High‐pressure short time behavior of traction fluids

The squeeze film formation ability of traction fluids is studied under impact load by dropping a steel ball‐bearing against a flat anvil made of mild steel. The effect of the pressure–viscosity coefficient and of the viscosity is investigated for plastic impact. The depth difference between the lubricated surface dent and the dry dent increases linearly with the product αη of the pressure–viscosity coefficient α and the viscosity η. The importance of the lubricant parameter αη is observed under the squeeze film formation ability from contact voltage or elastohydrodynamic lubrication central film thickness measurement at rolling condition. The intensity of each impact collision is measured by means of an acoustic emission (AE) sensor. The high‐pressure short‐time solidification of traction fluids was confirmed by dent analysis after the impact tests and AE analysis under impact loads. Copyright © 2006 John Wiley & Sons, Ltd.     

高黏度油润滑弹塑性接触问题数值仿真*

针对高黏度润滑油工况下,已有弹塑性润滑模型计算结果失真的问题,采用半解析法建立弹塑性润滑接触模型,通过逐步增加润滑油初始黏度的方式来进行仿真计算,消除了接触区压力曲线的波动,从而克服先前计算失真的问题;基于各向同性强化准则下的J2流动理论,采用径向返回算法求解塑性应变,并且将塑性应变引起的残余变形考虑至润滑油膜厚度方程中。研究结果表明：弹塑性润滑压力主峰相比于弹流润滑结果明显降低,二次压力峰相对变化较小;弹流润滑的中心膜厚与弹塑性润滑中心膜厚接近,但最小膜厚稍大;对于较高的速度和黏度工况,塑性应变区域会向表面及接触区出口处移动。     

A critical evaluation of film thickness‐derived pressure–viscosity coefficients

A single parameter, the pressure–viscosity coefficient, α, quantifies the pressure dependence of the viscosity of the liquid in elastohydrodynamic lubrication (EHL). Most published values of α have not been obtained from measurements of viscosity as a function of pressure. Rather, these effective pressure–viscosity coefficients have been derived from the measurement of the EHL film thickness, a more difficult procedure. In this article, five well‐characterized liquids that should be Newtonian in the EHL inlet are identified for which film‐derived coefficients have been reported. These coefficients are compared with coefficients derived from published viscosity correlations and new viscosity measurements. The film‐derived coefficients are found to not be an accurate representation of the piezoviscous response. The procedure of deriving a pressure–viscosity coefficient from a film thickness measurement does not offer an alternative to the simpler and easier viscometer measurement. Copyright © 2014 John Wiley & Sons, Ltd.     

高速重载弧齿锥齿轮点接触热弹流综合分析*

针对高速重载弧齿锥齿轮节圆位置,基于热弹流润滑理论进行齿面润滑特性分析,研究不同工况锥齿轮油膜各特征（压力、膜厚、温升）二维轮廓曲线的变化情况。结果表明：高速重载的工况使得Hertz压力峰与二次压力峰出现合并的现象,并且弹流润滑中经典的中央油膜平坦现象并不显著,仅当温度降低使润滑油黏度增加时,才逐渐出现了中央油膜平坦的现象。为了在工程实践中能够有针对性地调整工况参数来改善齿轮的润滑状态,分析油膜特征参数对输入参数的敏感性,发现工况参数中对油膜最大压力的影响程度由大到小为弹性模量、黏度、转速、功率;对油膜最大温升与最小油膜厚度的影响程度由大到小为黏度、转速、弹性模量、功率。     

A non-averaging method of determining the rheological properties of traction fluids

Traction machines have been frequently used to study the rheological responses of lubricants in elastohydrodynamic lubrication (EHL) contacts. Fundamental properties are inferred from EHL traction measurements based on the average pressures and temperatures in the contact. This average approach leads to uncertainty in the accuracy of the results due to the highly nonlinear resonse of the fluid such as viscosity to both pressure and temperature. A non-averaging method is developed in this paper to study the elastic and plastic properties of traction fluids operating in EHL contacts at small slide-to-roll ratios. A precision line-contact traction rig is used to measure the EHL traction at a given oil temperature and Hertz pressure. By choosing a sensible pressure-property expression, the parameters of the expression can be determined through the initial slope and peak traction coefficient of the traction measurements. The elastic shear modulus and the limiting shear stress of the lubricant corresponding to a single pressure can then be calculated for a range of pressures and temperatures of practical interest. Two high-traction fluids are studied, and their elastic moduli and limiting shear stresses presented.     

Investigation into the Normal Contact Stiffness of Rough Surface in Line Contact Mixed Elastohydrodynamic Lubrication

In this work, the statistical asperity microcontact models in combination with the acoustic spring model and the load sharing concept are utilized to study the interfacial normal contact stiffness for a rough surface in line contact elastohydrodynamic lubrication (EHL). Two different statistical microcontact models of Greenwood and Williamson (GW) and Kogut and Etsion (KE) are employed to derive the normal contact stiffness expressions for a dry rough line contact considering the purely elastic contact and the multiple regimes elastic–elastoplastic–fully plastic contact, respectively. The liquid film stiffness is calculated based on the relationship between film thickness and bulk modulus of the lubricant. The lubricant film thickness equations are employed in conjunction with the load sharing concept and the empirical formulas for the maximum contact pressure in a dry rough contact are fitted for the GW model and the KE model, to evaluate the relationship between film thickness and motion velocity for the purely elastic GW microcontact model and the multiregime KE microcontact model, respectively. The comparison with experimental results shows that the KE model predicts closer total contact stiffness results than the GW model. The stiffness contributions from the solid asperity contact and lubricant film are obtained and effects of surface roughness, applied load, motion velocity, and type of lubricant on the normal contact stiffness are analyzed.     

弹性流体动力润滑的热效应

简述热弹性流体动力润滑的概念、理论的发展及其科学基础。在给出一组典型的点接触热弹流数值解之后,通过实例集中描述5种热效应,即摩擦因数与滑滚比之间的关系、入口温升导致油膜减薄、尺度效应、热黏度楔效应和固体温度效应。澄清了润滑工程界对热弹流润滑的几个模糊理解,指出热弹流研究面临的主要困难,并展望其发展前景。     

Inverse approach for calculating temperature in EHL of line contacts

This paper proposes a thermal elastohydrodynamic lubrication (TEHL) inverse approach to estimate the pressure, temperature rise, and apparent viscosity distributions in an EHL line contact. Once the film shape is measured, the pressure and estimated film thickness distributions can be calculated from force balance and elastic deformation theories. By using these smoothing pressure and film thickness distributions, the Gauss-Seidel iteration is employed to calculate the temperature rise distribution from energy, surface temperature, and rheology equations. This approach overcomes the problems of pressure and temperature rise fluctuations, and generates accurate results of pressure and temperature rise distribution from a small number of measured points of film thickness, which also saves computing time. Results show that the direct inverse method requires a lot of measured points to establish the amplitude and location of the pressure and temperature rise spikes, whereas the inverse approach can obtain the accuracy results with only 31 measured points. With the error from the resolution in the film thickness measurements, this approach also presents a smooth curve of the pressure and temperature rise distributions with a small error. Furthermore, this approach still provides a good solution in apparent viscosity, whereas the direct method provides a much larger error in apparent viscosity.     

Elastohydrodynamic Lubrication with Oil Droplets

In oil–air lubrication, lubricants are supplied in the form of oil droplets to tribo-pairs. Numerical work has been carried out to investigate transient EHL characteristics when a series of oil droplets are entrained along the center line of the contact zone. Results show that the spacing distance between oil droplets is an important parameter for continuous EHL film formation. For oil droplets with the same volume, the effective lubrication time increases first and then decreases as the droplet distance increases. An optimum droplet distance can be found for the maximum effective lubrication time with continuous EHL films. Moreover, entrainment speed, lubricant viscosity and oil/solid interface can also affect the effective lubrication time significantly and change the optimum droplet distance accordingly. Numerical results showed a close correlation to the experiments. This study is useful to basic understanding of lubrication by limited lubricant supply.     

Microscopic study of thin film lubrication and its contributions to macroscopic tribology

This review article summarizes recent progress in investigation of nano‐rheology and thin film lubrication, as well as their contributions to conventional tribology. As the thickness of a lubricating film becomes comparable to molecular dimensions, a lubricant confined between solid walls undergoes a dramatic transition in its rheological properties and physical state, including the formation of ordered structure, enhanced viscosity and slow relaxation, glass transition or solidification, and consequent stick‐slip motion. As a result, it is recognized that there is special regime between EHL and boundary lubrication, identified as thin film lubrication, where lubricant flow and hydrodynamics are still in action but behave differently from expectations of the classical theory. Generalized theories of thin film lubrication are under development. Microscopic studies of thin film lubrication provide a solid theoretical basis to the development of high‐tech and micro devices, the understanding of lubrication failure, the generalization of classical lubrication theory, and friction control and interface design. This revised version was published online in June 2006 with corrections to the Cover Date.     

纳米级润滑膜的粘度修正与薄膜润滑计算

根据纳米级润滑膜的试验测试结果提出薄膜润滑状态的粘度修正公式 ,并在此基础上建立了润滑膜厚度计算的数值计算方程。将该数值计算结果与弹流理论计算值和试验值进行对比表明 ,在薄膜润滑条件下 ,膜厚与速度和润滑油粘度的关系与弹流润滑计算结果相差较大 ,可明显看出弹流润滑向薄膜润滑的过渡 ,所提出的粘度修正式与试验结果则有较好的一致性     

薄膜润滑与润滑状态图

讨论了速度、固体表面能、滑动比、润滑剂粘度和化学性能对薄膜润滑状态下油膜厚度的影响,以及弹流润滑向薄膜润滑转化条件和液体膜失效条件。进而提出了新的润滑状态划分准则以及不同润滑机理下膜厚的变化情况。     

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。     

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.     

指数率流体热弹流润滑分析

应用多重网格技术,求得了指数率非牛顿流体线接触热弹流润滑的数值解,分析了油膜压力、厚度和温度等随流变指数、速度参数、滑滚比及载荷参数的变化关系,并与相同工况下的等温解进行了比较。结果表明,随着流变指数的增加,油膜厚度和温度、入口处的当量粘度、最小膜厚、中心膜厚和最大温升均增大,而油膜压力和摩擦因数的变化较小。指数率流体弹流润滑问题的热效应不可忽略;与压缩功项相比,油膜能量方程中的热耗散项对温度的影响最大。同时,无量纲速度参数、滑滚比和载荷参数等均影响热弹流润滑特性。     

Starved Grease Lubrication of Rolling Contacts

Many grease lubricated roller bearings operate in the starved elastohydrodynamic (EHL) regime where there is a limited supply of lubricant to the contact (1). Under these conditions the film thickness drops to a fraction of the fully flooded value (2) and, thus, it is difficult to predict lubrication performance, or bearing life, from conventional EHL models. In this regime film thickness depends on the ability of the grease to replenish the track rather than the usual EHL considerations. The conventional view of grease lubrication is that base oil bleeds from the bulk reservoir close to the track, replenishing the inlet and forming a fluid EHL film (3). Resupply, under starved conditions, will thus depend on both operating conditions and grease parameters. The aim of this paper is to evaluate the influence of these parameters on starved lubrication in a rolling contact. Starved film thickness has been measured for a series of greases and the results have been compared to the fully flooded values. These show that the degree of starvation increases with increasing rolling speed, base oil viscosity and thickener content but decreases at higher temperatures. In many cases an increase in absolute film thickness is obtained when moving from high viscosity base oil to a low one, this result is the reverse of normally accepted EHL rules. Taking the fully flooded film thickness as a guide to lubrication performance is therefore not valid as grease film thickness in the starved regime is determined by local replenishment rather than bulk rheological properties.     

点接触弹流润滑供油条件退化的乏油分析

在点接触弹流润滑中,如果不能及时补充新油,则接触区的供油条件会随着润滑次数而退化。分析了供油油膜厚度、中心膜厚、最小膜厚和润滑油膜压力区形成位置与润滑次数的关系。结果表明:润滑开始时,由于供油油膜厚度较大,系统处于充分供油状态;随着润滑次数的增加,有一部分油从两侧泄漏,系统逐渐转到乏油状态,供油油膜厚度、中心膜厚和最小膜厚均逐渐变小,压力区形成位置则逐渐向Hertz接触区靠近;最终供油油膜厚度、中心膜厚和最小膜厚趋于定值,压力区趋于Hertz接触区,从而达到一种稳定乏油状态。     

Modélisation du contact lubrifié—exemple de la mise en forme des métaux

Lubricated contact modelling — the example of metal forming processes. The theory of hydrodynamic (HD) lubrication was developed after the derivation of the Reynolds' equation in 1886. It allowed us to understand firstly low pressure lubricated contacts, then, when coupled with elastic deformation equations, high pressure lubricated contacts in elasto-hydrodynamic (EHD) lubrication. In the 60's, the same techniques were transposed to plasto-hydrodynamic lubrication (PHD), where one of the solids in contact is under plastic deformation, such as in metal forming processes. With the example of wire-drawing, the application of PHD models to metal forming is recalled. The importance of temperature effects on film formation and evolution was then an incentive to transposing thermo-EHD models into thermo-PHD. The roughness–lubricant flow coupling is then described, in EHD then in PHD. Finally, models of the mixed lubrication regime are addressed, whereby average contact pressure is borne partly by solid–solid, or micro-EHD, or boundary films, and partly by the hydrodynamic or hydrostatic pressure in the lubricant. Following a discussion of a few results on strip cold rolling, perspectives for evolution of these mixed regime PHD models are presented, in view of recent mixed-EHD models from the literature.