The investigation of contact ratio in mixed lubrication

In order to describe the mixed lubrication in nano-scale which is constituted from dry friction, boundary lubrication, and thin film lubrication, a contact ratio between surfaces of a glass disk and a steel ball in a pure rolling process has been measured by the technique of Relative Optical Interference Intensity (ROII) with a resolution of 0.5 nm in the vertical direction and 1 μm in the horizontal direction. The relationships between the contact ratio and its influence factors have been investigated. Experimental results indicate that the contact ratio in the static state is related to the combined surface roughness, maximum Hertz pressure, and the combined elastic module of tribo-pair in an exponential function. The decrease of rolling speed or lubricant viscosity, and the increase of the pressure will enhance the dynamic contact ratio which is the contact ratio measured in the rolling process. The addition of polar additives into basic oil will reduce the contact ratio. The contact ratio between rough surfaces is larger than that between smooth surfaces in the higher speed region. However, the former becomes smaller than the later after speed decreases below a critical value. A formula for calculating the dynamic contact ratio is given in the end of the paper.     

Definition of the transition from fluid lubrication to mixed lubrication for rough surfaces

Fluid lubrication and mixed lubrication can both be phenomena in the study of the lubrication of rough surfaces. In this paper, we take the surface as random process and, by studying the contact of surfaces which present roughness, we can put forward a method which defines the transition from fluid lubrication to mixed lubrication, by looking for the first contact point between the two surfaces. This study suggests that the transition between fluid and mixed lubrication relates to the number of asperities on the contacting surfaces, an advance on former methods. We also apply this method to piston ring/cylinder lubrication research. The results show that the transition changes with time.     

粗糙表面微凸体对液黏传动的影响

为研究液黏传动过程中粗糙表面的承载特性,将分形理论引入到两粗糙表面摩擦过程之中,分析传动过程中混合摩擦和边界摩擦两阶段的微凸体承载过程,考虑微凸体弹塑性变形,对M-B模型进行修正,建立修正的微凸体承载模型。建立基于修正M-B模型的微凸体承载模型。通过数值仿真得到有效面积系数、分形参数对液黏调速离合器传动过程的影响规律;对修正的微凸体承载模型的计算结果与M-B模型的计算结果进行对比分析。结果表明:微凸体接触载荷和传递转矩随着面积比的增大而增大,当有效面积系数与尺度系数增大时,接触载荷与传递转矩均有所增大;分形维数为1.5时,微凸体接触载荷与传递转矩最小且随面积比的变化最为缓慢;在整个接触区域内,弹性变形区域的面积、接触载荷以及传递转矩最大,其次是弹塑性变形区域,塑性变形区域最小;考虑弹塑性变形时,微凸体接触载荷与传递转矩均有所下降;修正M-B模型和M-B模型间的修正系数范围在25%以内,修正系数随着有效面积系数、尺度系数的增大而增大,随着分形维数的增大而减小。     

密封环圆台型织构化粗糙表面对润滑性能的影响

针对密封环接触面之间的润滑问题,基于Reynolds方程,考虑粗糙度的影响,建立在流体动压润滑状态下圆台型表面织构的数学模型,对密封环接触表面在不同织构参数、不同粗糙度参数下润滑膜压力大小及分布情况进行研究。采用有限差分法、牛顿迭代法研究不同润滑介质下,圆台型微凹坑的几何参数及粗糙度参数对润滑膜平均压力的影响,并与理论数值结果进行对比验证。结果表明:密封环端面的平均膜压随圆台型织构间距、小径的增大而减小,随织构大径的增大而增大;存在最佳织构深度使平均膜压最大;润滑介质黏度越大,密封环端面平均膜压越大;粗糙峰峰高越大,端面平均膜压越小,而粗糙峰波长对端面平均膜压的影响较小,因此粗糙峰应尽可能小;存在织构参数、粗糙度参数的最优组合使润滑膜平均压力值达到最大。     

考虑摩擦的圆柱面切向接触刚度分形模型研究*

为了更准确地计算圆柱面切向接触刚度,本文考虑摩擦因素的影响,在圆柱面分形接触模型的基础上,引入存在摩擦时弹塑性变形的临界面积公式,并利用切向接触刚度的基本理论,推导考虑摩擦的圆柱面切向接触刚度分形模型,并通过Matlab对上述模型进行仿真,研究不同参数(摩擦因数、分形维数、粗糙度幅值 、材料的特性参数、曲率半径)以及接触的形式对切向接触刚度的影响。仿真结果表明：切向接触刚度与法向载荷成正比关系,但随分形维数取值范围的变化分别呈现指数与线性规律。摩擦因数与切向接触刚度成反比关系;材料的特性参数对切向刚度的影响,不仅与分形维数有关,还与自身取值关联;分形维数,粗糙度幅值与切向刚度的关系,受分形维数和材料特性参数的影响呈现正比或反比趋势。另外,内接触比外接触时的切向刚度大;随着曲率半径的变大,切向刚度增加。该研究为后续开展高副结合面动力学分析提供理论 基础。     

Investigating the Effect of Surface Finish on Mixed EHL in Rolling and Rolling-Sliding Contacts

Surface finish may significantly affect the lubrication performance of a tribological interface through the influence of topography on micro/nanoscale fluid flows around localized contacts at surface asperities. This paper aims to study the mixed lubrication performance of a group of engineered surfaces, including turned, isotropically finished, ground, and dimpled surfaces, under different operation conditions by means of a deterministic mixed elastohydrodynamic lubrication (EHL) model. The honed surface was used to mate with other surfaces. The results indicate that a longitudinal contact ellipse favors longitudinally oriented mating surface roughness and that a transverse contact ellipse, as well as a line contact, prefers a transversely orientated mating surface roughness for lubrication enhancement.     

Effect of surface texturing on rolling contact fatigue within mixed lubricated non-conformal rolling/sliding contacts

The rolling contact fatigue (RCF) life of highly loaded machine components is significantly influenced by the surface roughness features so that there is a continuous effort to design the topography of rubbing surfaces to enhance lubrication efficiency and prolong the operation of machine components. It can be suggested from the recent experimental results that lubricant emitted from shallow micro-dents could effectively lift off the real roughness features and reduce the asperities interactions within rolling/sliding mixed lubricated contacts. Thereby the additional supply of lubricant from surface features could help to reduce the risk of surface damage through the reduction of the interaction of rubbing surfaces during start-up or starvation. However, the introduction of such roughness features into the rubbing surfaces of highly loaded non-conformal contacts should consider not only the effects on lubrication film thickness but also on RCF.That is why this study is focused on the effects of surface texturing on RCF within non-conformal rolling/sliding contacts operated under mixed lubrication conditions. The principal task has been whether possible beneficial effect on film thickness is not accompanied by the reduction in RCF life. Textures with various sizes of micro-dents and their arrangement within the contacts have been considered. It has been found that results obtained with textured surfaces have exhibited no obvious reduction in RCF. Conversely, some increase in RCF using textured surfaces was observed that could be attributed to the positive contribution of micro-dents working as lubricant micro-reservoirs that reduce asperities interactions. Nevertheless, further experiments are necessary to confirm this possible beneficial contribution of surface texturing on RCF.     

Fatigue Life Reduction in Mixed Lubricated Elliptical Contacts

Highly loaded ball and rolling element bearings are often required to operate in the mixed elastohydrodynamic lubrication regime in which surface asperity contact occurs simultaneously during the lubrication process. Predicting performance of components operating in this regime is important as the high asperity contact pressures can significantly reduce the fatigue life of the interacting components. Rolling contact fatigue is one of the most dominant causes of failure of components operating in mixed lubrication regime. Contact fatigue begins with the initiation of microscopic fatigue cracks in the rolling contact surfaces or within the sub-surface regions due to cyclic shear stresses. Investigation of mixed lubrication effects on performance of machine components is of significant importance in order to understand and enhance their load carrying capacity. This article investigates the effects of mixed lubrication and surface roughness on machine components performance. Results from a mixed lubrication model are utilized to investigate the effects of different operating conditions on fatigue life of the components. Simple rough surfaces consisting of single hemispherical bump as well as complex rough surfaces consisting of a numerically generated 3D rough surface operating under mixed lubrication conditions are studied and results presented. The stress-based Ioannides and Harris model incorporating the fatigue limit is used to evaluate the fatigue life variation. Fast Fourier Transform (FFT) technique is used to significantly reduce the time required for the computation of internal stresses.     

基于粗糙接触的指尖密封热分析

提出了基于粗糙表面接触热阻的修正计算方法和考虑粗糙峰高度正态分布截断影响的修正系数拟合计算公式。根据等效的概念,将指尖密封系统中各接触副的接触热阻通过"圆柱桥"模型加以描述,在此基础上建立了指尖密封系统的有限元热分析模型。通过有限元计算,获得了指尖密封系统的温度场分布,以及系统最高温度随接触副表面粗糙度、转子过盈量和系统上下游气体压差等结构工况参数的变化规律。这一工作对于指尖密封的深入研究和设计具有较高的参考价值。     

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effect of surface roughness parameters on mixed lubrication characteristics

In this paper, a computer program was developed to generate non-Gaussian surfaces with specified standard deviation, autocorrelation function, skewness and kurtosis, based on digital FIR technique. A thermal model of mixed lubrication in point contacts is proposed, and used to study the roughness effect. The area ratio, load ratio, maximum pressure, maximum surface temperature and average film thickness as a function of skewness and kurtosis are studied at different value of rms. Numerical examples show that skewness and kurtosis have a great effect on the contact parameters of mixed lubrication.     

Effect of real longitudinal surface roughness on lubrication film formation within line elastohydrodynamic contact

In many applications (e.g. roller, barrel or needle bearings) surface features exhibit longitudinal alignment to the direction of motion. These features are produced by surface finishing techniques in the circumferential direction and are associated with line or very wide elliptical contact geometries. In such a case, the contact length in the direction of motion is considerably shorter comparing its width and the effect of a longitudinal roughness could significantly influence the lubrication film formation. Recent experimental studies have indicated less severe effect of a longitudinal roughness on lubrication film formation in the comparisons with that observed with transversely orientated roughness caused by the inlet perturbation. Nevertheless, these experimental studies have been focused on the behaviour of artificially produced asperities within a circular contact. The quantitative experimental study of longitudinal real surface roughness within a line contact has not been realized yet. That is why, in this study, the line contact formed between a steel tapered roller and glass disc is observed within an optical test rig and the effects of real surface roughness on lubrication film formation are studied. Experiments carried out under pure rolling conditions have shown that the depth is the key parameter that influences the effect on the film thickness. If the roughness features are shallow, the lubrication film shape within the contact follows the shape of the surface closely. However, the groove having only about 800 nm in depth divided the line contact into two parts that behave as two separate line contacts. Such an effect can increase the risk of the wear of rubbing surfaces as the lubrication film thickness between the real machine components can be significantly lower than expected.     

轴承表面弹性变形对倾斜轴颈轴承润滑性能的影响

采用平均Reynolds方程,在考虑润滑油粘压效应、轴承表面粗糙度的前提下,分析了轴承表面受载变形对倾斜轴颈轴承润滑性能的影响,并计算分析了不同表面粗糙度和表面方向参数下,考虑和不考虑轴承表面变形时的轴承润滑性能。结果表明,在分析倾斜轴颈轴承的润滑性能时,必须考虑轴承表面变形;在偏心率和轴颈倾斜角较大时,计及轴承表面变形以后,考虑轴承表面形貌参数对轴承润滑性能分析结果的影响不明显。     

考虑基体变形的混合润滑结合面接触特性

为研究混合润滑状态下粗糙表面基体变形对结合面接触特性的影响,建立了考虑基体变形的结合面接触刚度模型。首先,通过单微凸体-基体系统模型分别求解微凸体和基体的接触刚度,利用不动点迭代法获得微凸体真实变形量;其次,基于分形理论建立结合面固体接触刚度模型,通过固体接触刚度获得液体介质的接触刚度。根据仿真结果分析了基体变形、粗糙表面形貌以及润滑介质对结合面接触特性的影响规律。结果表明:当真实接触面积一定时,通过新模型计算的法向载荷小于忽略基体变形的模型;在接触前期,结合面的接触刚度主要由液体介质接触刚度主导,随着真实接触面积的增加,液体接触刚度占总刚度的比率越来越小,最后转变为固体的接触刚度主导结合面的接触刚度。该模型为研究混合润滑状态下结合面的接触特性提供了理论基础。     

Analysis of micro-elastohydrodynamic lubrication for engineering contacts

The paper describes methods which have been developed for theoretical analysis of elastohydrodynamic lubrication (EHL) in situations where the nominal oil film thickness is of the same order as the height of roughness asperities on the surfaces in contact. In such contacts the roughness significantly affects the distribution of pressure, and pressures much higher than predicted on the basis of smooth surface theory are obtained even under conditions where a full fluid film is present. This has consequences for surface fatigue processes such as pitting, and the presence of roughness is also considered to be a crucial factor in the occurrence of scuffing in which hydrodynamic film failure leads to adhesion and severe distress of the surfaces. The major aim of the work is to develop a better undertanding of the physics of scuffing based upon models of film failure in the presence of roughness.     

Analysis of Thermal Stability of High-Performance Rolling–Sliding Contacts in Mixed Lubrication

Thermal instability has been considered by pioneer researchers to be one of the most promising lines for a fundamental investigation into the failure mechanisms of rolling–sliding contacts. This article uses a recently developed mixed lubrication model that integrates interrelated topographical, mechanical, thermal, and tribochemical aspects to study the thermal instability of high-performance rolling–sliding contacts. The effects of various system parameters on the relation between the system bulk temperature and the heat generation in the contact are analyzed. The parameters include surface roughness; contact component size; surface and lubricant mechanical, thermal, and tribochemical properties; and operating conditions. Key results and their implications to system design and operation considerations are summarized in the Conclusion section of the article in relation to enhancing the thermal stability of the contact, particularly under adverse lubrication conditions.     

齿面粗糙度对齿轮传动接触疲劳应力的影响

对齿面粗糙度呈余弦分布的渐开线圆柱齿轮进行热弹流润滑数值计算,分析齿面粗糙度对齿轮传动接触疲劳应力的影响。结果表明:粗糙度会使轮齿接触区次表面发生明显的应力集中,粗糙度波长愈小,应力集中愈明显,且愈贴近齿轮表面;随着粗糙度波幅的增大,平均油膜厚度单调增大,而接触区次表面主剪应力的最大值呈抛物线变化;随着粗糙度波长的增大,平均油膜厚度迅速减小而主剪应力的最大值急剧增大,但当波长增至一定值时,二者各自趋于光滑齿面接触时的相应值。     

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.     

考虑摩擦的球面切向接触刚度分形模型研究

为准确且方便地计算两球面的切向接触刚度（TCS）,在前期对两球面接触分形模型研究的基础上,通过引入考虑摩擦因素的弹塑性变形临界面积计算公式,并基于接触面切向刚度基本理论,建立了考虑摩擦因素的两球面切向接触刚度的分形模型。对模型进行了仿真分析,结果表明：切向接触刚度与法向载荷成正比关系;摩擦因数与切向接触刚度的关系因分形维数的变化而呈现出不同的规律;受到分形维数变化的影响,切向接触刚度随接触面材料特性参数和分形粗糙度幅值的增大而增大;在一定工况下,切向接触刚度在分形维数取1.5时达到最大,且当分形维数在1.5左右时,其值增大最快;球面内接触比外接触时的切向刚度大;随着曲率半径的增大,切向刚度增大。研究结果为后续开展高副结合面（如轴承等）润滑及动力学分析提供了理论基础。     

Deterministic mixed lubrication modelling using roughness measurements in gear applications

The presence of surface roughness on the teeth of hardened and ground power transmission gears is an unavoidable consequence of their manufacture. The paper discusses the effect of surface roughness when the elastohydrodynamic lubricant film thickness developed between the gear tooth surfaces is small compared to the heights of the roughness features. The ratio of these quantities, called the Λ value, may be well below unity in typical applications. For such thin film conditions the moving roughness features cause the elastohydrodynamic contact between the gears to be highly transient in nature. Surface roughness features on the working surfaces of the gears move past each other during meshing and these asperity encounters are associated with extreme pressure perturbations, or with film breakdown and isolated asperity boundary lubrication events. The paper reviews approaches used to study this problem and describes a coupled approach to solving the elastic and hydrodynamic equations. This allows numerical solutions to be obtained for these extreme conditions so that transient contact events associated with mixed lubrication can be predicted in a unified numerical solution scheme. Typical results obtained from such an analysis are presented including surface fatigue modelling and contact strain energy calculations.