Temperature rise due to sliding in rolling/sliding elastohydrodynamic lubrication line contacts: an efficient numerical analysis for contact zone temperatures

An efficient numerical method based on Lobatto quadrature analysis is adopted for a rigorous analysis of temperature in elastohydrodynamic lubrication (EHL) line contacts. Temperature distributions are calculated for maximum Hertzian pressures and rolling speeds varying between 0.5 to 2.0 GPa and 1 to 30 m/s, respectively. Significant mid-film temperature and surface temperature increases have been observed at higher rolling speeds with an increase in loads and slip ratios. Results have been compared with the results of Manton, S. M., O'Donoghue, J. P. and Cameron, A., Temperatures at lubricated rolling/sliding contacts. Proceedings of the Institution of Mechanical Engineers, 1967–68, 182(417), 813–824. An empirical equation is presented for the prediction of non-dimensional maximum mid-film temperature in the contact zone in terms of the dimensionless thermal loading parameter Q, dimensionless load W and slip S, as:

     

Formulas Used in Thermal Elastohydrodynamic Lubrication

A numerical solution to the problem of thermal compressible elastohydrodynamic lubrication of rolling/sliding contacts has been tested over a wide range of operating parameters consisting of dimensionless load, speed, slip, and material parameters. A least squares exponential curve fit was used to develop simple formulas for the amplitude and location of the pressure spike, the minimum film thickness, and the maximum lubricant temperature as a function of the operating parameters. These equations can be used to evaluate parameters affecting the performance of rolling/sliding heavily loaded lubricated contacts.     

线接触热弹流润滑的数值分析

基于Ree—Eyring流变模型，建立线接触热弹流润滑方程，通过数值计算得出了载荷参数、速度参数、材料参数和滑滚比对于二次压力峰、最小油膜厚度和最大油膜温度的重要影响。     

Interferometry Measurement of Spin Effect on Sliding EHL

This paper describes interferometry measurement of the film profiles of sliding elastohydrodynamic lubrication (EHL) contacts with spin. In the custom-made EHL test rig, spin motion is introduced through adjusting the center offset of the ball-on-disc contact with respect to the disc rotation axis. A parameter, spin ratio S _sp, is employed to represent the spin level, which is defined as the ratio of the Hertzian contact radius to the center offset. Experimental results show that with spin the film shape is obviously skewed, and the film thicknesses at the two side lobes are no longer the same; therefore, the symmetry of the classical horseshoe film shape is lost. The film thickness dependences on entrainment speeds are significantly influenced by the spin ratio S _sp, and high spin ratios induce high speed indices. At a fixed spin ratio S _sp, with increasing sliding speeds the film thickness difference between the two side lobes becomes large, and the horseshoe film shape is more distorted. When applied loads are raised, more spin is introduced, film thickness decreases, and film shape is obviously twisted.     

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.     

Effect of Sliding Direction on EHL Film Shape Under High Sliding Conditions

It is well known that a sliding speed influences a lubricant film thickness of elastohydrodynamic rolling–sliding contacts significantly. The effect of sliding is described quite well for unidirectional rolling and sliding; however, there are a limited number of papers dealing with sliding in different directions. This study describes how the sliding direction influences elastohydrodynamic film shape under high sliding conditions. An optical ball-on-disc tribometer together with thin-film colorimetric interferometry method is used for a film thickness measurement. The results show that the sliding direction influences lubricant film shape and the effect is connected with dimple phenomena. The temperature–viscosity wedge effect is discussed as a possible mechanism. The results are important for a film thickness prediction under high sliding conditions and provide experimental evidence for an extension of elastohydrodynamic lubrication (EHL) theory.     

弹性流体动力润滑椭圆接触问题的热分析

本文通过一组完全数值解,在较宽的工作条件范围内分析了热效应对点接触弹流润滑性质的影响。在计算油膜温度分布和摩托车擦拖曳力的过程中,作者分别使用了热牛顿流体模型和Eyring流体模型。此外,作者还研制了光干涉弹流润滑实验台,对于不同的载荷、不同的滚动速度与相对滑动速度、不同的润滑剂和环境温度,能够测出点接触情况下的油膜形状、油膜厚度与摩擦拖曳力。经过对比可以看出,理论与实验相当一致。     

Experimental results and analytical film thickness predictions in EHD rolling point contacts

In this work, we consider several types of lubricants—including non-Newtonian fluids—that were studied in EHD pure rolling point contacts under various operating conditions, leading us to explore a wide range of dimensionless parameters. The experimental results are compared with predictions given by the usual analytical EHL relationships and by more recently developed models. This broad comparison conducted with particular emphasis on minimum film thickness (h_m) showed a fair agreement between experimental data and a few predictions including some obtained from extended models. Commonly used elastohydrodynamic lubrication (EHL) models did not systematically give accurate h_m estimation, whereas minimum film thickness not only is a yield value but also serves as a key parameter in estimating lubrication regimes.     

Influence of spinning on the rolling EHL films

Spinning cannot be ignored in some elastohydrodynamically lubricated contacts. In this paper, spinning is incorporated into an elastohydrodynamic lubrication (EHL) contact of pure rolling and its influences on EHL films are studied. Results show that with increase in spinning, the symmetry of the film shape gets lost, and the minimum film thicknesses, located respectively at the two side-lobes, decrease and show more dependence on loads. The speed indices of the film thickness at the side lobes are higher than those of the classical EHL theory predicted. Numerical work has also been carried out to clarify the experiment measurements.     

Effect of Interfacial Properties on EHL Under Pure Sliding Conditions

This paper presents an experimental study of the effect of boundary slip on the lubricating film shape and friction of an elastohydrodynamic lubrication (EHL) contact under isothermal conditions. Ball and disc pure sliding experiments were carried out with a high viscosity polybutene oil using a conventional optical EHL test rig. The film shape and friction were measured simultaneously. The results obtained from two discs with different coatings were compared. One disc was coated only with Cr, the partially reflective layer, and the other had an extra layer of SiO₂ coating on top. When running under mild conditions of low load and speed, there was no evidence of any boundary slip effect. However, when the load increased, the Cr-coated disc produced lower film thickness and friction than the SiO₂-coated disc. The Cr-coated surface had a larger contact angle, i.e., smaller surface energy, than the SiO₂ surface, which reflects the weak bonding between the molecules of the surface and the lubricant. The study concludes that surfaces with low surface energy promote boundary slip at the EHL contact, leading to a reduction in friction and film thickness.     

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.     

Thermal effects in elastohydrodynamic lubrication of line contacts using a non-Newtonian lubricant

A Reynolds' equation, using Winer's viscoplastic model to express the non-Newtonian fluid property, is derived for line-contact EHL problems. The numerical solutions are obtained to the incorporated Reynolds', elasticity, and energy equations for pressure, film thickness, and temperature distribution between two surfaces simultaneously having rolling and sliding motions. The results are presented for thermal non-Newtonian lubrication, to observe the difference between Winer's equation and Trachman's expression on temperature distribution, pressure, and film thickness. The variation in friction coefficient with slip shear rate is in agreement with other experimental data.     

圆弧齿轮热弹性流体动力润滑数值解

根据圆弧齿轮啮合点具有二维表面速度的点接触弹流模型,在变网格下联立求解能量方程、雷诺方程和弹性位移方程等,获得了齿面接触区内的温度、压力和润滑膜厚度分布。计算考虑了润滑剂粘度和密度随温度压力变化和挤压膜效应等因素。用恩瑞模型进行了齿面摩擦分析,讨论了工况变化对齿轮润滑性能的影响。结果表明：在中等载荷或转速时,圆弧齿轮的润滑膜厚度是渐开线齿轮的3倍以上,而齿面摩擦因数比渐开线齿轮小近一个量级;圆弧齿轮沿齿宽方向的滚动速度对润滑膜性态起主导作用,沿齿高方向的滑动速度对润滑膜温升及膜厚影响不大;齿面挤压膜效应对压力分布有一定影响。     

Effects of surface forces on pure squeeze thin film EHL motion of circular contacts

The pure squeeze thin film elastohydrodynamic lubrication (thin film EHL) motion of circular contacts with effects of surface forces taken into account is explored under constant load conditions. The difference between thin film EHL model and EHL model is apparent as the film thickness is thinner than 5 nm. The oscillation phenomena in pressure and film thickness come mainly from the action of solvation forces. The effects of surface forces become significant as the film thickness becomes thinner. Moreover, the viscosity is oscillatory due to its dependency on the hydrodynamic pressure which is affected by surface forces.     

Effect of Starvation on Traction and Film Thickness in Thermo-EHL Line Contacts with Shear-Thinning Lubricants

The effect of starvation on traction and film thickness behavior in thermo-EHL rolling/sliding line contacts has been studied using full EHL simulations. The simulations employed the free volume equation for viscosity–pressure–temperature relationship and Carreau viscosity model to describe the shear-thinning behavior of the EHL lubricant. The simulation results were used to develop equations for estimating the factors by which the traction coefficient increases and film thickness decreases as a function of the degree of starvation. For the situations involving inadequate lubricant supply at the inlet, these factors can be used to correct the traction coefficient and central film thickness predicted with the assumption of fully flooded condition.     

Occurrence of Wall Slip in Elastohydrodynamic Lubrication Contacts

Preliminary experimental work has been carried out to identify some of the boundary slip phenomena of highly pressurised polybutenes in an elastohydrodynamic lubrication (EHL) conjunction. The movement of the oil is signified using an entrapment that can be readily formed by the impact of a steel ball against a layer of oil on a glass block in an optical EHL test apparatus. The post-impact lateral movement of the entrapment was investigated under the conditions: (i) pure rolling, (ii) pure glass block sliding (steel ball stationary) and (iii) pure ball sliding (glass block stationary). It was observed that under pure rolling the entrapped oil travels within the contact region at the entrainment speed, which is correlated with EHL theory. Under pure glass block sliding conditions, the speed of the entrapped oil core is less than the entrainment speed, and in the extreme cases, this core can be nearly stationary. Under pure ball sliding conditions, the oil core moves at a speed greater than the entrainment speed. The observation indicates that the oil/steel ball interface can sustain higher shear stress than the oil/glass (chromium coated) interface and there is a boundary slip in terms of relative sliding at the latter interface under the experimental conditions. Furthermore, the amount of slip increases with an increase in the pressure. These experiments provide evidence of the existence of wall slippage, which leads to the abnormal EHL film profile characterised with an inlet dimple as reported earlier.     

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.     

Sixty years of EHL

It is now 60 years since Ertel produced the first solution to the elastohydrodynamic lubrication (EHL) problem. There has been enormous progress since then, both in numerical modelling and in experimental research on EHL. The moving, rough surface EHL problem can now be solved on laptop‐level computers, while maps of film thickness, pressure and temperature can be obtained experimentally from within rolling/sliding contacts. However, there remain some important questions that have not been fully resolved. One of the most contentious is how to describe the rheological properties of lubricants under the very severe conditions present in thin film EHL contacts. A second is how to model mixed lubricated contact, where the fluid film can break down at asperity conjunctions. But perhaps the greatest challenge to researchers in EHL is to produce useful design equations for predicting the performance of machine components operating in EHL and thereby ensure that EHL theory becomes an integral part of the design process. Copyright © 2006 John Wiley & Sons, Ltd.     

Elastohydrodynamic Lubrication in Extended Parameter Ranges — Part I: Speed Effect

Elastohydrodynamic Lubrication (EHL) has been given great attention in the last 40 years. Conventional theories by Dowson and Higginson for line contacts and Hamrock and Dowson for point contacts have been among the most important contributions and widely used in industries. However, commonly used film thickness formulae, developed more than 25–40 years ago when the computational power was very limited, were originally from curve-fitting based on limited numbers of numerical solutions obtained in relatively narrow parameter ranges. Actual operating conditions in typical engineering applications, such as gears, bearings, cams and traction drives, sometimes fall far outside those parameter ranges, and prediction through extrapolation is often difficult to give satisfactory results. As the computer technology and numerical simulation methods have been advancing greatly, one can now analyze cases in extended parameter ranges that cover various practical applications under severe conditions. This paper is Part I of a recent study, focusing on the speed effect on the EHL film thickness. In a relatively narrow speed range, the present results agree well with those from the conventional theory. In the extended speed and load ranges, however, the relationship between the film thickness and the rolling speed may no longer obey the simple power law described by the conventional theory. It appears to be a complicated function of speed, load and contact ellipticity. Commonly used formulae may often overestimate the film thickness especially when the load is heavy and the speed is not high.