Contact mechanics of rough surfaces in tribology: multiple asperity contact

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Contact analysis of three-dimensional rough surfaces under frictionless and frictional contact

A methodology for surface and sub-surface stress calculation of nominally flat on flat rough surface contact has been developed. This methodology is applicable for both large area contact (Hertzian contact) and small area of asperity contact (point load contact) with and without surface friction. A total of nine rough surfaces are generated by the computer with specified standard deviation of surface heights, σ, of 0.3, 1.0 and 3.0 nm, and correlation length, β^*, of 0.1, 0.5 and 0.9 μm. Under the typical applied load at the magnetic head slider-disk interface, small numbers of contact points are obtained and the deformation is purely elastic. Since these contact points are scattered and isolated, asperity contact behaves like point load contact. As β^* becomes larger, more adjacent points will be in contact at a certain contact spot and this is especially true at small σ. All the cases of flat on flat rough surface contact yield maximum von Mises stress on and near the surface at both frictionless and frictional contacts; no local maximum occurs in the sub-surface. In general, the friction effect in the vicinity of contact point is to increase the stress magnitude, while outside this region it also alters the stress distribution. For a surface of small β^* and large σ at high load of 1000 times of the nominal pressure at the head-disk interface, the contact pressure reaches the hardness at a few contact points and plastic deformation takes place in the near surface.     

粗糙表面滑动摩擦接触模型研究的进展

对近年来国内外粗糙表面模型的进展进行了概述,根据粗糙表面模型类型的不同,分为粗糙表面和平面接触模型以及双粗糙表面接触模型,在各自模型中按照静载和滑动接触类型的研究进展进行表述,并提出了一些目前研究中遇到的热力耦合的问题以及将来双粗糙分形表面模型的发展.     

The contact behavior of elastic/plastic non-Gaussian rough surfaces

A three-dimensional contact analysis was conducted to investigate the contact behavior of elastic--perfectly plastic solids with non-Gaussian rough surfaces. The effect of skewness, kurtosis and hardness on contact statistics and the effect of skewness and kurtosis on subsurface stress are studied. Non-Gaussian rough surfaces are generated by the computer with skewness, Sk, of −0.3, 0.0 and 0.3, and kurtosis, K, of 2.0, 3.0 and 4.0. Contact pressures and subsurface stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and patch solutions. Variation of fractional elastic/plastic contact area, maximum contact pressure and interplanar separation as a function of applied load were studied at different values of skewness and kurtosis. Contact pressure profiles, von Mises stresses, tensile and shear stress contours as a function of friction coefficient were also calculated for surfaces with different skewness and kurtosis. In this study, it is observed that surfaces with Sk = 0.3 and K = 4 in the six surfaces considered have a minimum contact area and maximum interplanar separation, which may provide low friction and stiction. The critical material hardness is defined as the hardness at which severe level of plastic asperity deformation corresponding to the Greenwood and Williamson’s cut-off A _plastic/A _real = 0.02 occurs for a given surface and load condition. The critical material hardness of surfaces with Sk = 0.3 and K = 4 is higher than that of other surfaces considered.     

Fractal prediction model of thermal contact conductance of rough surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces,which has been widely studied since last few decades,and for predicting which many theoretical models have been established.However,the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity.In this paper,a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes:elastic,elastoplastic and fully plastic.Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model.The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area.The larger the fractal dimension,or the smaller the fractal roughness,the larger the thermal contact conductance is.The thermal contact conductance increases with decreasing the ratio of Young’s elastic modulus to the microhardness.The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface,which provide certain reference to the further study on the issue of heat transfer between contact surfaces.     

齿廓修形斜齿轮沿接触线的弹流润滑计算

应用多重网格法，在三条接触线上同时获得具有典型弹流润滑特征的压力分布和油膜形状，进而计算了接触线上的载荷分布：通过修形，改善了齿面的润滑状况。提高了齿轮的抗胶合能力。     

Multi-point contact of the high-speed vehicle-turnout system dynamics

The wheel-rail contact problems, such as the number, location and the track of contact patches, are very important for optimizing the spatial structure of the rails and lowering the vehicle-turnout system dynamics. However, the above problems are not well solved currently because of having the difficulties in how to determine the multi-contact, to preciously present the changeable profiles of the rails and to establish an accurate spatial turnout system dynamics model. Based on a high-speed vehicle-turnout coupled model in which the track is modeled as flexible with rails and sleepers represented by beams, the line tracing extreme point method is introduced to investigate the wheel-rail multiple contact conditions and the key sections of the blade rail, longer nose rail, shorter rail in the switch and nose rail area are discretized to represent the varying profiles of rails in the turnout. The dynamic interaction between the vehicle and turnout is simulated for cases of the vehicle divergently passing the turnout and the multi-point contact is obtained. The tracks of the contact patches on the top of the rails are presented and the wheel-rail impact forces are offered in comparison with the contact patches transference on the rails. The numerical simulation results indicate that the length of two-point contact occurrence of a worn wheel profile and rails is longer than that of the new wheel profile and rails; The two-point contact definitely occurs in the switch and crossing area. Generally, three-point contact doesn’t occur for the new rail profile, which is testified by the wheel-rails interpolation distance and the first order derivative function of the tracing line extreme points. The presented research is not only helpful to optimize the structure of the turnout, but also useful to lower the dynamics of the high speed vehicle-turnout system.     

两弹塑性接触粗糙表面的静密封流量

当峰高的概率密度为指数分布时,利用泰勒公式推导了弹性载荷的近似解析解,给出了塑性载荷的严格解析解,导出了静密封流量的经验表达式。通过密封表面的泄漏量与表高标准差的3次方成正比。在塑性接触状态,存在一个临界塑性指数,当塑性指数大于临界塑性指数时,总载荷与塑性指数、粗糙度参数皆无关,量纲一的塑性泄漏量与较软材料的硬度有关,与两接触粗糙表面的复合弹性模量无关。     

单粗糙峰的时变等温线接触弹流润滑分析

求得了带单粗糙峰时变等温线接触弹流润滑问题的完全数值解,分析了单粗糙峰对压力、膜厚的影响。结果表明,单粗糙峰造成接触区对应位置油膜压力剧烈变化而膜厚变薄。讨论了单粗糙峰半波长、速度和载荷参数分别变化时对压力和膜厚的影响,最后比较了时变解和准稳态解。     

基于接触电阻法的表面膜损伤研究

为了研究摩擦副中表面膜的形成和损伤状态,用接触电阻法对润滑条件下往复运动的缸套/活塞环摩擦副进行了试验研究,提出了可揭示表面膜状态的表征方法,并成功观测到了磨粒对表面膜的损伤及恢复过程。研究表明:变载条件下表面膜状态发生显著变化;表面膜的损伤和愈合是动态的竞争过程。接触电阻可反映表面膜的实时信息。     

A Generalized Differential Colorimetric Interferometry Method: Extension to the Film Thickness Measurement of Any Point Contact Geometry

Whereas industrial elastohydrodynamic (EHD) contacts are generally noncircular, most experimental observations are made on sphere-on-plane conjunctions. The circular case is indeed a specific elliptical case, and it was widely investigated. The differential colorimetric interferometry (DCI) technique was often used to perform precise film thickness measurements in circular EHD contacts. From a single picture of the dynamic contact, it enables mapping the film thickness of the full conjunction, and postprocessing can be applied afterwards. Moreover, it is possible to record sequences at relatively high-frequency sampling. However, until now, the method could not be directly applied to noncircular conjunctions. In the present article, a generalized DCI method is proposed and assessed by several static and EHD validation cases for elliptical and torus-on-plane contact geometries. This new method no longer necessitates particular requirements on the contact shape while retaining the advantages of the original DCI method. It allows precise film thickness measurements in realistic industrial EHD contacts and opens the way for new experimental observations.     

Elastic/plastic contact of surfaces considering ellipsoidal asperities of work-hardening multi-phase materials

The importance of the plasticity index for defining the degree of elastic and plastic deformation of surface asperities is described. Some experimental validation of the argument is provided and the method is extended to cover the case of ellipsoidal asperity contacts and the effect of work-hardening for a general asperity height probability distribution. It is also shown how the model may be applied to study the behaviour of multi-phase composites. The arguments are based on Hertzian contacts without tractions but may be used with reasonable confidence for contacts where the coefficient of friction is less than 0.1.     

非参数似然率独立分量分析算法的OFDM系统载波频偏盲估计

研究提出了一种利用非参数似然比(NLR)新算法获得OFDM系统频偏估计的新方法,给出基于NLR的ICA算法的OFDM系统数学模型,利用NLR算法分离各个子载波,然后利用本地载波与子载波的频差估计出OFDM的频偏(CFO),该算法获得的CFO可以包括信道的传输特性对CFO的影响.经典的ICA算法(如FAST-ICA)对源信号的统计特性具有依赖性,源信号统计特性的变化可能使算法的性能降低甚至无法得到希望的分离信号,非参数似然算法(NLR)的独立分量分析(ICA),不依赖于源信号的统计特性,而且能够对混合信号实行连续分离,因此是一个全盲的算法.仿真结果表明,将跟踪到的频偏在接收端进行补偿后,减小了子载波的串扰,降低系统解调后的误码率,提高了OFDM系统性能.     

Automatic detection of onset and offset of QRS complexes independent of isoelectric segments

Accurate location to onset and offset of QRS complex from ECG signal is help measuring other features and it is a important and challenge task to recognize these onsets and offsets from ECG signal without isoelectric segment. The algorithm, which is introduced in this paper, does not depend on isoelectric segment and can accurately detect these onsets and offsets. In the algorithm, for every sample within about a cardio cycle of locally normalized ECG signal, two fitting straight lines are obtained respectively, from two sets of samples before and after the sample. And then two gradients and a smaller included angle corresponding to the two fitted lines are calculated. Third, those samples whose two gradients satisfied a pre-set value are taken as candidates for the R peak, and the sample with the minimal included angle is regarded as the R peak in this cardiac cycle. Finally, respectively before and after the detected R peak, the algorithm researches the onset and the offset of the QRS complex according to the same decision strategy. All 32 sets of 12-lead ECG records from http://physionet.org/pn3/twadb/ are employed to evaluate the method. The experimental results show that compared with three traditional methods, the method can more accurately detect all onsets and offsets and has better robust on interference.     

点啮合分度凸轮机构的接触域分析——渐开线螺旋廓面包络蜗杆分度凸轮机构

介绍了媒介共轭点啮合的由来和具体实施方法,它是将点啮合问题转化为两个线啮合问题来解决,从而利用成熟的线啮合理论来研究点啮合。讨论了点啮合副中的核心问题之一的接触域大小问题。利用微分几何和啮合原理推导出该机构的点啮合的诱导曲率方程,给出了接触域大小的计算公式。并对渐开线螺旋面包络蜗杆分度凸轮机构的接触域面积进了实例分析计算。结果证实与圆柱面相比渐开线螺旋面作为分度盘轮齿廓面,其点啮合诱导曲率相对较小,接触面积大。因而轮齿廓面的承载能力高、耐磨性强。     

Microtribological problems of physics and mechanics in smooth surface contact

This paper reviews a group of problems studied by a new scientific branch in tribology, viz. nanotribology. New feasibilities of analysing adhesional interaction of contacting surfaces are underlined in view of ‘molecular roughness’ and experimental verification of the calculated relationships by tunnelling and atomic force microscopes.     

数控车床对刀和原点偏置的机理分析及应用

结合西门子SINUMERIK 802DT数控车床系统,对手动试切法的对刀和原点偏置的原理进行了分析。明确了对刀和原点偏置的概念,归纳了对刀过程中相关参数的关系,并对有关结论进行推导。介绍了绝对对刀法和相对对刀法的概念及应用中的注意事项。     

基于弹流润滑的滚子轴承参数研究

基于弹流润滑理论研究滚子轴承结构参数对其润滑特性的影响。结合弹性接触变形方程以及流体动力学润滑方程,建立适合于滚子轴承的弹流润滑模型,研究在不同椭圆率、载荷、卷吸速度以及黏度等因素作用下滚子轴承的摩擦学性能变化规律。结果表明：椭圆率、载荷、卷吸速度以及黏度会不同程度地影响压力峰值及二次压力峰等参数;随着椭圆率的增大,油膜厚度以及压力显著增大;随着载荷的增大,总体压力、压力峰值、二次压力峰及其尖锐度明显增大,但最小油膜厚度略有下降;黏度与最小油膜厚度以及压力存在着明显正相关关系;卷吸速度与油膜厚度存在着微弱正相关关系,与油膜压力存在着微弱负相关关系。因此,一定程度上增大椭圆率并减小载荷,有利于提高润滑性能。     

Numerical and finite element contact temperature analysis of real composite-steel surfaces in sliding contact

Numerical techniques have been developed and used to evaluate the contact temperature distribution between real composite-steel surfaces in sliding contact. To characterise the contact temperature problem of composite materials new definitions for composite Peclet numbers have been introduced. In case of `slow sliding' problems a stationary numerical technique was applied, whereas for `intermediate and fast sliding' problems transient finite element (FE) solutions were preferred. At first sliding contacts of a single steel asperity over polyetheretherketone (PEEK) or carbon fibre (CF)/PEEK composite surfaces were modelled in order to study the contact temperature development on a microscopic level. It was followed by contact temperature results for real composite-steel sliding surfaces; the latter helped to provide information about the actual stress conditions, which are necessary to model the wear process of this pair of materials in future works.     

外摆线型单螺杆泵螺杆-衬套副的运动特性分析

通过分析外摆线型单螺杆泵螺杆-衬套副的相对运动,发现螺杆-衬套副的固定接触点出现在衬套骨线上,衬套可采用金属材料,螺杆可在金属基体表面黏接橡胶外套;用瞬心法推导出齿凸接触点和齿凹接触点处相对滑动速度的计算公式,并用MATLAB生成速度曲线,用SolidWorks建立螺杆泵实体模型,用SolidWorks Motion进行运动仿真,对比速度仿真值与速度公式曲线可知,拟合度很高,最大偏差率仅为-0.101%;将速度曲线与啮合状态进行对应,发现齿凹接触点处相对滑动速度的最大值发生在螺杆齿凸中点与衬套齿凹中点相接触处,齿凸接触点处相对滑动速度最大值发生在螺杆齿凸中点与衬套齿凸中点相接触处。