Thermoelastohydrodynamic Analysis of Spur Gears with Consideration of Surface Roughness

Thermoelastohydrodynamic lubrication (TEHL) analysis for spur gears with consideration of surface roughness is presented. The model is based on Johnson’s load sharing concept where a portion of load is carried by fluid film and the rest by asperities. The solution algorithm consists of two parts. In the first part, the scaling factors and film thickness with consideration of thermal effect are determined. Then, simplified energy equation is solved to predict the surfaces and film temperature. Once the film temperature is known, the viscosity of the lubricant and therefore friction coefficient are calculated. The predicted results for the friction coefficient based on this algorithm are in agreement with published experimental data as well as those of EHL simulations for rough line contact. First point of contact is the point where the asperities carry a large portion of load and the lubricant has the highest temperature and the lowest thickness. Also, according to experimental investigations, the largest amount of wear in spur gears happens in the first point of contact. Effect of speed on film temperature and friction coefficient has been studied. As speed increases, more heat is generated and therefore film temperature will rise. Film temperature rise will result in reduction of lubricant viscosity and consequently decrease in friction coefficient. Surface roughness effect on friction coefficient is also studied. An increase in surface roughness will increase the asperities interaction and therefore friction coefficient will rise.     

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。     

A measurement system for thin elastohydrodynamic lubrication films

An elastohydrodynamic lubrication (EHL) film measurement system using multi-beam interferometry is introduced in this paper. The measurement principle and the instrumentation are discussed. A simple and efficient method is suggested to obtain the fringe order of measured points. It is demonstrated that the presented measurement system can provide continuous measurement of lubricating films from nano to micro scales at a nano-level resolution, and can be used to investigate ultra-thin EHL films and tiny variations in EHL films. Translated from Tribology, 2006, 26(2): 150–153 [译自: 摩擦学学报]     

Basics of EHL for practical application

Elastohydrodynamic lubrication (EHL) is present in all lubricated components whose elements roll together, including gears, rolling bearing, cams and constant velocity joints. These are characterised by having very localised and thus very high pressure contact, of order 1 to 3 GPa, between the elements. Two important practical properties of EHL contacts are the lubricant film thickness and the friction, and lubricant and machine designers and users need to be able to predict both of these. In principle, they can be determined from full numerical solution of the elastohydrodynamic problem. However, this is quite difficult and time‐consuming and requires detailed knowledge of the rheology of the lubricant film at high pressure and shear rate. This paper is aimed at practising engineers and describes alternative approaches, i.e. how EHL can be applied to predict film thickness and friction in practical applications. Copyright © 2014 John Wiley & Sons, Ltd.     

固液两相流体弹流润滑研究

应用微极流体理论,考虑流体的可压缩性,建立线接触微极流体动力润滑的基本方程,进行固液两相流体稳态流动弹流润滑数值分析,获得了润滑油膜压力、形状以及摩擦力分布,分析了微极参数对润滑性能的影响,并与不可压缩流体结果进行比较。结果表明,固液两相润滑流体较单相牛顿流体,在增加膜厚、提高承载力方面有显著的作用,而接触表面的摩擦因数有所降低,流体的可压缩性降低了油膜压力与油膜厚度。     

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.     

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.     

The Effect of Grain Size on Stribeck Curve and Microstructure of Copper Under Friction in the Steady Friction State

In the present work, the effect of grain size on the friction and wear behavior of a copper (Cu) samples under different lubricant conditions was studied. The structural evolution of Cu subsurface layers under friction in different lubricant conditions was considered. All friction tests were conducted under laboratory conditions using a block-on-ring rig. The effects of sliding velocity and load on the friction coefficient and wear rate of Cu with different grain size (1, 30, and 60 μm) were analyzed. The Cu samples with the average grain size of 1 μm were obtained due to severe plastic deformation (SPD) by equal channel angular pressing (ECAP). The Stribeck curves for Cu samples with different virgin grain sizes were considered. Elasto-hydrodynamic lubrication (EHL) and boundary lubrication (BL) regions were mainly studied in the present work. Similar Stribeck curves were found out for Cu samples with different virgin grain size. A load of the transition from the EHL to BL region was increased with a decrease of the grain size. While the friction coefficients were similar in the EHL and BL regions for the samples with different grain sizes, the wear rate was increased remarkably with an increase the virgin grain size. Flow localization during friction in the BL region led to formation of the vortex structure in subsurface layers. Based on the dependence of the microhardness upon the depth, the degree of hardening (H) was evaluated. A correlation between the coefficient of wear and the deformation hardening of Cu samples with different virgin grain sizes was revealed. In order to take into account the effect of the grain size and to predict the Stribeck curve, a parameter, K, as the ratio between hardness of tested and annealed samples, was incorporated into the lubricant number. The theoretical values of the Stribeck curve calculated for preliminary deformed Cu samples (d = 1 μm) and annealed samples (d = 60 μm) were well coincided with the experimental results.     

Influence of a ring flat zone in the point contact surface on thermal elastohydrodynamic lubrication

This paper describes a geometrical profile, an elastohydrodynamically lubricated point contact surface with a ring flat zone, aimed at building up local line contact elastohydrodynamic lubrication (EHL) in point contact conjunctions to reduce the influence of side-leakage on the central film thickness. Effects of the ring flat zone on the thermal EHL characteristics are studied. A dimensionless coefficient, r_W, is defined to represent the relative half width of the ring flat zone in a point contact EHL surface. Thermal EHL numerical simulations have been performed to investigate the influence of r_W on the film thickness as well as pressure, temperature and friction coefficients under different operating conditions. In the range of 0≤r_W≤1.0 results show that the minimum film thickness decreases with increasing r_W and the central film thickness increases with increasing r_W, and the influence of r_W on the film thickness is more pronounced than those on the maximum pressure, the maximum temperature and the friction coefficients. It is revealed that the proposed ring flat zone with appropriate width is beneficial to the thermal lubrication.     

Friction Reduction in Mixed Lubrication

Minimization of frictional losses in the drivetrain of heavy-duty vehicles is important from both consumer satisfaction and environmental perspectives. Approaches to friction reduction in these components can be evaluated using simulation-based investigations. However, nearly all drivetrain components operate in the mixed lubrication regime which is difficult to model because both hydrodynamic lubrication and surface contact are significant and therefore, the total friction consists of hydrodynamic friction due to lubricant shearing and boundary film friction at asperity contact locations. Recent advances in simulation methods for mixed elastohydrodynamic lubrication (EHL) have enabled improved virtual design tools, such as those developed by Zhu and Hu and further improved by Liu et al. Here, these simulation tools are used to evaluate friction reduction and predict the effects on a mixed EHL interface under severe operating conditions. Three practical means of friction reduction are discussed based on the experimentally validated mixed lubrication friction model and its predictions made for representative, sample cases.     

A Quantitative Solution for the Full Shear-Thinning EHL Point Contact Problem Including Traction

We present a realistic elastohydrodynamic lubrication (EHL) simulation in point contact using a Carreau-like model for the shear-thinning response and the Doolittle-Tait free-volume viscosity model for the piezoviscous response. The liquid lubricant modeled is a high-viscosity polyalphaolefin which has been shown by high-pressure viscometry to possess a relatively low threshold for shear-thinning as a single-component liquid lubricant. As a result, the measured EHL film thickness is about one-half of the Newtonian prediction. We derived and numerically solved the two-dimensional generalized Reynolds equation for the modified Carreau model based on Greenwood. In this simulation, viscosity was not treated as an adjustable parameter; the models used for the pressure and shear dependence of viscosity were obtained entirely from viscometer measurements. Truly remarkable agreement is found in the comparisons of simulation and experiment for traction coefficient and for film thickness in both pure rolling and sliding cases.     

Influence of pressure and temperature dependence of thermal properties of a lubricant on the behaviour of circular TEHD contacts

The aim of this paper is to study the effects of pressure and temperature dependence of a conventional lubricant's thermal properties on the behaviour of heavily loaded thermal elastohydrodynamic lubrication (TEHL) contacts. For this purpose, a typical mineral oil (Shell T9) is selected and the dependence of its transport properties on pressure and temperature is investigated. Appropriate models are then developed for these dependencies. The latter are included in a TEHL solver in order to investigate their effect on the behaviour of circular EHD contacts. The results reveal the necessity of a thermal analysis including the pressure and temperature dependence of thermal properties for a good estimation of film thicknesses and mostly traction coefficients in circular EHD contacts operating under severe conditions. Numerical results are compared with experiments, showing a very good agreement over the considered ranges. This thorough validation of a thermal EHL framework for the calculation of film thickness and friction offers a previously unavailable opportunity to investigate the effects of variations in material properties.     

Friction and wear of copper samples in the steady friction state

The effect of sliding velocity and load on the friction and wear of Cu-steel pairs was studied. Elasto-hydrodynamic (EHL), mixed (ML) and boundary lubrication (BL) regions were analyzed using the Stribeck curve. The lubrication number of Schipper, Z, was used in the analysis of the Stribeck curve. Steady friction states were observed in the mixed EHL and BL regions, however two types of the ML region are revealed. The first type is the stable ML range. The second one is the range of unstable friction and wear when a decrease of the lubricant film leads to abrupt change of all controlled parameters. It was found that a transition to the unstable ML region occurs within a narrow range of Z parameter. Wear modes in the lubrication regions were studied. Deformation hardening in the lubricant regimes is discussed.     

Soft-tribology: Lubrication in a compliant PDMS–PDMS contact

We investigate the influence of surface roughness and hydrophobicity on the lubrication of a soft contact, consisting of a poly(dimethylsiloxane) (PDMS) sphere and a flat PDMS disk. The full Stribeck curves, showing boundary, mixed and elasto-hydrodynamic (EHL) lubrication, are presented for varying surface roughness and hydrophobicity. It is found that neither surface roughness nor hydrophobicity influence the friction coefficient (μ) within the EHL regime. However, increasing surface roughness decreases μ in the boundary regime, while extending the limits of the boundary and mixed lubrication regimes to larger values of the product of velocity and lubricant viscosity (Uη). The transition from the mixed lubrication to EHL regime is found to take place at lower values of the film thickness parameter Λ for increasingly rough surfaces. We found Λ=0.7 in the case of a root mean square (r.m.s.) surface roughness of 3.6 μm, suggesting that the effective surface roughness in a compliant compressed tribological contact is lower than that at ambient pressures. Rendering the PDMS surface hydrophilic promotes full-film lubrication and dramatically lowers μ in the boundary regime by more than an order of magnitude. This influence of surface wetting is also displayed when examining a range of lubricants using hydrophobic tribopairs, where the boundary μ decreases with decreasing lubricant–substrate contact angle. Implications of these measurements are discussed in terms of the creation of model surfaces for biotribological applications.     

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.     

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.     

纳米粗糙间隙中季戊四醇四酯的薄膜润滑行为

采用分子动力学模拟方法建立光滑和粗糙2种固体壁面结构,研究季戊四醇四酯润滑剂在不同压力、薄膜厚度下,在恒定剪切速度和温度下的薄膜润滑行为。分析壁面间润滑薄膜的密度分布,以及剪切过程中润滑剂的速度分布。输出固体壁面在x向和z向的力学响应,并计算摩擦因数。结果表明：表面纳米结构降低了润滑薄膜的厚度,减弱了润滑薄膜分层现象;当润滑薄膜厚度较大时,V形纳米沟槽有助于减小薄膜润滑系统的摩擦因数;润滑薄膜厚度较小时,V形纳米沟槽表面润滑状态容易从流体润滑转变到边界润滑状态,摩擦因数增大。     

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.     

N次谐波凸轮-挺柱副的润滑特性分析

将线接触弹流润滑理论应用于发动机配气机构,计算了某N次谐波凸轮-挺柱副润滑的稳态最小膜厚、膜厚比等参数,分析了凸轮．挺柱副稳态润滑在设计转速下随凸轮转角的变化特征,比较和讨论了发动机转速变化对润滑性能的影响。结果表明,凸轮桃尖区多为部分弹流润滑状态和边界润滑,工作段其它部分多为部分弹流、完全弹流和动力润滑状态。曲轴转速提高一般情况下对增加稳态最小膜厚有利,但由此导致的载荷波动量增加对最小膜厚的稳定性不利,从而使表面摩擦和磨损的可能性增加。     

Molecular dynamics characterization of thin film viscosity for EHL simulation

Molecular simulations were used to characterize changes in lubricant viscosity that may occur during thin film elastohydrodynamic lubrication (EHL). Molecular dynamics simulations were performed at variable wall speed and film thickness such that the effects of both parameters could be evaluated. Using this approach it was found that the viscosity of thin films under large shear is subject to both shear thinning and oscillation with film thickness. A composite model was developed that incorporated both effects. The expected impact that this model might have on an EHL interface was evaluated using a continuum simulation. An overall decrease in viscosity with some oscillation near the interface edges was predicted due to the molecularly modeled thin film effects.