Effect of non-spherical bearing geometry on transient elastohydrodynamic lubrication in metal-on-metal hip joint implants

Abstract

A transient elastohydrodynamic lubrication model for non-spherical bearing surfaces of artificial hip joint implants under walking conditions has been developed. A nominal ball-in-socket configuration was employed to represent the articulation between a spherical femoral head and a non-spherical acetabular cup in this study. The non-sphericity of the bearing geometry was described by an ellipsoid with the variation of three ellipsoidal semi-axis lengths relative to the nominal spherical surface. An appropriate spherical coordinate system and mesh grids were selected to facilitate the numerical simulation. Both the equivalent discrete spherical convolution model and the corresponding spherical fast Fourier transform technique were used to evaluate the elastic deformation of both the spherical head and non-spherical cup surfaces. The transient lubrication model was subsequently adopted to investigate the effect of nonsphericity of an ellipsoidal cup on the transient elastohydrodynamic lubrication in a typical metal-on-metal hip joint implant. It was found that the non-sphericity could have a large effect on the predicted film thickness and the maximum pressure by as much as ∼43 and 17 per cent respectively, for the conditions considered in this study, depending on the orientation of the non-spherical cup relative to the flexion-extension direction. Furthermore, the non-sphericity of the cup bearing surface, which can be caused by shape tolerance in manufacturing or wear in clinical application, was discussed, in relation to the lubrication.