Numerical and Experimental Studies on Tribological Behaviors of Cu-Based Friction Pairs from Hydrodynamic to Boundary Lubrication

When studying the tribological behaviors of a Cu-based friction pair in different lubrication regimes, calculation of the real contact area of asperity contacts is crucial but difficult. In this work, a mixed lubrication model in plane contacts is developed, and pin-on-disc tests are carried out. The real contact area ratio, load sharing ratio, and friction coefficient are investigated. Effects of sliding velocity, temperature, and pressure are considered. The results show that when the maximum contact area ratio is about 14.6%, the load sharing ratio of asperity contacts is about 95%. The friction coefficient obviously increases from less than 0.04 to about 0.15 as the regime changes from hydrodynamic to boundary lubrication. Asperities have a significant influence on the local lubrication of a Cu-based friction pair, and the action of hydrodynamic pressure cannot be ignored.     

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.     

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.     

Dynamic Friction Model of Lubricated Surfaces for Precise Motion Control

A model is developed to describe dynamic friction effects in lubricated surfaces. The model covers the hydrodynamic, mixed and boundary lubrication regions. The dynamic friction model can predict the friction force for time-varying velocity, and is useful in precise motion control. The model presented is for a short journal bearing, but can be extended to other geometries of sliding surfaces, such as point and line contacts or rolling element bearings. The friction is related to a time variable fluid film thickness, resulting from journal vibrations relative to the sleeve. The proposed model agrees qualitatively with experimental results for lubricated line contact. Both show similar hysteresis-type friction curves under oscillating velocity.     

A deterministic model for line-contact partial elastohydrodynamic lubrication

A deterministic model for partial elastohydrodynamic lubrication (EHL) is presented in this paper. The modelling methodology adopts some of the concepts used in the stochastic modelling of partial EHL and some of the procedures for deterministic calculation of asperity pressures. The model is shown to be capable of simulating the basic process of asperity interaction and solid-to-solid contact within an EHL conjunction of rough surfaces. Deterministic results of transient partial EHL in line contacts are obtained when one pair or multiple pairs of asperities collide. The model may help to gain a fundamental understanding of the transient behaviour of asperity interactions in lubricated concentrated contacts of rough surfaces. Asperity pressures may be calculated more accurately than the conventional analyses under dry and static contact conditions. The work represents a first attempt in deterministic modelling of tribo-contacts operating in the mixed regime of micro-EHL and boundary lubrication. Future work will aim at developing more realistic models incorporating factors such as three-dimensional asperity contacts, asperity plastic deformation, thermal effects and the effect of tribo-chemistry.     

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.     

Refined simulation of friction power loss in crank shaft slider bearings considering wear in the mixed lubrication regime

Friction reduction is a fundamental factor in decreasing fuel consumption of internal combustion engines. During the design stage of the engine the simulation of friction in the crank mechanism plays a vital role to develop optimum solutions. Due to the interaction of oil and elastic structures with rough surfaces in slider bearings, complex simulation models have to be used for representing the relevant physical behavior. The following article is focused on crank shaft slider bearings of large engines.The article describes a procedure evaluated by measurements showing how to model wear profiles of slider bearings to reach a high quality friction forecast. A fundamental influencing factor of bearing friction is given by the mixed lubrication regime and it is considered in the simulation model as part of asperity contact friction and hydrodynamic friction. Further effects result from the compliance in radial and width directions of the bearing structure and the wear of the bearing surface. Furthermore, the specific operating conditions of the slider bearing such as load, temperature, shaft speed and oil characteristics are essential and have to be taken into account.The objective of this investigation is to propose the wear profile of the bearing surface for the simulation model to be treated iteratively, where simulation results for the amount of mixed lubrication are successively assessed. For this purpose an iterative procedure is introduced and validated by measurements on a slider bearing test rig.The applied simulation method is based on elastic multi-body systems; the lubrication film contact is calculated based on Reynolds differential equation via the pressure balance calculated iteratively in the time domain. The model accounting for the mixed lubrication regime is based on the theory of Greenwood and Tripp.     

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.     

大偏心下滑动轴承热弹流润滑状态及特性*

滑动轴承在大偏心条件下工作时，热效应及弹性变形使得油膜润滑状态发生变化，进而影响摩擦特性。为此建立耦合轴瓦弹性变形、轴颈轴瓦粗糙峰接触、油膜温度分布及黏温-黏压关系的滑动轴承混合润滑模型，采用有限差分法求解得到不同工况下油膜压力场、温度场分布，分析热效应及弹性变形对润滑状态转变及轴承各特性参数的影响；搭建实验台测量试件内表面温度分布，测试结果验证了计算模型的正确性。结果表明：大偏心时热效应和弹性变形使得油膜润滑状态出现转化；粗糙峰的接触使摩擦热增加，且在最小油膜处形成温度峰值；热效应和轴瓦弹性变形使得接触压力峰值集中在轴承两端，承载能力和摩擦力均有所下降。     

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.     

UHMWPE复合材料水润滑轴承润滑状态转变性能研究

水润滑轴承润滑介质的黏度较低,轴承动压润滑难以形成。研究水润滑轴承润滑状态转变特性,可为水润滑复合材料轴承的设计和优化提供依据。建立水润滑轴承流固耦合计算模型,研究轴承承载力、水膜压力、轴承变形量随工况的变化关系,提出水膜厚度测试方法,研究轴承摩擦因数、水膜厚度随转速、负载的变化规律。研究结果表明:随偏心率和转速增大,轴承承载力、最大水膜压力和最大变形量均逐渐增大;随转速增大,轴承承载力、最大水膜压力和最大变形量的增幅逐渐减小。试验发现随着负载增大,改性UHMWPE轴承从混合润滑向动压润滑转变的膜厚比逐渐减小。     

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.     

Experimental and Numerical Study of Micropitting Initiation in Real Rough Surfaces in a Micro-elastohydrodynamic Lubrication Regime

Micropitting is a form of surface fatigue damage that happens at the surface roughness scale in lubricated contacts in commonly used machine elements, such as gears and bearings. It occurs where the specific film thickness (ratio of smooth surface film thickness to composite surface roughness) is sufficiently low for the contacts to operate in the mixed lubrication regime, where the load is in part carried by direct asperity contacts. Micropitting is currently seen as a greater issue for gear designers than is regular pitting fatigue failure as the latter can be avoided by control of steel cleanliness. This paper describes the results of both theoretical and experimental studies of the onset of micropitting in test disks operated in the mixed lubrication regime. A series of twin disk mixed-lubrication experiments were performed in order to examine the evolution of micropitting damage during repeated cyclic loading of surface roughness asperities as they pass through the contact. Representative measurements of the surfaces used in the experimental work were then evaluated using a numerical model which combines a transient line contact micro-elastohydrodynamic lubrication (micro-EHL) simulation with a calculation of elastic sub-surface stresses. This model generated time-history of stresses within a block of material as it passes through the contact, based on the instantaneous surface contact pressure and traction at each point in the computing mesh at each timestep. This stress time-history was then used within a shear-strain-based fatigue model to calculate the cumulative damage experienced by the surface due to the loading sequence experienced during the experiments. The proposed micro-EHL model results and the experimental study were shown to agree well in terms of predicting the number of loading cycles that are required for the initial micropitting to occur.     

进水温度对水润滑轴承润滑特性的影响

为研究进水温度变化对水润滑轴承润滑特性的影响,采用有限差分法建立水润滑轴承弹流润滑模型,分析不同进水温度和载荷条件下水润滑轴承润滑特性的差异,并且通过试验验证摩擦因数的变化规律。研究发现：随着进水温度升高,轴承的水膜压力下降,但在水膜压力峰区域最大水膜压力升高、最小水膜厚度减小、偏心率增大,表明进水温度升高对润滑性能有着负面影响;在相同的载荷和转速下,轴承摩擦因数随着进水温度升高而下降,且高载荷下进水温度对摩擦因数的影响更大。通过试验发现进水温度越高对摩擦因数变化的影响越大,不同进水温度下载荷越低,载荷的变化对摩擦因数变化量的影响越大。     

Calculation of Stribeck curves for (water) lubricated journal bearings

This paper describes a mixed elastohydrodynamic lubrication (EHL) model for finite length elastic journal bearings. The finite element method was employed to discretise the coupled system of 2D–3D Reynolds-structure equations and to compute Stribeck curves at constant load. As underrelaxation strategies have been found to be insufficient for an iterative solution of this problem, artificial dynamics have been added to the numerical structure equations in order to solve for stationary solutions of the fluid–structure problem. An ideal plastic asperity contact model together with an effective film thickness formulation according to Chengwei and Linqing was employed in order to compute the contact pressure in mixed lubrication. The method presented in this paper is applied to a typical water lubricated journal bearing problem. Computed Stribeck curves are presented and the numerical performance of the method is evaluated.     

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.     

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.     

表面织构对水润滑轴承混合润滑性能的影响

为分析表面织构对水润滑轴承混合润滑性能的影响,基于平均Reynolds方程及JFO空化边界条件建立带有表面织构的水润滑轴承混合润滑模型并数值求解,获得不同织构参数下水润滑轴承的Stribeck曲线。研究结果表明:表面织构是否能改善润滑性能与其深径比及面密度参数密切相关,织构的引入并不一定能降低水润滑轴承的摩擦因数;表面织构的面密度和深径比存在最优值,能使水润滑轴承获得最大的膜厚比与最小的摩擦因数,并在较低的转速下由混合润滑状态进入流体动压润滑状态。     

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。