Characterization of interface stresses and lubrication of rough elastic surfaces under ball-on-disc rolling

Abstract

This paper presents a statistical method for characterizing the interface stresses between an elastic rough ball and a smooth rigid disc under lubrication by considering the percolation effect of lubricant flow. The statistical analysis was carried out to integrate the random, microscopic asperity deformation with the asperity–lubricant interaction. An efficient solution process with the aid of the fast Fourier transform was developed for the multi-scale analysis. To avoid numerical instability, the Poiseuille term of the average Reynolds equation was turned off when the average lubricant film thickness was below the percolation threshold and the average hydrodynamic pressure was solved by using the Couette term. This successfully overcomes the limitation in the conventional statistical treatment of mixed lubrication. Moreover, it enables a smooth transition from mixed to boundary lubrication and allows a large range of dimensionless rolling speed, which cannot be achieved by conventional approaches. Also, an empirical formula was developed to evaluate the average central and minimum film thicknesses between lubricated rough surfaces in contact. It was found that the method developed can precisely predict the effect of surface roughness on contact stresses, can effectively estimate the contribution of the direct asperity–disc contacts, and can be used to describe the lubricant performance at a rolling–sliding contact interface.

Keywords

Statistical analysis mixed lubrication elastohydrodynamic lubrication rough surface

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