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.     

Theoretical and Experimental Investigations on EHL Point Contacts with Different Entrainment Velocity Directions

Film thickness prediction plays an important role in evaluating the performance and durability of machine elements under elastohydrodynamic lubrication (EHL). However, current formulae may not be appropriate for general conditions occurring in real contacts. This study investigates the effect of different lubricant entrainment velocity angles on film thickness distribution. For this purpose, a steady-state isothermal EHL model is used under a wide range of parameter sets including varying sum velocity, contact pressure, and sum velocity angle. Considerable differences in the trend of the central film thickness with respect to the lubricant entrainment velocity angle for low and high loaded contacts are shown. The results are compared with experimental measurements by means of an optical ball-on-disc tribometer and a twin-disc machine using capacitance method. Good agreement between numerical results and experimental measurements was found.     

An Investigation into Grease Behavior in Thermal EHL Circular Contacts

The behaviors of two lithium lubricating greases were investigated under EHL circular contact through measurements of traction coefficients on a self-made rig in which the contact was continuously fed with fresh grease. The average values of Erying shear stress and shear modulus of the two lithium greases were obtained from traction experimental data using this rig. Based on the Evans-Johnson model and thermal analysis, we calculated the values of shear stress and traction coefficients of the two greases. The results show that the calculated traction coefficients agree fairly well with the measured data.     

Numerical Simulation of Double Conformal Contacts Involving Both Interference and Clearance

Cylindrical conforming contacts are of great practical importance in engineering applications. Their contact behavior and stress fields need to be determined for desired configurations in order to achieve successful designs. A common configuration involving a ring has double interfaces, but their collective behavior is not well studied. Due to the fact that in a great number of designs the ring is constrained by an interference, this article focuses on simulating loaded double conforming contacts when at least one interface is subject to an interference while the other interface can have a clearance. This development is built upon analytical solutions of normal surface displacement and fast Fourier transform (FFT)-based contact algorithms presented in an earlier model. However, the model is novel in its ability to deal with interference in double-interface contact problems. The effects of microgeometry feature/deviations on the contact behavior are investigated with quantitative results from the model. This simulation model can be useful for design engineers in various engineering fields.     

A Limiting Solution for the Dependence of Film Thickness on Velocity in EHL Contacts with Very Thin Films

In recent years there have been substantial improvements in the capabilities of numerical modeling of elastohydrodynamic lubricant (EHL) films and it is now possible to analyze a very wide range of conditions rather than needing to rely on extrapolation using classical film thickness regression equations such as those of Dowson and Higginson. However, a new controversy has arisen concerning the film thickness-velocity dependence in EHL contacts at very low speeds and high loads, with some predictions showing a film thickness much less than that predicted by the classical equations. The present article applies the well-established limiting analysis, first presented by Grubin-Ertel, to the inlet of the EHL contact. It is shown that when the load is high and the speed is low (and the pressure gradient is very high in the inlet) an accurate resolution of the inlet pressure rise is critical for the determination of the film thickness. Discretization errors of this type might be responsible for discrepancies between the classical equations and some recently published numerical predictions.     

Film Formation in EHL Point Contacts under Zero Entraining Velocity Conditions

The contacts of adjacent balls in a retainerless bearing are subjected to the zero entrainment velocity (ZEV). The existence of an effective elastohydrodynamic lubrication (EHL) film between contacts running under ZEV conditions has long been proven experimentally. However, the classical EHL theory predicts a zero film thickness under ZEV conditions. Mechanisms, such as the thermal viscosity wedge effect and immobile film theory, have been proposed to tentatively explain the phenomenon. However, detailed numerical results are needed to provide theoretical evidence for such film formations. This paper aims to simulate, based on the viscosity wedge mechanism, the film formation of EHL point contacts under ZEV conditions. Complete numerical solutions have been successfully obtained. The results show that the thermal viscosity wedge induces a concave film profile, instead of a parallel film (Hertzian) as postulated by some previous researchers. By the simulation solver developed, the variation of film thickness with loads, oil supply conditions and ellipticity parameters have been investigated. Some unique lubrication behaviors under ZEV conditions are demonstrated. Furthermore, preliminary quantitative comparisons with the latest optical EHL experiments are finished. Both results are in good correlation.     

纯滚动集中接触润滑入口区热效应的数值分析

在对入口区膜厚形状和压力分布的简化处理前提下，采用数值分析方法全面地分析了纯滚动集中接触润滑入口区的热效应，得到了的结论与其它学者的试验及分析结果较为一致。     

重载下非牛顿流体线接触弹性流体动力润滑的数值解

对重载下线接触流体润滑时 ,润滑剂的流变学作用和表面变形进行了理论分析 ,从而导出了非牛顿流体的模型 ,指数模型就是其中之一。当指数 n增大时 ,油膜厚度随之上升 ,并且油膜破裂点向接触区中心移动 ,同时润滑油的等效粘度也随之上升 ,当 n=1时计算结果与牛顿流体基本一致。     

齿轮啮入冲击的弹流润滑数值分析

考虑单个轮齿的啮入冲击载荷以及曲率半径、速度沿啮合线的变化，用多重网格法模拟了轮齿从啮入到啮出的整个时间历程，分析了沿啮合线的油膜压力与膜厚的变化，并与静态结果进行了比较。     

A Critique of Rolling Contact Fatigue Criteria for Bearing Rings with Hoop Stresses

Tensile residual and interference fit stresses not treated in classical bearing formulations are known to reduce bearing rolling contact fatigue (RCF) life. Recent modifications of such theory to account for these stresses have simply included them in the computation of a single yield stress type criterion—either maximum shear or equivalent stress. An alternative modification is proposed and demonstrated for fatigue crack initiation that recognizes the primary influence of the maximum range of shear stress but includes the effect of normal stress on the critical planes, as in other successful bulk fatigue criteria for multiaxial nonproportional stress cycle fatigue.     

Modeling of Dynamic Friction in Lubricated Line Contacts for Precise Motion Control

A simple dynamic friction model for an elastohydrodynamic lubrication sliding and rolling line contact has been developed. This model uses the technique introduced earlier by Harnoy and Friedland (1). The model includes low-velocity regions where friction is a combination of contact and elastohydrodynamic friction. The study shows that the lime-variable friction is not only a function of instantaneous sliding velocity, but is also a memory function of the velocity history. Simulation of the model for an oscillating velocity exhibits similar hysteresis effects in friction-velocity curves as observed earlier in several experimental studies. The model can be useful for friction compensation to enhance the precision of motion in control systems.     

Stress Analysis on Layered Materials in Point Elastohydrodynamic-Lubricated Contacts

For multilayered or coated substrates in elastohydrodynamic-lubricated (EHL) contacts, the subsurface stress distributions under a normal load combined with shear traction have been analyzed in this article through computer simulations. The Papkovich-Neuber potentials and Fourier transform are adopted to deduce the pressure–displacement, pressure–stress, and shear traction–stress response functions in frequency domain for the coated substrates, and to calculate distributions of pressure and subsurface stress. The results from the analysis of EHL contacts on coated substrates are compared with those from dry contact model in which shear traction is assumed to obey Coulomb’s law. Effects of the Young’s modulus of coatings, the properties of lubricants, and the magnitude of traction are discussed. Similar to the results in dry contacts, hard coatings in lubricated cases tend to increase the von Mises stress, whereas soft coatings decrease the stress. Shear traction makes the max von Mises stress increasing and moving closer to surface. However, the changes in subsurface stress due to shear traction are less obvious in lubricated contacts. Comparison between EHL and dry contact models reveals that lubrication can reduce the von Mises stress in the coating layer due to smaller shear traction. The analyses show that pressure, film thickness, and subsurface stress distributions are influenced by surface coatings, sliding velocity, rheological models, and pressure–viscosity behaviors.     

Measurement of Pressure Distribution in EHL—Development of Method and Application to Dry Static Contacts

The development and application of a new technique to measure the pressure distribution in an elastohydrodynamic contact is described. The method uses optical interferometry to measure the local compression of a thin elastic layer sandwiched between the loaded surfaces. The elastic-layer thickness is mapped as a line profile across the contact and the measured compression is calibrated to give a pressure distribution. The data are acquired through a single triggered image rather than a scanning system so that transient pressures can be measured. The current study is limited to static contacts, and pressure profiles are presented for a number of contact conditions. These include smooth and textured surfaces and entrained debris. The results are compared to theoretical predictions for smooth surfaces.     

Mapping Shear Stress in Elastohydrodynamic Contacts

A new method has been, devised for investigating the theological properties of lubricant films in two-dimensional EHD contacts. A lubricated, sliding contact is produced between a sapphire flat and a steel ball. Thermal infrared emission microscopy is then employed to obtain 2-D maps of the variation of temperature rise due to friction across the contact. These maps are then used in conjunction with moving heal source theory to produce maps of energy dissipation and thus shear strength, of the lubricant film across the contact.

A series of mixtures of two lubricants, one giving high traction and one with low traction, have been studied using this technique to investigate the influence of lubricant, blending on shear stress and traction.     

The Influence of Moving Dent on Point EHL Contacts

A transient analysis for a dent passing through the conjunction of a point EHL contact was developed and solved numerically by using the multigrid method. Results show that the presence of sliding produces a noticeable pressure ridge and thus, a surface indentation at either leading side of the dent if the dent moves slower than the opposite surface, or at the trailing side if the dent moves faster than the opposite surface. The pressure ridge and surface indentation extend their lengths forward or backward from the dent in the sliding direction at a rate approximately half the sliding speed. The pressure fluctuation associated with the dent increases with increasing slide-to-roll ratio and dent depth, and decreases with increasing dent width in both x- and y-directions. The agreement between numerical simulation and experimental results obtained by Wedeven and Cusano (I) is remarkably close.     

On the Numerical Accuracy of Rough Surface EHL Solution

Numerical solution of rough surface elastohydrodynamic lubrication (EHL) is of great importance. In recent years, research efforts have been focused on deterministic modeling, because it is proven to be capable of predicting detailed contact and lubrication characteristics based on measured three-dimensional machined surface topography in a wide range of operating conditions. The accurate calculation of roughness derivatives, ?S/?X and ?S/?T, is found to be crucial for numerically solving EHL problems, especially if machined roughness with high-frequency components is involved. When discretized rough surfaces are employed, one may have to handle three different discretization grids, one for the stationary solution domain of the Reynolds equation and the other two for the moving rough surfaces in contact. Two numerical ways can be employed to fulfill the computation of ?S/?X and ?S/?T. One is to interpolate the topographic heights into the solution domain grid and then conduct the derivation calculations there. The other is to do derivations first in the surface grids and then interpolate the obtained derivatives into the solution mesh. In order to compare these two ways based on an accuracy analysis, a transverse sinusoidal rough surface is exploited and the effects of mesh spacing, differential scheme, interpolation method, and roughness wavelength on numerical errors of ?S/?X and ?S/?T are investigated. It is found that the appropriate way to minimize the errors is to ensure that the surface grids are considerably denser than that of the solution domain and to conduct derivation calculation first on the surface grids. A densified surface mesh may lead to a great reduction in numerical errors without causing any significant increase in the computing time. Densification of the solution domain mesh, on the other hand, is more difficult because it would result in a large increase in computational burden. It is also found that high-order differential schemes and interpolation methods are helpful to improve accuracy. Large roughness wavelengths lead to smaller numerical errors, but roughness amplitude has no influence on numerical accuracy.     

A Model for the Effect of Humidity on Stiction of the Head/Disk Interface

A model has been developed for the effect of humidity on stiction of the head/disk interface. The model combines the meniscus force of the adsorbed water film at the interface with the Greenwood-Williamson surface model, and takes into account the effects of suspension load as well as surface roughness and material properties of both the head and the disk. It correctly predicts the trend for stiction vs. relative humidity as obtained from experimental data.     

Prediction of Real Rough Surface Deformation in Pure Rolling EHL Contact: Comparison with Experiment

The ability to predict the in-contact deformation of surface topography is very important for the design of machine components with respect to minimizing the friction and wear of rubbing surfaces. In this study the amplitude attenuation principle is verified as a simple tool for this purpose. Measured lubricant film profiles are compared with prediction based on this principle. From the results obtained it appears that the amplitude attenuation principle provides reasonable estimation of the deformation of rubbing surfaces that can be used for the prediction of in-contact behavior of surface roughness. Good agreement was obtained under pure rolling conditions, which provides a good initial point for the other studies under rolling/sliding conditions where the wear of rubbing surfaces is of key importance.     

A Simplified Model to Study EHL Film Collapse During Rapid Halting Motion

A theoretical model for describing the EHL film thickness during rapid deceleration is presented. The theory is based on the pioneer work of Ertel (1939) and Grubin (1949), who gave the first analytical solution for the elastohydrodynamic lubrication of a line contact under stationary operating conditions. An extension is made here for rapid halting motion. The proposed model is well adapted when the halting period is small in comparison to the transit time (i.e. 2b/u, ratio between the contact width and the rolling speed). This work completes the model of Glovnea and Spikes (2001b), appropriate for slow halting motion but which suffers from experimental fitting, and the model of Chang (2000) that is more suitable for speed or load oscillations at a wavelength close to the transit time.

This behavior implies that stop-start, reciprocating or rapidly halting machine components may be able to maintain a separating film for longer than would be expected based on steady-state EHL theory. An application to a ball bearing arrangement in a space mechanism is finally made in order to assess the model capabilities.     

凸轮弹性流体动力润滑油膜厚度计算的新方法

本文先给出了全膜线接触弹流膜厚计算的统一公式，应用弹性流体动力润滑理论，探讨了凸轮油膜厚度的计算方法，利用MATLAB软件编制的程序可计算凸轮弹性流体润滑油膜厚度，凸轮膜厚比λ，从而能判断摩擦副之间的润滑状态，并对判断凸轮表面损伤坏形式，减少两接触表面的磨损，凸轮参数优化设计和使用寿命预测等具有重要意义。