A theoretical contact model for rough elastic spheres

Investigating the contact of rough spheres is constructive to wide engineering applications and scientific research. However, the coexistence of global curvature and surface roughness brings difficulty in the analysis of this problem. In this work, we present a theoretical model for the contact between a rough elastic sphere and a rigid plane. As a fundament, the whole-range contact of nominally flat Gaussian rough surfaces is dealt with by using finite element method. With the load-area relation for the contact of nominally flat rough surfaces, the local real contact area of rough spherical contact is determined, in which the local pressure is given by the Hertzian model. Then, the total real contact area of rough spherical contact is obtained by integrating over the Hertzian contact area. It is found that the load-area relation for the contact of rough spheres is linear at light loads and converges to the result of smooth spherical contact as the load increases. This rough spherical contact model is validated through direct finite element simulations.