Compliance of rough cylinders in compression

Compression of a rough turned cylinder between two hard, smooth, flat plates has been analysed with the aid of a mathematical model based on statistical analysis. It is assumed that the asperity peak heights follow Gaussian or normal and beta distribution functions and that the loaded asperities comply as though they are completely isolated from the neighbouring ones. Equations have been developed for the loadcompliance relation of the real surface using a simplified relation of the form W₀ = K₁ δⁿ for the load-compliance of a single asperity. Parameters K₁ and n have considerable influence on the load-compliance curve and they depend on the material, tip angle of the asperity, standard deviation of the asperity peak height distribution and the density of the asperities.     

Temperature Analysis in Lubricated Simple Sliding Rough Contacts

A temperature analysis of dry sliding fully plastic contact is extended to calculate the asperity temperatures between a sliding lubricated rigid smooth plane and a stationary elastic rough surface. First, surface roughness is generated numerically to have a Gaussian height distribution and a bilinear autocorrelation function. Lai and Cheng's elastic rough contact computer program is then used to determine the asperity contact loads and geometries of real contact areas. Assuming different frictional coefficients for shearing the lubricant film at the noncontact areas, shearing the surface film at the asperity contacts and shearing the oxide film as the asperity temperature exceeds a critical temperature, asperity temperature distributions can be calculated. Eight cases in Durkee and Cheng's scuffing tests of lubricated simple sliding rough contacts are simulated by using 20 computer-generated rough surfaces. The results show that scuffing is correlated to high-temperature asperities which are above the material-softening temperature.     

考虑微凸体水平距离分布及相互作用的结合面法向接触刚度建模

在涉及微凸体侧接触的粗糙表面接触建模过程中,通常需要假定微凸体之间侧接触的角度分布规律。提出一种考虑微凸体水平距离分布及相互作用的结合面法向接触刚度建模方法,该方法不再需要假定角度分布规律,而是基于首次发现的单个粗糙表面微凸体水平距离正态分布规律,根据统计学理论进行考虑微凸体相互作用的结合面法向接触刚度建模。对模型进行数字仿真发现：结合面法向接触刚度与接触载荷均随着微凸体水平距离标准差的减小而增大,并且考虑微凸体相互作用会使得结合面的法向接触刚度减小。结合面法向接触刚度随弹性模量的增大而减小,随材料硬度的增大而增大。通过有限元仿真结果与模态试验结果对比可知,基于模型的有限元仿真前三阶固有频率与试验所得结果基本吻合,并且误差相对GZQ模型更小。旨在通过研究单个粗糙表面微凸体水平距离分布,突破侧接触建模时接触角度分布函数仍需假设的理论瓶颈,为更加准确地预测结合面接触特性奠定基础。     

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.     

Transient Heat Conduction Between Rough Sliding Surfaces

When two rough bodies slide against each other, asperities on the opposing surfaces interact with each other, defining a transient contact and heat conduction problem. We represent each body by a Greenwood and Williamson asperity model with a Gaussian height distribution of identical spherical asperities. The heat transfer during a typical asperity interaction is analyzed, and the results are combined with the height distributions to determine the mean heat flux and the mean normal contact pressure as functions of the separation between reference planes in the two surfaces. We find that the effective thermal conductance is an approximately linear function of nominal contact pressure, but it also increases with the square root of the sliding speed and decreases with the 3/4 power of the combined RMS roughness. The results can be used to define an effective thermal contact resistance and division of frictional heat in macroscale (e.g., finite element) models of engineering components, requiring as input only the measured roughness and material properties.     

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.     

Predicting the Material Removal in Polishing: The Applicability of Two Types of Statistical Models

This article develops two statistical rough surface models to investigate the material removal rate in surface polishing. Model I implies that the contact between two surfaces is equivalent to that between a composite surface and a plane; but Model II is without the equivalent surface concept. The prediction differences of the two models were first investigated with the aid of contact mechanics. The analysis shows that the relative error of the predictions by the two models could be minimized by considering the interactions between asperities, and that this error increases with the separation of the mean planes, but decreases with the asperity density, asperity radius and standard deviation of the asperity height. By extending the models to study the material removal rate in polishing, it was found that asperity interaction is an important factor in a statistical modelling of polishing, and that with a given separation of the reference planes of the pad and workpiece surfaces, the material removal rate increases with the volume concentration of abrasive particles and varies with the pad roughness. The study also showed that the microstructure of a polishing pad has a significant effect on the material removal rate of a polishing.     

Abrasive wear between rough surfaces in deep drawing

In tribology, many surface contact models are based on the assumption that surfaces are composed of a collection of small asperities of which the tips are equally sized and spherically shaped and have some kind of statistical height distribution. This approach was used in 1966 by Greenwood and Williamson and was successfully followed by many researchers during the following decades. The statistical representation of surface topography enables calculation of contact forces and asperity deformations with reasonable accuracy using well established equations. Although this approach has proven to be suitable for static contact situations, alternative representations of the surface topography are required when modelling abrasive wear. In the current work an elastoplastic contact model is developed in which a representation of the surface topography is obtained by best fit approximations of the micro-contacts, obtained from real, measured surface height data. In this deterministic surface representation, the tips of the contacting asperities are assumed to have an ellipsoidal shape. Given the material parameters and contact conditions, the load and deformation of a single asperity can be computed. Subsequently, the wear induced by each individual asperity is obtained by inserting its size and shape and the conditions into a “single asperity micro-abrasion model”. By summing the contributions of all individual asperities, the total abrasive wear volume is obtained. The results of the developed abrasive wear model are compared with results obtained using a statistical approach.     

接触热导率数值预测研究

假设粗糙表面轮廓高度服从高斯分布,并将两粗糙表面间的接触等效为粗糙表面与光滑刚性表面的接触。由均方根粗糙度和平均凸峰坡度得出接触点的平均半径和单位面积内的接触点个数,分别建立了用圆柱体和圆锥台来表现接触粗糙峰的两种有限元模型,对接触热导率进行了数值预测。通过对比发现,用圆柱体来表现粗糙峰的模型计算出的结果与试验吻合较好,且其误差随界面载荷的增大而减小。     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

尺度相关的分形结合面法向接触刚度模型

基于分形理论,利用双变量Weierstrass-Mandelbrot函数模拟三维分形结合面,建立尺度相关的三维分形结合面法向接触刚度模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定结合面上各等级微凸体的面积分布密度函数,推导出法向接触刚度和法向接触载荷的解析表达式。计算结果表明：当结合面上的微凸体只能发生弹性变形,即自身等级小于弹性临界等级的微凸体,该部分微凸体引起的法向接触刚度和对应法向载荷关系呈非线性。当微凸体的等级大于弹性临界等级,在结合面接触过程中,微凸体弹性变形引起的法向接触刚度与对应的法向载荷关系为线性,非弹性变形引起的法向接触刚度与法向载荷关系为非线性。微凸体的等级范围对结合面的刚度影响较大,在相同的法向载荷作用下,高等级微凸体的结合面产生较高的法向接触刚度,即结合面越平整,结合面的法向刚度越高。     

Thermomechanical aspects of mixed friction in concentrated contacts

Important aspects of partial elastohydrodynamic lubrication are discussed. For heavily loaded counterformed machine parts such as cams and followers, gear teeth, and ball- and roller-bearing elements working in the mixed friction regime, thermomechanical effects on the micro scale have been investigated. The temperature distribution resulting from friction has been determined, assuming that an axially symmetrical source of heat occurs on the peak of the contacting asperity.The thermal deformations and stresses in interacting asperities are obtained with the finite element method. A statistical analysis of the thermomechanical quantities has been carried out. Conclusions about the temperatures and the thermal stresses in contacting asperities have been formulated. A thermoelastic coupling of the interacting rough surfaces has been proposed as a mechanism of the scuffing mode of failure in concentrated contacts.     

Surface density of asperities and real distribution of asperity heights on rubbed surfaces

Methods for obtaining the surface density of asperities and the real distribution of asperity heights, which differs from the distribution appearing on the surface profile curve, are considered for isotropic and anisotropic surfaces. For isotropic surfaces the asperities are assumed to be spherical at least near their peaks, and the surface density of asperities and the real distribution of asperity heights are obtained from the number of asperity peaks within a defined traverse length of the profile curve. For anisotropic surfaces the asperities are assumed to be ellipsoidal at least near their peaks. A method is derived by which the ellipsoidal asperities are replaced by equivalent spherical asperities. Comparison of theoretical and experimental results using Pyrex glass specimens showed that for worn surfaces the experimental and theoretical results agreed.     

Elastohydrodynamic Analysis of a Rotary Lip Seal Using Flow Factors

An elastohydrodynamic analysis of a rotary lip seal is performed numerically, incorporating both the fluid mechanics of the lubricating film and the elastic deformation of the lip. Asperities on the lip surface dominate the behavior of the flow field in the lubricating film and are taken into account through the use of flow factors. Because previous analyses treated those asperities deterministically, they required very large computation times. The present approach is much less computationally intensive because the asperities are treated statistically. Because cavitation and asperity orientation play important roles, these are taken into account in the computation of the flow factors. An asperity distortion analysis is introduced to model the complex variations in the asperity distribution on the surface of the lip. Results of the analysis show how the operating parameters of the seal and the characteristics of the asperities affect such seal characteristics as the thickness of the lubricating film, reverse pumping rate, power dissipation, and liftoff speed.     

Analyzing Elastic-Plastic Real Rough Surface Contact in Running-in

A numerical method is presented for evaluating the elastic-elastic contact of real rough surface contacts during running-in. For the surface contact, an elastic-plastic model based on the variational method is applied to analyze the pressure distribution and contact area of worn surfaces during running-in. In conjunction with the classical statistic model of Greenwood and Williamson, the numerical result showed that the plasticity index Ψ was decreased to one in the elastic range as running-in proceeded. In comparison with the Hertzian solution, the influence of the asperities is very significant on the pressure distribution, thereafter causing a higher peak value of contact pressure. For the subsurface, the interior stress from the von Mises criterion was calculated to evaluate the subsurface stress field subject to both normal and tangential forces. In the calculated of the interior stress, the total stress is decomposed into a fluctuating component and a smooth component. The fluctuating part is solved by using FFT from the concept of the convolution theorem while the smooth part is obtained directly by analytical solution. Calculations of contact area and subsurface stress on experimentally produced surfaces whose topography has been determined using an atomic force microscope and friction coefficient front sliding have been carried out. The results showed that asperities and friction coefficient gave rise to stress increase in the near-surface stress field and produced a high stress zone towards the surface. As a result, transverse asperity cracking was produced. The calculations and supporting experimental evidence clearly confirmed that the reduction of peak pressure during running-in decreased the plastic deformation of contact.     

Surface topography and properties of frictional contacts

The influence of surface topography on contacting solids is considered. The rough surface model is suggested and is used for the calculation of some tribological contact characteristics. A rough surface is modelled by a set of asperities of regular shape (wedge, cone, cylindrical, spherical segment), of differing height. A simple height distribution function and asperity shape function are used. These functions may be integrated analytically in further calculations.The surface model is used for calculation of one of the main contact parameters - real contact pressure (or real contact area) and other principal contact parameters, such as deformation, number of contact spots, average spot area, average distance between contact spots and intercontact gap.It is shown how the above parameters may be used for the calculation of such operational contact characteristics as friction coefficient, wear rate and electrical and thermal resistance.     

Effects of distribution of surface slopes and flow pressures of contact asperities on contact between solid surfaces

An analysis of the mechanism of contact between two solids was carried out considering the distribution of the surface slopes of conical asperities and the variation of the flow pressure of each contact asperity due to work-hardening and the work-hardened layer of the softer surface. From the analysis, where the distributions of the surface heights and the surface slopes are Gaussian the number of contact points decreases and their mean radius increases with increasing ranges of the distribution of the surface slopes for a given value of the mean surface slope. The number of contact points, the total real area, the separation and the radius of the contact points are influenced by the variation of the flow pressure of each contact asperity due to work-hardening of the contact asperities or the work-hardened layer of the softer surface.The validity of the theory was checked by comparing the theoretical and experimental results of the number, the separation and the distribution of the radii of contact points.     

Elastic–plastic adhesive contact of rough surfaces based on plastic asperity concept

The paper describes an analysis of adhesive contact between rough surfaces with small-scale surface asperities using an elastic–plastic model of contact deformation based on fictitious plastic asperity concept developed by Abdo and Farhang [Int. J. Non-Linear Mech. 40 (2005) 495]. The model considers simultaneous occurrence of elastic and plastic behaviours for an asperity. The well-established elastic adhesion index and plasticity index are used to consider the different contact conditions that arise as a result of varying load and material parameters. The load-separation behaviour for different combinations of these parameters is obtained. Comparison with previous elastic–plastic model that was based on elastic-then-plastic assumption is made showing significant differences.