Roughness effect on friction for multi-asperity contact between surfaces

A combined adhesion-roughness model of friction, originally developed for contact between a narrow slider and a single asperity, is applied to the case of multiple asperity contact between rough surfaces. An analytical model, based on the Greenwood-Williamson model of asperity contact, leads to a simple roughness-dependent expression for the friction coefficient. For elastic deformation at each contact point, the contribution due to roughness is half that suggested by the single asperity analysis. When contact is largely plastic, the roughness contribution is half the elastic contribution. The reduction is mainly due to cancellation when forces at the various asperities in contact are summed. Example calculations are performed for rough diamond surfaces, using numerically generated surfaces.