A study of the effect of model geometry and lubricant rheology upon the elastohydrodynamic lubrication performance of metal-on-metal hip joints

Lubrication modelling is of great importance in the design of artificial hip joints, especially for the demand of long life expectancy of those joints employing a metal-on-metal bearing. Through lubrication analysis, the dimensions of the head/cup and the clearance between them can be reasonably determined, and thus, if fluid film lubrication can be generated in artificial hip joint replacements, the wear and related failure can be reduced. In the majority of published numerical studies of the lubrication of hip joints, the synovial fluid for the natural joint and bovine serum used for in vitro simulator testing of joint replacements have always been treated as isoviscous, incompressible Newtonian fluids because the viscosity of these lubricants is almost unchanged at high shear rate. However, all these biological lubricants generally exhibit non-Newtonian characteristics of shear thinning, particularly under relatively low shear rates, and display a second Newtonian plateau at high shear rates.

In this paper, model geometry is investigated first to show that the ball-on-plane model is a reasonable approximation to a typical metal-on-metal hip joint bearing considered. Then, in order to accurately predict the film thickness and pressure, the Reynolds equation considering the shear thinning effect of biological lubricants is derived, based on the Rabinowitsch model and following Greenwood's approach. The non-Newtonian effect was considered through two effective flow factors in the sliding and leakage directions, respectively. Numerical simulations were conducted on the basis of an equivalent ball-on-plane model with an effective radius determined from the head radius and the radial clearance, showing the influence of the shear thinning effect. The general lubrication model based on the unified Reynolds equations model was solved for the film thickness and pressure distribution, and the FFT-based approach was utilized to speed up the time-consuming calculation of elastic deformation in a fully numerical lubrication analysis. The results showed that the predicted film thickness when considering the shear thinning effect was slightly larger than that from the isoviscous model. It was found, however, that if the viscosity of the lubricant is adopted as the asymptotic value at high shear rate, the isoviscous Newtonian model can also give accurate predictions of film thickness. This is due to the relatively high shear rate in the contact zone.