Analyses of wear rate due to micro-asperities and transferred particles on hard asperities

Assuming that micro-asperities and transferred particles on semicylindrical harder asperities with spherical ends ploughed a softer surface and that transferred particles at the front of harder asperities supported normal load, the effects on the wear rate of the parameters of surface topography, such as the mean height of micro-asperities, the radii of curvature at the tips of semicylindrical asperities and the length of an asperity, were analysed. The theoretical trends agreed well with the experimental wear rate trends for the polymers rubbed on harder surfaces with various roughnesses and those for various metals rubbed on the virgin surfaces of abrasive papers. The theoretical results showed that the wear rate decreased with a decrease in mean height of the micro-asperities and with increases in the radii of curvature at the tips of semicylindrical asperities and in the lengths of asperities. Furthermore, it was found, under the condition of abrasive wear, that the decrease in wear rate resulted from wear debris adhering to the front faces of the abrasive grains.     

Development of a wear equation for polymer-metal sliding in terms of the fatigue and topography of the sliding surfaces

A wear equation has been derived using the concept of fatigue failure due to asperity interactions in the contact region between sliding bodies. One of the three principal stresses that arise in the contact zone under the effect of a normal as well as a tangential load is of tensile nature. It is this principal stress that has been considered to be responsible for the initiation and propagation of fatigue cracks. It is assumed that the deformation in the contact zone is of elastic nature and that both the contacting surfaces are covered with asperities that have spherical tips. The wear equation involves the asperity height distribution φ(z). The particular distribution for a sliding situation is determined from experimental studies of the topography of sliding surfaces. The wear equation indicates that the wear rate depends upon the fatigue properties of the weaker material, normal load, sliding speed, coefficient of friction, moduli of elasticity of the contacting materials, asperity density, asperity radius of curvature and the distribution and standard deviation of asperity heights. The variation of wear with these parameters as indicated by the wear equation is in agreement with the experimental studies already reported in the literature.     

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.     

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.     

Friction characteristics of nanoscale sliding contacts between multi-asperity tips and textured surfaces

Nanoscale sliding contacts of smooth surfaces or between a single asperity and a smooth surface have been widely investigated by molecular dynamics simulations, while there are few studies on the sliding contacts between two rough surfaces. Actually, the friction of two rough surfaces considering interactions between more asperities should be more realistic. By using multiscale method, friction characteristics of two dimensional nanoscale sliding contacts between rigid multi-asperity tips and elastic textured surfaces are investigated. Four nanoscale textured surfaces with different texture shapes are designed, and six multi-asperity tips composed of cylindrical asperities with different radii are used to slide on the textured surfaces. Friction forces are compared for different tips, and effects of the asperity radii on the friction characteristics are investigated. Average friction forces for all the cases are listed and compared, and effects of texture shapes of the textured surfaces are discussed. The results show that textured surface II has a better structure to reduce friction forces. The multi-asperity tips composed of asperities with R=20r0 （r0=0.227 7 nm） or R=30r0 get higher friction forces compared with other cases, and more atoms of the textured surfaces are taken away by these two tips, which are harmful to reduce friction or wear. For the case of R=10ro, friction forces are also high due to large contact areas, but the sliding processes are stable and few atoms are taken away by the tip. The proposed research considers interactions between more asperities to make the model approach to the real sliding contact problems. The results will help to vary or even control friction characteristics by textured surfaces, or provide references to the design of textured surfaces.     

Evaluating the role of particle distribution and shape in two-body abrasion by statistical simulation

Previous work suggests that particle shape—specifically, its variation with particle size—is unlikely to be the dominant cause of the particle size effect (PSE) encountered in abrasion. In theory, the statistically similar nature of particle geometry implies that wear rate in two-body abrasion should be independent of particle size when all other conditions are unchanged and boundary effects are negligible. In practice, however, the severity of wear can be influenced substantially by the cumulative effect of relatively small variations of each governing factor. This paper deals with numerous issues related to the shape of abrasive particles and surfaces, with the view of understanding how shape contributes to wear and the manifestation of the PSE. It has been discovered, for example, that among the various solids of revolution used in the past to model the asperities of particles, the most representative possesses a power-law generatrix. Particle shape alone, however, constitutes a modest part in determining the properties of abrasive tools, such as grinding wheels and abrasive coated paper. Consequently, the density and distribution of the particles on the surface must also be given due consideration. To this end a statistical simulation of two-body abrasion has been developed. The effects of varying asperity shape and distribution on wear rate are clearly demonstrated and compared to results obtained from two-body experiments.     

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.     

Fatigue wear: A contribution to the wear phenomena of ion-plated thin metallic films

A wear model based on the fatigue failure of asperities on ion-plated surfaces is presented. It is suitable for ion-plated hard substrates sliding against hard counterfaces where asperity penetrations do not occur. The constants specific to the analysis are evaluated. A wear equation which is dependent on the mechanical properties of the system, the surface topography and the operating conditions is obtained. The wear rates are expressed as functions of the normal load, the sliding speed, the track width, the standard deviation of the surface asperities, the mean radius of the asperities, the stiffness of the asperities and the static yield strength of the multilayered material.     

Computational micro- and macroscopic models of contact and friction: formulation, approach and applications

This paper is dedicated to new asperity-based constitutive models of contact interfaces. These models have been obtained through a combination of finite element analysis of surface asperities and statistical homogenization techniques, to predict macroscopic, phenomenological behavior of the interface. This new approach has generalized the existing asperity-based models of contact and friction by considering realistic, complex shapes and mechanical properties of surface asperities, as opposed to previous simplified analytical solutions. This has been achieved by application, at the stage of asperity modeling, of the finite element method, which takes into account arbitrary shapes of asperities, non-linear material properties, molecular-range adhesion forces, and sliding resistance on the contact surface. The h–p adaptive mesh refinement techniques, adaptive timestepping and other adaptive methods are used to assure high accuracy of the solution. The result of this development is a new family of constitutive interface models, consistent with surface micromechanics and applicable to studies of static and dynamic friction phenomena. They are also extendible to calculation of thermal or electrical resistances, wear modeling, and other applications. This paper presents the theoretical formulation, numerical methodology and sample models of contact, adhesion and friction obtained through these homogenization techniques.     

The role of prow-deposits in the wear of abrasive grits by superficial fracture

Prevailing concepts of wear of abrasive grits assume a mechanism of slow attritious wear land formation or one of cutting edge destruction by chipping. A second attritious wear mechanism is reported, involving rapid land wear by superficial fracture.Transfer of prow-deposits from the workpiece to wear lands accompanies rapid land wear by fracture. Crack nucleation, in the region of tensile stress generated at asperity junctions, leads to crater generation. Fragment production yields larger individual wear particles than competing attrition processes. The resulting wear rate of an abrasive is 10 to 50 times larger than attrition wear rates generating polished surfaces.Differences in fracture wear rate, among the abrasives studied, result from the varied character of microstructural flaws in the grits. The spacing, size and shape of these flaws affect the fragment size and fracture frequency.Adherent prow-deposits of various sizes form on abrasive grits contacting metal workpieces during sliding, micromilling and grinding. Deposition on the wear lands depends on workpiece properties and environmental conditions. Strong adhesion and ductility of the workpiece favor formation of prow-deposits on grit asperities.     

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.     

A Comparative Study on Asperity Peak Modeling Methods

The peak identification scheme based method(three-point definition) and the spectral moments based method(spectral moment approach) are both widely used for asperity peak modeling in tribology. To discover the differences between the two methods, a great number of rough surface profile samples with various statistical distributions are first randomly generated using FFT. Then the distribution parameters of asperity peaks are calculated for the generated samples with both methods. The obtained results are compared and verified by experiment. The variation rules of the differences between the two methods with statistical characteristics of rough surfaces are investigated. To explain for the discovered differences, the assumptions by spectral moment approach that the joint distribution of surface height, slope and curvature is normal and that the height distribution of asperities is Gaussian, are examined. The results show that it is unreasonable to assume a joint normal distribution without inspecting the correlation pattern of [z], [z′] and [z′′], and that the height distribution of asperities is not exactly Gaussian before correlation length of rough surface increases to a certain extent, 20 for instance.     

Microscopic asperity contact and deformation of ultrahigh molecular weight polyethylene bearing surfaces

The effect of the roughness and topography of ultrahigh molecular weight polyethylene (UHMWPE) bearing surfaces on the microscopic contact mechanics with a metallic counterface was investigated in the present study. Both simple sinusoidal roughness forms, with a wide range of amplitudes and wavelengths, and real surface topographies, measured before and after wear testing in a simple pin-on-plate machine, were considered in the theoretical analysis. The finite difference method was used to solve the microscopic contact between the rough UHMWPE bearing surface and a smooth hard counterface. The fast Fourier transform (FFT) was used to cope with the large number of mesh points required to represent the surface topography of the UHMWPE bearing surface. It was found that only isolated asperity contacts occurred under physiological loading, and the real contact area was only a small fraction of the nominal contact area. Consequently, the average contact pressure experienced at the articulating surfaces was significantly higher than the nominal contact pressure. Furthermore, it was shown that the majority of asperities on the worn UHMWPE pin were deformed in the elastic region, and consideration of the plastic deformation only resulted in a negligible increase in the predicted asperity contact area. Microscopic asperity contact and deformation mechanisms may play an important role in the understanding of the wear mechanisms of UHMWPE bearing surfaces.     

The effect of zinc di-n-butyl dithiophosphate on bronze wear in a lubricated bronze-on-steel contact

The tribological behaviour of zinc di-n-butyl dithiophosphate in steel-on-bronze contacts has been studied in a three-pin-on-disc wear machine under closely controlled conditions, whilst parameters such as load, sliding speed, additive concentration and roughness of the steel disc were varied systematically. Most of the work was carried out with a mineral base oil having a low sulphur content. The work has shown that there are several ways in which the presence of the zinc di-n-butyl dithiophosphate in the oil can influence the wear of the bronze.Firstly, the zinc di-n-butyl dithiophosphate modifies the top surface layer of the bronze which results in a decrease of mechanical wear, i.e. adhesive and abrasive wear processes, but which promotes chemical wear. The net effect is to promote wear when the concentration of the additive is high and the lubrication conditions are mild, i.e. smooth discs and high sliding speeds. It has been observed that the net effect can also be to inhibit wear at low concentrations of the additive and intermediate roughnesses of the steel disc.Secondly, the zinc di-n-butyl dithiophosphate interacts with the steel surface by protecting the asperity tips on the steel against wear. With the base oil alone the asperities are allowed to run in and thereby reduce wear, but the additive prevents running in. This mechanism predominates when the roughness of the steel disc is high.     

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。     

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.     

Modeling of lubrication in micro contact

A thorough understanding of the mechanisms of micro contactlubrication and failure is required in order to optimize machinecomponent design for extreme operating conditions. In the verylow ratio, the ratio of lubricant filmthickness to surface roughness, asperity contacts play animportant role. Analysis of lubrication and failure of microcontact should include details of surface topography and itscharacterization, asperity contact pressure, micro lubricationpressure and film shape, as well as micro contact temperature.These aspects are discussed in this paper and typical numericalresults are given. Modeling and simulation tools are availableto describe the solid contact of asperity tips and the collapseof the lubricant film. It appears possible to investigate thetransition from full EHL to boundary lubrication by using themodel developed.     

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.