Simulation and characterization of fractal rough surfaces

In order to investigate the fractal characterization, namely the statistically self-affine of the engineering surfaces in different scale, two methods, the random-mid-displacements method and Weierstrass-Mandelbrot function method, are employed to simulate the profiles and 3D topography of rough surfaces. The power spectra of the surface profile is analyzed and the relationship of fractal dimension and its power spectra is built. From the graph of the power spectrum, the power spectrum of single fractal surface only has one segment, but the power spectrum of bifractal surface has two distinct segments, the different fractal dimensions are shown on the spectra graph. It is verified by calculation that fractal dimensions of the generated surfaces are in good agreement with the specified values. To compare with the traditional statistic parameters, the fractal dimensions and characteristic scale are scale independence to some extent. According to statistics, the two generated surfaces both have the character of the Gauss distribution. The scale independence of fractal characterization and statistical properties of the generated surfaces are discussed, through which it is concluded that a sophisticated description of rough surfaces should include both fractal and statistic features.