Wear and Lubrication Behaviors of Cu-Based Friction Pairs with Asperity Contacts: Numerical and Experimental Studies

This paper aims to investigate the wear and lubrication behaviors of wet Cu-based friction pairs. A mixed lubrication model in plane contacts is developed, and the tests of pin-on-disk are carried out. Wear losses are measured by the oil spectrum analysis method. The wear loss, the real contact area ratio, and the load sharing ratio are analyzed. Effects of sliding velocity, temperature, and pressure are considered. The results show that the temperature is the most significant influence on the wear loss of lubricated Cu-based friction pairs. As the temperature rises from 30 to 150 °C, wear loss increases from less than 0.4 mg to about 2.3 mg. The wear factor of the lubricated Cu-based friction pair in asperity contact areas is \(K_{c} = 9.4 \times 10^{ - 9}\) (g/Nm). When the lubricated wear is slight, the oil spectrum analysis method is an effective approach to accurately determine the wear loss.     

Deterministic solutions and thermal analysis for mixed lubrication in point contacts

A deterministic numerical model has been developed for simulation of mixed lubrication in point contacts. The nominal contact area between rough surfaces can be divided into two parts: the regions for hydrodynamic lubrication and asperity contacts (boundary lubrication). In the area where the film thickness approaches zero the Reynolds equation can be modified into a reduced form and the normal pressure in the region of asperity contacts can be thus determined. As a result, a deterministic numerical solution for the mixed lubrication can be obtained through a unite system of equations and the same numerical scheme. In thermal analysis, the solution for a moving point heat source has been integrated numerically to get surface temperature, provided that shear stresses in both regions of hydrodynamic lubrication and asperity contacts have been predetermined. A rheology model based on the limit shear stress of lubricant is proposed while calculating the shear stress, which gives a smooth transition of friction forces between the hydrodynamic and contact regions. The computations prove the model to be a powerful tool to provide deterministic solutions for mixed lubrication over a wide range of film thickness, from full-film to the lubrication with very low lambda ratio, even down to the region where the asperity contact dominates.     

A numerical method for the calculation of lubricant pressures in bearings with mixed lubrication

A model for mixed lubrication, assuming that the total normal load applied to the plane of the lubricated surfaces is carried partly by the hydrodynamic action of the lubrication film and partly by asperity contacts and that the total friction force between the lubricated surfaces is partly due to viscous friction and partly to asperity contacts, was used to develop a numerical solution for pressure distribution in a bearing experiencing mixed lubrication. The geometry treated and the pressure distribution obtained were for a simple slider bearing, but the method could easily be extended to other shapes. The model is based on measured roughness of a real surface. Real load carrying capacity and drag can therefore be determined since they are related directly to bearing pressure distribution     

A multi-scale model for friction in cold rolling of aluminium alloy

A simple and robust friction model is proposed for cold metal rolling in the mixed lubrication regime, based on physical phenomena across two length scales. At the primary roughness scale, the evolution of asperity contact area is associated with the asperity flattening process and hydrodynamic entrainment between the roll and strip surfaces. The friction coefficient on the asperity contacts is related to a theoretical oil film thickness and secondary-scale roll surface roughness. The boundary friction coefficient at the “true” asperity contacts is associated with tribo-chemical reactions between fresh metal, metal oxide, boundary additives, the tool and any transfer layer on the tool. The asperity friction model is verified by strip drawing simulations under thin film lubrication conditions with a polished tool, taking the fitting parameter of the boundary lubrication friction factor on the true contact areas equal to 0.1. Predicted values of average friction coefficient, using a boundary friction factor in the range 0.07–0.1, are in good agreement with measurements from laboratory and industrial rolling mill trials.     

Effects of Friction on the Contact and Deformation Behavior in Sliding Asperity Contacts

Finite-element analyses are carried out to study the effects of friction on the contact and deformation behavior of sliding asperity contacts. In the analysis, on elastic-perfectly-plastic asperity is brought in contact with a rigid flat at a given normal approach. Two critical values of the normal approach are used to describe the asperity deformation. One is the approach corresponding to the point of initial plastic yielding, and the other at the point of full plastic flow. Additional variables used to characterize the deformation behavior include the shape and size of the plastic zone and the asperity contact size, pressure, and load capacity. Results from the finite-element analysis show that the two values of critical normal approach decrease significantly as the friction in the contact increases, particularly the approach that causes plastic flow of the asperity. The size of the plastically deformed zone is reduced by the friction when the contact becomes fully plastic. The reduction is very considerable with a high friction coefficient, and the plastic deformation is largely confined to a small thin surface layer. For a low friction coefficient, the contact size, pressure and load capacity of the asperity are not very sensitive to the friction coefficient. For a moderate friction coefficient, the contact pressure is reduced and the junction size increased; the load capacity of the asperity is not significantly affected due to the compensating effects of the pressure reduction and the junction growth. For a high friction coefficient, the pressure-junction compensation is not longer sufficient and the asperity load capacity is reduced. The degree of the friction effects on these contact variables depends on the applied force or the normal approach. Although the analyses are conducted using a line-contact model, the authors believe that the effects of friction in sliding asperity contacts of three-dimensional geometry are essentially the same and the same conclusions would have been reached. These results may provide some guidance to the modeling of rough surfaces in boundary lubrication, in which the asperity friction coefficient can be high and vary significantly both in time and from one micro-contact to another.     

Enhanced friction model for high-speed right-angle gear dynamics

The modeling of elastohydrodynamic lubrication friction and the analysis of its dynamic effect on right-angle gears, such as hypoid and spiral bevel types are performed in the present study. Unlike the classically applied empirical constant coefficient of friction at the contacting tooth surfaces, the enhanced physics-based gear mesh friction model is both spatial and time-varying. The underlying formulation assumes mixed elastohydrodynamic lubrication (EHL) condition in which the division and load distribution between the full film and asperity contact zones are determined by the film thickness ratio and load sharing coefficient. In the proposed time-varying friction model, the calculation of friction coefficient is performed at each contact grid inside the instantaneous contact area that is being subjected to mineral oil lubrication. The effective friction coefficient and directional parameters synthesized from the net frictional and normal contact forces are then incorporated into a nonlinear time-varying right-angle gear dynamic model. Using this model, the effect of friction on the gear dynamic response due to the transmission error and mesh excitations is analyzed. Also, parametric studies are performed by varying torque, surface roughness and lubrication properties to understand the salient role of tooth sliding friction in gear dynamics. The simulation results are included. But experimental verification is needed.     

船用发动机重载工况下凸轮-滚轮副混合热弹流润滑分析

凸轮-滚轮副是大功率船用发动机配气机构的关键摩擦副,除受到弹簧力和自身的惯性力之外,还受到来自喷油器的极高燃油压力,工作条件极为苛刻。为了分析该摩擦副的性能,建立船用发动机重载工况下凸轮-滚轮副的混合热弹流润滑模型,计算燃油压力作用下的摩擦副油膜润滑、摩擦温升和磨损性能。结果表明：喷油器的燃油压力会显著降低凸轮-滚轮摩擦副之间的油膜厚度,同时产生较为严重的微凸体接触;随着环境温度的提高,凸轮-滚轮副的油膜厚度以及油膜温升会有所下降,而微凸体接触压力、摩擦力以及摩擦功率均会显著增加;滚轮打滑会造成凸轮-滚轮摩擦副的油膜厚度下降,同时导致油膜温升以及微凸体接触压力增大和并且致使表面磨损显著加剧。     

考虑边界膜强度的滑动摩擦副混合润滑模型研究

针对边界膜对摩擦副润滑状态的影响，提出一种能够综合反映压力及剪切速率对边界膜失效综合影响的边界膜强度模型，并基于润滑状态测试结果通过拟合获得模型参数；将该边界膜强度模型与流体动压润滑模型、粗糙表面接触模型耦合，建立考虑边界膜强度的混合润滑模型，并通过轴瓦摩擦实验机润滑测试结果对模拟结果进行验证。和现有典型混合润滑模型相比较，该混合润滑模型可以更准确地反映摩擦副的实际润滑状态以及摩擦因数变化规律。运用考虑边界膜强度的混合润滑模型分析轴瓦零件润滑状态转化特性和机制。结果表明：在存在边界润滑的混合润滑条件下，当加载力小于临界载荷，边界膜几乎未发生破裂，摩擦因数随载荷增加缓慢变大，其数值均较小；当加载力加至临界载荷，边界膜破裂，摩擦副微凸体接触区域出现干摩擦，摩擦因数出现突然增加，表明该摩擦副由边界润滑为主的混合润滑状态过渡到以干摩擦为主的润滑状态。     

Investigation of the strain distribution with lubrication during the deep drawing process

A lubrication/friction model can be implemented in FEM codes to predict the contact area ratio, friction coefficient and strain distribution in lubricated deep drawing process. In the lubrication analysis, the surface roughness effect on lubrication flow is included by using Wilson and Marsault's average Reynolds equation that is appropriated for mixed lubrication with severe asperity contact. With regard to the asperity contact theory, the well-known flattening effect is considered. Friction is expressed in terms of variables such as lubricant film thickness, sheet roughness, lubricant viscosity, interface pressure, sliding speed, and strain rate. The proposed lubrication/friction model combined with a finite element code of deep drawing process to predict the contact area ratio, friction coefficient and strain distribution. Numerical results showed that the present analysis provides a good agreement with the measured strain distributions.     

等温密封环摩擦状态演变预测与试验研究

结合浮动密封环的工作特点,提出一种基于载荷分配概念的密封摩擦状态演变预测模型。设定载荷分配系数,对粗糙表面微凸体接触和流体润滑接触两个部分摩擦力进行建模计算,根据微凸体承载力和总承载力等参数信息获得总摩擦因数值。模拟计算获得反映密封接触特性的摩擦因数与转速、压力以及表面粗糙度的关系曲线,仿真曲线历经完整的摩擦与润滑区,能够对不同摩擦状态下的接触特性进行预测。利用密封系统试验台对模型进行分析和验证,结果表明两者变化趋势保持一致,具有共同特征,说明密封摩擦预测模型能够真实反映密封摩擦副的接触规律及其变化情况,是预测密封摩擦状态的有效方法。     

Effect of laser textured dimples on the lubrication performance of cylinder liner in diesel engine

Laser surface texturing (LST) technique was utilised on a cylinder liner in a diesel engine. In order to analyse the effect of LST micro‐dimples on the lubrication and friction properties of cylinder liner–piston ring (CL–PR), we developed a new mixed lubrication model on the basis of the average Reynolds equation and asperity contacts equation. The model can consider the coupling effects between the surface roughness of non‐texturing regions and micro‐dimples and the synergistic effects of multi‐micro‐dimples. The results show that cylinder liner surface by LST can form effective hydrodynamic lubrication effect in most regions of the strokes, only near the dead points, the friction pair is in mixed lubrication state, asperity contact plays a major role in balancing the external load and the asperity friction force is obvious. The micro‐dimple parameters were optimised to obtain a better lubrication effect with the following optimised results: r_p = 30–60 µm, S_p = 0.2–0.4 and e = 0.03–0.1. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of rough line contacts operating under mixed elastohydrodynamic lubrication conditions

Heavily loaded machine elements, such as gears, usually operate in the mixed lubrication regime. Surface roughness has a significant effect on the pressure distribution, the subsurface stress field, and the friction coefficient. Based on the superposition of a dry rough and a fully flooded smooth contact, a mixed lubrication model has been developed. The roughness profile is assumed to be known. Surface deformation is calculated by taking into account the pressure distribution that is built up by asperity contacts, asperity interactions, and lubricant flow. Thermal and sliding effects are incorporated into the analysis. Non‐Newtonian lubricant behaviour is considered by using a power‐law rheological model. The pressure distribution, subsurface stress field, and friction coefficient were calculated from the model at several points along the contact path for an FZG type C gear pair. It was shown that a significant part of the load is carried by the contacting asperities. The position of the maximum shear stress is very close to the surface.     

基于分形理论的滑动摩擦表面接触力学模型

依据分形理论,考虑微凸体变形特征及摩擦作用的影响建立滑动摩擦表面接触力学模型。采用一个三次多项式来表达弹塑性变形微凸体的接触压力与接触面积的关系,从而满足在变形状态转变临界点处的微凸体接触面积与接触压力转化皆是连续和光滑的条件。推导出滑动摩擦表面临界弹性变形微接触面积、临界塑性变形微接触面积、量纲一真实接触面积的数学表达式。理论计算结果表明,表面形貌一定时,真实接触面积随着载荷的增大而增大;载荷一定时,真实接触面积随着特征尺度系数的增大而减小,随着分形维数的增大先增大后减小;当表面较粗糙时,摩擦因数对真实接触面积的影响很小;随着表面光滑程度的增大,摩擦因数对真实接触面积的影响增大,真实接触面积随着摩擦因数的增大而增大,特别是当摩擦因数较大时,真实接触面积增大的幅度也较大。接触力学模型的建立,为研究滑动摩擦表面间的摩擦磨损性能提供了依据。     

A Theoretical Analysis of Mixed Lubrication by Macro Micro Approach: Part I—Results in a Gear Surface Contact

Mixed lubrication is a key to bring the performance analysis to the failure analysis in most tribological components. A macro-micro approach to mixed lubrication has been developed in the present model. The relation between the average contact pressure and the average gap for a typical rough contact patch is first determined numerically in micro scale. Using this relation, the average gap, average oil-film pressure, and average contact pressure in a mixed-lubricated elastohydrodynamic contact can be solved simultaneously in macro scale by treating the contact to be smooth. The total pressure is assumed a superposition of average asperity contact pressure and lubricant pressure. The new approach is simple, efficient and robust, and covers entire range of the load ratio, from unity (dry contact) to zero (full-film EHL). In addition, it can be used for a wide range of operating conditions and on a much larger contact area with a much less computing time than deterministic simulation of mixed lubrication. Implementation of the Fast Fourier Transform (FFT) allows for a rapid calculation of the elastic deformation and asperity con/act pressure. As a demonstration to this new approach, a parametric study of dimensionless speed, load and contact shape on the load ratio and gap ratio was conducted for a gear rough surface of the load ratio, from unity (dry contact) to zero (full-film EHL). In addition, it can be used for a wide range of operating conditions and on a much larger contact area with a much less computing time than deterministic simulation of mixed lubrication. Impletmentation of the Fast Fourier Transform (FFT) allows for a rapid calculation of the elastic deformation and asperity contact pressure. As a demonstration to this new approach, a parametric study of dimensionless speed, load and contact shape on the load ratio and gap ratio was conducted for a gear rough surface     

The effect of laser texturing of SiC surface on the critical load for the transition of water lubrication mode from hydrodynamic to mixed

Experiments were carried out to verify if the low friction range of SiC in water lubrication can be expanded by micro-pores on the contact surface. Pores were formed by laser, with a diameter of 150 μm and a depth of about 8–10 μm and were distributed in a square array on the contact surface. Seven kinds of textured specimens with different intervals between the pores were tested and compared with the untextured specimen. The effect of the pore area ratio on friction coefficient and the critical load for the transition from hydrodynamic lubrication to mixed lubrication was reported and discussed.     

表面织构特征对其摩擦润滑特性的影响

为研究织构阵列的形貌、排布方式对织构化滑动摩擦副摩擦学特性的影响,利用三维CFD仿真方法,基于Navier-Stokes(N-S)方程建立不同形貌、排布的织构阵列摩擦副的润滑模型,分析不同形貌及排布方式对压力分布和承载特性的影响;在此基础上,研究6种形貌、2种排布方式织构的润滑特性及摩擦性能。结果表明,流体流入收敛楔产生正的流体动压,流入发散楔产生负的流体动压,规则排布的织构单元摩擦性能优于错开排布的织构单元。在最优的雷诺数条件下,不同形貌的织构单元平均摩擦系数随面积率的增加而减少,菱形织构和球冠形织构面积率从4.5%增加到12.5%时,摩擦系数分别降低了81%和76%。因此,合理的选择织构形貌、尺寸有助于改善织构化滑动摩擦副的摩擦学特性。     

A simple theory of asperity contact in elastohydro-dynamic lubrication

The Greenwood and Williamson theory of random rough surfaces in contact has been combined with established elastohydrodynamic theory to provide a theoretical approach to highly loaded lubricated contacts in which the load is shared between hydrodynamic pressure and asperity contact. It is shown that, provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given (to a first approximation) by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. It then follows that the asperity pressure, both real and apparent, is determined primarily by the ratio of theoretical film thickness to the combined roughness of the two surfaces (h_o/σ). A corollary of this result is that an increase in total load, which has only a small influence on the film thickness, is carried by an increase in fluid pressure and only gives rise to a small increase in asperity contact pressure.     

考虑软三体接触的粗糙界面混合润滑模型研究

软三体颗粒润滑是利用大量松散的固体软颗粒在界面中的承载和剪切行为实现特殊环境下界面的减摩,因此研究软颗粒介质摩擦界面在剪切过程中的受力情况,对软三体颗粒润滑机理的分析以及润滑装置的设计都具有重要意义。研究中将第三体颗粒类比为流体,基于雷诺方程、黏度方程、Greenwood和Williamson接触模型（G-W模型）等建立了含大颗粒粗糙界面的混合润滑模型。该模型中摩擦副的总载荷及总摩擦力由流体、微凸体和大颗粒三部分共同构成。通过采用有限差分法对上述物理模型进行求解分析,探究膜厚比、第三体大颗粒的质量浓度、粒径以及试件的表面形貌、弹性模量对三体接触界面的承载和摩擦力的影响情况,进而分析大颗粒粒径和接触表面粗糙度耦合时软三体接触界面的力学性能。基于对所构建的软三体接触界面混合润滑模型的研究可知：合理选择大颗粒质量浓度、粒径以及试件的表面形貌、弹性模量有助于提高承载、减小摩擦力,使得软三体颗粒流具有更好的减摩润滑性能。     

Parametric Analysis of Rolling–Sliding Line Contacts Under Boundary and Near Boundary Lubrication Conditions

This article reports a parametric analysis of rolling–sliding line contacts in boundary and near-boundary lubrication with relevance to the contacts in rotorcraft drive systems in loss of lubrication. A recently developed mathematical model for boundary lubrication with friction, temperature, and tribochemistry is used in the analysis. The parameters studied include radius of the line contact, surface hardness, boundary film shear strength, fluid–solid load sharing, system bulk temperature, load, speed, and slide-to-roll ratio. The contact condition is measured by the temperature and friction power intensity along with the boundary film integrity and mode of deformation. The results of the analysis led to a number of suggestions and elaborations listed in the Conclusion regarding various design considerations of the contacts in rotorcraft drive systems against loss of lubrication.