Asymptotic analysis of a lubricated heavily loaded spinning and rolling ball in a parabolic raceway

In the paper, the previously developed asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts is applied to a lubricated point contact with rolling and spinning. It is shown that the whole contact region can be subdivided into three subregions. The central region can be subdivided into the Hertzian region and two adjacent boundary layers — the inlet and exit zones. The main results of the paper are threefold: (i) it is shown that in the central parts of the inlet and exit zones, the mechanisms and the equations controlling the behaviour of the lubrication contact parameters in heavily loaded point and line EHL contacts are identical, (ii) asymptotically precise formulas for the central and exit lubrication film thickness for pre‐critical and over‐critical starved and fully flooded lubrication regimes are analytically derived, and (iii) the inlet and exit zone asymptotically valid equations are uniform across all steady heavily loaded line and point EHL contacts for lubricants with the same rheology. These asymptotically valid equations were analysed and numerically solved in previously published work based on the stable methods utilising the specific regularisation approach developed for lubricated line contacts. Cases of pre‐critical and over‐critical lubrication regimes are considered. The formulas for the lubrication film thickness for pre‐critical and over‐critical starved and fully flooded lubrication regimes allow for simple analysis of the film thickness as a function of spinning angular speed, angle of the entrained lubricant and other pertinent contact characteristics. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymptotic analysis of lubricated heavily loaded point contacts

The paper is devoted to the development of an asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts. It is shown that the whole contact region can be subdivided into three subregions: the central one that is adjacent to the other two regions occupied by the ends of the horseshoe‐shaped pressure/gap distribution zone. The central region, in turn, can be subdivided into the Hertzian region and its adjacent inlet and exit zones that, in turn, are adjacent to the inlet and exit boundaries of the contact, respectively. Moreover, in the central region, in the inlet and exit zones of heavily loaded point EHL contact, the EHL problem can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of heavily loaded line EHL contacts. The latter means that many of the well‐known properties of heavily loaded line EHL contacts are also valid for heavily loaded point EHL contacts. These asymptotically valid equations can be analysed and numerically solved based on the stable methods using a specific regularisation approach that were developed for lubricated line contacts. Cases of pre‐critical and over‐critical lubrication regimes are considered. The by‐product of this asymptotic analysis is an easy analytical derivation of formulas for the lubrication film thickness for pre‐critical and over‐critical lubrication regimes. The method is validated by the results of some experimental and numerical studies published by a number of researches. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymptotic analysis of lubricated heavily loaded point contacts with skewed direction of entrained lubricant

The paper is devoted to the application of the early developed asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts with skewed direction of entrained lubricant. It is shown that the whole contact region can be subdivided into three subregions: the central one, which is far away from the other two regions occupied by the ends of the horseshoe‐shaped pressure/gap distribution. The central region, in turn, can be subdivided into the Hertzian region and two adjacent boundary layers — the inlet and exit zones. Moreover, in the central region in the inlet and exit zones, the EHL problem can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of heavily loaded line EHL contacts. These equations can be analytically analysed and numerically solved on the basis of the stable methods using a specific regularization approach, which were developed for lubricated line contacts. Cases of pre‐critical and over‐critical lubrication regimes are considered. The by‐product of this asymptotic analysis is an easy analytical derivation of formulas for the lubrication film thickness for pre‐critical and over‐critical starved and fully flooded lubrication regimes. The latter allows for simple analysis of the film thickness as a function of the contact eccentricity and the direction of the entrained lubricant at the inlet in the contact. Copyright © 2013 John Wiley & Sons, Ltd.     

The Failure and Damage Mechanisms Under Friction of Copper in the EHL and Mixed EHL Regions

Recently, friction and wear behaviour of Copper (Cu)–steel pairs rubbed under different lubrication conditions were studied. The Stribeck curve was used to identify the different regimes of friction of copper with different virgin grain sizes: the elasto-hydrodynamic lubrication (EHL), mixed lubrication and boundary lubrication (BL) regimes. The aim of this work is the detailed analysis of the damage evolution under friction in the EHL and mixed EHL regions. The effects of load on the friction and the wear and damage mechanisms have been studied. The surfaces of Cu samples before and after friction have been analysed using SEM and AFM techniques as well as roughness and hardness measurements. It was shown that the mechanisms of damage and failure of Cu samples under friction in the EHL region are similar to the damage and failure mechanisms in Very High Cycle Fatigue. Friction in the EHL region is accompanied by initiation and coalescence of pores and microcracks. The effects of the coalescence of pores and microcracks observed in the EHL region are enlarged with a subsequent loading in the mixed EHL region. The effect of the loading rate on the transition from the EHL to BL region has been studied. It was shown that decreasing the loading rate increases significantly the load of the transition from the EHL to BL region. The pore and microcrack coalescence remain as the dominant damage mechanism under friction in the mixed EHL region with the low loading rate, while a lot of ploughing tracks and large delaminated regions appeared on the surface of Cu sample after friction with the higher loading rate.     

A Lubrication Deviation From the Classical EHL Theory by the Lubricant Viscoplasticity: Part II — Boundary of Lubrication Regimes

This paper distinguishes elastahydrodynamic lubrication (EHL) regimes in isothermal pure rolling case as three kinds according to lubricant rheology. In these regimes, the lubricants are respectively viscoelastic, viscoplastic, and non-continuum. Mathematical expressions are introduced ta describe the boundaries among these three regimes. H_c - r_it and U - W charts respectively plot the operational scopes of these lubrication regimes. The present study holds significance to understanding EHL film formation and more clearly embodies elastohydrodynamic film failure stage transitions.     

Friction, wear and structure of Cu samples in the lubricated steady friction state

Friction and wear of copper rubbed with lubrication in wide range of loads and sliding velocities were studied. The results of friction and wear experiments are presented as the Stribeck curve where the boundary lubrication (BL), mixed (ML) and elasto-hydrodynamic lubrication (EHL) regions are considered. The structural state of subsurface layers in different lubricant regions is studied by X-ray photoelectron spectroscopy, optical, transmission and scanning microscopy analysis. Dislocation density of dislocations in EHL and BL lubricant regimes was determined. Nanohardness at thin surface layers rubbed under different lubricant regimes is compared. The dominant friction and wear mechanisms in different lubrications regions are discussed.     

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     

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。     

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.     

Thermal transient rough EHL line contact simulations by aid of computational fluid dynamics

Reynolds equation is the pre-dominantly used PDE for modelling the fluid flow or more accurately the fluid pressure in an elastohydrodynamic lubrication (EHL) contact. The equation is derived by combining the two conservation equations of momentum and continuity into a single equation for the fluid pressure. The numerical approach for theoretical investigations performed on EHL contacts in this work is somewhat different. The modelling of the fluid flow is based on a computational fluid dynamic (CFD) technique. The fluid flow is simulated by aid of the equations of momentum and continuity in a more complete form and when the thermodynamics is incorporated, the equation of energy. The aim of the investigation was to examine whether the CFD technique could be used to handle thermal transient rough EHL line contacts. It is shown that commercial CFD software can be modified to meet such requirements. The influence of thermal effects on the flow under sliding motion was investigated. The non-Newtonian model used in this work is the Ree-Eyring model. It is shown that the choice of the Eyring stress in the model influences flow in the contacts. If the thermal properties of the surrounding solids differ, it has been shown experimentally and theoretically that a dimple or increased central film thickness may appear in the EHL contacts. This work shows that the governing mechanisms that result in the dimple are also present in thermal transient rough EHL line contacts.     

Application of Transient Elastohydrodynamic Lubrication Analysis for Gear Transmissions

Transient elastohydrodynamic lubrication theory which deals with the lubrication of gear transmission is presented. A numerical procedure was developed to solve the governing equations for the transient EHL with variable load, curvature, and rolling velocity along the line of action. The compressibility of the fluid is taken into consideration. Results are presented for the pressure distribution and the film thickness successively along the line of action as a function of time. A parametric study was conducted to investigate the effects of geometry factors on the lubrication behavior of a gear transmission. Parameters of interest are gear ratio, central distance, gear tooth module, and profile shift of gear tooth. The results of extensive simulations for gear tooth lubrication show that the equivalent curvature radius of gear teeth plays an important role on the EHL film formation.     

全膜润滑到边界润滑的过渡研究

摩擦副在工作中经历不同的润滑状态,利用数值模拟的方法研究了从全膜润滑到边界润滑的过渡。数值实验显示,从全膜到边界润滑是个光滑的过渡过程。对于光滑表面,在较低速度下过渡到混合润滑;而对于粗糙表面,全膜到混合润滑的过渡发生在较高速度下。     

水润滑塑料合金轴承润滑机理分析

根据水润滑塑料合金轴承润滑机理,建立了润滑基本方程组,采用多重网格法对润滑机理进行离散并求解,得到了符合精度的数值解,进而证明了弹流润滑的存在。     

界面滑移条件下点接触Stribeck曲线的实验研究

采用高黏度聚异丁烯润滑油,在光学弹流实验机上考察球-盘接触纯滑条件下的摩擦因数随卷吸速度和载荷的变化。结果表明,随着卷吸速度的增加,球-盘接触副进入弹流润滑并向流体动压润滑转变的过程中,摩擦因数并不像传统的Stribeck曲线一样,随着卷吸速度的增加而单调增加,而是呈现先上升、后下降、再上升的趋势,其中摩擦因数下降时的起始速度大致为凹陷出现的速度,摩擦因数再上升时的速度大致是润滑进入动压润滑的速度。初步论证界面滑移为产生上述波动的主要原因。     

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.     

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。     

Tribological Behavior of Self-mated Ti3SiC2 in Short-Chain n-Alcohols,Glycol and Glycerol under Boundary Lubrication

The tribological behavior of self-mated Ti₃SiC₂ in bath of alcohols are investigated at sliding velocity ranging from 0.005 to 0.3 m/s. The results show that the friction coefficient and wear rates of self-mated Ti₃SiC₂ are reduced greatly under lubrication of alcohols compared to that under dry condition. In alcohols, smooth worn surfaces of Ti₃SiC₂ can be obtained. The mechanical wear is inhibited and the oxidized Ti and Si species on the worn surface are TiO₂ and silica gel. The friction coefficients decrease with carbon numbers and sliding velocity in the n-alcohols. The friction coefficient decrease with sliding velocity in glycol and glycerol as well. The decrease is determined by the increase of the viscosity of alcohols. In glycerol, at 0.1 m/s and 5 N, the friction coefficient of self-mated Ti₃SiC₂ is 0.08 which is the lowest in this paper. The lubrication regimes are calculated according to classical lubrication theory. At velocity from 0.005 to 0.3 m/s, in all of the alcohols except glycerol, the λ are below 1 which indicates that the lubrication regime is BL. While in glycerol, the lubrication regimes vary from BL to BL and EHL, then to EHL as the velocity increases.     

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 load and elastic properties on the rolling and sliding friction of lubricated compliant contacts

Lubricated “soft” contacts, where one or both contacting solids have a low elastic modulus, are present in many practical engineering and biological applications including windscreen wipers, wet tyres, elastomeric seals, contact lenses and the tongue/palate system. In such contacts, the prevailing lubrication mode is “isoviscous EHL” (elastohydrodynamic lubrication). Unlike in steel–steel contacts, rolling friction can be considerable and this originates in part from the viscoelastic properties of the compliant surfaces.In this paper the influence on friction of both applied load and the elastic properties of the solids is studied using a mini traction machine. In this machine, the rolling and sliding friction can be separately determined. The viscoelastic properties of the polymers employed are measured using a dynamic mechanical analysis apparatus. The measured friction is compared to theoretical models for soft EHL and the viscoelastic energy losses arising from the contact deformation. Consideration of the frequency dependence of the substrate viscoelasticity enables reasonably accurate predictions of the rolling friction coefficient, especially within the mixed and boundary lubrication regimes.     

齿轮传动系统的动态-瞬态弹性流体动力润滑

本文给出了考虑齿轮传动系统振动影响的瞬态弹性流体动力润滑方程组及其求解方法。在瞬态弹流润滑理论的研究中综合考虑了变载荷、变曲率和变速度的瞬态效应,并被用于渐开线直齿轮的润滑问题。其中,变载荷是考虑到实际齿轮传动中所存在的系统振动所引起的动载荷,该动载荷由一个8质量、16自由度的振动方程求解而得。沿啮合点的动态-瞬态弹流润滑被作为一个时间过程作了完全数值求解。文中给出了一个算例,求得了沿啮合线上啮合时的二次压力峰及油膜厚度的变化曲线,并给出了七个特殊啮合点上的压力分布及油膜形状。