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 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.     

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.     

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.     

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.     

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.     

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.     

Modeling of lubrication in micro contact

A thorough understanding of the mechanisms of micro contactlubrication and failure is required in order to optimize machinecomponent design for extreme operating conditions. In the verylow ratio, the ratio of lubricant filmthickness to surface roughness, asperity contacts play animportant role. Analysis of lubrication and failure of microcontact should include details of surface topography and itscharacterization, asperity contact pressure, micro lubricationpressure and film shape, as well as micro contact temperature.These aspects are discussed in this paper and typical numericalresults are given. Modeling and simulation tools are availableto describe the solid contact of asperity tips and the collapseof the lubricant film. It appears possible to investigate thetransition from full EHL to boundary lubrication by using themodel developed.     

Effect of surface texturing on the elastohydrodynamic lubrication analysis of metal-on-metal hip implants

With the development of surface processing techniques, applications of bearing components have been introduced with specific surface textures to take advantage of lubrication.An advanced numerical model was established to simulate the mixed EHL problem of a metal-on-metal hip prosthesis with dimpled surface texturing. The surface texture with simple cylindrical dimples was numerically simulated, under both steady state and walking conditions.The present results showed that surface texturing may have a potentially beneficial effect on the reduction of asperity contact ratio and the improvement of lubrication performance of metal-on-metal hip replacements, particularly under predominant boundary lubrication conditions.     

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.     

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.     

A Transient Thermal Model for Mixed-Film Contacts

A thermal model is presented in this paper for deterministic calculations of the contact temperatures in mixed-film lubrication. A first-principal approach is taken to obtain the temperature results by solving transient energy equations in a domain consisting of three solid-film-solid regions. Various modeling techniques are used to feature model simplicity and to achieve a proper balance among solution accuracy, model robustness and computational efficiency. This thermal model may be incorporated into other deterministic isothermal mixed-film models to form a complete base model for mixed-film lubrication. It provides a platform upon which to model other effects such as lubricant additives, asperity plastic deformation and surface coating.     

A microwedge model of sliding contact in boundary/mixed lubrication

A refined friction model of sliding contact in boundary/mixed lubrication regime is developed. In addition to the well-known asperity flattening and roughening effects, significant deformation of asperities can be incited by the elastic microwedges on the tool surface. A model of asperity deformation, which includes the effects of smoothing, roughening, and microwedge, is proposed for processes where smooth tool and rough workpiece are used. A finite element formulation incorporating the microwedge effect in the Reynolds equation for lubricant flow is also derived. Numerical results showed that the inclusion of microwedge in the analysis provides a good agreement with the experimental measurements, especially with many interesting phenomena that can be neither explained nor predicted by the other friction models.     

螺旋槽机械密封瞬态启动过程润滑特性

建立了螺旋槽机械密封瞬态启动过程润滑特性的计算模型,耦合求解了含流量因子、接触因子及质量守恒空化边界的雷诺方程、弹塑性粗糙峰接触方程及动力学方程,比较了不同运行工况及结构参数的润滑状态转变过程。结果表明：增速阶段流体承载力与液膜厚度不断增大,粗糙峰承载力逐渐减小至消失;相比较于流体动压润滑状态,混合摩擦状态的液膜刚度较大且振荡幅值明显,在到达脱开转速时刻有较大的轴向速度突变。受挤压效应影响,较小的启动加速度可以在低转速下进入流体润滑状态,较高的外压和较低的内压均有利于润滑状态的转变。随槽数的增加,脱开转速呈先增大后减小趋势,螺旋角与槽深的减小或槽坝比的增大均对润滑状态转变能力起促进作用。     

边界润滑下滑动接触表面破坏行为的数值分析

针对边界润滑条件，本文用有限元方法分析了当滚动接触处于准静态情况下，接触表面覆盖有水边界膜而且接触区内存在微观突起和微观裂纹的接触状态，阐明了液体对表面微观裂纹的影响。分析结果表明液体的存在改变了接触区的受力状态，表面裂纹造成接触区应力分布的不连续；有水存在时，最高接触压力降低并且分布均匀，但造成应力强度因子K1增大，促进裂纹的扩展。     

Some insights into asperity temperatures in mixed-film lubrication

This paper investigates some fundamental thermal behavior of asperity contacts in mixed-film lubrication. First, the thermal interaction between the contacting asperity and the lubricant is studied. The analysis is based on transient simulations of a mixed-film contact problem under various contact conditions. The results suggest that the solid/fluid thermal interaction can be strong. The lubricant is shown to play an important role in asperity temperature. It not only generates heat through viscous shearing but also plays a role of cooling by transporting heat out of the thermally intensive asperity contacts. The interaction can significantly reduce asperity temperatures especially under high-speed conditions. The interaction also increases the lubricant temperature away from the asperity contact, thus facilitating thermal coupling among contacting asperities. Another thermal behavior of mixed-film contact studied is the effect of heat flow in the asperity contact in the direction perpendicular to the lubricant entrainment. Results suggest that the effect of this thermal side-flow is significant in low-speed contacts and diminishes when the entraining velocity becomes high. Further, the side-flow effect is much weaker in the mixed-film contact than in the dry contact and may be neglected in the modeling of complex mixed lubrication problems.     

On Mechanisms of Fatigue Life Enhancement by Surface Dents in Heavily Loaded Rolling Line Contacts

This paper studies mechanisms of surface dents in enhancing the fatigue life of rolling bearings previously reported in Akamatsu et al. (1). First, transient micro-EHL analyses of heavily loaded contacts between rough surfaces with multiple dents are conducted under near rolling conditions. Contacts with various dent dimensions, dent arrangements under different loading and kinematic conditions are investigated. Results show that surface dents generate no favorable micro-EHL effects to enhance the contact fatigue life. Subsequent analyses, in conjunction with other published studies, suggest that the fatigue life enhancement likely comes from the reduced local traction at asperity contacts through the “oil pots” effects of the dents. The effects of the surface dents on contact fatigue life may depend on the lubrication regime in which the contact is operating being favorable in poor lubrication conditions but adverse in well-lubricated contacts. Since rolling bearings are usually designed to operate in a healthy regime of lubrication, fatigue life enhancement by artificially introducing dents on bearing surfaces may not extend to field applications.     

Investigation into the Normal Contact Stiffness of Rough Surface in Line Contact Mixed Elastohydrodynamic Lubrication

In this work, the statistical asperity microcontact models in combination with the acoustic spring model and the load sharing concept are utilized to study the interfacial normal contact stiffness for a rough surface in line contact elastohydrodynamic lubrication (EHL). Two different statistical microcontact models of Greenwood and Williamson (GW) and Kogut and Etsion (KE) are employed to derive the normal contact stiffness expressions for a dry rough line contact considering the purely elastic contact and the multiple regimes elastic–elastoplastic–fully plastic contact, respectively. The liquid film stiffness is calculated based on the relationship between film thickness and bulk modulus of the lubricant. The lubricant film thickness equations are employed in conjunction with the load sharing concept and the empirical formulas for the maximum contact pressure in a dry rough contact are fitted for the GW model and the KE model, to evaluate the relationship between film thickness and motion velocity for the purely elastic GW microcontact model and the multiregime KE microcontact model, respectively. The comparison with experimental results shows that the KE model predicts closer total contact stiffness results than the GW model. The stiffness contributions from the solid asperity contact and lubricant film are obtained and effects of surface roughness, applied load, motion velocity, and type of lubricant on the normal contact stiffness are analyzed.     

A Study of Dynamically Loaded Finite Journal Bearings in Mixed Lubrication Using a Transient Thermohydrodynamic Analysis

A transient analysis of dynamically loaded finite journal bearings in mixed lubrication is made by solving the modified generalized Reynolds equation, 2-D energy equation in the oil, and heat conduction equation in the journal simultaneously including mass conserving cavitation. ISOADI (isothermal shaft and adiabatic bushing inner surface) thermal boundary condition is used. Journal temperature is treated as quasi-steady over one loading cycle. Two kinds of contact model are used. Numerical solutions using the finite difference method are presented. Results shows that the bearing behavior is closely tied to the roughness texture and topography, asperity contact load, bearing geometry, and operating conditions.