Theoretical investigation of transient elastohydrodynamic lubrication with newtonian solid‐liquid lubricants

This paper reports a theoretical investigation of transient elastohydrodynamic lubrication of a line contact. A time‐dependent Reynolds equation and elasticity equations for compressible solid‐liquid lubricants were solved using finite volume and multigrid techniques. The lubricants used were mineral oils mixed with very small solid particles, MoS₂ and PTFE, which can be treated as Newtonian fluids. The two surfaces were initially at rest and in contact. The transient oil film pressure and oil film thickness were calculated numerically. This simulation showed the significant effects of solid particles on the lubrication characteristics.     

Theoretical investigation of transient elastohydrodynamic lubrication with newtonian solid–liquid lubricants

This paper reports a theoretical investigation of transient elastohydrodynamic lubrication of a line contact. A time‐dependent Reynolds equation and elasticity equations for compressible solid–liquid lubricants were solved using finite volume and multigrid techniques. The lubricants used were mineral oils mixed with very small solid particles, MoS2 and PTFE which can be treated as Newtonian fluids. The two surfaces were initially at rest and in contact. The transient oil film pressure and oil film thickness were calculated numerically. This simulation showed the significant effects of solid particles on the lubrication characteristics. Copyright © 2006 John Wiley & Sons, Ltd.     

The Influence of Lubricant Upon EHD Film Behavior During Sudden Halting of Motion

Although steady state elastohydrodynamic (EHD) lubrication is quite well understood both from the theoretical and from the experimental point of view, studies of transient effects in EHD are currently far less developed. This paper describes an experimental investigation into EHD film behavior during sudden halting of motion. A technique has been devised which enables both central lubricant film thickness and film thickness profiles to be measured every millisecond during halting of a ball on flat, sliding contact. This has enabled detailed information of influence of lubricant on film collapse during halting to be obtained. It is shown that film collapse occurs in two stages. The first is a very rapid reduction in film thickness with only very small changes in film geometry and thus pressure distribution. This is followed, as soon as entrainment ceases, by the formation of a lubricant entrapment, and subsequent slow leakage of fluid from the central film region. This paper focussed on the formation of this entrapment and the influence of the rheological properties of the lubricant, i.e. viscosity and pressure-viscosity coefficient, on its development and behavior.     

Application of Transient Elastohydrodynamic Lubrication Analysis for Gear Transmissions

Transient elastohydrodynamic lubrication theory which deals with the lubrication of gear transmission is presented. A numerical procedure was developed to solve the governing equations for the transient EHL with variable load, curvature, and rolling velocity along the line of action. The compressibility of the fluid is taken into consideration. Results are presented for the pressure distribution and the film thickness successively along the line of action as a function of time. A parametric study was conducted to investigate the effects of geometry factors on the lubrication behavior of a gear transmission. Parameters of interest are gear ratio, central distance, gear tooth module, and profile shift of gear tooth. The results of extensive simulations for gear tooth lubrication show that the equivalent curvature radius of gear teeth plays an important role on the EHL film formation.     

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.     

弹流润滑状态下润滑剂的边界滑移问题

根据大量的实验事实和观察,本文对润滑剂中极性分子与金属界面间相互作用作了初步分析,从而提出了弹流润滑状态下润滑剂在固液界面发生滑移的力学模型,并分析了由于润滑剂在边界滑移对弹流润滑性能的影响。结果表明边界滑移是造成弹流润滑油膜破裂的关键因素。     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

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.     

Theoretical Modelling of Film-Forming Mechanisms Under Transient Conditions: Application to Deceleration and Experimental Validation

This paper proposes an analytical model for line (1D) and point contacts (2D), based upon the Ertel’s hypothesis to predict the evolution of film thickness in steady-state and transient conditions in elastohydrodynamic lubrication. This theoretical approach, applied to a velocity ramp at constant deceleration, is perfectly supported by experimental results in terms of film thickness distribution during the deceleration process and in terms of central film thickness at the vanishing of the entrainment velocity. This work emphasizes the role of the transport effects of the lubricant at the instantaneous entrainment velocity on the time and length scales at which the film thickness disturbances induced by the deceleration process occur until the complete halting of the surfaces.     

齿轮瞬态弹流润滑的多重网格数值分析

利用多重网格技术，考虑了轮齿上的载荷、啮合点的卷吸速度与综合曲率半径随啮合线的变化，求得了齿轮传动瞬态弹流润滑的完全数值解。揭示出最小膜厚、最大压力沿啮合线的变化，讨论了齿轮传动比对压力与膜厚的影响．给出了几个导致润滑失效的危险啮合点的压力与膜厚分布。     

A simple theory of asperity contact in elastohydro-dynamic lubrication

The Greenwood and Williamson theory of random rough surfaces in contact has been combined with established elastohydrodynamic theory to provide a theoretical approach to highly loaded lubricated contacts in which the load is shared between hydrodynamic pressure and asperity contact. It is shown that, provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given (to a first approximation) by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. It then follows that the asperity pressure, both real and apparent, is determined primarily by the ratio of theoretical film thickness to the combined roughness of the two surfaces (h_o/σ). A corollary of this result is that an increase in total load, which has only a small influence on the film thickness, is carried by an increase in fluid pressure and only gives rise to a small increase in asperity contact pressure.     

点接触润滑状态转化的实验观察

利用球-盘接触润滑油膜厚度的光干涉测量法，通过卷吸速度或载荷的改变实验研究了弹性流体动力润滑与流体动力润滑转化过程中油膜厚度的变化规律。实验结果显示这2种润滑状态之间存在明显的过渡区。与已有的理论一致，在弹性流体动力润滑区和流体动力润滑区，油膜厚度与卷吸速度或载荷在对数坐标中呈直线关系。在两者的过渡区，固体表面的弹性变形量随卷吸速度或载荷的变化发生明显的变化，油膜厚度与速度或载荷的关系不再为对数坐标中简单的线性关系。使用已有的润滑状态区理论不能得到实验观测到的润滑状态的转化过渡区。     

Power law fluid model incorporated into elastohydrodynamic lubrication theory of line contact

An algorithm is developed for the study of the infinitely long slider bearing in general form, considering the lubricant to be an incompressible power law fluid in isothermal conditions. The earlier works on this topic were considered by taking cavitation boundary conditions when a cylinder moves over a plane lubricated with a power law fluid and in EHL solution in a particular case, viz. pure rolling of a cylinder over an identical cylinder. We have considered a general solution including elastohydrodynamic lubrication (EHL) for different values of power law exponent. Deviation of values of central film thickness for different values of power law exponent from those for Newtonian lubricants are presented. The effects of the power law exponent on the central film thickness, minimum film thickness and load capacity are analysed. The effects of rolling and sliding velocities of contact surfaces are also analysed in terms of an equivalent radius of a cylinder moving over a moving plane. Film shapes and pressure distributions are also calculated numerically and presented graphically for various values of central film thickness considered in this paper. A number of observations obtained here with pseudoplastic nature of lubricants are in good agreement with the experimental results. The theoretical observations suggest the behaviour of common lubricants as pseudoplastic fluids in the cases of slowly moving surfaces and motion under heavy load.     

Analysis on Isothermal Elastohydrodynamic Lubrication of Orthogonal Face Gear

Face-gear drives have been applied in aviation transmissions, in particular, helicopter transmissions, and the lubrication characteristics are an important indicator for estimating the load-carrying capacity of face-gear teeth. In order to analyze the lubrication performance of the face gear under load, equations for the contact path of the face gear loaded tooth contact analysis (LTCA) were established on the basis of the load equivalent error of alignment (LEEA) and the load distribution among the teeth was calculated. Then a method for calculating the contact area and tooth surface velocity of face-gear drives was studied. Face-gear isothermal elastohydrodynamic lubrication (EHL) dimensionless equations are presented. A multigrid algorithm was used to complete the solution of the minimum film thickness and film pressure of face-gear drives. The lubricant film thickness and film pressure variation in the mesh cycle are expressed using example calculations that provide a theoretical basis for face-gear lubrication design.     

Effect of surface texturing on elastohydrodynamically lubricated contact under transient speed conditions

Effect of surface topography modifications on lubrication film thickness within non-conformal lubricated contact operated under transient speed conditions is observed. Optical test rig is used to observe the lubricant film behaviour between the flat surface of a chromium coated glass disc and a steel ball under simplified operational conditions modelling the cam and tappet contact. Numerical simulation was used to be able to choose the operating conditions suitable for experiments. An array of micro-dents was produced on the ball surface to be able to demonstrate the effect of surface topography on lubrication film formation. Experiments were carried out under elastohydrodynamic lubrication conditions. Obtained results have shown that surface texturing could represent the way how to increase lubrication efficiency of rolling/sliding non-conformal contacts under transient operational conditions through the lubricant emitted from micro-dents. It was found that the lubricant emitted from the micro-dents helps to separate rubbing surfaces especially under thin film lubrication conditions where the rubbing surfaces moves in the opposite direction.     

Tribological characteristics of aloe mucilage

Abstract

Increased concerns about environmental damage caused by many lubricants, has created a growing worldwide trend of promoting new environmentally friendly lubricants. The tribological characteristics of aloe mucilage as a kind of original biolubricant have been investigated in the present work. The experimental results indicate that the variation of the film thickness of aloe mucilage is not the same as that in traditional elastohydrodynamic lubrication, but conforms to the lubrication regime of thin film lubrication under the present experimental conditions. The coefficient of friction (COF) of the aloe mucilage among different tribological pairs is significantly decreased by the increase in velocity, while there is little variation when the normal load is increased. The COF of aloe mucilage between WC and DLC surfaces is very small with a value of 0˙04, and the wear resistance of the aloe mucilage between WC/DLC is better than that between WC/Si and WC/steel.     

On the shear stress of elastohydrodynamic lubrication in elliptical contacts

Results of mathematical modelling of elastohydrodynamic lubrication of rolling contacts are presented. Effects of dimensionless parameters such as speed, normal load, elliptical parameters and coefficient of limiting shear stress on shear stress distributions have been studied. Moreover, profiles on hydrodynamic pressure and film thickness in EHD contacts have been studied. It has been found that shear stress profiles on two contact surfaces in entraining direction are similar with each other in some way. Shear stresses of fluid film on contact surfaces vary with many factors, which reveals the mechanism of traction in elastohydrodynamically lubricated contacts.     

Approaching Mixed Elastohydrodynamic Lubrication of Smooth Journal-Bearing Systems with Low Rotating Speed

When a conformal interface is under low velocity and heavy load conditions, solid contact (or dry contact) may occur even in a system with smooth surfaces. This paper presents two approaches for solving steady-state and transient mixed elastohydrodynamic lubrication problems of journal bearings with smooth surfaces under low rotating speed. The first approach uses the reduced Reynolds equation with a combined finite element–backward finite difference scheme and the second applies a zero film thickness equation to describe the mechanical behavior of mating surfaces at solid contact points. The major advantages of these two approaches are (1) no division of the solution domain into a lubricated area and a solid contact area is necessary and (2) the solid contact pressure, lubricant pressure, and eccentricity ratio can be solved simultaneously. Numerical examples are presented for the application of these approaches. For the steady-state cases under low velocity studied in this work, pressure distributions approach those found in a dry contact state. This comparison confirms that the contact treatments are proper. Moreover, a transient case under sinusoidal loading was analyzed with these two approaches, and the results showed good agreement. This comparison further supports the use of these approaches.     

Elastohydrodynamic lubrication of circular contacts at pure squeeze motion with non-Newtonian lubricants

In this study a numerical method for general applications with non-Newtonian fluids is developed to investigate the pure squeeze motion in an isothermal elastohydrodynamic lubricated spherical conjunction under constant load conditions. The coupled transient modified Reynolds, the elasticity deformation, and the load equilibrium equations are solved simultaneously. Computer simulation is carried out to investigate the effects of flow rheology and operations on the relationship between the pressure and film thickness distributions. The simulation results reveal that the larger the flow index (n), the larger the film thickness and the smaller the maximum central pressure. This results in larger time needed to obtain maximum central pressure. In addition, the elastic deformation is more significant for the lower flow index. Therefore, the smaller the flow index becomes, the greater the difference between the hydrodynamic lubrication (HL) solution and elastohydrodynamic lubrication (EHL) solution becomes.     

Lubrication in helical gears

In this paper, a method to determine elastohydrodynamic film thickness in helical gears is developed by combining the Dowson-Higginson elastohydrodynamic lubrication (EHL) formulation with helical gear geometry and kinematics. Comparisons are made with traditional gear film thickness models. This analysis is then used to characterise the film thickness and lambda ratio in an automotive planetary gearset. Methods to measure surface roughness in fine-pitch gears are described.