The contact mechanics in metal-on-metal hip implants employing a cobalt chromium acetabular cup with an ultra-high molecular weight polyethylene (UHMWPE) backing were analysed in the present study using the finite element method. A general modelling methodology was developed to examine the effects of the interfacial boundary conditions between the UHMWPE backing and a titanium shell for cementless fixation, the coefficient of friction and the loading angle on the predicted contact pressure distribution at the articulating surfaces. It was found that the contact mechanics at the bearing surfaces were significantly affected by the UHMWPE backing. Consequently, a relatively constant pressure distribution was predicted within the contact conjunction, and the maximum contact pressure occurred towards the edge of the contact. On the other hand, the interfacial boundary condition between the UHMWPE backing and the titanium shell, the coefficient of friction and the loading angle were found to have a negligible effect on the contact mechanics at the bearing surfaces. Overall, the magnitude of the contact pressure was significantly reduced, compared with a similar cup without the UHMWPE backing. The importance of the UHMWPE backing on the tribological performance of metal-on-metal hip implants is discussed.

The elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a 28 mm diameter metal-on-metal hip prosthesis employing a metallic cup with an ultra-high molecular weight polyethylene (UHMWPE) backing under a simple steady state rotation representing the flexion/extension during walking. Both Reynolds and elasticity equations were coupled and solved numerically by the finite difference method. The elastic deformation was determined by means of the fast Fourier transform (FFT) technique using the displacement coefficients obtained from the finite element method. Excellent agreement of the predicted elastic deformation was obtained between the FFT technique and the conventional direct summation method. The number of grid points used in the lubrication analysis was found to be important in predicting accurate film thicknesses, particularly at low viscosities representative of physiological lubricants. The effect of the clearance between the femoral head and the acetabular cup on the predicted lubricant film thickness was shown to be significant, while the effect of load was found to be negligible. Overall, the UHMWPE backing was found not only to reduce the contact pressure as identified in a previous study by the authors (Liu et al., 2003) but also significantly to increase the lubricant film thickness for the 28 mm diameter metal-on-metal hip implant, as compared with a metallic mono-block cup.

Complete numerical solutions were obtained for the time-dependent thermal elastohydrodynamic lubrication (EHL) of line contacts under combined vertical and longitudinal vibrations. It was assumed that the contact was composed of two in®nitely long steel rollers. These rollers were then simpli®ed as an in®nite plane and an equivalent roller. The lubricant was assumed to be a Ree±Eyring non-Newtonian¯uid. The time-dependent numerical solutions were achieved instant after instant in each period of vibrations. The periodic error was checked at each end of the vibration period until the responses of pressure, ®lm thickness and temperature were all periodic functions with the frequency of the roller's vibrations. At each instant, the pressure ®eld was solved with a multi-grid method, the surface deformation was solved with a multi-level multi-integration technique, and the temperature ®eld was solved with a ®nite difference scheme through a sweeping process. It was shown that the normal vibration dominated the EHL characteristics and could be either strengthened or weakened slightly depending on the phase of the tangential vibration. It was also found that the vibration of the roller could produce transient surface dimples within the contact conjunction.

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