A full numerical analysis of hydrodynamic lubrication in artificial hip joint replacements constructed from hard materials

Abstract
A full numerical analysis of the hydrodynamic lubrication problem of artificial hip joint replacements with surfaces of high elastic modulus materials, such as metal-on-metal or ceramic-on-ceramic, under cyclic walking conditions is reported in this paper. The Reynolds equation in spherical coordinates has been solved for both entraining and combined entraining and squeeze film motions under a three-dimensional variation in both the load and the speed experienced in hip joints during walking. It has been shown that a finite lubricating film thickness can be developed during the walking cycle owing to the combined action of the squeeze film and entraining motions under some conditions. It has been found that the design parameters for plain spherical bearings, such as the femoral head radius and the radial clearance between the femoral head and the acetabular cup, have a large effect on the magnitude of the predicted lubricating film thickness. Some interest has been shown in recent years in the performance of metal-on-metal bearings in which a dimple has been machined at the pole of the acetabular cup. It is shown that a dimple on the acetabular cup can significantly increase the film thickness throughout the walking cycle, particularly for relatively large depths and if the location of the dimple coincides with the direction of the resultant force acting on the joints. It is concluded that there is a good possibility that a full continuous hydrodynamic lubricating film can be developed in ceramic-on-ceramic hip joint replacements, and perhaps for some well-finished metal-on-metal implants with a relatively small radial clearance. For some metal-on-metal configurations, the effect of elastic deformation of the bearing surfaces must be taken into account in the lubrication analysis, particularly for a relatively large radial clearance.