Similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure

Some modern scaling and fractal approaches to the characterization of surface roughness are under consideration. A new mathematical model of a multilevel profile suitable for flexible simulation of roughness is presented as a development from these approaches. The iterative construction of the model is described. It is shown that the profile is a hierarchical structure with self-affine and fractal features. Its geometrical properties are studied both analytically and numerically, and some of them are proved to be of the renormalization type. The profile contour length can be finite or infinite depending on the chosen values of the structural parameters. Some characteristics including the bearing curve and the upper volume function of the profile and the corresponding prestructures are calculated. (C) 1999 Elsevier Science Ltd. All rights reserved.