Non-newtonian thermal analysis of an EHD contact lubricated with MIL-L-23699 oil

A thermal and non-Newtonian fluid model under elastohydrodynamic lubrication conditions is proposed, integrating some particularities, such as the separation between hydrodynamic and dissipative phenomena inside the contact. The concept of apparent viscosity is used to introduce the non-Newtonian behaviour of the lubricant and the thermal behaviour of the contact into the Reynolds equation, acting as a link element between the hydrodynamic and dissipative components of the EHD film, independently of the rheological and thermal models considered. The apparent viscosity enables the application of the rheological model better adapted to each lubricant, without appealing to special formulations of the EHD problem.The Newton–Raphson technique is used to obtain the lubricant film geometry and the pressure distribution inside the EHD contact. The shear stresses developed in the fluid film are evaluated assuming the non-linear Maxwell rheological model. The surfaces and lubricant temperature distributions are determined using the simplified Houpert's method, applied to the inlet contact zone, and the thermal method proposed by Tevaarwerk is applied in the high pressure contact zone.The non-Newtonian thermal EHD model is applied to the analysis of a contact lubricated with MIL-L-23699 oil. Significant results are obtained for the centre and minimum film thickness, for the inlet shear heating and film thickness reduction factor (φ_T), for the temperature rise of the lubricant and of the surfaces and for the friction coefficient inside the contact, considering wide ranges of the operating conditions (maximum Hertzian pressure, inlet oil temperature, rolling speed and slide-to-roll ratio).Finally, the numerical traction curves determined are compared with the corresponding experimental results, showing very good correlation.     

The influence of the slide-to-roll ratio on the friction coefficient and film thickness of EHD point contacts under steady state and transient conditions

The effect of different slide-to-roll ratios has been experimentally investigated under steady state and transient conditions using a steel ball in contact with the plane surface of a glass disc. Under transient conditions the entraining velocity has been varied with a sinusoidal law at two different frequencies. Measurements of the friction force and film thickness using optical interferometry have been made.For the same working conditions, different friction coefficient trends found for positive and negative slide-to-roll ratios can be related to different film thickness values and shapes. The combination of different thermal effects could be a possible explanation for the obtained results.     

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.     

一个表面带单粗糙峰的线接触时变微弹流润滑数值分析

通过数值求解研究了一个固体表面的单粗糙峰对两固体形成的线接触时变弹流润滑区压力、膜厚分布曲线的影响。结果表明：粗糙峰的出现，使其对应位置上的压力、膜厚发生急剧变化；粗糙峰的移动，对压力和膜厚的变化、固体表面的凹陷现象以及Hertz接触区的出口颈缩均有不同的影响；另外，压力峰和油膜形状随着粗糙峰幅值和半波长的变化而变化。结果亦表明：准稳态解比时变解过高地估计粗糙峰对压力和膜厚的影响。     

Squeeze fluid film of spherical hydrophobic surfaces with wall slip

Isothermal squeeze film flow of Newtonian fluid between spherical hydrophobic surfaces with wall slip is investigated using a limiting shear stress model and complementary algorithm. Wall slip velocity is controlled by the liquid–solid interface limiting shear stress. It is found that the wall slip dramatically decreases the hydrodynamic support force of the squeeze fluid film. In the case of large wall slip the hydrodynamic support force increases only slightly with the decrease in the film thickness. We find that wall slip decreases with increasing film thickness and limiting shear stress, but increases with increasing fluid viscosity and approaching velocity. An empirical equation is given for prediction of the fluid load support capacity. The possible effect of pressure on wall slip is also discussed. It is found that fluid pressure suppresses wall slip after the proportionality coefficient of limiting shear stress reaches a critical threshold. However, almost no effect is found when it is below this critical threshold. Good agreements exist between the present theoretical predictions and some existing experimental observations.     

极限剪切状态下的线接触Reynolds方程

本文导出了考虑极限剪切状态的线接触流变热弹流Reynolds方程,该方程以Evans—Johnson流变模型为基础,可用于求解线接触流变热弹流润滑问题的油膜厚度、压力分布、剪应力分布和牵曳系数曲线。计算实例表明,润滑油的流变特性对弹流润滑的油膜形状和压力分布影响不大,但对Hertz接触区的剪应力分布有显著影响。     

Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts

A fast multigrid approach is presented for the analysis of thermal elastohydrodynamic lubrication (EHL) under rolling/sliding circular contacts at high loads and high slip ratios with low computing time on a personal computer. This fast solver combines directiteration, multigrid, Newton-Raphson, Gauss-Seidel iteration, and multilevel multi-integration methods into one working environment that can reduce the computational complexity from O(n³ to O(nlnn) for the thermal EHL problem under rolling/sliding circular contacts. Since the couped Reynolds and energy equations are simultaneously solved by the Newton-Raphson scheme, the iteration for the convergence solution is less than those of the classical approach. Results show that thermal effects on the pressure profile and film thickness are significant for a wide range of loads, speeds and slip ratios. The maximum midfilm and surface temperature rise in the Hertzian contact region increases with increasing slip ratio, dimensionless speed, and load. The minimum film thickness decreases with increasing load and slip ratio, and decreasing dimensionless speed.     

Influence of temperature distributions in EHL film on its thickness under high slip ratio conditions

This paper describes the influence of temperature rise of oil film in Hertzian contact area on the film thickness or profile under high slip ratio conditions. Temperatures of both surfaces of a ball and a disk as well as average temperature across the oil film were measured by means of an improved infrared. Two kinds of optical band-pass filters were used to separate the radiations from the ball surface and the oil film through an infrared transparent disk made of sapphire glass. In case of temperature measurement of the disk surface, another sapphire glass disk was coated with 300 nm chromium layer on the contact surface to radiate the infrared from the disk surface and also to intercept the radiation from the ball surface and the oil film. Temperature profiles across the oil film were estimated by assuming a parabolic profile with the measured three kinds of temperatures.For case within 200% in slip ratio, both minimum and central film thickness decreased under constant entrainment velocity as slip ratio increased. Measured film shapes were not flat at central Hertzian contact region under high-slip condition and differed from the results by the conventional EHD theory assuming constant viscosity in the direction of film thickness. The profile of Couette flow varied due to the distribution of oil film temperature in thickness direction. The viscosity wedge action, that is the variation of the profile of Couette flow causes reduction of film thickness or deformation of film profile. For case over 200% in slip ratio, the relation between central film thickness and slip ratio under constant relative slide speed had a great difference from the results calculated from the formula presented by Chittenden et al.     

基于弹流润滑的无级变速器滑移控制安全区域分析

针对无级变速器滑移模式下传动失效概率增大的问题，基于弹流润滑理论分析了不同传递转矩和相对滑动速度情况下，从动轮摩擦副油膜压力、厚度及其剪切应力变化情况，建立了安全裕度模型，基于油膜极限剪切应力与最大剪切应力计算了摩擦副的安全裕度，并确定了滑移控制的安全工作区域，为滑移控制策略的制定与优化提供了依据。研究结果表明：随着从动带轮传递转矩、相对滑动速度的增大，摩擦副的安全裕度逐渐减小；当传递转矩小于130 N·m时，在所有相对滑移速度范围内均可保证摩擦副油膜处于安全状态;当传递转矩大于130 N·m时，随着相对速度的增大，摩擦副油膜失效概率增大。     

Behavior of real roughness features within mixed lubricated non-conformal contacts

A combination of thin film colorimetric interferometry and phase shifting interferometry was used to study the effect of slide-to-roll ratio on the micro-elastohydrodynamic action and asperity-contact mechanism on the real asperity scale. The behavior of the roughness features of different scales in very thin film, real rough surface elastohydrodynamic contacts was observed from chromatic interferograms evaluated by thin film colorimetric interferometry. Obtained film thickness distribution was compared with undeformed ball surface topography measured by phase shifting interferometry. It was confirmed that the presence of deep grooves within lubricated contact can result in lubrication film breakdown under positive slide-to-roll ratio conditions when the rough surface is moving slower than the smooth surface. Negative slide-to-roll ratio conditions are much less critical from this point of view. Moreover, shallow pits formed naturally on rubbing surface as a result of surface finishing process were observed to significantly influence the film thickness formation. They act as lubricant micro-reservoirs and emit the lubricant into the contact under rolling/sliding conditions that enlarges film thickness. Such a behavior also suggests the possible beneficial tribological effect of surface texturing based on shallow micro-cavities under mixed lubrication of non-conformal surfaces.     

The First Normal Stress Difference in a Shear-Thinning Motor Oil at Elevated Pressure

Currently, the only aspect of non-Newtonian behavior being modeled in lubrication is the shear dependence of viscosity. However, shear thinning is accompanied by a large difference between the normal stress in the flow direction and the cross-film direction. This stress difference can increase the load capability of a lubricant film without increased frictional penalty.

A commercial 10W-40 motor oil was characterized at elevated pressures. Three different high-pressure instruments were employed: a falling-body viscometer, a thin-film Couette viscometer, and a parallel-plate rheogoniometer. Ordinary shear thinning with a second Newtonian inflection was observed. A first normal stress difference of 0.6 MPa was measured under what may be mild conditions for a crankshaft journal bearing. Elevated pressures are essential to the measurement of rheological properties that govern hydrodynamic film thickness and friction in automotive components.

Time–temperature–pressure superposition was validated for the first normal stress difference. The first normal stress difference in the terminal regime may be estimated from the upper-convected Maxwell model, where the shear modulus is assumed to be equal to the Newtonian limit shear stress obtained from a measurement of shear thinning. The first normal stress difference in the shear-thinning regime may be estimated from an extant empirical rule.

These results will be of substantial importance when analytical techniques are developed for hydrodynamic lubrication with real non-Newtonian shear response. The results are immediately useful for calculating the shear stress for cavitation in ambient pressure high-shear viscometers.     

Numerical analysis of grease thermal elastohydrodynamic lubrication problems using the Herschel-Bulkley model

Grease thermal elastohydrodynamic lubrication (TEHL) problems of line contacts are analysed numerically. The effects of temperature and rheological parameters on grease TEHL are investigated using the Herschel-Bulkley model as a rheological model of greases. The pressure distribution, the shape of grease film, mean film temperature and surface temperature of solid wall in line contacts are obtained. It is found that thermal effects on the minimum film thickness become remarkable at high rolling speeds. The effect of yield stress of the Herschel-Bulkley model on minimum film thickness is negligible, while the flow index and viscosity parameter have significant effects on minimum film thickness.     

Thermal effects of different kind influencing lubricated non-conformal contacts

Three steel spherical specimens with different diameters are tested against a glass disc under the same working conditions in several rolling speeds and slide-to-roll ratios. The same tests are carried out with the specimens connected to a steel shaft with and without a ceramic insert purposely designed for limiting the transfer of the heat generated by the shaft seals and bearings to the specimens, in order to evaluate the influence of the experimental apparatus on friction results. A general increase in friction is found when the ceramic insert is used probably related to a greater local lubricant viscosity inside the contact due to the reduction in the specimen surface temperature. However, the configuration of the experimental apparatus does not influence in a significant way the shape of the friction curves as a function of the entraining speed and of the slide-to-roll ratio. The analysis of the interference images of the contact shows that the thermal insulation due to the ceramic insert does not affect particularly the film thickness.     

Analysis of Micropolar and Power Law Fluid–Lubricated Slider and Journal Bearing with Partial Slip–Partial Slip Texture Configuration

An analysis of micropolar and power law fluid–lubricated partial slip–partial slip texture slider and journal bearings is presented. The nondimensional pressure and shear stress expressions for a partial slip texture configuration are analyzed using narrow groove theory. The parameters used in the analysis are nondimensional partial slip length, nondimensional partial slip–partial slip texture length, nondimensional depth of recess, ratio of land with slip to recess, nondimensional slip coefficient, coupling number; ratio of characteristic length to film gap, and power law index. A partial slip configuration with a higher slip coefficient yields an improvement in load capacity and reduction in coefficient of friction compared to a partial slip texture configuration for micropolar and power law shear thinning (pseudoplastic) fluid-lubricated slider and journal bearings.     

A computer model of mixed lubrication in point contacts

A numerical model of mixed lubrication is presented in this paper. The idea introduced here is that asperity contact may be viewed as a result of a continuous decrease in film thickness, so that the transition between contact and non-contact is continuous and the same mathematical model should work for both regions. The pressure over the thin films is assumed to obey the Reynolds equation, and the solution of the equation, under the condition of h→0, is expected to be the same as that predicted by the theory of elasticity. To achieve convergent and stable solutions, the left-hand side terms of the Reynolds equation are switched off when the local film thickness approaches zero, leading to a reduced Reynolds equation. Pressure distributions over the entire computation domain are thus obtained through solving a unified equation system without identifying hydrodynamic or asperity contact regions. Computations were conducted for several example cases and results show that convergent solutions are achievable on different types of roughness, over a wide range of λ ratios (0.01 to infinity), and for different slide-to-roll ratios (0.0–2.0).     

界面滑移对圆柱形凹坑织构滑动轴承摩擦力的影响

为研究不同的滑移情况对圆柱形凹坑织构滑动轴承摩擦力的影响,建立含有圆柱形凹坑织构的滑动轴承在不同界面滑移状态下的摩擦力计算模型,探究影响织构化滑动轴承摩擦力的参数,并借助ANSYS分析不同滑移情况下界面滑移对圆柱形凹坑织构滑动轴承摩擦力的影响规律。结果表明:织构化滑动轴承的摩擦力主要是由轴颈线速度、油膜滑移比、轴承的进出油口压力、织构处油膜压力、织构深度、油膜厚度和承载力决定;不同滑移情况下织构模型的摩擦力均小于无织构模型;且在上下表面均滑移时,圆柱形凹坑织构在出口位置时表现出最优的承载和减摩效果;适当地增加圆柱形凹坑织构的深度可以改善模型的摩擦性能,但是过深的凹坑织构并不能发挥出其性能。     

Analyses of thermal hydrodynamic lubrication in high-speed rolling. Part I: the effect of the roller's elastic deformation

A study of thermal hydrodynamic lubrication for high-speed strip rolling, which includes the roller's elastic deformation, was developed for a lubricant whose rheological behaviour satisfies the Barus' model. The difference in lubricating performances between an elastic roller and a rigid roller was assessed using parameters such as film thickness and pressure; temperature distributions in the fluid film, roller, and workpiece; separating force and shear torque. The elastic roller was made either of a unique material or its substrate was coated with one layer of a harder material to improve the wear resistance. The elastic deformation of the roller was obtained with the aid of Hitchcock's elastic-deformation theory and the biharmonic equation of Airy's stress function. It was found that the elastic deformation produces a substantial effect on some rolling characteristics.     

Thin-Film Lubrication of Dented Surfaces

Surface microfeatures introduced to conformal surfaces have been proved in the last decade to provide beneficial tribological performances. They were found to significantly improve load capacity, wear resistance, or friction coefficient in applications that involve mechanical seals, piston rings, thrust bearings, or ultra-high-density magnetic disc drives. Recent studies have suggested that such an approach could be used to improve the lubrication capabilities under thin-film lubrication of highly loaded non-conformal contacts. However, surface micro-features influence the film thickness and pressure distribution within concentrated contacts that could result in surface failures. In this paper, thin-film colorimetric interferometry has been used to study the effects of an artificially produced micro-dent on film thickness distribution within thin-film lubricated contacts. Obtained results have shown that the behavior of dented surfaces significantly depends on the slide-to-roll ratio. An increase in the lubricant film thickness has been observed just upstream of the trailing edge of the micro-dent when the disc is moving slower than the ball with the micro-dent. In the reverse conditions, for a positive slide-to-roll ratio, the presence of the micro-dent within the concentrated contact results in the film thickness reduction located downstream of the leading edge of the micro-dent. This reduction can cause the local film breakdown of very thin films. Nevertheless, it has been observed that highly viscous boundary films can avoid it and rubbing surfaces have been completely separated using the formulated oil even under very thin lubrication conditions.     

The influence of the viscoplastic and viscoelastic character of a lubricant on elastohydrodynamic lubrication

The non-newtonian constitutive equation proposed by Johnson and Winer is discussed. Derivations of the lubrication equations suitable for the viscoplastic rheological model and the viscoelastic model are presented. The full numerical elastohydrodynamic lubrication solutions for the viscoplastic model and the viscoelastic model are obtained in order to observe the effects of the elastic shear modulus of the fluid and the limiting shear stress on the pressure distribution, film thickness and coefficient of friction.     

Thermal point contact EHL analysis of rolling/sliding contacts with experimental comparison showing anomalous film shapes

The paper presents an experimental and numerical investigation of non-conformal lubricated contacts in which anomalous film shapes occur. The experiments were concerned with the contact between a steel ball and the plane surface of a glass disc at various slide-roll ratios. A paraffin base mineral oil was used as a lubricant and friction coefficients and film thicknesses were measured. It was found that for slide-roll ratios with the disk moving faster anomalous elastohydrodynamic lubrication (EHL) films were obtained characterized by a “dimple” in the central region of the contact. Numerical thermal-elastohydrodynamic analyses were carried out to simulate both film thickness and friction corresponding to the experimental conditions using Newtonian and Ree-Eyring rheological models. Initial results from this study suggest that neither of these lubricant models predict the correct detailed film shape and the experimental friction at the same time. An alternative lubricant model including both thermal and limiting shear stress effects (wall slippage) is currently under development.