How to determine the number of asperity peaks, their radii and their heights for engineering surfaces: A critical appraisal

At present there are no generally accepted and experimentally confirmed, 2D or 3D, deterministic, asperity-deformation models to evaluate the real contact area in tribological applications. One of the key obstacles is that there are no clear and experimentally verified criteria about how to define and consequently determine the “actual” load-carrying asperity peaks. As a result, this work attempts to clarify how different, arbitrarily selected, asperity-peak identification criteria affect the calculated asperity-peak properties, i.e., the number, radii and heights. Such an analysis is still missing from the literature on 2D and 3D, asperity-peak analyses and is required for a better understanding of the physical meaning and engineering feasibility, and thus more realistic assumptions about these criteria. Different criteria that take into account the number of required neighbouring points (i.e., 3, 5 and 7 points), the peak-threshold value (z-direction) and the effect of the data resolution in the x-direction were applied in this study. Five different real surface roughnesses in the broad engineering range from Ra=0.003 μm to Ra=0.70 μm were evaluated. The results show the huge influence of these pre-selected criteria for which no verified guidelines exist. Although contact-deformation conditions based on experimental evidence are still required, several obvious and relevant conclusions can be drawn: (i) the 3-point asperity-peak criteria are more trustworthy than the 5 or 7 point criteria, (ii) an x-direction data resolution Δx below 1 μm should be used to limit the important effect on the calculated number of asperity peaks, and (iii) the peak threshold value (z-direction criteria) depends to a large extent on the surface roughness and lacks guidelines for use in its current form.