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

A full numerical analysis of the hydrodynamic lubrication problem of artifi cial hip joint replacements with surfaces of high elastic modulus materials , such as metal-on-metal or ceramic-on-ceramic, under cyclic walking condit ions is reported in this paper. The Reynolds equation in spherical coordina tes 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 fi nite lubricating film thickness can be developed during the walking cycle o wing to the combined action of the squeeze film and entraining motions unde r some conditions. It has been found that the design parameters for plain s pherical bearings, such as the femoral head radius and the radial clearance between the femoral head and the acetabular cup, have a large effect on th e 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 acet abular cup. It is shown that a dimple on the acetabular cup can significant ly increase the film thickness throughout the walking cycle, particularly f or 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 lubri cating film can be developed in ceramic-on-ceramic hip joint replacements, and perhaps for some well-finished metal-on-metal implants with a relativel y small radial clearance. For some metal-on-metal configurations, the effec t of elastic deformation of the bearing surfaces must be taken into account in the lubrication analysis, particularly for a relatively large radial cl earance.