Effect of ultra-high molecular weight polyethylene thickness on contact mechanics in total knee replacement

One of the important design parameters in current knee joint replacements is the thickness of the ultra-high molecular weight polyethylene (UHMWPE) tibial insert, yet there is no clear definition of the upper limit of the 'thick' polyethylene insert. Using one design knee implant and subjecting it to the physiological loads encountered throughout the gait cycle, measurements of the lengths of contact imprints generated were compared with the corresponding theoretical predictions for different insert thicknesses under the same applied load. Multiple regression analysis was applied to test whether the dimensions of contact imprints are influenced by UHMWPE thickness. Good agreement was obtained between the theoretical predictions and the experimental measurements of the dimensions of contact imprints when the knee was at 60 degrees flexion. Therefore, it was possible to estimate the contact pressure at the articulating surface using the theoretical model. Contact imprint dimensions increased with increasing applied load. Statistical analysis of the experimental data revealed that, at 0 degree flexion, the overall imprint dimensions increased as the UHMWPE thickness increased from 8 to 20 mm. However, the increment was not significant when the thickness subinterval 10-15 mm was considered. Furthermore, at 60 degrees flexion, thickness was not a significant factor for the overall imprint dimensions. No evidence was found from the data to suggest that an increment in polyethylene thickness over 10 mm would significantly reduce the contact imprint dimensions. These findings suggest that thicker inserts can be avoided, as they require unnecessary bone resection.     

Analysis of contact mechanics in McKee-farrar metal-on-metal hip implants

Contact mechanics analysis for a typical McKee-Farrar metal-on-metal hip implant was carried out in this study. The finite element method was used to predict the contact area and the contact pressure distribution at the bearing surfaces. The study investigated the effects of the cement and underlying bone, the geometrical parameters such as the radial clearance between the acetabular cup and the femoral head, and the acetabular cup thickness, as well as other geometrical features on the acetabular cup such as lip and studs. For all the cases considered, the predicted contact pressure distribution was found to be significantly different from that based upon the classical Hertz contact theory, with the maximum value being away from the centre of the contact region. The lip on the cup was found to have a negligible effect on the predicted contact pressure distribution. The presence of the studs on the outside of the cup caused a significant increase in the local contact pressure distribution, and a slight decrease in the contact region. Reasonably good agreement of the predicted contact pressure distribution was found between a three-dimensional anatomical model and a simple two-dimensional axisymmetric model. The interfacial boundary condition between the acetabular cup and the underlying cement, modelled as perfectly fixed or perfectly unbonded, had a negligible effect on the predicted contact parameters. For a given radial clearance of 0.079 mm, the decrease in the thickness of the acetabular cup from 4.5 to 1.5 mm resulted in an increase in the contact half angle from 15 degrees to 26 degrees, and a decrease in the maximum contact pressure from 55 to 20 MPa. For a given acetabular cup thickness of 1.5 mm, a decrease in the radial clearance from 0.158 to 0.0395 mm led to an increase in the contact half-angle from 20 degrees to 30 degrees, and a decrease in the maximum contact pressure from 30 to 10 MPa. For zero clearance, although the contact pressure was significantly reduced over most of the contact area, the whole acetabular cup came into contact with the femoral head, leading to stress concentration at the edge of the cup. Design optimization of the geometrical parameters, in terms of the acetabular cup thickness and the radial clearance, is important, not only to minimize the contact stress at the bearing surfaces, but also to avoid equatorial and edge contact.     

Prediction of scratch resistance of cobalt chromium alloy bearing surface, articulating against ultra-high molecular weight polyethylene, due to third-body wear particles

The entrapment of abrasive particles within the articulation between a cobalt chromium alloy (CoCrMo) femoral component and an ultra-high molecular weight polyethylene (UHMWPE) cup of artificial hip joints or tibial inserts of artificial knee joints usually scratches the metallic bearing surface and consequently increases the surface roughness. This has been recognized as one of the main causes of excessive polyethylene wear, leading to osteolysis and loosening of the prosthetic components. The purpose of this study was to use the finite element method to investigate the resistance of the cobalt chromium alloy bearing surface to plastic deformation, as a first approximation to causing scratches, due to various entrapped debris such as bone, CoCrMo and ZrO2 (contained in radiopaque polymethyl methacrylate cement). A simple axisymmetric micro contact mechanics model was developed, where a spherical third-body wear particle was indented between the two bearing surfaces, modelled as two solid cylinders of a given diameter, under the contact pressure determined from macro-models representing either hip or knee implants. The deformation of both the wear particle and the bearing surfaces was modelled and was treated as elastic-plastic. The indented peak-to-valley height on the CoCrMo bearing surface from the finite element model was found to be in good agreement with that reported in a previous study when the third-body wear particle was assumed to be rigid. Under the physiological contact pressure experienced in both hip and knee implants, ZrO2 wear particles were found to be fully embedded within the UHMWPE bearing surface, and the maximum von Mises stresses within the CoCrMo bearing surface reached the corresponding yield strength. Consequently, the CoCrMo bearing surface was deformed plastically and the corresponding peak-to-valley height (surface roughness) was found to increase with both the hardness and the size of the wear particle. Even in the case of CoCrMo wear particles, with similar mechanical properties to those of the CoCrMo bearing surface, a significant plastic deformation of the bearing surface was also noted; this highlighted the importance of considering the deformation of the wear particles. These findings support the hypotheses made by clinical studies on the contribution of entrapped debris to increased surface roughness of CoCrMo femoral bearing surfaces.     

Analysis of elastohydrodynamic lubrication in McKee-Farrar metal-on-metal hip joint replacement

An elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a typical McKee-Farrar metal-on-metal hip prosthesis under a simple steady state rotation. The finite element method was used initially to investigate the effect of the cement and bone on the predicted contact pressure distribution between the two articulating surfaces under dry conditions, and subsequently to determine the elastic deformation of both the femoral and the acetabular components required for the lubrication analysis. Both Reynolds equation and the elasticity equation were coupled and solved numerically using the finite difference method. Important features in reducing contact stresses and promoting fluid-film lubrication associated with the McKee-Farrar metal-on-metal hip implant were identified as the large femoral head and the thin acetabular cup. For the typical McKee-Farrar metal-on-metal hip prosthesis considered under typical walking conditions, an increase in the femoral head radius from 14 to 17.4 mm (for a fixed radial clearance of 79 microm) was shown to result in a 25 per cent decrease in the maximum dry contact pressure and a 60 per cent increase in the predicted minimum film thickness. Furthermore, the predicted maximum contact pressure considering both the cement and the bone was found to be decreased by about 80 per cent, while the minimum film thickness was predicted to be increased by 50 per cent. Despite a significant increase in the predicted minimum lubricating film thickness due to the large femoral head and the thin acetabular cup, a mixed lubrication regime was predicted for the McKee-Farrar metal-on-metal hip implant under estimated in vivo steady state walking conditions, depending on the surface roughness of the bearing surfaces. This clearly demonstrated the important influences of the material, design and manufacturing parameters on the tribological performance of these hard-on-hard hip prostheses. Furthermore, in the present contact mechanics analysis, the significant increase in the elasticity due to the relatively thin acetabular cup was not found to cause equatorial contact and gripping of the ball.     

Temperature Modeling in a Total Knee Joint Replacement Using Patient-Specific Kinematics

This paper reports the implementation of a computer modeling approach that uses fluoroscopically measured motions of total knee replacements as inputs and predicts patient-specific implant temperature rises using computationally efficient dynamic contact and thermal analyses. The multibody dynamic simulations of two activities (gait and stair) were generated from the fluoroscopic data to predict contact pressure and slip velocity time histories for individual elements on the tibial insert surface. These time histories were used in a computational thermal analysis to predict average steady-state temperature rise due to frictional heating on each element. For the standard condition, which assumes an ultra-high molecular weight polyethylene (UHMWPE) tibial component and cobalt-chrome femoral component, 1Hz activity frequency, friction coefficient of = 0.06, and convective heat transfer coefficient of h = 30 (W/(m²·K)), the predicted maximum temperature rise on the medial compartment was 9.1 and 14°C for continuous activities of gait and stair respectively. The sensitivity of the temperature rise to activity rate, heat partitioning to the femoral component, and convective heat transfer coefficient was explored. The model is extremely sensitive to the thermal properties of the femoral component and predicts order of magnitude changes in contact temperature with order of magnitude changes in thermal conductivity. A survey of thermal conductivity for current and proposed scratch resistant femoral component implant materials shows variations greater than an order of magnitude.     

Importance of pin geometry on pin-on-plate wear testing of hard-on-hard bearing materials for artificial hip joints

The contact mechanics between the pin and the plate used in simple wear screening tests were investigated in this study. Both soft-on-hard, such as ultra-high molecular weight polyethylene (UHMWPE)-on-metal or UHMWPE-on-ceramic, and hard-on-hard, such as metal-on-metal, bearing couples were considered. The effect of the pin geometry and the misalignment between the pin and the plate were investigated on the predicted contact pressure distribution at the bearing surfaces using the finite element method. It was demonstrated that in the case of soft-on-hard bearing couples, neither the geometrical discontinuity of the pin surface nor the misalignment could cause a significant increase in the contact stress. However, for hard-on-hard combinations, even with a very small misalignment of 0.5 degrees between the pin and the plate, the geometrical discontinuity could lead to a more than tenfold increase in the predicted contact stress. This elevated contact stress may lead to a large scatter in the wear data and, even more importantly, structural damage of the bearing surfaces.     

大功率密度柴油机主轴承混合润滑分析

针对某型柴油机功率提升后主轴承润滑性能出现恶化的现象,计及表面形貌和弹性变形等因素影响,建立12V150柴油机主轴承润滑分析模型。运用弹性流体润滑、轴承动力学及Greenwood-Tripp微凸峰接触理论,分析功率提升后的主轴承润滑性能,提出需要改进的参数。分析表明:主轴承润滑性能变差的原因主要是功率提升后,曲轴和主轴承承受载荷加剧,油膜压力增加,引起轴颈弯曲或倾斜,导致主轴最小油膜度减小。研究曲轴平衡率、轴承宽度和润滑油黏度等参数对主轴承润滑性能的影响,提出了将曲轴平衡率由70%增大至90%,轴承宽度由46 mm增大至48 mm,并合理增加润滑油黏度的改进方案。结果表明:曲轴平衡率能有效地减小主轴颈倾斜角度,而轴承宽度和润滑油黏度对轴颈倾斜几乎没有影响;改进后主轴承最小油膜厚度提升了16.08%,峰值粗糙接触压力减小了37.11%,平均摩擦损失总功减小了13.08%。     

工况对盾构机主驱动轴承润滑特性的影响

以某隧道工程实际工况条件为例,建立盾构机主驱动轴承载荷分布计算模型和等温线接触弹流润滑模型,通过数值分析得到极限工况和占比99.9%的工况条件下盾构机主驱动轴承的油膜厚度及油膜压力分布;依据实际工况条件分析不同工况对轴承油膜厚度、油膜压力的影响规律,以及滚子所处位置不同时滚子负载与油膜压力和膜厚之间的变化关系。结果表明：不同工况下主轴承油膜厚度、油膜压力分布规律相似,均出现二次峰值;同一工况下,随着滚子于主轴承所处位置不同,油膜压力及膜厚最值随滚子负载的增大而减小;同一位置处二者最值随主轴承受力的增大而减小。     

Transient elastohydrodynamic lubrication in artificial knee joint with non-Newtonian fluids

This paper presents the transient analysis of a human artificial knee joint under elastohydrodynamic lubrication (EHL) for point contact with non-Newtonian lubricants. The artificial knee joints use ultra high molecular weight polyethylene (UHMWPE) against metal with time-varying speed and load during walking. This numerical simulation employed a perturbation method, Newton Raphson method and multigrid method with full approximation technique to solve simultaneously both the time-dependent Reynolds equation, with non-Newtonian fluid based on a Carreau model, and the elasticity equation.The general numerical schemes are implemented to investigate the characteristics of elastohydrodynamic lubrication in human artificial knee joints; profiles of pressure and film thickness are determined, with varying material and lubricant properties, applied loads and speeds. The results show that the elastohydrodynamic fluid film thickness between the metallic component of the artificial knee joint and the soft polyethylene bearing becomes larger as the contact area increases and the fluid film pressure decreases. At the beginning of the first walking cycle, the film thickness is lower than in subsequent cycles because of the time required to develop the fluid film; after the first cycle, the fluid film is similar for every cycle and is dependent on transient applied load and speed during human movement.     

Elasto-plastic contact analysis of an ultra-high molecular weight polyethylene tibial component based on geometrical measurement from a retrieved knee prosthesis

The wear phenomenon of ultra-high molecular weight polyethylene (UHMWPE) in knee and hip prostheses is one of the major restriction factors on the longevity of these implants. Especially in retrieved knee prostheses with anatomical design, the predominant types of wear on UHMWPE tibial components are delamination and pitting. These fatigue wear patterns of UHMWPE are believed to result from repeated plastic deformation owing to high contact stresses. In this study, the elasto-plastic contact analysis of the UHWMPE tibial insert, based on geometrical measurement for retrieved knee prosthesis, was performed using the finite element method (FEM) to investigate the plastic deformation behaviour in the UHMWPE tibial component. The results suggest that the maximum plastic strain below the surface is closely related to subsurface crack initiation and delamination of the retrieved UHMWPE tibial component. The worn surface whose macroscopic geometrical congruity had been improved due to wear after joint replacement showed lower contact stress at macroscopic level.     

Microscopic asperity contact and deformation of ultrahigh molecular weight polyethylene bearing surfaces

The effect of the roughness and topography of ultrahigh molecular weight polyethylene (UHMWPE) bearing surfaces on the microscopic contact mechanics with a metallic counterface was investigated in the present study. Both simple sinusoidal roughness forms, with a wide range of amplitudes and wavelengths, and real surface topographies, measured before and after wear testing in a simple pin-on-plate machine, were considered in the theoretical analysis. The finite difference method was used to solve the microscopic contact between the rough UHMWPE bearing surface and a smooth hard counterface. The fast Fourier transform (FFT) was used to cope with the large number of mesh points required to represent the surface topography of the UHMWPE bearing surface. It was found that only isolated asperity contacts occurred under physiological loading, and the real contact area was only a small fraction of the nominal contact area. Consequently, the average contact pressure experienced at the articulating surfaces was significantly higher than the nominal contact pressure. Furthermore, it was shown that the majority of asperities on the worn UHMWPE pin were deformed in the elastic region, and consideration of the plastic deformation only resulted in a negligible increase in the predicted asperity contact area. Microscopic asperity contact and deformation mechanisms may play an important role in the understanding of the wear mechanisms of UHMWPE bearing surfaces.     

Journal bearing housing design—A statistical study with FEM

When designing journal bearing housings for construction equipment, one goal is to get an even pressure distribution over the length of the bushing. This is to avoid excessive wear due to contact pressure peaks.A housing that is considered good, does not allow the pin to deflect and keeps the stresses low in the weld. To do this it must be stiff and this will lead to high contact pressures on the edges of the bushing, which is not preferable since wear is highly dependent on the contact pressure level.If the distribution of the contact pressure could be smoothed out over the bushing, the material might be used more efficiently. The normal way to do this is to crown the bushing to allow for pin deflection. However this leads to reduced area in contact. Another method to avoid high pressures in the bearing is to optimize the bearing housing for optimum stiffness.This paper describes one way to optimize journal bearing housings in regard to the contact pressure in the tribo-contact. A statistical approach was applied to a parameterized finite element model with contact elements. Three parameters were analyzed at different loads; set ring thickness, set ring width and fillet weld size.The contact pressure distributions were evaluated in two different ways to a single value to meet the statistical demand of measurable result. The results show that the set ring thickness and width are the parameters that influence most the contact pressure distribution. To reduce the maximum contact pressure the set ring thickness should be kept small.     

考虑粗糙度的船舶水润滑高分子轴承弹流润滑性能研究

为了揭示表面粗糙度对船舶水润滑高分子材料轴承润滑性能的影响规律,开展水润滑轴承弹流混合润滑理论研究;建立考虑内衬材料粗糙度和弹性变形的水润滑轴承混合润滑模型,并对模型进行仿真验证;分析内衬粗糙峰对水膜厚度、水膜压力分布和承载能力的影响规律。研究结果表明：在转速增大的过程中,内衬粗糙度的增大会减缓水膜厚度的增幅比,使轴承需要更高的转速来进入流体动压润滑状态;减小轴承内衬粗糙度能有效降低轴承起飞转速,加快轴承由混合润滑转变为流体动压润滑的过程,减小轴承与轴颈的局部接触,降低轴承异常振动噪声发生的可能性。研究结果揭示了内衬粗糙度变化对轴承润滑特性的影响机制,为水润滑轴承的优化设计提供理论参考。     

海水润滑塑料轴承的微观热弹流润滑分析

考虑轴承表面海水润滑膜温度场和轴承表面横向粗糙度等因素,对塑料轴承的弹流润滑问题进行了研究。利用压力求解的多重网格法和弹性变形求解的多重网格积分法以及温度求解的逐列扫描技术,得到塑料轴承微观热弹流润滑问题的完全数值解,讨论了连续波状粗糙度、载荷、轴承转速对海水润滑膜压力及膜厚的影响。数值计算结果表明：轴承表面粗糙度对润滑膜压力和膜厚分布都有一定影响,连续波状粗糙度使润滑膜压力和膜厚分布产生振荡;转速和载荷对压力分布影响较小,随转速的增大、载荷的减小,膜厚都有明显的增大。     

基于Abaqus的井下U形金属密封环性能研究

为满足井下流量控制阀在高温高压、强腐蚀工况下的密封要求,提出一种可用于径向密封的U形金属密封环;利用Abaqus软件建立密封环的二维有限元分析模型,计算在预紧和井下实际工况条件下的最大Mises应力和接触压力的分布情况,分析初始压缩量、密封环厚度和井下压力对密封性能的影响.结果 表明:随着初始压缩量的增加,最大接触压力...     

Elastohydrodynamic lubrication analysis of metal-on-metal hip prostheses under steady state entraining motion

The elastohydrodynamic lubrication problem of metal-on-metal hip joint replacements was considered in this study. A simple ball-in-socket configuration was used to represent the hip prosthesis. The Reynolds equation in a spherical coordinate was adopted for the fluid-film lubrication analysis, to account for the ball-in-socket geometry. The corresponding elastic deformation was calculated by means of the finite element method in order to consider the complex ball-in-socket geometry as well as the backing materials underneath the acetabular cup. Both the Reynolds and the elasticity equations were solved simultaneously using the Newton-Raphson finite difference method. The general methodology developed was then applied to a recent experimental prototype metal-on-metal hip implant. It was shown that the backing materials underneath the acetabular cup had little influence on the predicted contact pressure and the elastic deformation at the bearing surfaces for this particular example. Both the film thickness and the hydrodynamic pressure distributions were obtained under various loads up to 2500 N. The predicted minimum lubricating film thickness from the present study was compared with a simple estimation using the Hamrock and Dowson formulae based upon an equivalent ball-on-plane model and excellent agreement was found. However, it was pointed out that for some forms of metal-on-metal hip prostheses with a thin acetabular cup, a polyethylene inlay underneath a metallic bearing insert or a taper connection between a bearing insert and a fixation shell, the general methodology developed in the present study should be used and this will be considered in future studies.     

Steady-state elastohydrodynamic lubrication analysis of a metal-on-metal hip implant employing a metallic cup with an ultra-high molecular weight polyethylene backing

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.     

大偏心下滑动轴承热弹流润滑状态及特性*

滑动轴承在大偏心条件下工作时，热效应及弹性变形使得油膜润滑状态发生变化，进而影响摩擦特性。为此建立耦合轴瓦弹性变形、轴颈轴瓦粗糙峰接触、油膜温度分布及黏温-黏压关系的滑动轴承混合润滑模型，采用有限差分法求解得到不同工况下油膜压力场、温度场分布，分析热效应及弹性变形对润滑状态转变及轴承各特性参数的影响；搭建实验台测量试件内表面温度分布，测试结果验证了计算模型的正确性。结果表明：大偏心时热效应和弹性变形使得油膜润滑状态出现转化；粗糙峰的接触使摩擦热增加，且在最小油膜处形成温度峰值；热效应和轴瓦弹性变形使得接触压力峰值集中在轴承两端，承载能力和摩擦力均有所下降。     

考虑粗糙度时不同衬层材料水润滑轴承润滑特性比较*

以水润滑轴承为研究对象,考虑表面粗糙度的影响,针对丁腈橡胶（NBR）、赛龙、飞龙、超高分子量聚乙烯(UHMWPE)4种新型非金属衬层材料建立润滑数学模型,并推导水膜厚度方程;采用有限差分法,研究考虑实际表面粗糙度时4种新型衬层材料的衬层变形、水膜厚度和水膜压力的变化规律,分析最大水膜压力和承载力随转速的变化,并与表面光滑轴承进行对比。结果表明：考虑表面粗糙度时水润滑轴承的衬层变形和水膜厚度均呈波状分布,衬层变形减小,最小水膜厚度变薄,而水膜压力有轻微的局部突变,最大水膜压力增大,承载力下降;4种材料的变形量和最小水膜厚度由大到小均依次是NBR、赛龙、飞龙、UHMWPE,水膜压力由大到小依次是UHMWPE、飞龙、赛龙、NBR。在相同工况下,NBR衬层材料比其他3种衬层材料相对容易形成润滑水膜,而UHMWPE衬层材料可以保证系统承受较大的承载力。研究结果对水润滑轴承材料选型和加工装配有一定的参考意义。     

Size and shape of the resection surface geometry of the osteoarthritic knee in relation to total knee replacement design

This study examines the resection surface geometry of the femur, tibia, and patella in relation to the design of total knee implants. Using a technique known as principal component analysis (PCA), the variation in the resection geometry of the knee was summarized. Of the total variation of the knee, 58 per cent was due to variation in size and 14 per cent was due to varying femoral intercondylar notch width. A PCA was performed on each bone separately and it was found that 60 per cent, 76 per cent and 71 per cent of variation was due to size for the femur, tibia, and patella respectively. Femoral and tibial size were highly correlated (r = 0.95) while patellar size had poorer correlation with both femoral and tibial size (r < 0.7). Simple linear dimensions (femoral epicondylar width or tibial mediolateral width) were reliable indicators of knee size. The effect of shape variation, which is generally not accounted for in implant design, was measured. The resected surfaces of each subject were compared with a model of the resection surfaces of the knee which varied in size but not shape. The maximum overhang and underhang of the model on the resection surfaces were measured. There was average maximum model overhang of 3.6 mm and underhang of 3.9 mm in the femur, 2.3 mm overhang and 1.9 mm underhang in the tibia, and 2.6 mm overhang and 2.5 mm underhang in the patella. The maximum coverage that an implant can be expected to provide for a population is quantified. Implant designs which include some shape as well as size variation improve on the implant fit.