A model for nonlinear viscoelastic torsional response of an elastomeric bushing

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 the sleeve. The relation between the force or moment applied to the shaft or sleeve and the relative displacements or rotations is nonlinear and exhibits features of viscoelasticity. A force(moment)-displacement(rotation) relation for elastomeric bushings is important for multibody dynamics numerical simulations. A boundary value problem for the bushing response leads to a relation which requires extensive computation time to implement and is hence unsuitable. In a separate study, a force(moment)-displacement(rotation) relation for single mode response has been proposed which can be used in multi-body dynamics simulations. The relation is expressed in terms of a force (moment) relaxation function for the bushing, and a method for its determination by experiments on bushings has been presented. The applicability of this relation for torsional mode bushing response is evaluated in the present work. A boundary value problem is formulated for torsional mode bushing response. Numerical solutions of the boundary Value problem represent the exact bushing response and act as numerically generated experimental data. The proposed moment-rotation relation is constructed using this data. Numerical solutions of the boundary value problem also allow for comparison between the exact moment-rotation behavior and that predicted by the proposed model. It is shown that the method for determining the bushing relaxation function and the predictions of the proposed moment-rotation relation are in very good agreement with the exact results.