Stiffness analysis of leaf spring system under large deformation

Abstract

The paper proposes a semi-analytical model to analyze large deformation elastic behavior of leaf spring under static load. The model treats leaf spring system as a curved beam with one end directly hinged to a fixed support and the other end being attached to another fixed support through a rigid link (shackle). Constrained motion of the shackle with large deformation of curved beam is modeled using a rotational spring at fixed hinge point of the shackle. Two more physically plausible models for the restraint motion are also proposed, which are derived from the main model through post processing. In the first derived model, the constrained motion is captured by defining a longitudinal spring in a virtual rod connecting the curved beam ends, whereas in the second derived model, the restrained motion is modeled through vertical stiffness of the system. Due to combined complications coming from non-conventional boundary condition, asymmetric geometry, non-uniform curvature, and nonlinear kinematics, the problem is analyzed through successive geometry updation. Governing equation for the curved beam is derived in body fitted curvilinear frame considering combined bending–stretching effects. Global solution for the total system is then obtained by incorporating the elastically restrained shackle motion through satisfaction of kinematic and kinetic constraint relations. As the governing equation and the constraint conditions involve geometric nonlinearity, a numerical iterative scheme is developed and implemented in MATLAB®. For the purpose of validation, the theoretical model is simulated in commercial finite element package ABAQUS®. Comparison of deflection profiles with the finite element model validates the proposed leaf spring model. After the validation study, observations on effects of system parameters and curved leaf profile shape on system stiffnesses are furnished. Effects of the parametric study are presented through true and total system stiffnesses. The parametric study may lead toward optimized design of the system.

Keywords

Leaf spring curved beam elastically restraint boundary asymmetric large deformation geometric nonlinearity geometry updation

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