The effects of relative angular motions on friction at rough planar contacts

Changes in friction due to angular motions at rough planar contacts are investigated using a compliant contact model that isolates an angular degree-of-freedom. Expressions are developed that relate the real area of contact, the contact forces and the line-of-action of the resultant normal contact force to the angular displacement for both periodic and random rough surfaces. We assume that the friction force is proportional to the real area of (elastic) contact. For a periodic rough surface, consisting of an array of hemispherical asperities of equal height and radius, the friction force is shown to be independent of angular displacement. The normal force increases and its line-of-action shifts away from the center of the contact as angular displacements increase. Therefore, the coefficient of friction decreases with angular displacement. In contrast, for a randomly rough surface, the contact area and normal contact force are shown to be non-linearly dependent on angular displacement, but remain proportional to each other in the presence of relative angular motion. Therefore, for the randomly rough surfaces the coefficient of friction is independent of angular motion.