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

Abstract

An elastomeric bushing is a device used in automotive suspension systems to cushion the force 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 applied to the shaft or sleeve and their deformation is non-linear and exhibits features of viscoelasticity. A force–displacement relation for elastomeric bushings is important for multi-body dynamics numerical simulations. A boundary value problem for the bushing response leads to a force–displacement relation which requires extensive computation time to implement and is hence unsuitable. In a separate study, an explicit force–displacement relation has been introduced which can be used in multi-body dynamics simulations. The relation is expressed in terms of a force relaxation function, and a method for its determination from experiments on bushings has been developed. These are evaluated in the present work. A boundary value problem is formulated for axial mode bushing response, i.e. deformation of the non-linear viscoelastic cylinder when the shaft and sleeve undergo relative displacement along their common axis. Numerical solutions of the boundary value problem represent the exact bushing response for use in the method for determining the force relaxation function of the bushing. Solutions also allow for comparison between the exact force–displacement 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 force–displacement relation are in very good agreement with the exact results.