Analysis of the initial contact height when a curved body approaches a rough flat surface

Abstract

As a first approach to the study of various contact problems, including the locus of a ball rolling on a rough flat surface, the initial contact heights in the contact between a rough flat surface and a smooth curved body, in this case an elliptic paraboloid, were analysed theoretically. The statistical description of the initial contact heights can be represented by simple functions of one equivalent variable. This equivalent variable is given by σ p N 2 p R x when the rough flat surface has unidirectional roughness and by σ s N s R when the rough flat surface has non-directional roughness, where σ p , N p , σ s and N s are the surface roughness parameters and R x and R are the principal radius and the equivalent radius of the curved body. The statistical description of the initial contact heights for the rough flat surface was replaced by the envelope curve obtained with a profilometer whose stylus was the tip of a curved body to confirm the theoretical results experimentally.