Mechanisms of elastic contact and friction between rough surfaces

The mechanisms of elastic contact and friction between two rough surfaces were analysed, assuming that the surface asperities were spherical, at least near their summits, and that they contacted elastically. It was found that the real contact area and the number of contact spots are approximately proportional to the load, whereas the mean area of contact spots and the mean pressure at the contact areas are almost independent of load. The frictional force F is almost equal to sA_r, where s is the shearing strength at the contact area and A_r is the real contact area. The experimental results using Pyrex glass specimens agreed within experimental limits with the theoretical results.     

Prediction of contact parameters from the topographies of contacting surfaces

An image analysing technique has been used to examine the distribution of sizes of micro-contacts produced by impressing hard, rough surfaces into soft, optically flat surfaces. Comparisons with a statistical theory of contact indicated the correct values of mean surface slope required for the accurate prediction of the microscopic contact configuration.     

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.     

三维真实粗糙表面弹性接触的全域数值解

本文提出了三维真实粗糙表面弹性接触问题的全域数值求解方法。这种方法采用网格规则划分和局部柔度矩阵存储解决了计算机存储问题;采用求解域收缩和逐次低松弛迭代解决了接触方程求解问题。运用这种方法可以获得真实粗糙表面弹性接触时全接触域内的压力分布与总载荷、接触图象及其实接触面积、接触变形与接触刚度等参数。计算结果与实测结果符合得较好。     

Tribological Behavior of Ti<Subscript>3</Subscript>SiC<Subscript>2</Subscript> Sliding Against Ni-based Alloys at Elevated Temperatures

Understanding the mechanism of “rubbing” noise and low-amplitude friction exited vibration generation in steady sliding can be helped by models describing the contact interactions. In the current article, we consider a simple microscopic contact model for surfaces in sliding, which is based on the adhesion theory of friction. In the proposed model, we consider that the formation and shearing of a junction contributes to a small change in the real contact area. The model incorporates random size and random spacing between junctions. We investigate the dependence of the instantaneous real contact area on the average size and number of junctions. We find that from the viewpoint of vibration reduction, it is advantageous if the real contact area needed to support the given load is obtained as a sum of many small-sized micro-contacts, instead of few large-sized micro-contacts. The above result is in agreement with experimentally observed reduction of vibrations of a hard-disk slider after texturing.     

The elastic contact of a rough surface

The elastic contact of an isotropically rough surface with a plane is treated by approximating the summits of a random process model by paraboloids with the same principal curvatures and applying the classical Hertzian solution for their deformation. The errors in this approximation are computed in terms of the separation and of a bandwidth parameter α. Load and real contact area are derived as functions of separation. For large separation the fractional area of real contact is found to be half the bearing area fraction and the separation may be eliminated to give direct porportionality between load and area. For all separations the load is approximately proportional to the contact area. The constant of proportionality depends only on the Hertzian elastic modulus and the profile absolute mean slope. Experimental measurements of the latter and of α for a variety of surfaces show little variation in either, and the measured values of α are within the range of applicability of the model. The theory is critically compared with existing theories.     

Surface separation and contact resistance considering sinusoidal elastic–plastic multi-scale rough surface contact

The current work considers the multi-scale nature of surface roughness in a new model that predicts the real area of contact and surface separation as functions of load. This work is based upon a previous rough surface multi-scale contact model which used stacked elastic–plastic spheres to model the multiple scales of roughness. Instead, this work uses stacked 3D sinusoids to represent the asperities in contact at each scale of the surface. By summing the distance between the two surfaces at all scales, a model of surface separation as a function of dimensionless load is obtained. Since the model makes predictions for the real area of contact, it is also able to make predictions for thermal and electrical contact resistance. In accordance with concerns in previous works that the iterative calculation of the real contact area in multi-scale methods does not converge, this work not only tests but also gives conditions required for convergence in these techniques. The results are also compared to other existing rough surface contact models.     

Contact properties of a wet clutch friction material

Wet clutches are required to transmit torque and also prevent motion in automatic transmissions. Their performance is critically dependent on a friction material which comprises one of the contacting surfaces. Friction materials are usually a composite of fibres, naturally occurring minerals and particles of silicon and graphite, which are all bonded together with a resin. The material formed has very rough surfaces with much steeper slopes than normally-finished steel surfaces. When the friction material is loaded against a relatively flat counterface the real area of contact is only a small percentage of the nominal area and consists of many small, independent “contact units”. It is important to know the conditions present in the contact units (spatial dimensions and pressure) in order to understand and model wet clutch lubrication.In this study, the contact units formed between a paper based friction material and a glass counterface have been investigated under different pressures and during rubbing. A contact visualisation technique is used to directly view and capture images of the contact. The real area of contact and the number of individual units is subsequently determined by image analysis. It is found that the real area of contact increases approximately linearly with applied load, and increases rapidly with rubbing, due to wear. As the load is increased, the number of individual contact units increases up to a critical pressure, suggesting more parts of the material support the load. Above the critical pressure the contact units may be deforming elastically and/or plastically to form larger units. After rubbing, large contact units are formed by flat areas on the tops of the contacting fibres, which are formed during wear. The topography of individual fibres is studied before and after the wearing process using atomic force microscopy, and the results support the truncating wear mechanism.     

不同滑动速度下干接触体瞬态温度场计算

工程实际中,由于摩擦力的存在,接触副的运动将导致接触区内产生大量的摩擦热,使接触副温度升高;由此产生的瞬时高温会使接触副更易发生弹塑性变形、引起表层下裂纹的萌生及扩展,甚至使接触副表面发生化学变化。建立了不同滑动速度下干接触体的滑动接触模型,利用快速傅立叶变换,通过求解拉普拉斯热传导方程,获得光滑及粗糙表面接触副的瞬时温升以及接触体内部各离散点的温度分布,即半无限体干接触的温度场。结果表明,相同载荷及摩擦因数条件下,相对滑动速度对接触体的温升及其温度分布有重要影响;粗糙峰表面接触处的瞬时温升远高于光滑表面接触处的瞬时温升。     

微观随机粗糙表面接触有限元模型的构建与接触分析

基于相关文献提出粗糙表面模拟方法,通过软件工具在ANSYS中建立微观粗糙表面接触有限元模型,利用该模型分析载荷对弹塑性变形和接触面积的影响。结果表明:随着正压力的增大,粗糙表面上不断地有微凸峰与平面发生弹性接触变形,接触斑点(或接触斑点群)的数目逐渐增加,斑点中心区域的弹性变形很快达到最大,微凸峰负荷变形的同时也使斑点四周区域受到挤压;初始接触时,轮廓高度较大的微凸峰率先发生弹性变形,随着压力的增大,金属材料所受应力达到屈服极限同时粗糙表面的弹性变形和塑性变形的集中区域不断增加,真实接触面积不断增大;接触区数目的增多和接触区面积的增加都可以导致接触面上真实接触面积增加;随着压力的增大,真实接触面积的增大并不是由于接触区数目的增多,而是微观接触区面积的增大。     

A multiscale analysis of elastic contacts and percolation threshold for numerically generated and real rough surfaces

In this paper, we present numerical investigation of the contact between an elastic solid and a randomly rough surface. In agreement with recent results, we find that the contact area vs load relation depends on the statistical parameters only through the root mean square slope of the heights distribution. Such result extends to contact pressure regimes where the area/load relation is non-linear.Moreover, we show that fractal self-affine surfaces give a good representation of real surfaces from both topographical and contact mechanics points of view.Finally, we investigate how the network of non-contact areas evolves as the real contact area is increased, finding that the percolation threshold is smaller than the one predicted by Bruggeman's theory.     

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.     

混合润滑下粗糙表面的接触刚度研究*

针对润滑状态下结合面的接触刚度问题,建立一种混合润滑状态下粗糙表面接触刚度等效薄层模型,将接触界面的总刚度等效为固体接触刚度和润滑剂接触刚度之和,研究不同实际接触面积下的表面形貌和润滑剂类型对法向接触刚度的影响,并讨论固体刚度和润滑剂刚度占总法向刚度的比例。结果表明：粗糙界面的法向接触刚度随法向载荷的增加而增加,且混合润滑状态下的接触刚度大于干接触条件下的接触刚度;在初始接触时,法向接触刚度敏感地依赖于润滑性能;随着实际接触面积的增大,表面形貌对接触刚度的影响变得更加明显。     

基于分形几何的表面微观形貌模拟及粘着弹性接触计算研究

基于Ausloos和Berman提出的推广的W-M函数对具有分形特征的粗糙表面进行仿真模拟,分析了函数中与尺度无关的特征参数对表面微观形貌的物理意义。同时,基于Yan和Maugis的理论研究,用模拟的分形表面建立了考虑表面效应的弹性接触模型,通过数值方法对整个过程进行迭代求解,得到了两接触面在不同的接触条件下各个接触斑点上的载荷分布和真实接触面积以及接触斑点的数量和尺寸。由于真实接触面积的尺寸敏感地反应表面微观几何形貌的变化,因此该方法为研究粘着机制和减小微尺度粘着效应提供了思路。     

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.     

The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

Three-dimensional contact model for numerically analyzing pressure distribution in wear

Although FEM is adequate in solving most elastic and rough surface contact problems with acceptable accuracy, its requirement for a large number of elements jeopardizes its effective use in analyzing real surface contacts, the contact stresses and the surface profile over a finite area between two rough contact surfaces. To overcome this problem, a technique, for constructing 3D surface in a computer by modifying the available 2D finite impulse response (FIR) digital filter methods and using the fast Fourier transform (FFT) procedure, is proposed, by referring to SEM morphology and experimental results. The technique, incorporating the variatonal approach in minimizing the stored contact energy, eliminates the additional iteration needed in determining contact area. It can be used to predict: (i) the contact pressure distribution and contact statistics of 3D real rough surfaces, (ii) the real contact stresses between a rigid flat and various coated specimens, (iii) the contact stress distribution profile, (iv) the role of friction and stress distribution in wear process. This revised version was published online in August 2006 with corrections to the Cover Date.     

Static contact under load between nominally flat surfaces in which deformation is purely elastic

In considering the contact between two rough surfaces, an asperity-based model has been obtained by applying the most general Hertzian equations for elastic deformation to the random surface model of Longuet-Higgins. For a given separation, general formulae for the expectations and variances of the load and real contact area and for the mean number of contacts are given, whilst for the variance of the number of contacts an upper bound has been derived. The formulae, involving analytically intractable integrals, have been evaluated in a special case by Monte Carlo techniques.     

A finite element-based model of normal contact between rough surfaces

Engineering surfaces can be characterized as more or less randomly rough. Contact between engineering surfaces is thus discontinuous and the real area of contact is a small fraction of the nominal contact area. The stiffness of a rough surface layer thus influences the contact state as well as the behavior of the surrounding system. A contact model that takes the properties of engineering surfaces into account has been developed and implemented using finite element software. The results obtained with the model have been verified by comparison with results from an independent numerical method. The results show that the height distribution of the topography has a significant influence on the contact stiffness but that the curvature of the roughness is of minor importance. The contact model that was developed for determining the apparent contact area and the distribution of the mean contact pressure could thus be based on a limited set of height parameters that describe the surface topography. By operating on the calculated apparent pressure distribution with a transformation function that is based on both height and curvature parameters, the real contact area can be estimated when the apparent contact state is known. The model presented is also valid for cases with local plastic flow in the bulk material.     

Normal contact between rough surfaces by the Discrete Element Method

This paper presents the study of nonadhesive, frictionless contact between elastic solids realized by the Discrete Element Method. This numerical method dedicated to multi-contact problems is applied to the field of tribology by studying the normal contact between a rigid rough surface and an elastic body modeled by spheres. A specific interparticle stiffnesses derived from homogenization techniques is implemented. From numerical tests carried out on spheres packings, we observe that the desired main macroscopic elastic constants are correctly modeled. Concerning the study of normal contact between rough surfaces, the obtained results are in accordance to existing theoretical models and numerical results from the literature, thereby demonstrating the potential of the Discrete Element Method to study the normal contact between contacting elastic bodies with rough surfaces. In particular, we recover the linear dependence of the real contact area with the normal load. In addition, we show that decreasing the surface roughness increases the average contact pressure.