrealist material in nature, this system is designed and modelled through CAD software, dimensions and loading data are arrived from literature reviews. FEA based static analysis will be conducted to study the behaviors of existing and heterogeneous models and the effectiveness of new model will be evaluated. The heterogeneous model is very economical alternative to many composite models proposed in the literature review and easy to manufacture, recyclable, and maintainable.

Keywords CAD, FEA, Leaf Spring, Heterogeneous


      1. Suspension and Leaf Springs

        Suspension can be considered as a link between the wheels and the body. It absorbs quick loadings and collects the elastic energy. Design fundamentals are based on the strength and comfort. The strength characteristics are usually determined according to the suspension type and loading. The comfort design fundamentals originate from the fluctuation and vibration point of view. The basic idea for the design is to generate the wanted elasticity and maintain the driving comfort. The leaf spring is one of the oldest suspension types. Nowadays it is widely used in heavy duty vehicles and work machines. Sometimes it is also called as a semi-elliptical spring; as it takes the form of a slender arc shaped length of spring steel (Fig.1.1) of rectangular cross section. The center of

        the arc provides the location for the axle, while the tie holes are provided at either end for attaching to the vehicle body.

        Supports the chassis weight, controls chassis roll more efficiently-high rear moment center and wide spring base, controls rear end wrap-up, controls axle damping, controls braking forces and regulates wheelbase lengths (rear steer) under acceleration and braking.

        Fig 1: Leaf Springs

      2. Spring Material Property

        The most common leaf spring material used is silicon steel and the properties of the same if given below.

        Name : 65Si7 (Isotropic) Youngs modulus (E) : 2.1e5 N/mm2 Poissons Ratio : 0.266

        BHN : 400-425

        UTS : 1940 MPa

        Tensile strength Yield : 1450 MPa Spring stiffness : 221.5 N/mm2

        Density : 7850 Kg/m3

      3. Mechanical Properties of Rubber

        Rubber is a unique material that is both elastic and viscous. Rubber parts can therefore function as shock and vibration isolators and/or as dampers. Although the term rubber is used rather loosely, it usually refers to the compounded and vulcanized material. In the raw state it is referred to as an elastomer. Vulcanization forms chemical bonds between adjacent elastomer chains and subsequently impart dimensional stability, strength, and resilience. An unvulcanized rubber lacks structural integrity and will flow over a period of time. Rubber mechanical properties as follows,

        Hardness, shore A 1090

        Tensile strength 11 N/mm²

        Elongation at break 1001100%

        Maximum temperature +300 °C

        Minimum temperature -120 °C

        E 9.70e5 N/mm²

        Poisson Ratio 0.45

      4. Rubber Compounding

        Typical rubber compound formulations consist of 10 or more ingredients that are added to improve physical properties, affect vulcanization, prevent long-term deterioration, and improve process ability. These ingredients are given in amounts based on a total of 100 parts of the rubber.

      5. Elastomer

        Both natural and synthetic elastomer is available for compounding into rubber products. The American Society for Testing and Materials (ASTM) designation and composition of some common elastomers are shown in Table 1 Some elastomers such as natural rubber, Neoprene, and butyl rubber have high regularity in their backbone structure. They will align and crystallize when a strain is applied, with resulting high tensile properties. Other elastomers do not strain- crystallize and require the addition of reinforcing fillers to obtain adequate tensile strength. Natural rubber is widely used in shock and vibration isolators because of its high resilience (elasticity), high tensile and tear properties, and low cost. Synthetic elastomers have widely varying static and dynamic properties. Compared to natural rubber, some of them have much greater resistance to degradation from heat, oxidation, and hydrocarbon oils. Some, such as butyl rubber, have very low resilience at room temperature and are commonly used in applications requiring high vibration damping. The type of elastomeric used depends on the function of the part and the environment in which the part is placed. Some synthetic elastomers can function under conditions that would be extremely hostile to natural rubber. An initial screening of potential elastomers can be made by determining the upper and lower temperature limit of the environment that the part will operate under. The elastomer must be stable at the upper temperature limit and maintain a given hardness at the lower limit. There is a large increase in hardness when approaching the glass transition temperature. Below this temperature the elastomer becomes a glassy solid that will fracture upon impact. Further screening can be done by determining the solvents and gases that the part will be in contact with during normal operation and the dynamic and static physical properties necessary for adequate performance.

      6. Finite Element Analysis

    Traditional approach to design analysis involves the application of classical or analytical techniques. This approach has the following limitations: Stresses and strains are obtained only at macro level. This may result in inappropriate deployment of materials. Micro level information is necessary to optimally allocate material to heavily stressed parts. Adequate information will not be available on critically stressed parts of the components. It may be necessary to make several simplifications and assumptions to design complex components and systems, if design analysis is carried out in the conventional manner.

    Manual design is time consuming and prone to errors. Design optimization is tedious and time consuming. FEA is a convenient tool to analyze simple as well as complex structures. The use of finite element analysis is not restricted to mechanical engineering systems alone. EA finds extensive application in electrical engineering, electronics engineering, micro electro mechanical systems, biomedical engineering etc. In manufacturing, FEA is used in simulation and optimization of manufacturing processes like casting, machining, plastic molding, forging, metal forming, heat treatment, welding etc. Structural, dynamic, thermal, magnetic potential and fluid flow problems can be handled with ease and accuracy using FEA. FEA was initially developed in 1943 by R. Courant to obtain approximate solution to vibration problems. Turner et al published in 1956 a paper on Stiffness and Deflection of Complex Structures. This paper established a broader definition of numerical analysis as a basis of FEA. Initially, finite element analysis programs were mainly written for main frame and mini computers. With the advent of powerful PCs, the finite element analysis could be carried out with the help of several FEA software packages. Finite element method can be applied to a variety of design problems concerning automobiles, airplanes, missiles, ships, railway coaches and countless other engineering and consumer products.


      1. Problem Description

        Leaf springs experience fluctuating loads with static loads of the vehicle and pay loads during its life time cycle. The springs were arranged in concentric arc model where each of them has contact at all loading conditions, the loads are transferred to the vehicle chassis through this contact load transfer, and this causes each leaf members experience the stress under all loading conditions. These leaf springs absorb road loads and shocks. While in riding, continuous change in the road surfaces bumps and pot holes make fluctuation loads in the spring members, this decrease service life of the spring members and in turn the whole system. Minimization of the load absorption between leaf members or minimize contact will increase the life. But, the cost of the new or modified system must be an economical one and in terms of maintenance and replacement. So, there is a strong need for a new and innovative economical stress minimization system.

      2. Proposed Solution

    It is clear that, minimizing contact loading will yield improvement in the service life of the leaf spring system. The literature reviews provides enough guidance in leaf spring dimensional details, static loading details from experiment and finite element analysis. Most of the authors proposed composite material model as a better alternate for the leaf spring system, even though it has advantages in strength and fatigue life, it is nerve an economical model for vehicles in the present situation, more over the manufacturing and serviceability is difficult for them. Considering all these factors, a Hyper elastic material (Synthetic Rubber) as an interleaf between leaf springs is proposed in this project work. Rubber can elongate several hundred times than its original shape and retain the same after loading, this behavior is called Hyper elastic, by introducing this Hyperelastic material

    between leaf spring members will absorb the loads and stress due them. The behaviors of this proposed heterogeneous model will be evaluated through static analysis and compared with the existing model.


    The above figure shows the meshed model of the leaf assembly. It contains 193313 nodes and 47666 elements made of tetra and Hexa type 3d elements. The following figure shows the boundary condition. The master leaf eyes are fixed.

      1. Model

        The following figures show the solid models of the leaf spring system that is taken for the analysis. The model dimensions are taken from the literature review [5].and tested with the given condition and compared with the experimental results.

        Since the eye diameter and U-bolt dimensions are not specified in any of the literature review, the FEA results may vary ± 10% from the actual.

        Fig. 2 Leaf Spring with Rubber Insert Model

        Fig. 3- Steel Spring Model

      2. Leaf Dimension

        Length of full length leaves

        (L-1 and L-2) : 1450 mm each

        Width of all leaves : 70mm

        Thickness of all leaves : 12mm No. of extra full length leaf : 1

        No. of graduated length leaves : 07

        (L-3, L-4, L-5, L-6, L-7, L-8 and L-9) : 1320,1140,940,



      3. Boundary Conditions

        The eyes of the leaf springs are fixed and a static loading of 35000 N, will be applied for static analysis.

      4. Static Analysis

        The following figure shows the imported model of the leaf spring assembly for performing static analysis.

        Fig. 4 – Leaf Spring Assembly

        The assembly contains 9 leafs, two of them are master leafs and other seven are graduated leafs.

        Fig 5 – Mesh

        Fig. 6 – Boundary Condition

        The following figure shows the loading condition of the model, the static loading of 35000 N is applied on the master leaf spring.

        Fig. 7 – Loading Condition

        The static loading condition is arrived from the literature reviews, for the same model the load is applied at the masters leafs top face. When the model is taken cambered the load must be applied at the bottom leaf to simulate the real situation. Here the un-cambered model is taken and applied at the top. The following figure show the maximum deflection that the leaf assembly experience under static loading condition. The maximum value is 156.85 (153 + 3.85) mm.

        Fig.8- Total Deformation

        The following figure shows the VonMises stress of the leaf assembly, it is maximum (1054.1 MPa) at the leaf eyes and it is understandably so, because of the one fixed and one movable ends.

        Fig.9 – VonMises Stress

        The Tensile stress of the spring material is 1470 MPa which is much higher than the induced VonMises stress.

      5. Heterogeneous Model Analysis

    The following figure shows the heterogeneous model, the model consists of 9 steel leafs, which are interleafed with

    4.1 Static Analysis


    synthetic rubber. The thickness of the rubber sleeves are same thickness (12 mm) as steel leafs.

    The static analysis of the steel leaf model shows the following results

    Fig. 10 Heterogeneous Model

    The following figure shows the meshed model, contains 101616 nodes and 118608 elements.

    Fig. 11 Meshed Model

    3.6 Boundary Condition

    The following figure shows the boundary condition, fixed ends and loading of 35000 N.

    Table 1 Results Comparison


    Experimental [5]




    Load (N)




    Max. Stress (MPa)



    + 10

    Deflection (mm)




    The result shows that the value gives acceptable nearer results to the experimental result.

    4.2 Heterogeneous Model Static Analysis

    The following table shows the comparison results of the normal steel and heterogeneous model.

    Table 2 Result Comparison

    3.7 Results

    Fig. 12 Fixed Eye

    Fig. 13 Loading

    Experience a maximum of 1057.3 MPa. The induced is below the yield limit of 1470 MPa.






    Load (N)




    Max. Stress (MPa)









    Loa (N)




    Max. Stress (MPa)





    Static analysis of steel and heterogeneous leaf springs was numerically investigated and the results show effectiveness of heterogeneous model. From the literature review static loading with specification of leaf spring were extracted and the same is used for modeling the leaf spring. Steel leaf spring is modeled followed by heterogeneous; both were undergone static analysis which shows heterogeneous is far better than steel. The heterogeneous is modeled using silicon rubber leafs

    The following figure shows the VonMises stress. The maximum value shows 146.30 MPa.

    inserted between steel leafs provides best result in reducing stress, rubber leafs absorbed around 86% of stress in static loading.

    The present research can be extended for experimental investigation to establish a better relationship between analytical, numerical and experimental results. This can be used to form empirical relation among the design parameters of leaf spring.

    Fig. 14 VonMises Stress

    The following figure shows the maximum shear stress in the model. The value shows 77.722 MPa.

    Fig. 15 Shear Stress


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