Inclusion of “interaction” in the Greenwood and Williamson contact theory

Recent direct implementation of asperity theories is reinterpreted here to formulate an improved version of the Greenwood and Williamson GW) theory with the inclusion of interaction between asperities. This is achieved by treating the contact pressures as uniformly distributed over he apparent contact area and the resulting deformation as uniform. The correction is equivalent to an increase of the effective separation of the ean planes by a quantity proportional to the nominal pressure, resulting in a reduction of the “real” area of contact and of total load for a given eparation. However, the area–load relationship is unchanged. The correction effectively depends on the ratio between the nominal pressure and he elastic modulus multiplied by the ratio between the size of the nominal contact area and standard deviation of the asperity heights. For contacts uch larger than the size of roughness, uniform interaction effects would be dominant at relatively modest pressures (particularly for soft materials). his also means that the effect of interaction is unlimited. However, the only significant change is in the prediction of gas-tightness, it is harder to eal a large area than a small one. The modification of the theory has a significant effect on stiffness and conductance. Indeed, a parallel is drawn etween this correction and the “clustering” terms of resistance in the Holm–Greenwood formulae for a cluster of circular spots. Finally, numerical ontact simulations using Weierstrass–Mandelbrot (WM) surfaces show a general agreement with the improved theory but also significant scatter or low load levels. Taking into account the effect of asperity interaction, the improved GW theory is now able to predict the numerically obtained ontact response for intermediate load levels. 2008 Published by Elsevier B.V.