Analysis of a contact problem in leaf springs

Abstract

In this investigation, a nonlinear elastic model of leaf springs is developed for use in the computer simulation of multibody vehicle systems. In the leaf spring model developed in this investigation, the distributed inertia and stiffness of the leaves of the spring are modeled using the finite element floating frame of reference formulation that accounts for the effect of the nonlinear dynamic coupling between the finite rotations and the leaf deformation. The leaf spring geometry and deformations are modeled using nodal degrees of freedom defined with respect to the spring body coordinate system. By assuming that the leaf deformation can be large but the leaf deformed shape remains simple, component mode synthesis techniques can be used to significantly reduce the number of deformation coordinates. The nonlinear stiffness matrix is first developed for the finite element of each leaf and is used to determine the overall leaf spring stiffness matrix. The pre-stresses, the contact and friction that characterize the nonlinear behavior of leaf springs are discussed. Using the nonlinear leaf spring formulation presented in this study, a detailed multibody model for a sport utility vehicle is developed. It is shown that the proposed leaf spring model that accounts for the effect of windup, contact and friction between the spring leaves can be effectively used for assessing the dynamic stability of sports utility vehicles.