Contents I. Introduction
Friction is often modeled in Coulomb model, using a constant called friction coefficient, which is the quotient of tangential friction force and active force. Particularly, in mechanical system involving contact between hard surfaces, friction coefficient is often predetermined in various experiments, and then is used popularly in researches [1]. Traditionally, friction between 2 contacting surfaces is described by modeling perfectly smooth surfaces with given geometry (usually represented by continuous functions), allowing quick evaluating magnitude and direction of forces. Therefore, friction force distribution can be found easily in Coulomb model with cumulative friction moments, by intergrating the distribution over the whole surface with the marginal conditions. In this smooth surface, cumulative friction torque linearly relates with load. However, perfectly smooth surfaces are ideal in nature. There are always irregular values, known as asperities [2]. Asperities change over time and surface deformation, in conformation with friction distribution [3]. Different friction distributions lead to different values of accumulated friction moment which can not be observed in smooth surface model. Therefore, a 3D mathematical model, on an uneven geometry, is needed to quantitatively analyze the Relationship of uneven property of surface on cumulative friction torque.
