A model for non-linear viscoelastic coupled mode response of an elastomeric bushing

Abstract

An elastomeric bushing is a device used in automotive suspension systems to cushion the loads transmitted from the wheel to the frame of the vehicle. A bushing is essentially an elastomeric hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. The shaft is connected to the suspension and the sleeve is connected to the frame. The elastomeric cylinder provides the cushion when it deforms due to relative motion between the shaft and sleeve. The relation between the force or moment applied to the shaft or sleeve and the relative displacements or rotations is non-linear and exhibits features of viscoelasticity. An explicit force–displacement relation for elastomeric bushings is important for multi-body dynamics numerical simulations. A boundary value problem for the bushing response leads to an implicit relation which requires extensive computation time to implement and is hence unsuitable. In the present work, an explicit relation for coupled axial and torsional mode response is introduced and studied. A boundary value problem is formulated for coupled axial and torsional mode bushing response. A constitutive model is defined in which the axial force and torsional moment are each expressed explicitly in terms of axial displacement and rotation. Each relation contains a relaxation function which depends on the axial displacement and rotation. The relaxation functions are constructed using numerical results obtained by solving the boundary value problem. Numerical solutions of the boundary value problem also allow for comparison between the exact coupled mode response and that predicted by the proposed model. It is shown that the predictions of the proposed moment–rotation relation are in very good agreement with the exact results.