Numerical simulation of friction between contacting rough surfaces

A model for predicting the friction of contacting rough surfaces is presented. Numerical simulation techniques are used to generate randomly rough surfaces with Gaussian statistics, An elastic Hertzian analysis is then used to calculate the contact of each generated surface with a rigid, perfectly smooth, half plane of specified applied load. The number, location and size of the contact points are determined. Contact is also calculated according to simple plasticity theory, and the authors show how the results from the elastic analysis tend to the plasticity results, as surface roughness increases. For each calculated contact profile, the friction coefficient for that contact is calculated, using two method, one 'microscopic' and one 'macroscopic'. For the microscopic method he calculates the adhesive force required to break each junction, and sum these to produce the total frictional force. This assumes that each contact point must be broken simultaneously, and is likely to overestimate the frictional force for a large number of contact points. In the macroscopic approach the total frictional force is related to the total true contact area, but does not take account of the details of each individual contacting junction. He presents results from the models, showing the effects of applied load, and of surface and material properties, on quantities such as the total contact area, mean contact pressure and mean surface separation, and hence on frictional force. The numerical approach allows one to study the typical variations in friction that might reasonably be expected to arise from the statistical nature of the surface contact. He finds that these variations are generally smaller than those measured in a typical friction experiment. Model predictions are compared with experimental measurements of the friction of MoS2 coated substrates. The macroscopic model is shown to predict the variation of friction with roughness, whereas the microscopic model performs better when studying the effect of applied load on friction. In both cases, agreement is better for the metallic substrates than for the ceramic substrate. Reasons for these results, and possible extensions of the model, are discussed.