Fractal characterization and simulation of rough surfaces

Roughness measurements on a variety of machined steel surfaces and a textured magnetic thin-film disk have shown that their topographies are multiscale and random. The power spectrum of each of these surfaces follows a power law within the length scales considered. This spectral behavior implies that when the surface is repeatedly magnified, statistically similar images of the surface keep appearing. In this paper the fractal dimension is identified as an intrinsic property of such a multiscale structure and the Weierstrass-Mandelbrot (W-M) fractal function is used to introduce a new and simple method of roughness characterization. The power spectra of the stainless steel surface profiles coincide at high frequencies and correspond to a fractal dimension of 1.5. It is speculated that this coincidence occurs at small length scales because the surface remains unprocessed at such scales. Surface processing, such as grinding or lapping, reduces the power at lower frequencies up to a certain corner frequency, higher than which all surfaces behave as unprocessed ones. The W-M function is also used to simulate deterministically both brownian and non-brownian rough surfaces which exhibit statistical resemblance to real surfaces.