A Multi-Scale Model for Contact Between Rough Surfaces

This work describes a non-statistical multi-scale model of the normal contact between rough surfaces. The model produces predictions for contact area as a function of contact load, and is compared to the traditional Greenwood and Williamson (GW) and Majumdar and Bhushan (MB) rough surface contact models, which represent single-scale statistical and fractal analyses, respectively. The current model incorporates the effect of asperity deformations at multiple scales into a simple framework for modeling the contact between nominally flat rough surfaces. Similar to the “protuberance upon protuberance” theory proposed by Archard, the model considers the effect of having smaller asperities located on top of larger asperities in repeated fashion with increasing detail down to the limits of current measurement techniques. The parameters describing the surface topography (areal asperity density and asperity radius) are calculated from an FFT performed of the surface profile. Thus, the model considers multi-scale effects, which fractal methods have addressed, while attempting to more accurately incorporate the deformation mechanics into the solution. After the FFT of a real surface is calculated, the computational resources needed for the method are very small. Perhaps surprisingly, the trends produced by this non-statistical multi-scale model are quite similar to those arising from the GW and MB models, but seem largely unaffected by the sampling resolution at the employed surface data.