Roughness, friction and wear: The effect of contact planform

Abstract

Recent theoretical and experimental findings suggest that the statistical properties which affect friction vary slowly with the dimensions of the nominal area. This variation is due to the existence of random long spatial fluctuations which are outside the bandwidth of features imposed by the surface preparation process and which longer wavelengths completely dominate contact behaviour. This leads to the suspicion that the second of Amontons' laws, i.e. that the limiting static friction is independent of the shape of the nominal area, is not absolutely true. A relation is derived which connects the limiting static friction with the statistical contact properties and with a dimension of the nominal area. In an experiment devised to test this relation, the limiting static friction was measured for three rectangular steel specimens whose nominal area and normal load were kept constant and whose length to breadth ratio varied. The limiting static friction was found to be linearly related to the specimen length in agreement with theoretical predictions. Regression analysis of 36 measurements established that the probability of this result being due to chance was less than 1 in 500. Supporting evidence for this hypothesis has also been found from wear experiments reported in the literature.