Film pressure distributions in point contacts predicted by thermal EHL analyses

In general, lubricated rolling/sliding contact fatigue problems have been investigated by assuming Hertzian contact pressure distributions. In this paper, thermal EHL analyses in consideration of the variations in oil properties in all directions within the film have been carried out under conditions of circular and elliptical contacts. It has been found that the actual film pressure distributions differ markedly from the Hertzian pressure distribution depending on the thermal conductivities of both contacting surfaces, slide–roll ratios and viscosity–pressure coefficients.     

Numerical analysis of TEHL line contact problem under reciprocating motion

This paper presents a full numerical analysis to simulate the thermal elastohydrodynamic lubrication (TEHL) of steel–steel line contact problem under reciprocating motion. The equation system is solved using multigrid techniques. General tribological behaviors of TEHL under reciprocating motion are explained. Comparison between thermal and isothermal results reveals the importance of thermal effect in prediction of the traction coefficient and film thickness. The influences of frequency, stroke length, and applied load on the variations of film thickness, pressure and traction coefficient during one working cycle are discussed. Furthermore, the influence of slide–roll ratio on tribo-characteristics of oil film under same entraining velocity is revealed.     

Effect of Surface Velocity Directions on Elastohydrodynamic Film Shape

This article is focused on the effects of the angle between lubricant entrainment velocity and sliding velocity on elastohydrodynamic film thickness distribution. Thin-film colorimetric interferometry was used to evaluate the film thickness distribution in smooth glass–steel contacts to provide basic data on the effects of the slide–roll ratio and the direction of sliding with respect to entrainment velocity. It was observed that as the sliding perpendicular to the entrainment velocity increased, the overall film thickness was reduced and asymmetry of the film profile with respect to the direction of the entrainment velocity increased. The asymmetry of the film profile with respect to the direction of the entrainment velocity increased with the entrainment speed or the overall film thickness. When the speed of the glass disk was larger than that of the steel ball, a dimple was formed even if there was a difference in direction between the entrainment and sliding velocities. A part of the dimple was exhausted from the elastohydrodynamic lubrication (EHL) conjunction as the angle between the entrainment and sliding velocities approached 90°.     

Film Formation in EHL Point Contacts under Zero Entraining Velocity Conditions

The contacts of adjacent balls in a retainerless bearing are subjected to the zero entrainment velocity (ZEV). The existence of an effective elastohydrodynamic lubrication (EHL) film between contacts running under ZEV conditions has long been proven experimentally. However, the classical EHL theory predicts a zero film thickness under ZEV conditions. Mechanisms, such as the thermal viscosity wedge effect and immobile film theory, have been proposed to tentatively explain the phenomenon. However, detailed numerical results are needed to provide theoretical evidence for such film formations. This paper aims to simulate, based on the viscosity wedge mechanism, the film formation of EHL point contacts under ZEV conditions. Complete numerical solutions have been successfully obtained. The results show that the thermal viscosity wedge induces a concave film profile, instead of a parallel film (Hertzian) as postulated by some previous researchers. By the simulation solver developed, the variation of film thickness with loads, oil supply conditions and ellipticity parameters have been investigated. Some unique lubrication behaviors under ZEV conditions are demonstrated. Furthermore, preliminary quantitative comparisons with the latest optical EHL experiments are finished. Both results are in good correlation.     

椭圆接触弹流润滑油膜形状的实验研究

采用多光束干涉测量技术,在自制光弹流实验机上进行了椭圆接触弹流润滑油膜形状的实验测量,观察了椭圆接触区短轴与卷吸方向之间的夹角θ、速度、施加载荷等对油膜形状的影响。结果表明：夹角θ较小时,油膜厚度整体上更大,接触区较窄,入口区油膜更陡峭;低速时,夹角及载荷基本不影响膜厚;高速、轻载时,夹角θ对膜厚影响更显著;载荷及夹角越大,动压油膜越难建立。     

弹流润滑中局部油膜增厚的数值模拟

通过理论计算模拟了Kaneta等在光干涉弹流试验中观察到的,当接触区钢球表面和玻璃盘表面反向运动时出现的反常油膜局部增厚现象,即润滑固体表面在接触区出现凹陷.对钢球-玻璃盘接触副进行了热弹流问题的完全数值求解,发现润滑中的热效应是形成凹陷的根本原因.当盘快球慢时有凹陷出现;而盘慢球快时无凹陷出现.讨论了凹陷的深度、位置和形状随运动条件、粘压系数及载荷等的变化.     

Experimental observation of a dimple-wedge elastohydrodynamic lubricating film

One of the main features of typical elastohydrodynamic lubricating (EHL) contacts is the unique horseshoe film shape, which can be readily observed by using interferometry and quite accurately modelled by the well-established EHL theory. However, an anomalous EHL film, characterized by a wedge shape together with a tiny dimple at the inlet region, is observed under pure sliding conditions with ultra slow speeds of 3–800 μm/s in an optical EHL test rig. The variations of the wedge and the inlet dimple with different sliding speeds and loads are investigated using a series of polybutene oils of high viscosities. It is found that the inclination of the wedge is dependent on sliding speeds, loads and oil viscosities. The dimple always occurs at the inlet. The appearance of an inlet dimple together with a wedge film shape is reported for the first time. The phenomenon can be attributed to a non-Newtonian characteristic of the lubricant: the limiting shear strength. Additionally, the influence of starvation on the film shape is also examined.     

EHL Performance of the Lubricant With Shear Strength: Part I — Boundary Slippage and Film Failure

This paper analytically investigates the isothermal line contact elastohydrodynamic lubrication of three lubricants with much different shear strengths under the nondimensional operating parameters of w = 2.15e-4 and U = 2.53e-10 applying the lubricant ideal viscoplastic rheological model. The boundary slippage of the low-shear-strength lubricant occurring in the EHL inlet zone was found and results in a much thinner film compared to the classical EHL theory prediction. The film boundary slippage and its growth with the slide/roll ratio variation of tile low-shear\- strength lubricant exhibit special phenomena, which are much different from those of the high-shear-strength lubricant. The easy occurrence of film failure in concentrated contact in the case of high sliding speed, heavy load, large slide/roll ratio, and low-shear-strength lubricant was concluded due to the severe friction heating on the surface conjunction and the lubricant thermal desorption on tile lubricant/surface boundary. The EHL film failure mechanism was further recognized.     

Simplified multigrid technique for the numerical solution to the steady-state and transient EHL line contacts and the arbitrary entrainment EHL point contacts

A simplified multigrid (MG) method is developed based on that presented by Venner et al. The full approximate scheme (FAS) right-hand side of the film thickness equation is ignored and only the Gauss–Seidel iteration is employed throughout the calculating procedure. The algorithm can be used in both steady state and transient isothermal line contact elastohydrodynamic lubrication (EHL) analyses and can also be extended to solve the elliptical contact problem with arbitrarily directed entrainment, with high computational efficiency and good numerical stability. A unique method is proposed to tackle the entrainment direction of the elliptical contacts.     

斜齿圆柱齿轮的热弹流润滑理论

将斜齿圆柱齿轮在某一啮合瞬时啮合线上的热弹流润滑问题近似等效为两反向圆锥滚子的准稳态热弹流润滑问题。应用多重网格法和逐列扫描法数值求解一对斜齿圆柱齿轮某啮合瞬时的准稳态热弹流润滑现象。结果表明：第一,斜齿圆柱齿轮接触线上各点的压力、膜厚、油膜温度和两齿面的温度均不相同,且温度分布的差异较明显。在接触区内,最低温升接近于零,最高温升则超过100 K。这是由于压力和膜厚的分布主要取决于沿滚子长度方向各点等效半径的分布曲线,而温度的分布则主要由沿滚子长度方向各点滑滚比的取值而定。第二,端部修形虽然可以降低端部高压和高温,但端部的压力和温度仍比中部高,膜厚比中部薄。对应到两齿面上,油膜中压力和温度较高,厚度较薄的位置最易发生点蚀和胶合破坏。     

The Effect of the Electric Double Layer on Very Thin Thermal Elastohydrodynamic Lubricating Film

The effect of the electric double layer (EDL) of friction surface on lubrication is significant under the condition of very thin lubricating film. This article presents a theoretical evaluation concerning the effect of the EDL on the film thickness and the pressure distribution of the elastohydrodynamic lubricating water film. These numerical analyses are based on the modified Reynolds equation that considers the EDL. Owing to the temperature risen readily in elastohydrodynamic lubrication (EHL) contact area, the influence of the temperature rise on the EDL effect was also investigated. The analysis results show that the EDL leads to a noticeable increase in the film thickness but has few influences on the pressure. Further, the analytical comparisons between isothermal and thermal conditions reveal that the temperature rise in the contact area weakens the effect of the EDL on the EHL film. Overall, consideration of the EDL effect gives a thicker EHL film, but once the temperature rise in the EHL regime is taken into account, the film thickness is correspondingly decreased.     

变速点、线接触副弹流润滑油膜的观测

应用光干涉方法,在自制的光弹流试验机上分别对纯滚动条件下点接触和线接触形成的弹流油膜进行变卷吸速度实验,并进行油膜测量。结果表明,在卷吸速度为零时都有封油现象的出现。随着卷吸速度的增加,油膜厚度增加,点接触形成的弹流油膜具有典型的马蹄形特征,线接触形成的弹流油膜在接触区端部有类似点接触的马蹄形收缩。要达到同样的最大赫兹接触压力,施加在线接触实验上的载荷要比施加在点接触实验上的载荷大40倍左右。     

一种离子液体的热弹流润滑数值模拟

离子液体因微观结构与普通润滑油不同,使其具有较低的黏压系数。采用光干涉油膜测量技术标定一种离子液体的黏压系数,并通过等温数值计算验证其可靠性。使用标定的黏压系数,对该离子液体进行膜厚、温升、摩擦因数和接触区中心黏度等热弹流润滑数值计算,并与具有相同黏度的普通润滑油的算例进行比较。计算结果显示,离子液体与同黏度润滑油相比具有突出的摩擦学性能,体现在离子液体在较宽速度和滑滚比范围内有非常低的温升和摩擦因数,而膜厚仍保持在同黏度润滑油的40%以上。离子液体的这种热弹流特性主要归因于其较低的黏压系数。     

Experimental study on lubrication regime variation in point contacts

The change between elastohydrodynamic lubrication (EHL) and hydrodynamic lubrication (HL) under a wide range of entrainment speeds and applied loads was studied using an optical EHL apparatus. A log-log scale linear relationship was demonstrated in the two lubrication regions between the film thickness and the entrainment speed (or load). A transition region can be clearly discerned between these two regions in which the film thickness no longer bears a linear relationship with the entrainment speed (or load). It is shown that a piezoviscous effect can be distinguished in the HL region by the speed exponent or the load exponent, and that relative sliding has a significant influence on the transition region.     

重载变速工况下弹流润滑的实验研究

为了揭示重载变速工况下的弹流润滑特性,在自行开发的光干涉弹流实验装置上,开展了相关的实验研究。实验主要针对钢球点接触,在重载(0.83GPa)和超重载(1.44GPa)两种载荷和变卷吸速度工况条件下,对弹流油膜进行了测量,获得了有效的实验数据。结果表明:重载和超重载条件下形成的弹流油膜都具有马蹄形特征。但超重载的没有重载的马蹄形特征明显。卷吸速度为零时有明显的封油现象,随着卷吸速度的增加,由卷吸速度产生的流体效应使得膜厚增加。另外,在进行超重载实验时,随着实验时间的延长,镀铬膜玻璃表面会有较多划痕,甚至出现玻璃表面被压溃的现象。     

Theoretical investigation on the dimple occurrence in the thermal EHL of simple sliding steel–glass circular contacts

The conical depression (surface dimple) phenomena observed by Kaneta et al. (Kaneta M, Nishikawa H, Kameishi K, Sakai T. Effects of elastic moduli of contact surfaces in elastohydrodynamic lubrication. ASME J. Tribol. 1992;114:75–80; Kaneta M, Nishikawa H, Kanada T, Matsuda K. Abnormal phenomena appearing in EHL contacts. ASME J. Tribol. 1996;118:886–892.) in optical interferometry experiments are simulated numerically by a complete solution to the simple sliding circular contact thermal elastohydrodynamic lubrication (TEHL) problem. Good agreement is displayed between the theoretical and experimental results. This agreement is explained by the “temperature–viscosity wedge” mechanism, which was first proposed by Cameron (Cameron A. Hydrodynamic lubrication of rotating discs in pure sliding, a new type of oil film formation. J. Inst. Petrol 1951;37:471.). Effects of the viscosity–pressure coefficient, the ambient viscosity, and the entrainment velocity on the behavior of the surface dimples are discussed.     

Inverse approach for estimating rheological characteristics of adsorption layer in thin film EHL contacts

A modified Reynolds equation is derived for thin film elastohydrodynamic lubrication (TFEHL) by means of the viscous adsorption theory. This TFEHL theory can be used to explain the deviation between the measured film thickness and that predicted from the convenient elastohydrodynamic lubrication (EHL) theory under very thin film conditions. Results show that the thinner the film, the greater the ratio of the adsorption layer to the total film thickness becomes, and the greater the value of the pressure–viscosity index (z′). An inverse approach is proposed to estimate the pressure distribution based upon the film thickness measurement and to determine the pressure–viscosity index of oil film, and the thickness (δ) and the viscosity ratio (η^*) of the adsorption layer in TFEHL circular contacts. Based on TFEHL theory, the inverse approach can reduce z′ error, and provides a reasonably smooth curve of pressure profile by implementing the measurement error in the film thickness. This algorithm not only estimates the pressure, but also calibrates the film shape. Consequently, it predicts z′, η^*, and δ with very good accuracy. It can also be used to evaluate the lubrication performance from a film thickness map obtained from an optical EHL tester. Results show that the estimated value of z′ is in very good agreement with the experimental data.     

Analysis on the thermal elastohydrodynamic lubrication of tapered rollers in opposite orientation

Faced to the lubrication of the meshing teeth of helical gears, thermal elastohydrodynamic lubrication (TEHL) of two tapered rollers located in opposite orientation was studied numerically. It has been found from the full numerical solution that the lubricating performances of two tapered rollers differ significantly from that of a finite line contact. For tapered rollers, the distributions of pressure and film thickness depend strongly on the distribution of the effective radius in the direction of the roller length, and the distribution of temperature rise depends strongly on the local slide-roll ratio in the direction of the roller length. Side-leakage is inevitable in the elastohydrodynamic lubrication (EHL) of two tapered rollers, and thin films are produced in the ends by side-leakage, but the high pressures in the ends could be decreased by the end-shape modification, which is beneficial to the end lubrication. The temperature distribution is interesting, and the lowest temperature in the high-pressure area is close to the ambient temperature, which occurs in a place where the local slid-roll ratio is zero.     

Transient increase of film thickness in micro-textured EHL contacts

In this paper, the transient lubrication phenomena induced by isolated circular micro-cavities passing through an EHL point contact are analysed. A 52 100 steel ball was micro-machined using a femtosecond pulse laser, and is tested with an EHL tribometer. The experiments are simulated numerically with a 2D-multigrid solver. Under rolling–sliding conditions, the film thickness distribution is modified, and two opposite effects are observed. Deep micro-cavities induce an oil film decrease. On the contrary, a shallow micro-cavity locally generates a large increase in the film thickness. When the ball surface is the slowest, the propagation velocity of the local oil film reinforcement increases.     

自旋对角接触球轴承弹流润滑与油膜刚度的影响

根据角接触球轴承自旋运动特征,同时考虑弹流润滑效应,建立角接触球轴承考虑自旋运动的弹流润滑模型;采用多重网格法求解弹性变形,利用有限差分法迭代求解雷诺方程,得到较为精确的数值解;分析不同赫兹接触压力、滚道表面粗糙度下自旋对角接触球轴承弹流润滑和油膜刚度的影响。结果表明：考虑自旋时随着Hertz接触压力、自旋角速度增大,油膜厚度减小,油膜压力增大,油膜承压区域呈细长状,并向接触中心靠近;随着滚道表面粗糙度幅值增大,油膜压力和膜厚均出现了波动,且考虑自旋运动时,轴承油膜厚度明显减小,油膜局部压力峰值更大;随着卷吸速度、润滑油黏度增大,油膜刚度减小,而考虑自旋运动时油膜刚度值更大;随着自旋角速度增大,油膜刚度逐渐增大。