The effects of size distribution functions on contact between fractal rough surfaces

In the fractal rough surface characterized by Weierstrass-Mandelbrot function, the amount of asperities with frequency index n is γ times the amount of asperities with frequency index n-1. According to the property, the revised size distribution functions and truncated size distribution functions of asperities with frequency index n are developed for the two-dimensional and three-dimensional fractal rough surfaces, respectively. The relations between real contact area and total contact load are obtained. The comparison between predictions of present model, the revised MB model and experimental data are given. The results show these asperities whose frequency indexes range from nmin to nmin+5 are major contribution to real contact area and total contact load. For given initial frequency index and total contact load, the real contact area of present model is smaller than that of the revised MB model. With an increase in initial frequency index, the results of present model gradually approach to that of the revised MB model. When initial frequency index nmin is less than the elastic critical frequency index nec, the trends of present model are in better agreement with experiment than that of the revised MB model.