An Analytical Solution to an Archard-Type Fractal Rough Surface Contact Model

摘要

Due to the existence of multiple scales of features on surfaces, during the past two decades models have been developed that employ a fractal description of the rough surface profile. Most of these models use a truncation calculation to predict the contact area. The load corresponding to the truncated area of the fractal surface is then calculated using elastic and elastic- plastic asperity contact models. The current work instead uses a stacked asperity model that was first introduced by Archard to predict contact area as a function of load. From this the elastic contact of multiscale rough surfaces can be solved analytically, providing a closed-form solution for certain cases of surface profiles. The results of the model are then compared to a two-dimensional (2D) deterministic model of rough surface contact. Finally, the analytical relationships are used to create models for three-dimensional (3D) elastic and elastic-plastic contact of fractal/multiscale rough surfaces.