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 pro_le suitable for ~exible simulation of roughness is presented as a development from these approaches[ The iterative construction of the model is described[ It is shown that the pro_le is a hierarchical structure with self!a.ne 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 pro_le contour length can be _nite or in_nite depending on the chosen values of the structural parameters[ Some characteristics including the bearing curve and the upper volume function of the pro_le and the corresponding prestructures are calculated