A model for non-linear viscoelastic coupled mode 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 su rface. The shaft is connected to the suspension and the sleeve is connected to the frame. The elastomeric cylinder provides the cushion when it deform s 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 displa cements or rotations is non-linear and exhibits features of viscoelasticity . An explicit force-displacement relation for elastomeric bushings is impor tant for multi-body dynamics numerical simulations. A boundary Value proble m for the bushing response leads to an implicit relation which requires ext ensive computation time to implement and is hence unsuitable. In the presen t work, an explicit relation for coupled axial and torsional mode response is introduced and studied. A boundary value problem is formulated for coupl ed axial and torsional mode bushing response. A constitutive model is defin ed in which the axial force and torsional moment are each expressed explici tly in terms of axial displacement and rotation. Each relation contains a r elaxation function which depends on the axial displacement and rotation. Th e relaxation functions are constructed using numerical results obtained by solving the boundary value problem. Numerical solutions of the boundary val ue problem also allow for comparison between the exact coupled mode respons e and that predicted by the proposed model. It is shown that the prediction s of the proposed moment-rotation relation are in very good agreement with the exact results. (C) 1999 Published by Elsevier Science Ltd. All rights r eserved.