Analysis of biphasic lubrication of articular cartilage loaded by cylindrical indenter

Combination of theoretical biphasic analyses and corresponding experimental measurements for articular cartilage has successfully revealed the fundamental material properties and time-depending mechanical behaviors of articular cartilage containing plenty of water. The insight of load partitioning between solid and fluid phases advanced the prediction of the frictional behavior of articular cartilage. One of the recent concerns about biphasic finite element (FE) analysis seems to be a dynamic and physiological condition in terms of mechanical functionality as a load-bearing for articular joint system beyond material testing, which has mainly focused on time-dependent reaction force and deformation in relatively small and low speed compression. Recently, the biphasic FE model for reciprocating sliding motion was applied to confirm the frictional effect on the migrating contact area. The results indicated that the model of a cylindrical indenter sliding over the cartilage surface remarkably sustained the higher proportion of fluid load support than a condition without migrating contact area, but the effectiveness of constitutive material properties has not been sufficiently evaluated for sliding motion. In our present study, at the first stage, the compressive response of the articular cartilage was examined by high precision testing machine. Material properties for the biphasic FE model, which included inhomogeneous apparent Young's modulus of solid phase along depth, strain-dependent permeability and collagen reinforcement in tensile strain, were estimated in cylindrical indentation tests by the curve fitting between the experimental time-dependent behavior and FE model simulation. Then, the biphasic lubrication mechanism of the articular cartilage including migrating contact area was simulated to elucidate functionality as a load-bearing material. The results showed that the compaction effect on permeability of solid phase was functional particularly in the condition without the migrating contact area, whereas in sliding condition the compaction effect did not clearly show its role in terms of the proportion of fluid load support. The reinforcement of solid phase, which represented the collagen network in the tissue, improved the proportion of fluid load support especially in the sliding condition. Thus, a functional integration of constitutive mechanical properties as a load-bearing was evaluated by FE model simulation in this study.     

Tribology-optimised silk protein hydrogels for articular cartilage repair

Porous hydrogels were made from silk fibre as potential materials for cartilage repair. The aim was to develop materials which mimicked the tribological behaviour of cartilage, with controlled pore-sizes and optimised mechanical properties. Mechanical tests showed hydrogels had a comparable compressive modulus to cartilage, with stiffness improved by decreasing pore size. Under static loading and during shear hydrogels demonstrated significant interstitial fluid support. Friction testing showed the hydrogels had a cartilage-like frictional response, dominated by this interstitial fluid support. Silk hydrogels showed little wear, early signs of which were changes in surface morphology that did not correlate with the equilibrium friction coefficient. Consequently both wear and friction should be monitored when assessing the tribological performance of hydrogels.     

Experimental and numerical investigation of the behaviour of articular cartilage under shear loading—Interstitial fluid pressurisation and lubrication mechanisms

In this paper, the mechanical and frictional responses of articular cartilage when subjected to alternating shearing forces under a constant load were investigated. Shear testing was performed at physiological contact pressures to ascertain the influence of interstitial fluid support on the evolution of frictional forces during cyclic loading.Numerical studies were also performed using the finite element software Abaqus. The tissue was modelled as a biphasic material with strain dependent permeability. The influence of the material characteristics on the lubrication mechanisms occurring when cartilage is subject to compression and shear was studied to corroborate the experimental findings.     

Mechanical and tribological properties of poly(hydroxyethyl methacrylate) hydrogels as articular cartilage substitutes

Poly(hydroxyethyl methacrylate) (p(HEMA)) hydrogels have been proposed as promising biomaterials to replace damaged articular cartilage. A major obstacle to their use as replacement bearing tissue is their poor mechanical properties in comparison with healthy articular cartilage. The purpose of this study was to obtain p(HEMA) hydrogels with physicochemical and mechanical properties close to healthy articular cartilage, by introducing a hydrophilic monomer, namely acrylic acid (AA). Formulations of hydrogels with different amounts of hydrophilic monomer (acrylic acid, AA) were synthesized and tested: p(HEMA), p(HEMA-co-5%AA), p(HEMA-co-25%AA). The macro-mechanical tests were reproduced at nanoscale in order to verify if the superficial properties of the hydrogels are similar to the bulk ones.     

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.     

Influence of protein conformation on frictional properties of poly (vinyl alcohol) hydrogel for artificial cartilage

Poly (vinyl alcohol) (PVA) hydrogel is one of the anticipated materials for artificial cartilage. In our previous studies, wear of PVA hydrogel depended on content of proteins in lubricants. The secondary structures of bovine serum albumin (BSA) and human gamma globulin (HGG) were investigated in circular dichroism spectroscopy to clarify the influence of the proteins on frictional properties. BSA and HGG were mainly composed of the α-helix and the β-sheet, respectively. BSA containing the α-helix structure showed low friction compared to HGG composed of the β-sheet structure in mixed or boundary lubrication mode. The α-helix structure forms low shear layer because the α-helix structure is easily released from surfaces and low cohesive strength. HGG forms uniform adsorption layer, but showed higher friction than BSA in the rubbing with single protein. In the repeated rubbing with changing of lubricants from HGG to BSA, however, the final friction was reduced, because an optimum layered structure of proteins was formed. Hence, layered structure of proteins appears to play an important role to protect rubbing surfaces and to reduce friction. In heat treatment tests, heat-induced BSA showed very low friction because of reduction of the α-helix structure. Heat-induced HGG did not show large differences from native HGG, but could not bring low friction with heat-induced BSA. Thus it was shown that the protein conformation has effective influences on friction.     

Analysis of the dynamics of a slider-crank mechanism with hydrodynamic lubrication in the connecting rod-slider joint clearance

The conventional slider-connecting rod-crank mechanism is widely applied in mechanical systems. The use of hydrodynamic bearings in the mechanism joints is of particular interest in reducing friction, mainly in special conditions of lubrication such as the connecting rod-slider joint. This bearing belongs to a class of bearings with alternating rotational motion. This paper proposes a mathematical model for this particular problem, considering the dynamics of the slider-connecting rod-crank system interacting with the lubrication phenomenon in bearings with alternating motion. Two models were used to analyze the dynamics of the system. The first model (by Eksergian Equation of Motion) represents the system when the connecting rod end is in contact with the bearing surface, assuming, in this condition, the same behavior as that of rigid bearings (without clearance). The second model (by Lagrange Method) represents the system when the connecting rod end is in the hydrodynamic lubrication mode in the slider bore clearance. In this condition, the slider moves in relation to the connecting rod, presenting a problem of multi-degrees-of-freedom. The mathematic model of hydrodynamic lubrication was introduced to obtain more realistic results of the system's dynamic behavior.     

Optimum shape design for surface of a thermohydrodynamic lubrication slider bearing

This paper utilises a thermohydrodynamic model of bearing to optimise the shape of slider bearing. Friction is minimised subject to load and centre of pressure requirements using a sequential quadratic programming algorithm. A generalised Reynolds equation is solved simultaneously with an energy equation using the finite volume method to obtain bearing characteristics, such as friction, load and centre of pressure. Results show that the coefficient of friction is reduced by the optimisation approach. Results also show that larger temperature–viscosity coefficient and inlet viscosity tend to yield smaller optimal friction, whereas larger thermal conductivity tends to yield larger optimal friction. Copyright © 2012 John Wiley & Sons, Ltd.     

Development of a detailed model for piston-ring lubrication in IC engines with circular and non-circular cylinder Bores

Over recent years a detailed model for piston-ring lubrication has been developed by the authors. The computer model incorporates a finite difference solution of the two-dimensional Reynolds equation with the squeeze effect for fully flooded lubrication as well as a flow-continuity algorithm for ‘starved' lubrication. It can be used to evaluate the tribological performance of piston rings operating in both circular and distorted bores. The influences of many factors, such as level of bore distortion, ring conformability, axial motion of the ring, and circumferential variation of the ring face profile are taken into account. An improved method for determining oil availability in a ring pack was also developed by considering the effect of relative locations of rings on the piston and oil accumulation in front of the ring. This paper summarises the development of the model and presents some selected results. It should be noted that much of the material presented has been drawn from other publications by the authors for the purpose of review and summary.     

Hydrodynamic lubrication of rubber seals for reciprocating motion; leakage of seals with an O-ring

The solution of design and operational problems in sealing technology requires definition of the lubrication parameters underneath the sealing ring. Knowledge of the film thickness enables one to define the out-leakage, the most important sealing parameter. A review of theoretical and experimental equations defining the lubricating film thickness is presented. An original method of measuring the film thickness is described, and an attempt is made to explain the differences that exist between the theoretical and experimental equations.     

A theoretical simulation of thermal elastohydrodynamic lubrication for a Newtonian fluid in impact motion

In this work, the thermal elastohydrodynamic lubrication (TEHL) in an impact motion is explored using multigrid (MG) method and column by column scanning techniques. A steel ball impacts onto an infinite steel plane lubricated with a thin layer of oil. The study starts from a smooth contact problem and the results are compared with the corresponding isothermal ones. Then surface waviness is imposed on the steel ball surface to check the fluctuation in the oil film.     

A numerical method for the calculation of lubricant pressures in bearings with mixed lubrication

A model for mixed lubrication, assuming that the total normal load applied to the plane of the lubricated surfaces is carried partly by the hydrodynamic action of the lubrication film and partly by asperity contacts and that the total friction force between the lubricated surfaces is partly due to viscous friction and partly to asperity contacts, was used to develop a numerical solution for pressure distribution in a bearing experiencing mixed lubrication. The geometry treated and the pressure distribution obtained were for a simple slider bearing, but the method could easily be extended to other shapes. The model is based on measured roughness of a real surface. Real load carrying capacity and drag can therefore be determined since they are related directly to bearing pressure distribution     

The ultra-low friction of the articular surface is pH-dependent and is built on a hydrophobic underlay including a hypothesis on joint lubrication mechanism

In this study, the influence of pH on interfacial energy distributed over the phospholipids-bilayer surface model and the effect of hydrophobicity on coefficient of friction (f) were investigated by using microelectrophoresis. An important clinical implication of deficiency in hydrophobicity is the loss of phospholipids that is readily observed in osteoarthritis joints. This paper establishes the influence of pH on interfacial energy upon an increase f, which might be associated with a decrease of hydrophobicity of the articular surface.     

Analysis of the piston ring lubrication with a new boundary condition

Research on the inlet and outlet lubricational characteristics of the piston ring have been intense and ongoing. Many researchers had considered that the entire surface of the ring was enveloped in an oil film, but much experimental research has discovered that not all the entire surface was soaked. To consider a partially lubricated ring, the following conditions are presupposed; oil starvation is applied to the inlet region and the open-end assumption to the outlet region. This algorithm confirms flow continuity and permits the nadir of the pressure to go down to the saturation pressure. Using these new boundary conditions, the actual effective width participating in ring lubrication is determined and the minimum film thickness and flow rate for the ring pack can be calculated. The effective width is expected to be about 20 to 30 percent of the whole width of the ring, and the minimum film thickness is less than the result obtained by using the Reynolds cavitation boundary condition.     

Development of a laboratory test device for electrorheological fluids in hydrostatic lubrication

Electrorheological (ER) fluids exhibit changes in their rheological behaviour in the presence of an external electric field. Research and development activities related to ER fluids and their applications have increased dramatically during the last few decades. If commercialised, ER fluids could have a significant impact on hydraulic equipment, and be utilised in the automotive, marine, aerospace, robotics, and machinery industries. The objective of the present study is to demonstrate the feasibility of using ER fluids to produce ‘smart’ lubricants that can control friction and wear of sliding components. The ER lubricant effect is demonstrated using a unique test machine that utilises hydrostatic lubrication. It is found that the friction torque increases by as much as 30% when a voltage of 2000 V is applied to an ER fluid in the newly developed test machine.     

Fluid film lubrication in the presence of cavitation: a mass-conserving two-dimensional formulation for compressible,piezoviscous and non-Newtonian fluids

A mass-conserving formulation of the Reynolds equation has been recently proposed by some of the authors to deal with cavitation in lubricated contacts [1]. This formulation, based on the mathematical derivation of a linear complementarity problem (LCP), overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. In the present paper, the methodology favoured in [1], already successfully applied to solve textured bearing and squeeze problems in the presence of cavitation in a one dimensional domain for incompressible fluids, has been extended to include the effects of fluid compressibility, piezoviscosity and the non-Newtonian fluid behaviour and it has been also applied to the analysis of two dimensional problems. The evolution of the cavitated region and the contact pressure distribution are studied for a number of different configurations which can be considered as relevant benchmarks.In particular, some of the results obtained with the proposed scheme are critically analysed and compared with the predictions obtained using alternative formulations, including full CFD calculations. The stability of the proposed algorithm and its flexibility in terms of implementation of different models for compressibility, piezoviscosity and non-Newtonian behaviour are highlighted.     

Filtration characteristics of magnetic fibrous polymer as a new oil filter material for lubrication systems

Magnetic fibrous polymeric filter (MFPF) elements for lubrication systems were obtained by pneumoextrusion of a thermoplastic polymer (polyamide) containing a magnetic particulate filler (barium ferrite), and treating it subsequently in magnetic fields. Using a standard laboratory oil filtration test rig, metallic particle quantifier, and an image analyser system, the dependence of the filtration characteristics of the magnetic filter medium on the magnetic parameters was investigated. The variation of pressure drop and filtration efficiency with the packing density of the lubricating filter elements was measured. A conventional lubricant filter for an internal combustion engine was also tested for comparison with the filtration performance of the magnetised filter medium. Increasing the magnetic force of the filter medium made the MFPF material more effective in filtering fine ferrous particles, without changing the pressure drop. It was concluded that MFPF can be used as an effective filter in lubrication systems.     

Self-healing behavior of a polyelectrolyte-based lubricant additive for aqueous lubrication of oxide materials

We report on the self-healing behavior of a polyelectrolyte-based aqueous lubricant additive, poly(l-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG), during aqueous lubrication of an oxide-based tribosystem. Combined pin-on-disk tribometry and fluorescence microscopy experiments have shown that stable lubricating performance was enabled by means of rapid healing of the worn tribopair surface by polymers dissolved in the adjoining bulk lubricant. This rapid ‘self-healing’ of PLL-g-PEG is attributed to electrostatic interactions between the polycationic poly(l-lysine) (PLL) backbone of the polymer and negatively charged oxide surface. In contrast, a similar healing effect was not readily achievable in the case of methoxy-poly(ethylene glycol)-trimethylsilylether (Sil-PEG), a lubricant additive that is covalently bonded to the surface prior to tribological stress.     

Elastohydrodynamic lubrication analysis of a functionally graded layered bearing surface,with particular reference to 'cushion form bearings' for artificial knee joints

Elastohydrodynamic lubrication of a functionally graded layered (FGL) bearing surface, whose elastic modulus increases with depth from the bearing surface, was investigated in this study. The finite difference method was employed to solve the Reynolds equation, simultaneously with the elasticity equation of the bearing surface, under circular point contacts. The finite element method was adopted to solve the elasticity equation for the FGL bearing surface. The displacement coefficients thus obtained were used to calculate the elastic deformation of the bearing surface, required for the elastohydrodynamic lubrication analysis. Good agreement of the predicted film thickness and pressure distribution was obtained, between the present method and a previous study for a single layered bearing surface with a uniform elastic modulus. The general numerical methodology was then applied to an FGL bearing surface with both linear and exponential variations in elastic modulus, with particular reference to the 'cushion form bearing' for artificial knee joints. The predicted film thickness and pressure distribution were shown to be quite close to those obtained for a single layer under typical operating conditions representative of artificial knee joints, provided that the elastic modulus of the single layer was chosen to be the average elastic modulus of the graded layer.     

A new mechanism design of electro-magnetic actuator for a micro-positioner

This paper proposes a new type of non-conventional electro-magnetic actuator (EMA) for micro-positioning. It is a repulsive magnetic system consisting of a motion pad and two active coils. The motion of the pad is caused by the repelling force between the coils and the permanent magnets on the pad. First, the dynamic model is derived and analyzed. Next, an adaptive sliding mode controller is developed to deal with the unknown parameters with the objective of precision positioning. The experimental results demonstrate satisfactory performances including regulation accuracy and control stiffness for the system.