基于不同微观固体接触模型的轮轨表面变形特性分析

针对轮轨表面接触变形问题,采用不同的统计型微观固体接触模型,即Greenwood-Williamson （GW）模型,Chang-Etsion-Bogy （CEB）模型和Zhao-Maietta-Chang （ZMC）模型,研究轮轨接触表面变形特性。利用Newton-Raphson方法对微观固体接触模型公式进行求解,并同时求解间隙方程和载荷平衡方程。考虑不同粗糙度和不同塑性指数下各微观固体接触模型的压力分布情况,以及接触半径随载荷的变化情况。并将不同微观固体接触模型的结果和Hertz模型结果对比,结果表明弹塑性微观接触模型（CEB,ZMC）比弹性模型（GW）有着更小的接触压力以及更宽的接触半径,最大压力均小于最大Hertz接触压力,接触半径均大于Hertz接触半径。     

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 statistical model of elasto-plastic asperity contact between rough surfaces

This work models statistically elasto-plastic contact between two rough surfaces using the results of a previous finite element analysis of an elasto-plastic sphere in contact with a rigid flat. The individual asperity contact model used accounts for a varying geometrical hardness effect that has recently been documented in previous works (where geometrical hardness is defined as the uniform pressure found during fully plastic contact). The contact between real surfaces with known material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. The asperity is modeled as an elastic-perfectly plastic material. The model produces predictions for contact area, contact force, and surface separation. The results of this model are compared to other existing models of asperity contact. Agreement exists in some cases and in other cases it corrects flaws, especially at large deformations. The model developed by Chang, Etsion and Bogy is also shown to have serious flaws when compared to the others. This work also identifies significant limitations of the statistical models (including that of Greenwood and Williamson).     

Evaluation of the real contact areas, pressure distributions and contact temperatures during sliding contact between real metal surfaces

A three-dimensional elastic contact algorithm has been developed to analyse the normal contact problems of bodies having rough surfaces. The algorithm can evaluate the real contact areas and contact pressure distributions using measured surface roughness data.

Following an approximate elastic-plastic contact solution the analysis produces more realistic elastic and plastic contact areas; in addition results of contact pressure distributions can be predicted according to a given maximum plastic limit pressure.

The technique can simulate (in an approximate way) the elastic-plastic sliding contact behaviour in the vicinity of asperities or concentrated contact areas by ignoring the effect of the tangential forces on the vertical displacement.

Assuming a certain sliding speed and a particular coefficient of friction the local temperature distribution due to the heat generation over the real contact areas can also be calculated for 'slow sliding' problems.

The results show the moving real contact areas and the contact temperature fields for an electric spark mechanical steel surface moving over a planed bronze surface. Changes of the rigid body displacement, as well as the average and maximum pressures are also presented during sliding.

The micro-contact or asperity contact behaviour for bodies having large nominal contact area and the macro-contact behaviour for bodies being in 'concentrated contact' are also compared. In the latter case an ideal smooth steel ball was slid over the previously mentioned bronze surface.     

On the Modeling of Elastic Contact between Rough Surfaces

The contact force and the real contact area between rough surfaces are important in the prediction of friction, wear, adhesion, and electrical and thermal contact resistance. Over the last four decades various mathematical models have been developed. Built on very different assumptions and underlying mathematical frameworks, model agreement or effectiveness has never been thoroughly investigated. This work uses several measured profiles of real surfaces having vastly different roughness characteristics to predict contact areas and forces from various elastic contact models and contrast them to a deterministic fast Fourier transform (FFT)-based contact model. The latter is considered “exact” because surfaces are analyzed as they are measured, accounting for all peaks and valleys without compromise. Though measurement uncertainties and resolution issues prevail, the same surfaces are kept constant (i.e., are identical) for all models considered. Nonetheless, the effect of the data resolution of measured surface profiles will be investigated as well. An exact closed-form solution is offered for the widely used Greenwood and Williamson (GW) model (Greenwood and Williamson, Proceedings of the Royal Society of London A, vol. 295, pp. 300–319), along with an alternative definition of the plasticity index that is based on a multiscale approach. The results reveal that several of the theoretical models show good quantitative and qualitative agreement among themselves, but though most models produce a nominally linear relationship between the real contact area and load, the deterministic model suggests otherwise in some cases. Regardless, all of the said models reduce the complicated surface profiles to only a few key parameters and it is therefore unrealistic to expect them to make precise predictions for all cases.     

An Analytical Solution for Elastic and Elastic-Plastic Contact Models

In tribology often a closed form solution for calculation of contact stress and real contact area is required for the purposes of, for example, developing wear maps and temperature profiles at asperities. In assuming a Gaussian distribution of asperity heights it is not possible to obtain an analytical solution for the contact load and real contact area for many analytical models such as those developed by Greenwood and Williamson (elastic model), Chang, et al. (elastic-plastic model) and Horng (elliptic elastic-plastic model). In this paper, two exponential functions have been derived from a fitting procedure applied to the numerical results of the Gaussian height distribution thus offering an analytical expression for the above three models. It has been demonstrated that the two exponential functions (φ₂* and φ₄*) can give a fair approximation to the contact load and the real contact area in the separation of 0 to 4σ. In addition, variations in plasticity index (ψ) and effective asperity radius (γ) do not significantly affect the approximated accuracy. The results obtained by the newly derived exponential functions have been compared with the exponential function φ₁*; suggested by Greenwood and Williamson, 1966 and it has been shown that use of φ₁* invariably gives a larger error than using two exponential functions over two ranges of separation distances.     

Micro-contact analysis for the initial contact in nanoindentation tests

The force-depth behavior of initial contact between a Berkovich indenter and S45C steel specimens has been examined. The indenter is considered as a rigid sphere with a radius of 300 nm since the blunt tip is dominant under initial contact. The S45C steel specimens were prepared to have different surface characteristics. The specimen surface profile was decomposed by Fourier cosine series; then the statistical evaluation for force and area of micro-contact was proposed. The influence of surface roughness on the real contact area and thus the contact pressure arising in the indentation test can be investigated from the proposed analyses. The force-depth responses obtained by the proposed method revealed good agreement with the experimental results for the prepared specimens with their different surface characteristics. The evaluated results of the force fractions in the elastic, elastoplastic, and plastic deformation regions showed that the S45C steel specimens had fully plastic deformation under the initial contact load of 5 μN. The average values of real contact pressure evaluated by the current method rapidly reached the hardness value. Through the proposed method, the dominant radii of summits were evaluated and their relation to the indentation depth was demonstrated.     

新的粗糙表面弹塑性接触模型

提出一种新型的粗糙表面弹塑性微观接触模型.该模型的建立基于接触力学理论和接触微凸体由弹性变形向弹塑性变形及最终向完全塑性变形的转化皆是连续和光滑的假设.研究单个微凸体在载荷逐渐增加时的变形规律,并重点推出弹塑性变形区间的接触方程.在此基础上应用概率统计理论导出了粗糙表面的接触载荷、平均分离和实际接触面积之间的数学关系式.在不同的塑性指数和载荷条件下,该模型与GW弹性模型和CEB弹塑性模型就实际接触面积和法向距离的预测结果进行了对比.结果表明,在同样塑性指数和载荷条件下比GW模型预测的实际接触面积大但法向距离小,且两者的差距随塑性指数和载荷的增加而增大.因此该模型的预测结果更加符合人们的试验观察和直觉,能够更加科学和合理地描述两个粗糙表面的微观和宏观接触状态.     

Application of Fractal Contact Model in Dynamic Performance Analysis of Gas Face Seals

Fractal theory provides scale?independent asperity contact loads and assumes variable curvature radii in the contact analyses of rough surfaces, the current research for which mainly focuses on the mechanism study. The present study introduces the fractal theory into the dynamic research of gas face seals under face?contacting conditions. Structure?Function method is adopted to handle the surface profiles of typical carbon?graphite rings, proving the fractal con?tact model can be used in the field of gas face seals. Using a numerical model established for the dynamic analyses of a spiral groove gas face seal with a flexibly mounted stator, a comparison of dynamic performance between the Majumdar?Bhushan(MB) fractal model and the Chang?Etsion?Bogy(CEB) statistical model is performed. The result shows that the two approaches induce differences in terms of the occurrence and the level of face contact. Although the approach distinctions in film thickness and leakage rate can be tiny, the distinctions in contact mechanism and end face damage are obvious. An investigation of fractal parameters D and G shows that a proper D(nearly 1.5) and a small G are helpful in raising the proportion of elastic deformation to weaken the adhesive wear in the sealing dynamic performance. The proposed research provides a fractal approach to design gas face seals.     

An analytical model of the material removal rate between elastic and elastic-plastic deformation for a polishing process

This paper develops an analytical model for the material removal rate during specimen polishing. The model is based on the micro-contact elastic mechanics, micro-contact elastic-plastic mechanics and abrasive wear theory. The micro-contact elastic mechanics between the pad-specimen surfaces used the Greenwood and Williamson elastic model. The micro-contact elastic-plastic mechanics between specimen and particle, as well as the micro-contact elastic mechanics between particle and pad, are also analyzed. The cross-sectional area of the worn groove in the specimen is considered as trapezoidal area. A close-form solution of material removal rate from the specimen surface is the function of average diameter of slurry particles, pressure, the specimen/pad sliding velocity, Equivalent Young’s modulus, RMS roughness of the pad, and volume concentration of the slurry particle.     

油封密封性能的有限元分析

利用大型有限元分析软件ANSYS建立了油封的二维轴对称有限元模型,分析了油封的腰厚、密封圈唇口平面到弹簧槽中心平面的距离以及过盈量3种重要参数对最大接触压力及其分布情况的影响。结果表明,采用该模型计算得到的油封在静态条件下的变形情况以及Von M ises应力分布情况与实际情况基本一致。在其它条件不变的情况下,随着油封腰部厚度t的增加,最大接触压力有递增的趋势,且随着油封尺寸的增大,在增加相同大小的腰厚时,最大接触压力增大的幅度将逐渐趋于平缓;最大接触压力随R值的增大而逐渐减小,且R值的改变对于小尺寸油封最大接触压力的影响较大;增大唇部过盈量,最大接触压力也随之而呈递增趋势,同样小尺寸油封递增幅度要大于大尺寸油封。     

Contact of surface asperities in wear

Stresses have been examined under the elliptical Hertzian contact area, which appear during a real contact between two asperities in the process of sliding friction. The stresses are found according to the Mises-Hencky criterion and characterize the ability of the material to change its shape. Relationships have been found of such a maximum stress under the surface of the contact area depending on the geometric parameters of the contact area, on the friction coefficient and the maximum pressure in the centre of contact area. The processing of the calculation data was conducted according to a special program on a computer and yielded an approximate relationship to calculate the maximum reduced stress. The distribution of dangerous stresses under the contact surface has been shown. The most critical points may be both within the surface layer of the material and on the contact area itself.     

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.     

<Emphasis Type="Italic">In situ</Emphasis> investigation of the contact area in elastic–plastic spherical contact during loading–unloading

The real contact area between a sphere and a flat during loading, unloading, and cyclic loading–unloading in the elastic–plastic regime of deformations was investigated experimentally. A direct optical technique was used to observe in situ the evolution of the contact area. The experimental results obtained with copper and stainless steel spheres of different diameters that were pressed against a sapphire flat were compared with existing theoretical models, and whenever possible, with previous experimental works. These models are based on the assumption of either perfect slip (i.e., frictionless) or full stick contact condition. Good agreement was found between the experimental and theoretical results for the contact area and mean contact pressure. The existing models for the unloading process fail to accurately predict the residual radius of curvature of fully unloaded spheres, and the irreversibility of multiple loading unloading cycles at least for the several initial cycles. Some recommendations to improve the models are provided.     

旋转冲击作用下凿岩机水封密封性能分析*

为探讨液压凿岩机冲洗机构水封在高频冲击和旋转运动复合作用下的泄漏情况,在分析钎尾冲击速度随时间变化规律基础上,通过求解广义雷诺方程分析密封区的流体力学特性,建立旋转冲击复合作用下凿岩机水封密封区膜厚及泄漏量的计算模型。基于ABAQUS分析冲击周期内变速度下的水封接触应力变化规律,分析不同流体压力、冲击速度幅值和转速对密封性能的影响。结果表明:最大接触压力的变化和内外行程有关,外行程最大接触压力随冲击速度幅值的增大而增大,随转速的增大而减小,内行程则相反;同时无转速时的最大接触压力明显小于有转速时的最大接触压力,外行程的整体的最大接触压力大于同位置内行程的最大接触压力;冲击速度幅值越大,一个周期内的实时泄漏量和净泄漏量越大;不同转速下的实时泄漏量比较接近,转速越大,净泄漏量越小,表明在一定的范围内提高转速有利于提升水封密封性能;随液体压力增大最大接触压力变大,实时泄漏量变小,而净泄漏量先变小再变大,表明在中等压力下水封的密封性能更好。     

Effect of asperity interactions on rough surface elastic contact behavior: Hard film on soft substrate

An improved elastic micro-contact model of rough surfaces accounting for asperity interactions is proposed. The contact behavior of a single asperity system is composed of a stiffer hemi-spherical asperity deformation and bellowing softer substrate deformation, which is then extended to rough surface contact including asperity interactions. Using the solution of substrate deformation, normal positions of individual asperities are adjusted during quasi-static contact, from which surface interactive forces are obtained. Analytical simulations are performed using the proposed rough surface contact model, whose results are compared to Greenwood-Williamson-based models and with experimental measurements.     

Analysis of wheel and rail adhesion under wet condition by using elastic–plastic microcontact model

This paper presents a numerical model to investigate the adhesion characteristics of the wheel/rail contact with consideration of surface roughness under wet conditions. The elastohydrodynamic lubrication theory is used to obtain the load carried by water, and the statistical elastic–plastic microcontact model presented by Zhao–Maietta–Chang is applied to calculate the load carried by asperities contact. Meanwhile, the thermal influencing reduction factor is used to consider the inlet heating effects on the film thickness, and the change of water viscosity is also taken into consideration due to the flash temperature generated by the moving rough surfaces. Furthermore, the present work investigates the dependence of the wheel/rail adhesion coefficient on train speed, surface roughness amplitude, the initial temperature, the plasticity index and the maximum contact pressure under wet condition. Copyright © 2014 John Wiley & Sons, Ltd.     

Synergetic effects of wafer rigidity and retaining-ring parameters on contact stress uniformity in chemical mechanical planarization

Here we use two-dimensional models of fluid film lubrication and contact mechanics to calculate the contact stress and fluid (i.e., slurry) pressure distributions on the wafer?Cpad interface in chemical mechanical planarization (CMP). In particular, the effective rigidity of the wafer (determined by the wafer carrier structure), the retaining-ring width and its back pressure are taken to be the design parameters. The purpose is to study the synergetic effects of such parameters on the contact stress uniformity, which directly affects the spatial uniformity of the material removal rate on the wafer surface. Our numerical results indicate that, for a given wafer rigidity, one may choose the retaining-ring width and back pressure to minimize the contact stress non-uniformity (NU). Also, the resulting minimum NU decreases with the effective wafer rigidity, suggesting that it is beneficial to use a soft (e.g., floating-type) wafer carrier. Moreover, for a soft wafer carrier, it is demonstrated that using a multi-zone wafer-back pressure profile is even more effective in reducing NU.     

In lubro 3D measurement of oil film thickness at the interface between tool and workpiece in sheet drawing using a fluorescence microscope

In order to understand quantitatively the micro-contact and lubricant behavior at the interface between a tool and a workpiece in sheet drawing, a method for mapping the oil film thickness in lubro has been developed. This is based on the use of a fluorescence microscope. It is shown, firstly, that the in situ oil film thickness between the tool and the workpiece can be measured three dimensionally, and, secondly, that the in situ surface topography of the workpiece can be visualized clearly. From the 3D surface topography, the permeation of the trapped lubricant into the real contact area can be observed.     

Effects of the Lubricant Piezo-Viscous Properties on EHL Line and Point Contact Problems

This paper presents the application of the free-volume viscosity model in a Newtonian elastohydrodynamic line and point contact simulation using a more effective multigrid approach. According to recent experimental studies using high pressure viscometers, the free volume-based pressure–viscosity relationship closely represents the realistic piezo-viscous behavior for the high pressure typically encountered in elastohydrodynamic applications [1]. The effects of different pressure–viscosity relationships, including the exponential model, the Roelands model, and the free-volume model are investigated through an example with poly-alpha-olefin lubricant. It is found that the real pressure–viscosity behavior predicted by the free-volume model yields a higher viscosity at the low-pressure area, which results in a larger central film thickness. The fact that film thickness is formed mainly by the entraining action at the inlet area significantly weighs the importance of viscosity variation from different models in this area. The inlet area is a low-pressure area, and accordingly, the real viscosity of the lubricant predicted by Doolittle model undergoes a rapid increase in a convex function, being apparently larger than the Roelands one. Furthermore, the Doolittle model leads to higher pressure spike amplitude than that observed using the Roelands model. To solve the problem, a full multigrid approach has been used upon the assumptions of isothermal condition. Multigrid is more effective because it uses coarser grid levels to remove errors of different frequencies, which could be more quickly smoothed away than those on simply the fine grid alone. The developed coarse grid correction cycle proves to be an efficient tool to solve the EHL problem for a wide range of load conditions.