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Derived from the Heterogeneous Multiscale Methods (HMM), a two-scale method is developed for the analysis of Elastohydrodynamic Lubrication (EHL) and micro-EHL in tilted-pad bearings with threedimensional topography. A relationship linking the pressure gradient to mass flow rate is derived and represented in the bearing domain through homogenisation of near-periodic simulations describing the Fluid Structure Interaction (FSI) of topographical features. For the parameters investigated the influence of compressibility and piezoviscosity was found to be more significant than that of non-Newtonian (shear-thinning) behaviour on textured bearing performance. As the size of topography increased twoscale solutions demonstrated that at constant load the coefficient of friction increased and the minimum film thickness decreased over a range of pad lengths and tilt angles.

Diameter and diametral clearance of the bearing surfaces of metal-on-metal hip implants and structural supports have been recognized as key factors to reduce the dry contact and hydrodynamic pressure and improve lubrication performance. On the other hand, application of aspherical bearing surfaces can also significantly affect the contact mechanics and lubrication performance by changing the radius of the curvature of a bearing surface and consequently improving the conformity between the head and the cup. In this study, a novel metal-on-metal hip implant employing a specific aspherical bearing surface, Alpharabola, as the acetabular surface was investigated for both contact mechanics and elastohydrodynamic lubrication under steady state conditions. When compared with conventional spherical bearing surfaces, a more uniform pressure distribution and a thicker lubricant film thickness within the loaded conjunction were predicted for this novel Alpharabola hip implant. The effects of the geometric parameters of this novel acetabular surface on the pressure distribution and lubricant thickness were investigated. A significant increase in the predicted lubricant film thickness and a significant decrease in the dry contact and hydrodynamic pressures were found with appropriate combinations of these geometric parameters, compared with the spherical bearing surface.

The lubrication regime in which artificial hip joints operate adds complexity to the prediction of wear, as the joint operates in both the full fluid film regime-specifically the elastohydrodynamic lubrication (EHL) regime-and the mixed or boundary lubrication regimes, where contact between the bearing surfaces results in wear. In this work, a wear model is developed which considers lubrication for the first time via a transient EHL model of metal-on-metal hip replacements. This is a framework to investigate how the change in film thickness influences the wear, which is important to further investigation of the complex wear procedure, including tribocorrosion, in the lubricated hip implants. The wear model applied here is based on the work of Sharif et al. who adapted the Archard wear law by making the wear rate a function of a relative film thickness nominalized by surface roughness for examining wear of industrial gears. In this work, the gait cycle employed in hip simulator tests is computationally investigated and wear is predicted for two sizes of metal-on-metal total hip replacements. The wear results qualitatively predict the typical wear curve obtained from experimental hip simulator tests, with an initial "running-in period" before a lower wear rate is reached. The shape of the wear scar has been simulated on both the acetabular cup and the femoral head bearing surfaces. Keywords:wear model; elastohydrodynamic lubrication (EHL); metal-on-metal total hip joint replacement; Archard law; numerical simulation Introduction:

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The frictional performance of a bearing is of significant interest in any mechanical system where there are lubricated surfaces under load and in relative motion. Surface topography plays a major role in determining the coefficient of friction for the bearing because the size of the fluid film and topography are of a comparable order. The problem of optimising topography for such a system is complicated by the separation in scales between the size of the lubricated domain and that of the topography, which is of at least one order of magnitude or more smaller. This paper introduces a multiscale method for optimising the small scale topography for improved frictional performance of the large scale bearing. The approach fully couples the elastohydrodynamic lubrication at both scales between pressure generated in the lubricant and deformation of the bounding surfaces. Homogenised small scale data is used to inform the large scale model and is represented using Moving Least Squares metamodels calibrated by cross validation. An optimal topography for a minimum coefficient of friction for the bearing is identified and comparisons made of local minima in the response, where very different topographies with similar frictional performance are observed. Comparisons of the optimal topography with the smooth surface model demonstrated the complexity of capturing the non-linear effect of topography and the necessity of the multiscale method in capturing this. Deviations from the smooth surface model were quantified by the metamodel coefficients and showed how topographies with a similar frictional performance have very different characteristics.