Computer aided FEA simulation of EN 45 A parabolic leaf spring

Article history: Received September252012 Received in revised format December 28 2012 Accepted January25 2013 Available online 25January 2013 This paper describes computer aided finite element analysis of parabolic leaf spring. The present work is an improvement in design of EN45A parabolic leaf spring used by a light commercial automotive vehicle. Development of a leaf spring is a long process which requires lots of test to validate the design and manufacturing variables. A three-layer parabolic leaf spring of EN45A has been taken for this work. The thickness of leaves varies from center to the outer side following a parabolic pattern. These leaf springs are designed to become lighter, but also provide a much improved ride to the vehicle through a reduction on interleaf friction. The CAD modeling of parabolic leaf spring has been done in CATIA V5 and for analysis the model is imported in ANSYS-11 workbench. The finite element analysis (FEA) of the leaf spring has been carried out by initially discretizing the model into finite number of elements and nodes and then applying the necessary boundary conditions. Maximum displacement, directional displacement, equivalent stress and weight of the assembly are the output targets of this analysis for comparison & validation of the work.


Introduction
Leaf springs are the components of the suspension system.They perform isolation task in transferring vibration due to road irregularities to driver's body.Increasing competition and innovations in automobile sector tends to modify the existing products or replacing old products by new and advanced material products.More efforts are taken in order to increase the comfort of user.To improve the suspension system, many modifications have taken place over the time.Inventions of parabolic leaf spring and use of composite materials for these springs are some of these latest modifications in suspension systems.The main advantages of parabolic leaf springs are that they are lighter, cheaper, better fatigue life, and they isolate more noise.CAE tools are widely used in the automotive industries.In fact, their use has enabled the automakers to reduce product development cost and time while improving the safety, comfort, and durability of the vehicles they produce.Aggarwal and Chawla (2007)described that fretting fatigue between leaves can be reduced by careful control of shot peening parameters.The bending strength of EN45A parabolic leaf spring is found to be higher as compared with semi-elliptic leaf spring.Kanbolat and Soner(2011)

FEA Simulation
A stress-deflection analysis is performed using finite element analysis (FEA).The complete procedure of analysis has been done using ANSYS-11.The CAD model of parabolic leaf spring is imported to ANSYS-11 workbench as shown in Figure-6 below.

Fig. 6. Model in ANSYS-11 Workbench
To conduct finite element analysis, the general process of FEA is divided into three main phases, preprocessor, solution, and postprocessor.

Preprocessor
The preprocessor is a program that processes the input data to produce the output that is used as input to the subsequent phase (solution).Following are the input data that needs to be given to the preprocessor: 1.Type of analysis 2.Element type 3.Real constants 4.Material properties 5.Geometric model 6.Meshed model 7.Loading and boundary conditions.

Solution
Solution phase is completely automatic.The FEA software generates the element matrices, computes nodal values and derivatives, and stores the result data in files.These files are further used by the subsequent phase (postprocessor) to review and analyze the results through the graphic display and tabular listings.

Postprocessor
The output from the solution phase is in the numerical form and consists of nodal values of the field variable and its derivatives.For example, in structural analysis, the output is nodal displacement and stress in the elements.The postprocessor processes the result data and displays them in graphical form to check or analyze the result.The graphical output gives the detailed information about the required result data.
Table 2 shows different parameters associated with material properties.Meshing of the model is done in which model is discretized into finite number of elements and nodes.This mesh along with material properties is used to mathematically represent the stiffness and mass distribution of the structure.As already discussed about parabolic leaf springs that rubber tip inserts has been provided between the leaves.Meshing has been done by properly selection of element type, relevance, refinement and sizing control.
A meshed view of the model & meshing details are shown in Fig. 7 and Table 3 below, respectively.These tip inserts are fixed on the upper face of leaf treated as bonded contact as shown in Fig. 8 while it is having no separation type of contact with the bottom face of upper leaf as shown in Fig. 9 to allow sliding motion between them.The boundary condition is the collection of different forces, pressure, velocity, supports, constraints and every condition required for complete analysis.Applying boundary condition is one of the most typical processes of analysis.A special care is required while assigning loads and constraints to the elements.Boundary condition of the leaf spring involves the fixation of one of the revolute joint and applying displacement support at the other eye end of leaf spring.A joint rotation of 2.2° has been taken for both revolute joints considering the no load camber.Loading conditions involves applying a load at the center of the leaf.As per specifications the spring is drawn at flat condition, therefore the load is applied in downward direction to achieve initial no load condition.The model under defined boundary conditions is shown in Fig. 10.The main leaf having two eye ends make revolute type of joint with pin inserted at both ends.Table 4 demonstrates the definition of both of the revolute joints.The details of load applied and different supports at both ends are defined in the Table 6.

Results and Discussions
As the FE Analysis of parabolic leaf springs has been done in the above section, and experimental results has been taken as the standards to compare with results obtained in the FE Analysis.Now it is necessary that we have some discussion on the both, experimental as well as FEA results and to reach for a conclusion.The result table of the FE analysis coming out of ANSYS-11 workbench is as under; Linear static loading was performed in FEA to reduce the design complexity, material saving and time saving too.The FEA deflection value is 56.806 mm having 16% deviation from experimental valuei.e. an acceptable deviation.On the other hand the equivalent von-mises stress is 1083.2MPa as obtained from computer aided finite element analysis through ANSYS.A stress deflection curve is plotted for rated load i.e. 3600N and full load 7600N as shown in Fig. 14, which is showing a straight line relation between stress and deflection.

Conclusions
A correlation of CAE Analysis with experimental results taken at industrial laboratory has been provided with this work.It is aimed to reach capability of manufacturing the right product at lower cost & at one sitting instead of repeated design and prototype costs that made by trial and error methods.The result section above depict the total deflection as 56.806 mm in the parabolic leaf spring at full load i.e. the deflection obtained from FEA results are close to the experimental value.The corresponding equivalent von-misesstress developed in the leaf spring at same full load is 1083.2MPa i.e. the equivalent von-misesstress is observed to be well below the yield stress indicating that the design is safe.The parabolic leaf spring was found to weigh 8.05 Kg recorded in the laboratory while FEA model of parabolic leaf spring weighs 8.62 Kg i.e. a negligible difference between them.All these conclusions give very close results proving the validation of the FEA model as well as of this work.
Fig. 2 CAD Model of Parabolic Leaf Spring Fig. 3. Taper Leaves of Assembly

Fig. 11 .
Fig. 11.Total deformation in the leaf spring Fig. 12. Deformation vectors showing their intensity As shown in above results the deflection and the von-mises stress are target results for comparison with the experimental results.

Fig. 13 .
Fig. 13.Von-Mises stress contour Fig. 13.Load-Deflection curve used a numerical approach to obtain the fatigue CAD modeling software is dedicated for the specialized job of 3D-modeling.The model of the multi leaf spring structures also includes many complicated parts, which are difficult to make by any of other CAD modeling as well as Finite Element software.The Chemical composition of EN45A spring steel by % weight is 0.61 C, 1.8 Si, 0.79 Mn, 0.02 S, 0.024 P and geometrical specification of leaf springs are; Span length = 940 mm, Seat Length = 100 mm, Number of leaf = 3, Rated load = 3600 N, Maximum Load= 7600 N, Width of leaf=60 mm, Tip Inserts: 50mm Diameter, Centre Rubber Pad=100mmX50mmX5mm

Table 2
Material properties of EN45A spring steel

Table 3
Meshing details in ANSYS-11 Report

Table 4
Revolute joint at eye ends between leaf and pin

Table 6
Details of force & supports applied

Table 7
Results showing deformation & equivalent stress