A general analytical solution to the problem of microelastohydrodynamic lubrication of low elastic modulus compliant bearing surfaces under line contact conditions

Abstract
A general governing equation for the pressure perturbation associated with the microelastohydrodynamic lubrication action generated by asperities superimposed upon compliant bearing surfaces of low elastic modulus has been derived in this study. It has been shown that the equation derived not only governs the lubrication of the asperities superimposed upon a macroelastohydrodyn-amic contact but also the asperity lubrication of a hydrodynamic lubrication conjunction such as a parallel face seal. Analytical solutions to the governing equation have been obtained under various conditions. The main characteristics associated with the microelastohydrodynamic lubrication mechanism predicted from the present analysis have been found to be in good agreement with the full numerical solutions presented by Dowson and Jin (1, 2) for the lubrication of normal human ankle joints. Furthermore, it is pointed out that the simple analytical method developed in this study can be applied not only to a layered surface on a rigid backing, as in the natural synovial joint, but also to the more general situation of semi-infinite solids with low elastic modulus.