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.     

An elastohydrodynamic lubrication (EHL) model of wear particle migration in an artificial hip joint

A full fluid ball-in-socket elastohydrodynamic lubrication (EHL) analysis of an artificial hip joint made of a metallic femoral head and ultra-high molecular weight polyethylene (UHMWPE) acetabular cup was considered. Since artificial hips operate in a mixed lubrication mode, wear occurs and wear particles lead to reduced hip lifetimes. This study involves simulating these particles within the lubrication regime. Hip deformation was compared to models employing finite element analysis and the spherical fast-Fourier transform technique. Particle modeling results were compared to suspension modeling experiments by other researchers. Results show a strong influence of lubricant fluid velocity on that of the wear particles.     

Metal-on-metal hip joint tribology

The basic tribological features of metal-on-metal total hip replacements have been reviewed to facilitate an understanding of the engineering science underpinning the renaissance of these hard-on-hard joints. Metal-on-polymer hip replacements operate in the boundary lubrication regime, thus leading to the design guidance to reduce the femoral head diameter as much as is feasible to minimize frictional torque and volumetric wear. This explains why the gold-standard implant of this form from the past half-century had a diameter of only 22.225 mm (7/8 in). Metal-on-metal implants can operate in the mild mixed lubrication regime in which much of the applied load is supported by elastohydrodynamic films. Correct tribological design leads to remarkably low steady state wear rates. Promotion of the most effective elastohydrodynamic films calls for the largest possible head diameters and the smallest clearances that can reasonably be adopted, consistent with fine surface finishes, good sphericity and minimal structural elastic deformation of the cup on its foundations. This guidance, which is opposite in form to that developed for metal-on-polymer joints, is equally valid for solid (monolithic) metallic heads on metallic femoral stems and surface replacement femoral shells. Laboratory measurements of friction and wear in metal-on-metal joints have confirmed their potential to achieve a very mild form of mixed lubrication. The key lies in the generation of effective elastohydrodynamic lubricating films of adequate thickness compared with the composite roughness of the head and cup. The calculation of the film thickness is by no means easy, but the full procedure is outlined and the use of an empirical formula that displays good agreement with calculations based upon the full numerical solutions is explained. The representation of the lambda ratio, lambda, embracing both film thickness and composite roughness, is described.     

Fatigue Life Reduction in Mixed Lubricated Elliptical Contacts

Highly loaded ball and rolling element bearings are often required to operate in the mixed elastohydrodynamic lubrication regime in which surface asperity contact occurs simultaneously during the lubrication process. Predicting performance of components operating in this regime is important as the high asperity contact pressures can significantly reduce the fatigue life of the interacting components. Rolling contact fatigue is one of the most dominant causes of failure of components operating in mixed lubrication regime. Contact fatigue begins with the initiation of microscopic fatigue cracks in the rolling contact surfaces or within the sub-surface regions due to cyclic shear stresses. Investigation of mixed lubrication effects on performance of machine components is of significant importance in order to understand and enhance their load carrying capacity. This article investigates the effects of mixed lubrication and surface roughness on machine components performance. Results from a mixed lubrication model are utilized to investigate the effects of different operating conditions on fatigue life of the components. Simple rough surfaces consisting of single hemispherical bump as well as complex rough surfaces consisting of a numerically generated 3D rough surface operating under mixed lubrication conditions are studied and results presented. The stress-based Ioannides and Harris model incorporating the fatigue limit is used to evaluate the fatigue life variation. Fast Fourier Transform (FFT) technique is used to significantly reduce the time required for the computation of internal stresses.     

A simple fully integrated contact-coupled wear prediction for ultra-high molecular weight polyethylene hip implants

A fully coupled contact and wear model was developed in the present study for hip implants employing an ultra-high molecular weight polyethylene (UHMWPE) cup in combination with a metallic or ceramic femoral head. A simple elasticity equation based on the concept of constrained column model was employed to solve the contact mechanics between the acetabular cup and the femoral head under the three-dimensional physiological loading condition. The wear model was based on the classical Archard-Lancaster equation in common with all other studies reported in the literature. The fully coupled contact and wear model was applied to both conventional and cross-linked UHMWPE cups under a wide range of design parameters such as the clearance and the femoral head radius. The predicted linear and volumetric wear as well as their rates for conventional UHMWPE cups were found to be in good agreement with those obtained from a similar analysis by Maxian but using the finite element method for the contact mechanics analysis. The predicted maximum contact pressure was found to decrease rapidly within the first 10(6) cycles, and below the limit to cause plastic deformation within the UHMWPE cup with a nominal radial clearance of 0.2 mm. The effect of the clearance between the head and the cup on the predicted wear was found to be negligible. For the cross-linked UHMWPE cup with relatively large diameters up to 48 mm and a fixed outside diameter of 50 mm, the predicted wear, which was found to increase with increasing femoral head radius, remained small owing to the small wear factor associated with these materials. Furthermore, if the head diameter increases beyond 42 mm, a rapid increase in the contact pressure was predicted, owing to the decrease in the wall thickness of the cross-linked UHMWPE cup.     

Integrated wear prediction model for cylindrical gear with variable hyperbolic circular arc tooth trace under mixed elastohydrodynamic lubrication

Cylindrical gear with variable hyperbolic circular arc tooth trace (VH-CATT) is a new type of gear. Sliding wear is the main mode of the surface failure of multiple mechanical parts. Both the lubrication state and contact temperature considerably influence wear characteristics, which may aggravate the transmission performance of gear pairs. Wear, contact temperature, as well as lubrication states are jointly explored. Therefore, an integrated wear prediction model was proposed through taking into account flash contact temperature and surface roughness of VH-CATT cylindrical gears in mixed elastohydrodynamic lubrication. According to the equivalent ellipse contact model of VH-CATT cylindrical gears and tooth surface equation, normal curvature and velocity relations for VH-CATT cylindrical gears were observed, and the normal meshing force was obtained through the consideration of load sharing coefficients and quality grades. Flash contact temperature was estimated by using the literature. This study proposes analytical solutions for investigating how various surface roughness, operation, and geometric parameters affect asperity contact ratio (ACR), asperity contact pressure (ACP), flash contact temperature (FCT), as well as wear depth (WD) related to driving gears. ACR, ACP, FCT, as well as WD initially decrease and then increase from engaging-in to engaging-out processes. The minimum occurs at the pitch point. The WD declines as module, cutter radius, and rotational velocity increase while augmenting when surface roughness and torques increase. The maximum and minimum wear depths in driving gears occur at the dedendum and pitch point, respectively. Its overall wear is reduced by 23.16 % compared to the wear of spur gears. The results are valuable for the studies of tooth pitting, wear resistance, and fatigue life improvement for VH-CATT cylindrical gear. These studies can provide verification data and references required for engineering designs and VH-CATT cylindrical gear operations.

     

A Model for Wear and Friction in Cylinder Liners and Piston Rings

Abstract

A one-dimensional elstohydrodynamic mixed lubrication wear and friction model is developed. The model can predict the effects of surface roughness, asperity contact, temperature-pressure-viscosity on wear, lubrication, and friction of the piston rings and cylinder liner. Wear is predicted based on the surface asperity contact pressure. The cylinder bore wear and the ring pack friction during an engine break-in are simulated and compared with the experimental results. The influence of cylinder wall temperature and surface roughness on friction and wear is investigated. The ring pack friction due to oil viscous shearing and asperity contact is found to reach its minimum at a certain oil temperature.     

Effect of wear of bearing surfaces on elastohydrodynamic lubrication of metal-on-metal hip implants

The effect of geometry change of the bearing surfaces owing to wear on the elastohydrodynamic lubrication (EHL) of metal-on-metal (MOM) hip bearings has been investigated theoretically in the present study. A particular MOM Metasul bearing (Zimmer GmbH) was considered, and was tested in a hip simulator using diluted bovine serum. The geometry of the worn bearing surface was measured using a coordinate measuring machine (CMM) and was modelled theoretically on the assumption of spherical geometries determined from the maximum linear wear depth and the angle of the worn region. Both the CMM measurement and the theoretical calculation were directly incorporated into the elastohydrodynamic lubrication analysis. It was found that the geometry of the original machined bearing surfaces, particularly of the femoral head with its out-of-roundness, could lead to a large reduction in the predicted lubricant film thickness and an increase in pressure. However, these non-spherical deviations can be expected to be smoothed out quickly during the initial running-in period. For a given worn bearing surface, the predicted lubricant film thickness and pressure distribution, based on CMM measurement, were found to be in good overall agreement with those obtained with the theoretical model based on the maximum linear wear depth and the angle of the worn region. The gradual increase in linear wear during the running-in period resulted in an improvement in the conformity and consequently an increase in the predicted lubricant film thickness and a decrease in the pressure. For the Metasul bearing tested in an AMTI hip simulator, a maximum total linear wear depth of approximately 13 microm was measured after 1 million cycles and remained unchanged up to 5 million cycles. This resulted in a threefold increase in the predicted average lubricant film thickness. Consequently, it was possible for the Metasul bearing to achieve a fluid film lubrication regime during this period, and this was consistent with the minimal wear observed between 1 and 5 million cycles. However, under adverse in vivo conditions associated with start-up and stopping and depleted lubrication, wear of the bearing surfaces can still occur. An increase in the wear depth beyond a certain limit was shown to lead to the constriction of the lubricant film around the edge of the contact conjunction and consequently to a decrease in the lubricant film thickness. Continuous cycles of a running-in wear period followed by a steady state wear period may be inevitable in MOM hip implants. This highlights the importance of minimizing the wear in these devices during the initial running-in period, particularly from design and manufacturing points of view.     

Design considerations for cushion form bearings in artificial hip joints.

Lubrication mechanisms and contact mechanics have been analysed in a new generation of 'cushion form' bearings for artificial hip joints, which comprise low elastic modulus layers on the articulating surfaces. Comparisons have been made with 'hard' bearings used in existing prostheses and also with the natural hip joint. Lubricating film thicknesses are enhanced by larger contact areas and lower contact pressures. For a fixed contact area, simultaneous changes in layer thickness and radial clearance have been shown to have a small effect on elastohydrodynamic film thickness. Hard bearings designed with the same contact area as the cushion bearings produced a similar film thickness, but lubricant film thickness is not optimized in current designs. The main advantage of using a cushion bearing with low elastic modulus layers was found to be associated with microelastohydrodynamic lubrication. Careful selection of the elastic modulus is important in order to ensure that this lubrication regime was effective. Low elastic modulus layers may also produce local deformations, which enhance squeeze film action. The elastic modulus of the material should not be lower than necessary to produce effective microelastohydrodynamic lubrication, as a further reduction in modulus only increases the strain distribution in the material. A lubricant film thickness of 0.3 microns has been predicted for a cushion hip prosthesis with a femoral head diameter of 32 mm and radius of contact zone of 16 mm, using a 2 mm thick layer with an elastic modulus of 20 MPa.     

轴颈倾斜对内燃机主轴承润滑和磨损的影响

建立内燃机主轴承热弹性流体动力润滑模型,考虑轴颈倾斜,以粗糙接触压力表征轴颈与轴瓦的磨损程度.通过对不同工况下主轴颈倾斜角度、粗糙接触压力等的计算,研究轴颈倾斜对主轴承润滑和磨损的影响.结果表明,轴颈不对中倾斜角度较小时,主轴承仍能够处于流体润滑状态;轴颈倾斜角度较大时,轴承处于边界润滑状态,出现偏摩擦磨损.转速和负荷对轴颈倾斜影响较大,高转速和满负荷时轴承的润滑不良,磨损较大.     

Effect of surface texturing on mixed lubricated non-conformal contacts

The behaviour of surface texturing based on shallow micro-dents was observed within mixed lubricated non-conformal contacts and compared with results obtained under thin film elastohydrodynamic conditions. Thin film colorimetric interferometry was used to observe the changes in lubrication film thickness. It was found that lubricant emitted by micro-dents could effectively lift off the real roughness features that provided an increase in average but also the local minimum film thicknesses. On the contrary to smooth contact conditions no film thickness reduction is obvious either downstream or upstream the micro-dent. The possible beneficial effect of surface texturing on mixed lubricated contact was checked through the qualitative wear test. It confirmed that an array of shallow micro-dents reduced asperity interactions of rubbing surfaces. Moreover, the effect of micro-dents on rolling contact fatigue was also considered in this study. It has been shown that individual dents would have to be much deeper compared to those used in surface texturing experiments to cause reduction in contact fatigue life. It can be suggested from the obtained results that properly designed surface texturing could help to increase the separation of rubbing surfaces under mixed lubrication conditions.     

An axisymmetric contact model of ultra high molecular weight polyethylene cups against metallic femoral heads for artificial hip joint replacements.

Contact mechanics of ultra high molecular weight polyethylene (UHMWPE) cups against metallic femoral heads for artificial hip joints is considered in this study. Both the experimental measurement of the contact area and the finite element prediction of the contact radius, maximum contact pressure and maximum Von Mises stress have been carried out for a wide range of contemporary artificial hip joints. Good agreement of the contact radius has been found between the experimental measurements and the finite element predictions based upon an elastic modulus of 1000 MPa and a Poisson's ratio of 0.4 for UHMWPE material under various loads up to 2.5 kN. It has been shown that the half contact angle for all the cup/head combinations considered in this study is between 40 degrees and 50 degrees under a load of 2.5 kN. The importance of this result has been discussed with respect to the anatomical position of the cup when placed in the body and the selection of a simple wear-screening test for artificial hip joints. The predicted contact radius and maximum contact pressure from the finite element model have also been compared with a simple elasticity analysis. It has been shown that the difference in the predicted contact radius between the two methods is reduced for more conforming contacts between the femoral head and the acetabular cup and smaller UHMWPE cup thickness. However, good agreement of the predicted maximum contact pressure has been found for all the combinations of the femoral head and the acetabular cup considered in this study. The importance of contact mechanics on the clinical performance of artificial hip joint replacements has also been discussed.     

Deterministic solutions and thermal analysis for mixed lubrication in point contacts

A deterministic numerical model has been developed for simulation of mixed lubrication in point contacts. The nominal contact area between rough surfaces can be divided into two parts: the regions for hydrodynamic lubrication and asperity contacts (boundary lubrication). In the area where the film thickness approaches zero the Reynolds equation can be modified into a reduced form and the normal pressure in the region of asperity contacts can be thus determined. As a result, a deterministic numerical solution for the mixed lubrication can be obtained through a unite system of equations and the same numerical scheme. In thermal analysis, the solution for a moving point heat source has been integrated numerically to get surface temperature, provided that shear stresses in both regions of hydrodynamic lubrication and asperity contacts have been predetermined. A rheology model based on the limit shear stress of lubricant is proposed while calculating the shear stress, which gives a smooth transition of friction forces between the hydrodynamic and contact regions. The computations prove the model to be a powerful tool to provide deterministic solutions for mixed lubrication over a wide range of film thickness, from full-film to the lubrication with very low lambda ratio, even down to the region where the asperity contact dominates.     

船用发动机重载工况下凸轮-滚轮副混合热弹流润滑分析

凸轮-滚轮副是大功率船用发动机配气机构的关键摩擦副,除受到弹簧力和自身的惯性力之外,还受到来自喷油器的极高燃油压力,工作条件极为苛刻。为了分析该摩擦副的性能,建立船用发动机重载工况下凸轮-滚轮副的混合热弹流润滑模型,计算燃油压力作用下的摩擦副油膜润滑、摩擦温升和磨损性能。结果表明：喷油器的燃油压力会显著降低凸轮-滚轮摩擦副之间的油膜厚度,同时产生较为严重的微凸体接触;随着环境温度的提高,凸轮-滚轮副的油膜厚度以及油膜温升会有所下降,而微凸体接触压力、摩擦力以及摩擦功率均会显著增加;滚轮打滑会造成凸轮-滚轮摩擦副的油膜厚度下降,同时导致油膜温升以及微凸体接触压力增大和并且致使表面磨损显著加剧。     

Effect of surface texturing on the elastohydrodynamic lubrication analysis of metal-on-metal hip implants

With the development of surface processing techniques, applications of bearing components have been introduced with specific surface textures to take advantage of lubrication.An advanced numerical model was established to simulate the mixed EHL problem of a metal-on-metal hip prosthesis with dimpled surface texturing. The surface texture with simple cylindrical dimples was numerically simulated, under both steady state and walking conditions.The present results showed that surface texturing may have a potentially beneficial effect on the reduction of asperity contact ratio and the improvement of lubrication performance of metal-on-metal hip replacements, particularly under predominant boundary lubrication conditions.     

Tribological assessment of a flexible carbon-fibre-reinforced poly(ether-ether-ketone) acetabular cup articulating against an alumina femoral head

New material combinations have been introduced as the bearing surfaces of hip prostheses in an attempt to prolong their life by overcoming the problems of failure due to wear-particle-induced osteolysis. This will hopefully reduce the need for revision surgery. The study detailed here used a hip simulator to assess the volumetric wear rates of large-diameter carbon-fibre-reinforced pitch-based poly(ether-ether-ketone) (CFR-PEEK) acetabular cups articulating against alumina femoral heads. The joints were tested for 25 x 10(6) cycles. Friction tests were also performed on these joints to determine the lubrication regime under which they operate. The average volumetric wear rate of the CFR-PEEK acetabular component of 54 mm diameter was 1.16 mm(3)/10(6) cycles, compared with 38.6 mm(3)/10(6) cycles for an ultra-high-molecular-weight polyethylene acetabular component of 28 mm diameter worn against a ceramic head. This extremely low wear rate was sustained over 25 x 10(6) cycles (the equivalent of up to approximately 25 years in vivo). The frictional studies showed that the joints worked under the mixed-boundary lubrication regime. The low wear produced by these joints showed that this novel joint couple offers low wear rates and therefore may be an alternative material choice for the reduction of osteolysis.     

Contact mechanics and lubrication analyses of ceramic-on-metal total hip replacements

Ceramic-on-metal (CoM) total hip replacements have shown reduced wear and friction. Lubrication and contact mechanics analyses play an important role in providing an overall understanding for the tribological performance of CoM bearings. In the present study, the steady-state contact mechanics and elastohydrodynamic lubrication (EHL) and transient EHL of CoM bearings were analyzed. The dry and lubricated contact pressures of CoM bearings showed typical characteristics of hard-on-hard hip bearings. The effects of head radius and radial clearance on the lubrication performance were predicted. CoC and CoM bearings are more likely to benefit full fluid film lubrication than MoM bearings.     

A New Approach Using Palm Olein,Palm Kernel Oil,and Palm Fatty Acid Distillate as Alternative Biolubricants: Improving Tribology in Metal-on-Metal Contact

Metal-on-metal (MoM) hip replacements are commonly used hip implants. However, one of the issues under debate is the interference of friction and wear. The purpose of this feasibility study is to elucidate the performance of palm lubrication between the femoral head and the acetabular cup. In the tribology of hip implants, the use of palm olein, palm kernel oil, and palm fatty acid distillate as synthetic lubricants for human joints has shown tremendous potential. A modified pin-on-disc as hip screening has been used to evaluate the friction and wear on an acetabular cup with an inner diameter of 28 mm. The wear debris was then observed with microscopy image analysis. This study revealed that the physical and unique chemical properties in palm oil can optimize the rate of friction and wear on the metal acetabular cup and thus allow for a stable implant of MoM.     

Lubrication of Strip Rolling in the Low-Speed Mixed Regime

An analytical model for strip rolling in the low-speed mixed lubrication regime is developed. An average Reynolds equation for longitudinal saw-tooth surfaces under conditions of high fractional contact area, is combined with an analysis for asperity flattening under conditions of bulk plastic flow, to treat lubrication in the mixed regime. Analyses for the inlet zone and work zone and the influence of pressure on viscosity are included in the model. The model indicates that hydrodynamic lubrication effects are important at much lower speeds than previously considered possible. The film thickness predicted by the model is somewhat smaller than that measured using the oil drop method in rolling aluminum alloy with a mineral oil.     

A multi-scale model for friction in cold rolling of aluminium alloy

A simple and robust friction model is proposed for cold metal rolling in the mixed lubrication regime, based on physical phenomena across two length scales. At the primary roughness scale, the evolution of asperity contact area is associated with the asperity flattening process and hydrodynamic entrainment between the roll and strip surfaces. The friction coefficient on the asperity contacts is related to a theoretical oil film thickness and secondary-scale roll surface roughness. The boundary friction coefficient at the “true” asperity contacts is associated with tribo-chemical reactions between fresh metal, metal oxide, boundary additives, the tool and any transfer layer on the tool. The asperity friction model is verified by strip drawing simulations under thin film lubrication conditions with a polished tool, taking the fitting parameter of the boundary lubrication friction factor on the true contact areas equal to 0.1. Predicted values of average friction coefficient, using a boundary friction factor in the range 0.07–0.1, are in good agreement with measurements from laboratory and industrial rolling mill trials.