Evaluation of the real contact areas, pressure distributions and contact temperatures during sliding contact between real metal surfaces

A three-dimensional elastic contact algorithm has been developed to analyse the normal contact problems of bodies having rough surfaces. The algorithm can evaluate the real contact areas and contact pressure distributions using measured surface roughness data.

Following an approximate elastic-plastic contact solution the analysis produces more realistic elastic and plastic contact areas; in addition results of contact pressure distributions can be predicted according to a given maximum plastic limit pressure.

The technique can simulate (in an approximate way) the elastic-plastic sliding contact behaviour in the vicinity of asperities or concentrated contact areas by ignoring the effect of the tangential forces on the vertical displacement.

Assuming a certain sliding speed and a particular coefficient of friction the local temperature distribution due to the heat generation over the real contact areas can also be calculated for 'slow sliding' problems.

The results show the moving real contact areas and the contact temperature fields for an electric spark mechanical steel surface moving over a planed bronze surface. Changes of the rigid body displacement, as well as the average and maximum pressures are also presented during sliding.

The micro-contact or asperity contact behaviour for bodies having large nominal contact area and the macro-contact behaviour for bodies being in 'concentrated contact' are also compared. In the latter case an ideal smooth steel ball was slid over the previously mentioned bronze surface.     

Coalescence and breakup of contact areas: Effects on surface temperatures

In a study of the mechanisms by which thin polymeric films can prevent or delay the onset of fretting corrosion, experimental observations were made of the apparent real area of contact and temperatures generated by friction in a dry-sliding system consisting of stationary polymer-coated steel balls loaded against a vibrating sapphire disk. Five different polymers were used in the original study at vibrating frequencies ranging from 100 to 200 Hz and amplitudes from 20 to 100 μm; but this paper focuses on only one of these—polystyrene coated steel balls in contact with sapphire. Surface temperatures generated by friction were measured using an infrared microscope system. A photomacro/video technique was developed to view the fretting contact interface and to measure the size and distribution of the real areas of contact. The experiments revealed several complex patterns and unusual phenomena. In one example of behavior, a number of small contact patches would suddenly coalesce into one larger contact patch and then break up again into a similar collection of separate patches. This coalescence and breakup occurred at a regular frequency which was much lower than the oscillating frequency. In addition, significant surface temperature spikes corresponding to the occurrence of coalesced areas were observed.A general thermal model previously developed was used to theoretically predict the temperatures corresponding to the experimental conditions [Furey MJ, Vick B, Foo SJ, Weick BL. A theoretical and experimental study of surface temperatures generated during fretting. In: Proceedings of Japan international tribology conference, Nagoya, Japan, 29 October 1990–1 November 1990, vol. II, pp. 809–14; Vick B, Furey MJ. A basic theoretical study of the temperature rise in sliding contact with multiple contacts. Tribology International 2001;34:823–29]. The thermal model consists of a sliding pair of any material combination with three-dimensional and transient conditions. The key feature is the contact area, which is modeled as a collection of rectangular patches in which each patch can have any specified size, shape, position, and time duration. In this way, each contact has a unique start and finish time and the entire collection of contacts can evolve with time in any specified manner. This provides the flexibility to model everything from hard, brittle surfaces such as ceramics to softer, deformable surfaces such as polymers.Using the changes in the apparent real area of contact as observed in the experiments, the theoretical model predicted surface temperatures in close agreement with experimental values. The results of this study show not only that the area of contact is complex and dynamically changing, but that the surface temperatures produced are extremely sensitive to the real area of contact. Although the fundamental mechanisms for the observed phenomena of breakup, coalescence and motion of contact areas are unknown, the study is important since it illustrates the connection between areas of contact and surface temperature—a key unknown which influences physical and chemical behavior in tribological processes.     

Effects of temperature,sliding velocity and non-friction time on severe-mild wear transition of iron

The effects of non-friction time along with temperature and sliding velocity on the distance to achieve severe-mild wear transition are discussed using a twin-ring sliding type wear test rig. It became clear that as the non-friction time increased, while keeping the same velocity, the severe-mild wear transition distance increased. On the other hand, the transition distance from severe to mild wear decreased, as the sliding velocity decreased or as the specimen temperature increased. From these results, it is concluded that the low sliding speed accelerates the severe-mild wear transition by increasing the real friction time at the real area of contact.     

Contact and thermal analysis of transfer film covered real composite-steel surfaces in sliding contact

For composite-steel surfaces in sliding contact an anisotropic numerical contact algorithm has been developed to study the ‘layer type’ problems. An FE contact analysis was applied to evaluate the contact parameters (real contact area, contact pressure distribution and normal approach). The contact temperature rise was determined by using both a numerical thermal algorithm for stationary and a FE transient thermal technique for ‘fast sliding’ problems.The effect of a continuous transfer film layer (TFL), that had built up during wear of the PEEK matrix material on the steel counterpart, was considered. Its thickness was assumed to be t=1 μm, and its material properties were that of PEEK at room temperature or, in the case of frictional heating, at a temperature of 150°C (i.e. above the glass transition temperature of the polymer matrix).Results are presented for a spherical steel asperity, with/without TFL, sliding over composite surfaces of different fibre orientation, and in addition, for real composite-steel surfaces (based on measured surface roughness data) in sliding contact. The TFL has an effect on the contact parameters especially at higher operating temperatures (i.e. 150°C); it results in the production of a larger contact area and a lower contact pressure distribution. The contact temperature rise is clearly higher if a TFL is present. Due to the low thermal conductivity of PEEK, the TFL is close to the melting state or it even gets molten within a small vicinity of the contact area.     

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.     

弹流润滑点接触Hertz区温度分布及其变化规律的实验研究

为实现对点接触赫兹接触区温度的测量,根据热辐射理论和红外热像仪的测温原理,利用红外热像仪测量被测物体表面真实温度以及分布情况,得到点接触区的温度分布规律,并与摩擦力进行对比分析.结果表明:在弹流润滑下,接触区温升与压力分布相对应,最大温升一般发生在Hertz接触区中心的附近;最大温升随载荷的增加而增大,与速度也有一定的关系.     

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。     

Contact Mechanics and Friction on Dry and Wet Human Skin

The surface topography of the human wrist skin is studied using an optical method and the surface roughness power spectrum is obtained. The Persson contact mechanics theory is used to calculate the contact area for different magnifications, for both dry and wet condition of the skin. For dry skin, plastic yielding becomes important and will determine the area of contact observed at the highest magnification. The measured friction coefficient [M.J. Adams et al., Tribol Lett 26:239, 2007] on both dry and wet skin can be explained assuming that a frictional shear stress σ_f ≈ 15 MPa acts in the area of real contact during sliding. This frictional shear stress is typical for sliding on polymer surfaces, and for thin (nanometer) confined fluid films. The big increase in the friction, which has been observed for glass sliding on wet skin as the skin dries up, can be explained as resulting from the increase in the contact area arising from the attraction of capillary bridges. This effect is predicted to operate as long as the water layer is thinner than ～14 μm, which is in good agreement with the time period (of order 100 s) over which the enhanced friction is observed (it takes about 100 s for ～14 μm water to evaporate at 50% relative humidity and at room temperature). We calculate the dependency of the sliding friction coefficient on the sliding speed on lubricated surfaces (Stribeck curve). We show that sliding of a sphere and of a cylinder gives very similar results if the radius and load on the sphere and cylinder are appropriately related. When applied to skin the calculated Stribeck curve is in good agreement with experiment, except that the curve is shifted by one velocity-decade to higher velocities than observed experimentally. We explain this by the role of the skin and underlying tissues viscoelasticity on the contact mechanics.     

磨粒微观滑动接触过程热效应的有限元分析

利用ANSYS有限元软件分析了磨粒与被磨损材料表面滑动接触过程中,在摩擦热和力场的耦合作用下,接触区表现出的局部温度变化、应力变化等特性。结果表明,在磨粒滑移过程中,磨粒相当于接受固定热源作用,接触区温度逐渐上升,温度存在起伏波动现象,瞬现温升最高点在磨粒接触区两侧,反映出接触状态的不连续性,接触区状态的非稳定性;被磨材料表面的各点在进入接触前、经历接触时、脱离接触时,接触区温度存在先升高再下降的变化过程,同时,接触区的应力、剪应力、接触压力也发生变化。磨粒滑动过程的热效应问题研究将有助于揭示接触过程中材料表面损伤机制。     

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。     

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.     

Friction of rubber on ice: A new machine,influence of rubber properties and sliding parameters

Friction of rubber on ice and snow is important for performance of vehicle tyres in winter. We introduce a new linear tribometer that was designed for measuring the friction of rubber on ice. We present a systematic study of rubber sliding on ice, investigating speed, load, temperature and rubber properties. The friction was linked to behaviour at the interface, particularly melt–water formation and real area of contact. Friction tends to decrease with conditions that promote melt–water formation, and tends to increase as real area of contact increases. We observe stick-slip behaviour with high real area of contact and high load.     

Calculation of sliding power loss in spur gear contacts

An engineering-level calculation model for sliding power loss in spur gear contacts is presented. Teeth contact through the line of action is modelled as a constantly changing roller contact whose radius, speed, and load can be calculated from the gear geometry under the given operating conditions. The gear mesh cycle is approximated by a large number of elastohydrodynamic contacts. A constant film thickness and a Hertzian pressure distribution are assumed in each contact. The model includes non-Newtonian lubricant behaviour together with temperature and mixed lubrication effects in contact. The numerical solver is reasonably fast in evaluating effectively the sliding power loss dependence on the essential gear and lubricant parameters. The features and behaviour trends of the calculated sliding power losses have a close similarity with published results obtained from measurements and experiment-based power loss models with mineral oil. The limiting shear stress of the lubricant is observed to have an essential role in the power loss behaviour especially at high loads.     

Numerical and Experimental Studies on Tribological Behaviors of Cu-Based Friction Pairs from Hydrodynamic to Boundary Lubrication

When studying the tribological behaviors of a Cu-based friction pair in different lubrication regimes, calculation of the real contact area of asperity contacts is crucial but difficult. In this work, a mixed lubrication model in plane contacts is developed, and pin-on-disc tests are carried out. The real contact area ratio, load sharing ratio, and friction coefficient are investigated. Effects of sliding velocity, temperature, and pressure are considered. The results show that when the maximum contact area ratio is about 14.6%, the load sharing ratio of asperity contacts is about 95%. The friction coefficient obviously increases from less than 0.04 to about 0.15 as the regime changes from hydrodynamic to boundary lubrication. Asperities have a significant influence on the local lubrication of a Cu-based friction pair, and the action of hydrodynamic pressure cannot be ignored.     

旋转齿轮瞬时接触应力和温度的分析模拟

建立了高速齿轮传动轮齿瞬时接触温度的分析方法和模型;采用赫兹接触理论和有限元接触分析方法分析了标准渐开线齿廓和齿顶修形齿廓的齿面接触压力;研究了啮合过程中轮齿的相对滑动速度和齿面摩擦因数以及摩擦热流密度的计算方法;建立了轮齿本体温度的有限元温度分析模型;计算了轮齿接触面的瞬时温升;分析了标准和齿顶修形渐开线齿轮的轮齿本体温度和瞬时接触温度及相关因素对它们的影响。     

A novel test rig for in situ and real time optical measurement of the contact area evolution during pre-sliding of a spherical contact

An experimental test rig was developed in order to investigate elastic–plastic single micro-spherical contact under combined normal and tangential loading. This novel apparatus allows in situ and real time direct optical measurement of the real contact area (RCA) evolution in pre-sliding. It also allows relative displacement measurements under very low rates of tangential loading (down to 0.01 N/s) to capture accurately the fine details at sliding inception. This is achieved by piezoelectric actuation in closed loop feedback control in addition to synchronization with data and image acquisition to obtain real time measurement. The RCA measurement is realized by direct optical observation technique, whereas two different image processing algorithms were implemented for the elastic and the elastic–plastic contact regimes. The various features and capabilities of the test rig are presented along with some preliminary experimental results of RCA and friction behavior to assess its performance.     

A basic theoretical study of the temperature rise in sliding contact with multiple contacts

The objectives of this paper are to develop a theoretical solution for the temperature rise due to sliding contact between surfaces with multiple, interacting asperities and to use this solution to examine the effects of the important contact area and system parameters. A solution based on the Green's function method is developed for the basic problem of two half-space regions in sliding contact with any arbitrarily specified arrangement of rectangular asperities.Studies are conducted to demonstrate the effects of the contact area parameters, namely the number, size, spacing and orientation of the contacts, as well as sliding velocity. Results indicate that the contact temperatures are extremely sensitive to the number and relative spacing between contacts, where subdivision of a single contact into separated pieces significantly reduces the contact temperature rises. The orientation of the contacts relative to the sliding direction is shown to have only a small influence on temperature. The shape of the contacts also has only a small influence, except in the case of contact patches with large aspect ratios where significantly lower surface temperatures can occur. Sliding speed is shown to be extremely important in that increased speed causes both higher temperature levels and greater interaction between contacts due to the convective effect.The current paper is intended to describe the basic solution methodology for calculating temperature rises due to multiple, interacting contacts and to show some fundamental trends for a selected set of regularly arranged contact area distributions.     

The Subsurface Stress Field Created by Three-Dimensionally Rough Bodies in Contact with Traction

A numerical simulation technique for calculating the complete subsurface stress field for three-dimensionally rough bodies in sliding contact is described. The stresses are calculated using real digitized three-dimensional surface profiles. The effects of the surface roughness and the sliding friction are presented. Using an existing contact simulation code, the digitized surfaces are mathematically pressed together and the real areas of contact and the asperity pressures are calculated. The surfaces are assumed to remain elastic throughout the contact simulation process. The shear forces at the asperity contact interfaces are assumed to be proportional to their calculated normal pressures. The subsurface stresses are then determined with these known normal and tangential forces at the surface.     

传热界面真实接触面积计算与分析

在热流通过两相互接触材料尤其是金属材料的界面时，真实接触面积是界面传热的一个主要影响因素。当承受大应力的两接触体之间具有相对滑动或相对滑动趋势时，粗糙表面在压力和粘着力及剪切力的作用下接触粗糙峰发生弹性、弹一塑性或完全塑性变形，真实接触面积与压力之间的关系随变形机制而发生变化，在力的作用下材料的变形机制由表面微观几何形貌和力学性质决定。计算表明，单个粗糙峰接触面积与载荷的关系受变形机制的影响，粘着力对接触面积的影响可以忽略，表面相对滑动将增加真实接触面积。     

Study of plastic shear deformation in surface layer at friction. Simulation results. Part II. Effect of friction parameters

Deformation and temperature in the surface layer of plastic material and thickness of the plasticized layer are calculated using the one-dimensional macroscopic friction model developed in the first part of the paper [1]. We have studied the effect of sliding velocity, contact spot area, hardening ability, and thermal conductivity of material on the frictional heating and plastic deformation of the surface layer during a single touch between the contact spot and counterbody. Repeated contacts of the specimen and counterbody are simulated and the accumulation of plastic shear is considered for different contact spot sizes.