Combined Force and Moment in a Three Dimensional Model of Elastic Contact of Nominally Flat Rough Surfaces

In this paper we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment and thereby contact moment is derived. Through this scheme it is possible to also define elastic contribution to friction since the half-plane tangential contact force on one side of an asperity is no longer balanced by the half-plane tangential force component on the opposite side. The elastic friction force however is shown to be of a much smaller order than the contact normal force. Approximate closed form equations are found for contact force and moment as functions of separation, asperity radius of curvature sum, mean plane slope and nominal contact dimension. The approximate equations are shown to give error within seven percent.