Effects of shape and scale in mechanics of elastic interaction of regular wavy surfaces

The physical effects associated with the shape and the scale of regular wavy surface asperities are investigated analytically. A special periodic analytical function, which is a generalization of a sine wave and allows to describe waviness of arbitrary smooth shape is suggested. The formulation and solution of the plane problem of elastic contact of a wavy surface with a half-plane is considered. Asperities of two-scale levels are taken into account-regular waviness with arbitrary shape (small-scale asperities) and regular sine-shaped roughness (large-scale asperities). The obtained pressure distribution for an arbitrary shaped one-scale wave is a generalization of the Westergaard's solution for a sine wave. The results show that the shape of asperities has significant influence on pressure distribution over the entire range of contact lengths. It is also shown that the elastic coupling of adjacent asperities and asperities of different scales increases the nonlinearity of the contact interaction. But for the small loads the problem can be approximately reduced to linear, and the contact area fraction can be obtained directly from the geometry of contacting surfaces.