The coefficient of proportionality K between real contact area and load, with new asperity models

Most recent numerical works on fractal surfaces have simply compared the low load limit of the coefficient of proportionality kappa of the relationship between real contact area and load In particular, that provided by Persson's theory, and that obtained from the Bush. Gibson and Thomas (BGT-A) asperity contact theory, which is a generalized form of the Greenwood and Williamson (GW) one. The two theories differ only by a numerical constant kappa = root 8/pi approximate to 1 6 vs kappa = root 2 pi approximate to 2 5, but neither of the two provide an accurate prediction, Persson's value being generally too low, and BGT-A's limit being only valid for extremely large separations A detailed numerical comparison using a range of generated fractal surfaces permits to compare the existing models, finding for example that bandwidth is more Important than Gaussianity of the surfaces. Then, we propose two new theoretical equations generalizing GW and BGT to take into account interaction effects in an approximate way (GW-I and BGT-I, respectively), which significantly improve the accuracy of original asperity models. Further, as a practical alternative to the tribologist, we suggest a new very simple discrete form of the GW model (called GW-RI) whose accuracy is similar to BGT-I, but with much lower computational cost, comparable to analytical solutions since the latter require the evaluation of the variance of the profile slopes, sigma(2)(m), with a surface defined at a given set of points The GW-RI model additionally avoids an ambiguity over how to define numerically the variance of the profile slopes, sigma(2)(m)