An Analysis of the Multi-scale Structure of Rough Surfaces

Abstract

Even with the various surface finishing techniques, all surfaces are rough with different structures and geometric characteristics over multiple scales. The roughness impacts significantly the friction, wear, and surface fatigue of applications, and also affects the electrical and thermal resistance. In this work, a profilometer was utilized to measure the profiles of different rough surfaces, and the profiles were characterized using a variety of statistical, multi-scale spectrum, and fractal methodologies. Since the fractal dimension, D, is a very popular and arguably important parameter in describing the fractal rough surfaces, four different methods are implemented in calculating the value and these four methods are then compared. The relationship between the fractal dimension, D, and the fractal scaling constant, G, is investigated as well. The measured rough surfaces are also compared with W-M function generated rough surfaces. After comparing a series of statistical and fractal parameters which are calculated based on the surface profile data, it can be found that the Weierstrass-Mandelbrot (W-M) function does not appear to be very suitable for characterizing real rough surfaces. Another important conclusion is that many surfaces are not consistent with the quality of self-affinity that many of the popular fractal models assume. Therefore, a discrepancy exists between idealized fractal equations and real surfaces.