Applicability of fractal concepts to surface roughness

The stochastic part of metal surface profiles can be described by means of fractal geometry. The scaling behaviour of the roughness-depth as function of the basis length is related to the non-integral fractal dimension. Regular fractals, which are constructed similarly to the Koch-curve, are not capable of reproducing typical roughness-depth distributions. More adequate is the Weierstra ss-Mandelbrot function, If the bearing area ratio approximately follows a power law, the parameters can be easily determined from the exponent and the form of the roughness-depth distribution, as is shown for a technical surface after cold-rolling. If the Weierstra ss-Mandelbrot function is used in two classical friction models, the influence of the parameters including the fractal dimension on the friction coefficient in the case of dry surfaces can qualitatively be estimated.