Estimating Mixed & Boundary Friction from the Lambda Ratio: Incorporating the Effect of Surface Character

The authors have previously reported a method to estimate boundary and mixed friction coefficients using lambda ratio values and friction data from Mini Traction Machines (MTM). This paper reports a more general approach which accounts for the surface height distribution of the topographies at the interface by employing the overlap functions of idealised probability height distributions of the interface components. The overlap coefficients of probability density functions relevant to engineering rough surfaces have been calculated, and simple analytical expressions have been obtained for exponential, Gaussian and Rayleigh distribution functions. This is believed to be the first time overlap coefficients of probability density functions have been calculated and applied in a tribological context. It has been found that the derived expressions can be used to predict mixed/boundary friction for rough surface lubricated contacts and are in good agreement with published experimental data. It has also been noted that rough surfaces with identical Gaussian distribution functions take an especially simple form and that surfaces that are described by the Rayleigh probability density function, provide a good model for “run-in” surfaces. This feature allows tribologists to make quick and simple comparisons of the friction of new and worn, or run-in, machine components.