An expert system to characterise the surfaces morphological properties according to their tribological functionalities: The relevance of a pair of roughness parameters

Knowing that a surface or profile can be characterized by numerous roughness parameters, the objective of this investigation was to present a methodology which aims to determine quantitatively and without preconceived opinion the most relevant pair of roughness parameters that describe an abraded surface. The methodology was firstly validated on simulated fractal profiles having different amplitudes and Hölder exponents and it was secondly applied to characterise different worn regions of a retrieved metallic femoral head articulated against an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup containing an embedded metallic fibber into its surface. The methodology consists in combining the recent Bootstrap method with the usual discriminant analysis. It was validated on simulated fractal profiles showing that, among more than 3000 pairs tested, the total amplitude Rt and the fractal dimension Δ is the most relevant pair of roughness parameters; parameters corresponding to the variables modulated in the analytical expression of the fractal function. The application of this methodology on a retrieved metallic femoral head shows that the most relevant pair of parameters for discriminating the different investigated worn regions is the arithmetic roughness parameter Ra paired with the mean peak height Rpm. This methodology finally helps in a better understanding of the scratch mechanism of this orthopedic bearing component.