Experimental and Theoretical Studies of the Fractal Scaling Parameter and the Lateral Scale Dependence of the Asperity Interference

The fractal scaling parameter was released in a recent study from its artificially assigned constant value to become a measurable parameter for simulated surface profiles. In the present study, this concept was extended to develop schemes for determining the fractal scaling parameter from experimental power spectral density data. The difference in the trends of peaks has been observed between experimental power spectral density data and those of the Weierstrass-Mandelbrot function. A modified W-M function was proposed based on a peak splitting behavior of the power spectrum. To verify a relationship between the interference and lateral length scale for asperities, which is commonly assumed in fractal modeling, a numerical scheme was developed to truncate measured surface profiles for finding asperity interferences for microcontacts of various sizes. This relationship was confirmed by the favorable results from a comparison of the power values obtained from truncation of a surface profile to those obtained by using the fast Fourier transform. A numerical scheme was developed to generate random power spectral density curves and fractal surface profiles for given values of the fractal scaling parameter.