Leiming Gao

Effect of 3D physiological loading and motion on elastohydrodynamic lubrication of metal-on-metal total hip replacements

An elastohydrodynamic lubrication (EHL) simulation of a metal-on-metal (MOM) total hip implant was presented, considering both steady state and transient physiological loading and motion gait cycle in all three directions. The governing equations were solved numerically by the multi-grid method and fast Fourier transform in spherical coordinates, and full numerical solutions were presented included the pressure and film thickness distribution. Despite small variations in the magnitude of 3D resultant load, the horizontal anterior-posterior (AP) and medial-lateral (ML) load components were found to translate the contact area substantially in the corresponding direction and consequently to result in significant squeeze-film actions. For a cup positioned anatomically at 45 degrees , the variation of the resultant load was shown unlikely to cause the edge contact. The contact area was found within the cup dimensions of 70-130 degrees and 90-150 degrees in the AP and ML direction respectively even under the largest translations. Under walking conditions, the horizontal load components had a significant impact on the lubrication film due to the squeeze-film effect. The time-dependent film thickness was increased by the horizontal translation and decreased during the reverse of this translation caused by the multi-direction of the AP load during walking. The minimum film thickness of 12-20 nm was found at 0.4s and around the location at (95, 125) degrees. During the whole walking cycle both the average and centre film thickness were found obviously increased to a range of 40-65 nm, compared with the range of 25-55 nm under one load (vertical) and one motion (flexion-extension) condition, which suggested the lubrication in the current MOM hip implant was improved under 3D physiological loading and motion. This study suggested the lubrication performance especially the film thickness distribution should vary greatly under different operating conditions and the time and location that potential wear may occur was very sensitive to specific loading and motion conditions. This may provide some explanation to the large variations in wear from hip simulators and clinical studies, and also stress the importance of using more realistic loading and motion conditions in the tribological study of MOM hip prostheses.

Contact mechanics and elastohydrodynamic lubrication in a novel metal-on-metal hip implant with an aspherical bearing surface

Diameter and diametral clearance of the bearing surfaces of metal-on-metal hip implants and structural supports have been recognised as key factors to reduce the dry contact and hydrodynamic pressures 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.

Comparison of numerical methods for elastohydrodynamic lubrication analysis of metal-on-metal hip implants: Multi-grid verses Newton-Raphson

Abstract Elastohydrodynamic lubrication (EHL) of a metal-on-metal hip implant was investigated under quasi-static operating conditions. Various numerical methods, such as Newton-Raphson (N-R), multi-grid (MG), multi-level multi-integration, and fast Fourier transform technique (FFT), were considered and compared in terms of the convergence and accuracy of the numerical solution. It was found that the numerical convergence for the MG method was much faster, and consequently the computational time required was significantly lower than the N-R method. This feature was particularly evident, when a tighter tolerance was specified on the pressure iteration and a high load or low viscosity was considered. Furthermore, the multi-integration method was found to be more effective, only when four-level grids were considered and compared with the FFT technique. It was concluded that the MG method has the potential to be applied efficiently and effectively for modelling realistic EHL problems of artificial hip joints such as under transient conditions of walking and when the surface topography is considered.

A Multiscale Framework for EHL and Micro-EHL

In this article, a heterogeneous multiscale method is introduced to analyze the microelastohydrodynamic lubrication (micro-EHL) of bearings with topological features. Two scales are adopted in the analysis: the large-scale simulations describe the entire bearing domain, and the small-scale simulations describe the fluid–structure interaction (FSI) at the small-scale features. Conservation of mass and momentum of the lubricant and the bearings elastic deformation are solved for. The relationship between the pressure gradient and mass flow is obtained from homogenized small-scale FSI simulations and applied on a global scale via a scattered data interpolation method. When the micro structure is periodic the exact model at micro scale is replaced by an effective derived equation, i.e., homogenized model. The elastic deformation of the textured bearing surface is addressed at both the large and small scales, by decomposing the displacement influence matrix into the diagonal terms and nondiagonal terms (sorted at the small scale and large scale, respectively). The multiscale method was demonstrated as being capable of modeling the global pressure and film thickness for a bearing with surface texture while maintaining the accuracy of the small-scale modeling features. The illustrative geometry was that of a linear converging pad bearing in two dimensions. The solutions were compared with those obtained using lubrication theory for the smooth surface case, and good agreement was obtained. The method was then demonstrated for geometries incorporating topographical features.

The effect of aspherical geometry and surface texturing on the elastohydrodynamic lubrication of metal-on-metal hip prostheses under physiological loading and motions

Abstract As an alternative material combination, metal-on-metal (MOM) hip replacement has attracted a revived interest due to its very low wear rates. In this article, an elastohydrodynamic lubrication analysis is performed for an MOM hip replacement with specific geometrical designs: a macro Alpharabola geometry of the cup bearing surface and micro-dimples on the head surface. The corresponding numerical methodology is presented and full numerical solutions are obtained. The effect of the macro- and micro-geometrical designs on the lubrication performance is investigated, under both simplified and physiological walking conditions. The real physiological loading and motion conditions are important to be considered when optimizing the conformity-associated geometry of hip bearings. The Alpharabola geometry of cup bearing surface is found to significantly improve the lubricating film thickness and reduce hydrodynamic pressure of MOM hip implants, when the Alpharabola minimum radius is aligned with the loading direction. Dimpled surface texturing has an adverse effect in a fluid film lubrication regime under the conditions considered in this study.

Effect of walking patterns on the elastohydrodynamic lubrication of metal-on-metal total hip replacements

The profiles of forces and kinematics can significantly affect the results of both hip simulators and computer simulations of hip implants, in terms of lubrication and wear. Most of the related studies have employed the simplified load and motion profiles to simulate walking. The purpose of this study is to investigate the lubrication of a typical metal-on-metal (MOM) total hip implant, under different loading and motions of walking; which included three patterns for hip simulators (Leeds Mk I, Leeds ProSim, and the ISO standard) and a combined walking-stopping-start-up-walking pattern. A general ball-in-socket lubrication model was solved and full numerical solutions of the elastohydrodynamic lubrication were presented. The multi-grid method was adopted to solve the Reynolds equation. A combined multi-level multi-integration and fast Fourier transform technique was used to obtain the elastic deformation of bearing surfaces. Complex three-dimensional loading and motion were found to result in large variations of the film thickness during one walking cycle, particularly for the physiological case considered in the Leeds Mk I simulator. Under such a physiological pattern, the squeeze film effect was generally greater than the other two hip simulator patterns, particularly during the swing phase, resulting in larger film thickness. The squeeze film effect was encouraged by the translation of the lubricating contact area in the entrainment direction. Small variations in the film thickness and friction torque were observed between the Leeds ProSim and ISO patterns. Intermittent breaks during steady walking were unlikely to cause complete depletion of lubrication in the MOM hip implants. At 5 s after stopping, the lubrication regime was shifted from full film lubrication to mixed lubrication. A lubricant pocket was developed quickly and the film profile finally achieved an equilibrium condition.

Predictive wear modeling of the articulating metal-on-metal hip replacements

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.

Numerical solutions for the elastic deformation of spherical bearing surfaces of metal-on-metalhip joint implants

Abstract On the elastohydrodynamic lubrication analysis, one of the most time-consuming issues is the calculation of surface deformation. Two methods are usually adopted to fasten the calculation: the multi-level multi-integration (MLMI) and the fast Fourier transform (FFT). However, in spherical models such as for hip joint replacements, the finite-element method has to be employed instead of analytical formulations to determine the influence coefficients. It limits the coarsest grid to 60 × 60 points to ensure numerical accuracy. This limitation prevents the MLMI to achieve high performance. Therefore, a combined MLMI and FFT method is proposed. The basic idea is to replace the direct summation on the coarse grids in the MLMI by the FFT algorithm. The combined method is validated by comparing to the individual MLMI and FFT. The combined method is found to perform fastest. In solving a quasi-static elastohydrodynamic lubrication solution, approximately 65 per cent less CPU time is required on grid 512 × 512, and the accuracy is not affected. For the usual semi-infinite plane models, sometimes a large number of levels can cause a lot of additional operations and storage space when translating data between the levels. The combined MLMI and FFT method can be an alternative way to choose the coarse grid more flexibly, reduce the number of grid levels, and optimize the computing performance.

Different Loading and Motion Applied on Hip Simulators Affects the Lubrication of Metal-on-Metal Hip Implants

The transient elastohydrodynamic lubrication for metal-on-metal (MOM) total hip replacement was numerically solved under three gait loading and motion patterns, according to Leeds Mk I hip simulator, Leeds ProSim and ISO standard, respectively. The Reynolds equation for pressure calculation was solved in spherical coordinate system using the multi-grid method and the elastic deformation of both acetabular cup and femoral head was obtained by spherical FFT technique. Full numerical solutions of EHL were obtained including the pressure and film thickness distribution, for MOM hip replacement under the three gait patterns. Large variations in the film thickness were observed for different patterns, especially when the three dimensional load applied on. For example, the film thickness was significantly increased using Leeds Mk I pattern. This may result in large difference of hip simulator wear testing.

Elastohydrodynamic Lubrication of Aspherical Metal-on-Metal Artificial Hip Joints

The effect of a novel aspherical bearing surface, Alpharabola, which is defined as equation (1), on lubrication of MOM hip implants was investigated. The Reynolds equation was solved by the multi-grid (MG) method and the elastic deformation equation was solved by multi-level multi-integration (MLMI) method with the elastic deformation influence coefficients being calculated by finite element method (FEM). Typical pressure distribution and film profile of this implant were predicted. The effects of different geometric parameters, α, on pressure and film thickness were investigated. By introducing the average clearance, the lubrication performance of this novel MOM implant and that of the conventional spherical implants were compared.