A modified rough interface model considering shear and normal elastic deformation couplings

Abstract

This paper presents an analytical description of frictional contact hysteresis behavior between two flat rough surfaces in partial and gross slip. Couplings between shear and normal forces in the contact interface are included by considering spherical asperities in oblique contact. In the oblique contact, the relation between shear and normal interface forces is determined using asperities tangential friction forces and Hertzian normal contact forces. The Mindlin elastic spherical contact solution is modified in this study using the rod contact model leading to higher maximum tangential friction force and pre-slip limit compared to the classical solution. Based on the proposed modified Mindlin spherical contact solution, this paper develops a modified two rough interface (MTRI) model using the multi-asperity contact theory. The MTRI model provides accurate estimates of the contact interface behavior in an explicit form by including the oblique contact effects and the rod solution.

In obtaining the hysteresis behavior of two flat rough interface contact, the contact regions associated with the pre-slip and sliding state at different tangential loading phases, i.e., virgin loading, unloading, and reloading, are determined. Then by the integration of pairs of asperities contact forces over the contacting regions at each state, restoring forces of contacting surfaces are obtained. The proposed MTRI model predictions are validated against experimental observations and found to be in good agreement.