Study on contact spots of fractal rough surfaces based on three-dimensional Weierstrass-Mandelbrot function

Abstract

All engineering surfaces are of certain degree of roughness and comprising asperities of various size. When two rough surfaces contact with each other, the contact load will be dispersed by numerous contact spots generated by the compressive deformation of asperities. Weierstrass-Mandelbrot function is widely used in fractal contact theories to model the roughness and self-affinity of engineering surfaces. It is found that the fundamental assumptions in conventional fractal contact models are unsuitable for the description of true conditions. A numerical statistical method is utilized on the calculated fractal rough surfaces by W-M function to investigate the exact formulation of the size distribution function and profile function of asperities in fractal contact theories. Based on the statistical results presented, a modified three-dimension fractal contact theory is proposed.