Numerical analysis of rough surface characteristics and their contact behavior: The PSD Vs WM function generated self-affine fractal surfaces

As is well known, rough surfaces exhibit self-affine fractal. Synthesized artificial fractal surfaces with the power spectral density (PSD) and Weierstrass-Mandelbrot (WM) function methods are employed to facilitate contact research on friction, wear and lubrication. Since these two methods are independent, it is challenging to control the input parameters and ensure the creation of identical artificial surfaces with same roughness parameters. Nevertheless, comparisons between them are necessary for engineering research. In this paper, based on Nayak’s random process theory, a power spectral density that incorporates the WM function is established. The mathematical expression for the fractal roughness $G$ including $H$, $q_l$, $q_s$, $\zeta$, $h_{\mathrm{rms}}$ and $M$ is then derived, using the definition of the root mean square roughness as a reference, to match the WM and PSD surfaces. Through extensive numerical simulations, the asperity overlap is quantified for the first time, with $M=5$ specified, solving the problem of the WM function's inability to accurately represent rough surfaces. Additionally, we compare the multiasperity contact models with the Persson model. When the input parameters are the constant, rough surface characteristics and their contact behavior of the two surface types are nearly identical, so far both methods can be used for accurate simulation of fractal surfaces.