Explaining the mechanics of metallic sliding friction and wear in terms of slipline field models of asperity deformation

It is shown that the force which opposes the sliding of a hard relatively smooth surface over a softer surface can be explained as the force needed to push waves of plastically deformed material along the soft surface ahead of asperities on the hard surface. For rougher surfaces and/or poorer lubrication it is shown how the wave can be torn off or material removed by a chip formation process and wear particles formed. Coefficients of friction predicted from the corresponding asperity deformation models are shown to give good agreement with experimental results. For smooth well lubricated surfaces the wear of the softer surface is shown to occur as a result of the progressive damage to this surface brought about by the repeated passage of waves across it. Equations for predicting wear are derived from the asperity deformation models and a comparison made between predicted and experimental wear results. The paper ends by considering possible future trends in research into the mechanics of friction and wear.     

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.     

Prediction of Archard's wear coefficient for metallic sliding friction assuming a low cycle fatigue wear mechanism

A recently developed model for sliding friction, in which the frictional force is assumed to result from the pushing of waves of plastically deformed material in the soft surface ahead of asperities on the hard surface, is used to calculate the magnitude of the resulting plastic strain increments which progressively deform the soft surface. On the assumption that a low cycle fatigue mechanism eventually results in detachment of wear particles from the soft surface as a result of this cyclic working of the surface, the calculated strain increments (the magnitudes of which vary with the roughness of the hard surface and the boundary lubrication conditions) are used to estimate wear rates. The results are expressed in terms of Archard's wear coefficient and, for very smooth surfaces and good lubrication, this is predicted to have extremely low values as observed in wear tests for such conditions. For rougher surfaces and less efficient lubrication it is shown that the wear coefficient can increase dramatically.     

基于分形理论的滑动摩擦表面接触力学模型

依据分形理论,考虑微凸体变形特征及摩擦作用的影响建立滑动摩擦表面接触力学模型。采用一个三次多项式来表达弹塑性变形微凸体的接触压力与接触面积的关系,从而满足在变形状态转变临界点处的微凸体接触面积与接触压力转化皆是连续和光滑的条件。推导出滑动摩擦表面临界弹性变形微接触面积、临界塑性变形微接触面积、量纲一真实接触面积的数学表达式。理论计算结果表明,表面形貌一定时,真实接触面积随着载荷的增大而增大;载荷一定时,真实接触面积随着特征尺度系数的增大而减小,随着分形维数的增大先增大后减小;当表面较粗糙时,摩擦因数对真实接触面积的影响很小;随着表面光滑程度的增大,摩擦因数对真实接触面积的影响增大,真实接触面积随着摩擦因数的增大而增大,特别是当摩擦因数较大时,真实接触面积增大的幅度也较大。接触力学模型的建立,为研究滑动摩擦表面间的摩擦磨损性能提供了依据。     

A numerical model of friction between rough surfaces

This paper describes a computational method to calculate the friction force between two rough surfaces. In the model used, friction results from forces developed during elastic deformation and shear resistance of adhesive junctions at the contact areas. Contacts occur between asperities and have arbitrary orientations with respect to the surfaces. The size and slope of each contact area depend on external loads, mechanical properties and topographies of surfaces. Contact force distribution is computed by iterating the relationship between contact parameters, external loads, and surface topographies until the sum of normal components of contact forces equals the normal load. The corresponding sum of tangential components of contact forces constitutes the friction force. To calculate elastic deformation in three dimensions, we use the method of influence coefficients and its adaptation to shear forces to account for sliding friction. Analysis presented in Appendix A gives approximate limits within which influence coefficients developed for flat elastic half-space can apply to rough surfaces. Use of the method of residual correction and a successive grid refinement helped rectify the periodicity error introduced by the FFT technique that was used to solve for asperity pressures. The proposed method, when applied to the classical problem of a sphere on a half-space as a benchmark, showed good agreement with previous results. Calculations show how friction changes with surface roughness and also demonstrate the method's efficiency.     

Slip-line fields for explaining the mechanics of polishing and related processes

Two-dimensional rigid cylindrical asperities are used in modelling the friction and material removal mechanisms occurring in moving contact between engineering surfaces and particularly between abrasive or polishing grits and softer work-pieces. The contact zone of the circular section of the cylinder is approximated by a single chord or by two chords, thereby permitting slip-line fields to be constructed to represent the plastic deformation of the softer material. Account is taken of lubrication conditions. The single chord model is associated with low normal loads, low coefficients of friction and no wear but plastic working of the traversed surface. As normal load is increased there is a transition to the double chord model where the coefficient of friction is higher and where wear occurs due to a cutting action in conjunction with working of the traversed surface. Under certain conditions of lubrication and high loads wear can occur by a tearing mechanism. Experimental findings are cited which confirm that there can be no wear but working of the surface with low loads and wear plus working of the surface with high loads as predicted by the theory.     

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.     

Effects of Friction on the Contact and Deformation Behavior in Sliding Asperity Contacts

Finite-element analyses are carried out to study the effects of friction on the contact and deformation behavior of sliding asperity contacts. In the analysis, on elastic-perfectly-plastic asperity is brought in contact with a rigid flat at a given normal approach. Two critical values of the normal approach are used to describe the asperity deformation. One is the approach corresponding to the point of initial plastic yielding, and the other at the point of full plastic flow. Additional variables used to characterize the deformation behavior include the shape and size of the plastic zone and the asperity contact size, pressure, and load capacity. Results from the finite-element analysis show that the two values of critical normal approach decrease significantly as the friction in the contact increases, particularly the approach that causes plastic flow of the asperity. The size of the plastically deformed zone is reduced by the friction when the contact becomes fully plastic. The reduction is very considerable with a high friction coefficient, and the plastic deformation is largely confined to a small thin surface layer. For a low friction coefficient, the contact size, pressure and load capacity of the asperity are not very sensitive to the friction coefficient. For a moderate friction coefficient, the contact pressure is reduced and the junction size increased; the load capacity of the asperity is not significantly affected due to the compensating effects of the pressure reduction and the junction growth. For a high friction coefficient, the pressure-junction compensation is not longer sufficient and the asperity load capacity is reduced. The degree of the friction effects on these contact variables depends on the applied force or the normal approach. Although the analyses are conducted using a line-contact model, the authors believe that the effects of friction in sliding asperity contacts of three-dimensional geometry are essentially the same and the same conclusions would have been reached. These results may provide some guidance to the modeling of rough surfaces in boundary lubrication, in which the asperity friction coefficient can be high and vary significantly both in time and from one micro-contact to another.     

粗糙表面接触模型的研究进展

实际工程中的接触表面都不是绝对光滑的,当两物体相互接触时,真实表面的接触实际上是微凸体间的接触.粗糙表面间的接触行为对摩擦、磨损、润滑、密封和传热等有着重要的影响,是摩擦学研究的主要课题之一.介绍了Hertz弹性接触模型、统计学接触模型和分形接触模型,对粗糙表面接触模型的研究现状和进展作了分析和评述.由Hertz模型只能求解一些几何形状比较规则的物体,应用范围非常有限;各种统计学模型都是经过简化的理想模型,这些简化究竟能导致多大误差目前还没有精确的分析;分形模型利用了包含全部表面粗糙度信息的分形参数D和G,其对粗糙表面接触性质的预测不受仪器分辨率和取样长度的影响,使预测具有惟一性或确定性.     

Stribeck Curve Under Friction of Copper Samples in the Steady Friction State

The friction and wear of a pure copper block (99.98 wt% Cu) against a hardened steel disc were studied. The effect of sliding velocity and load on the friction coefficient and wear rate of Cu samples during steady tests was studied. Elasto-hydrodynamic (EHL), mixed (ML) and boundary lubrication (BL) regions were analyzed using the Stribeck curve. The lubrication number of Schipper, Z, was used in the analysis of the Stribeck curve. The transitions from one lubrication region to another are discussed. The mixed EHL region is characterized by stable low values of the friction coefficient, wear rate and temperature. Straight asperity contact is the dominant mechanism under friction of Cu–steel pair in the BL region. High-friction coefficients and wear rates, thin lubricant films and large wear grooves indicate straight asperity contact between rubbed surfaces in the BL region. Although the dominant mechanisms in the mixed EHL and BL regions are different in principle, a steady friction state is preserved in both cases. It is expected that the steady friction state in the BL and mixed EHL regions is associated with deformation and fracture of surface layers but these process occur at different scale levels. It was shown that under friction of Cu–steel pair, two types of ML regions are observed. The first is the stable steady friction of mixed EHL with low values of the friction coefficient and wear rate. The second type of the ML region is the region of unstable friction and wear when a decrease of lubricant film leads to a change of external (roughness, temperature, friction and wear) and internal (strain and stress) parameters. It was found out that a transition to the unstable ML region occurs within a narrow range of Z parameter under definite values of the load and sliding velocity.     

Model and computer simulation of friction

A model, consisting of the stochastic formulae which describe the relationship between the friction coefficient and the parameters known to be significant in dry friction, is proposed for dry sliding friction between two randomly rough surfaces. The model considers the frictional phenomena which dominate in energy dissipation and which may occur simultaneously between contacting elements. The kind of interaction in a given spot of asperity contact depends on the local energy flux density. The effect of several parameters on the friction coefficient, the real area of contact, and the number of contact spots can be calculated with the FRI-SIM program. A comparison of the simulation and experimental data shows a convergence of results.     

An upper-bound analysis of friction in metal forming

In the analysis of metal forming processes, a knowledge of friction is important, especially when the microstructure evolution and criteria for limiting phenomena are predicted by numerical simulation. The friction wave model has been studied by several researchers. Their analyses are mainly based on the assumption that there is no plastic deformation of the bulk material. However, it is necessary to clarify the influence of bulk material deformation on the surface asperity deformation. This paper deals with the development of a friction wave model by considering the influence of bulk material on the surface asperity deformation. The situation of rough tool—smooth workpiece (RT—SW) contact during forming process has been investigated. Based on this condition, an admissible velocity field is constructed for the upper bound analysis. The relationship between the normal pressure and the sliding resistance is established over a large range of pressure. The role of surface roughness, bulk displacement and bulk strain on metal forming friction is analysed.     

Theoretical analysis of the plastic yielding of a hard asperity sliding on a soft flat surface

When a hard material slides on a soft material, wear occurs generally on the soft material surface. Wear can also occur on the harder material but the conditions for this have not yet been elucidated.As plastic deformation of contact points is an important factor in the generation of wear particles, the condition under which the plastic yielding of each material occurs simultaneously and the condition under which the hard asperity yields before the soft flat surface were analysed theoretically. The analysis indicates that there is a critical value, which depends on the hardness ratio and the shear stress on the interface, for the top angle of the asperity. If the top angle of an asperity is less than this critical value, the asperity can yield plastically despite its being harder than the mating surface.     

The residual stress distribution in a plastically deformed model asperity

When rough metallic surfaces come into contact, plastic deformation may occur locally, even at the lightest loads. This plastic deformation is thought to be an important element in a wide range of contact failure mechanisms, including fatigue and nearly all forms of wear.In this paper a simple model of asperity plastic deformation is presented. The model is based on slip line field theory and is used to calculate residual and full-load stress distributions at fully plastic asperity contacts for normal and moderate tangential loads.Measurements of surface residual stress were carried out using two different techniques on a range of plastic contacts of various materials and geometries. The results show agreement with the main predictions of the theory.     

Investigation of the wear mechanism of carbon-fiberreinforced acetal

The friction and wear characteristics of acetal reinforced with 25 wt.% of randomly dispersed carbon fibers were investigated and compared with those of the base resin. The addition of carbon fibers to the polymer decreased the coefficient of friction and wear rate for the composite material sliding against a hardened and ground steel disk for extended periods of time. A number of surface topography parameters pertinent to the wear process, i.e. arithmetic average roughness, autocorrelation function, asperity density, tip radius of curvature, distribution of the radii of curvature and heights of asperity peaks, and ordinale heights, were calculated and evaluated for the sliding surface of the disk. The worn surfaces of filled and unfilled polymer pins were examined by scanning electron microscopy to investigate the probable wear mechanism for these materials. It was found that the wear of reinforced polymers proceeds by the pulling-out of the broken and worn fibers.     

Refined simulation of friction power loss in crank shaft slider bearings considering wear in the mixed lubrication regime

Friction reduction is a fundamental factor in decreasing fuel consumption of internal combustion engines. During the design stage of the engine the simulation of friction in the crank mechanism plays a vital role to develop optimum solutions. Due to the interaction of oil and elastic structures with rough surfaces in slider bearings, complex simulation models have to be used for representing the relevant physical behavior. The following article is focused on crank shaft slider bearings of large engines.The article describes a procedure evaluated by measurements showing how to model wear profiles of slider bearings to reach a high quality friction forecast. A fundamental influencing factor of bearing friction is given by the mixed lubrication regime and it is considered in the simulation model as part of asperity contact friction and hydrodynamic friction. Further effects result from the compliance in radial and width directions of the bearing structure and the wear of the bearing surface. Furthermore, the specific operating conditions of the slider bearing such as load, temperature, shaft speed and oil characteristics are essential and have to be taken into account.The objective of this investigation is to propose the wear profile of the bearing surface for the simulation model to be treated iteratively, where simulation results for the amount of mixed lubrication are successively assessed. For this purpose an iterative procedure is introduced and validated by measurements on a slider bearing test rig.The applied simulation method is based on elastic multi-body systems; the lubrication film contact is calculated based on Reynolds differential equation via the pressure balance calculated iteratively in the time domain. The model accounting for the mixed lubrication regime is based on the theory of Greenwood and Tripp.     

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.     

Microtribology

Contacts in microsystems are under very light loads, and contact elements are made of hard materials. However, contact surfaces are not always atomically smooth but have relatively high peaks of asperity. Silicon is hard but has poor anti‐wear properties. Good hard coatings thus become necessary for low wear. Liquid lubricants or adsorbed water generate meniscus forces and stiction. Therefore, a new lubrication method is required for coated surfaces. The present understanding of mechanisms of stiction and the generation of pull‐off force and high friction is reviewed for such contact conditions. New hard coating materials and a new concept of N2 lubrication that exhibit promising friction and wear behaviour are introduced. Copyright © 2006 John Wiley & Sons, Ltd.     

A microwedge model of sliding contact in boundary/mixed lubrication

A refined friction model of sliding contact in boundary/mixed lubrication regime is developed. In addition to the well-known asperity flattening and roughening effects, significant deformation of asperities can be incited by the elastic microwedges on the tool surface. A model of asperity deformation, which includes the effects of smoothing, roughening, and microwedge, is proposed for processes where smooth tool and rough workpiece are used. A finite element formulation incorporating the microwedge effect in the Reynolds equation for lubricant flow is also derived. Numerical results showed that the inclusion of microwedge in the analysis provides a good agreement with the experimental measurements, especially with many interesting phenomena that can be neither explained nor predicted by the other friction models.