Elastohydrodynamic lubrication analysis of a functionally graded layered bearing surface, with particular reference to 'cushion form bearings' for artificial knee joints

摘要

Elastohydrodynamic lubrication of a functionally graded layered (FGL) bearing surface, whose elastic modulus increases with depth from the bearing surface, was investigated in this study. The finite difference method was employed to solve the Reynolds equation, simultaneously with the elasticity equation of the bearing surface, under circular point contacts. The finite element method was adopted to solve the elasticity equation for the FGL bearing surface. The displacement codricjents thus obtained were mcd to calculate the elastic dcformation or the bearing surface, required for the elastohydrodynamic lubrication analysis. Good agrecinent of the piudicted film thickness and pressure distribution was obtained. beteen the present method and a previous study for a single layered bearing surface with a uniform elastic modulus. The general numerical methodology was then applied to an FGL bearing surface with both linear and exponential variations in elastic modulus, with particular reference to the 'cushion form bearing' for artificial knee joints. The predicted film thickness and pressure distribution were shown to be quite close to those obtained for a singie layer under typical operating conditions ncpresentativc of artificial knee joints, provided that the elastic modulus of the single layer was chosen to be the average elastic modulus or the graded layer.