On the size distribution of truncation areas for fractal surfaces

Abstract

The size distribution of contact spot areas is critical for the evaluation of contact behavior of rough surfaces. A size distribution law proposed by Mandelbrot has been used widely in multi-asperity fractal contact models to predict the rough contact behavior. However, the Mandelbrot law has a limitation on the representation of the truncation area distribution for rough surfaces. Therefore, the present study develops a new size distribution law of the truncation areas for fractal surfaces. Specifically, the three-dimensional Weierstrass-Mandelbrot (WM) function is used to characterize rough surfaces. A novel method is proposed to determine the fractal parameters of the WM function. Numerical investigation of rough surface truncation is conducted to obtain size distribution information of the truncation regions for various rough surfaces. Based on the numerical results, the new size distribution law of the truncation areas is proposed and validated by fractal surface and realistic rough surface. It is found that the proposed law can accurately reproduce the size distribution of the truncation areas for rough surfaces with a wide range of fractal parameters.