Feature Analysis of Fractal Surface Roughness Based on Three-dimensional W-M Function

Abstract

The three-dimensional W-M fractal function was used to simulate the rough surface, and the different fractal parameters correspond to the different surface morphology. In order to explore the influence rule of fractal dimension D and scale coefficient G on the surface profile, the fractal dimension D value was 2.5, and the scale factor G value was 1E-14. The mean height, standard deviation and spectrum characteristics of the surface contour were analyzed. The results show that under the action of a single fractal parameter, the surface roughness Ra and the surface contour height standard deviation std all decrease with the increase of D, and increase with the increase of G, and the change trend is basically the same. When D is kept constant and only G is a variable, the surface height value of frequency components remain unchanged, the amplitude of each frequency decreases with the decrease of G; G remains unchanged but only D is a variable, with the increase of D, the frequency amplitude changes slowly, and the amplitude decreases.