The planar contact problem of interaction between a rigid heat-conductive cylindrical die and an elastic layer in frictional heat emission

The paper presents discussion of a new planar problem of contact interaction between a rigid heat-conductive die of circular cross section and an elastic layer. The apparatus of integral transformation is used to obtain a precise solution of the nonstationary equations of heat conductivity for the layer and the cylindrical die. This method makes it possible to reduce the formulated problem to a system of integral equations with time-variable limits of integration; the structure of the equations is governed by the type of thermophysical conditions on the interaction surface. An algorithm is advanced for solving this type of integral equation; the variations in time of the contact pressure and the interaction area boundaries are explored. Thus, it is possible to make the problem’s mathematical formulation closer to the real distribution of thermoelastic stresses and to estimate more accurately the effect of temperature fields on the value and pattern of the contact-pressure distribution.     

Evolution of contact pressure during wear of the coating in a thrust sliding bearing

The evolution of contact pressure is analyzed during the wear of a thrust sliding bearing following the law of nonlinear wear. The coating’s deformation properties are described using the nonlinear Winkler model. It is demonstrated that steady wear can exist with a definite contact pressure distribution.     

地铁线路曲线段磨耗状态下轮轨滚动接触有限元分析

基于城市轨道交通曲线段不同磨耗程度的典型钢轨和车轮的实测型面,利用有限元分析软件ANSYS建立曲线段轮轨三维弹塑性接触有限元模型,对三种不同轮轨磨耗型面匹配工况下的地铁车辆的曲线通过性能以及轮轨接触应力进行计算分析,分析不同磨耗状态下车轮和钢轨接触时的接触应力和轮轨应力的分布状态,并研究其对钢轨磨耗的影响。发现钢轨使用初期,由于轮轨廓形不一致,轮轨间易出现应力集中,应力集中部位易出现磨损;随着钢轨侧磨的增加,轮轨接触状态逐渐由一点接触变为两点接触,且接触点的塑性变形部分和弹性部分的过渡区间易出现裂纹;两点接触状态下,外侧轨距角处接触面积及应力集中区域远大于钢轨侧面部分,轨距角易出现较大的接触压力,易加速钢轨磨耗与疲劳伤损的产生。     

Influence of the microprojection geometry on the elastic contact of surfaces with regular microrelief

The influence of surface microprojections—their shape and additional harmonics—on the elastic contact of a flat surface and a surface with regular microrelief is considered on the basis of the elastic contact of a half-plane and an undulatory surface. It is shown that the contact-pressure curve depends on the surface gradient of the microprojection and the mutual influence of adjacent microprojections.     

Simulation of combined wearing of the shaft and bush in a heavily loaded sliding bearing

The problem of simultaneous wear of an elastic cylinder and a cylindrical notch surface in an elastic space is discussed (in the planar formulation). The contact problem formulation omits the limitation of the contact area. The contact is solved in steps; the linear wear and contact parameters of the shaft and bush are solved at each step in time. The Multopp-Kalandia method is applied to the solution of the contact problem. The constructed model is used to investigate the evolution of contact pressure and form changes of the shaft and bush in the process of wear.     

滑动接触中摩擦发热的数值分析

在滑动接触中，存在摩擦起热问题，运动机理对接触行为参数特性的影响不同于纯滚动接触，采用有限元方法，利用ANSYS软件，对2维滚滑模型进行分析，通过研究接触区的温度，接触应力和变形在运动学状态下的变化特性，可以看到接触状态的非稳定性必定会造成实际摩擦状态的不同，这也是形成接触表面不均匀磨损的原因之一。     

隔膜压缩机金属膜片层间接触力学行为的研究

根据隔膜压缩机膜片的受力分析,建立了三层膜片层间接触力学模型。通过理论计算获得了不同挠度情况下膜片的挠度曲线、径向应力、周向应力及主剪切应力值。根据膜片不同挠度的应力分布,求出三层膜片接触面滑动区和黏着区的分布情况,发现可以通过改变膜片材料、膜片厚度来改善膜片层间接触状态,降低膜片层间摩擦磨损,对延长膜片的使用寿命具有重要意义。     

Forced vibrations of a rigid body on a three-parameter foundation

The dynamic characteristics of the foundation model proposed by Kerr¹ are studied in connexion with the problem of the forced vibrations of a rigid beam supported by an elastic medium of finite depth (the two-dimensional case). Smooth and permanent contact is considered. Damping is included by complex foundation parameters. A resonant effect concerning the bending moments in finite beams is pointed out. Frequency-response curves and contact-pressure distributions are given for both axi- and anti-symmetrical vibrations.     

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.     

Contact mechanics analysis of metal-on-metal hip resurfacing prostheses

Finite-element method was employed to study the contact mechanics in metal-on-metal hip resurfacing prostheses, with particular reference to the effects of bone quality, the fixation condition between the acetabular cup and bone, and the clearance between the femoral head and the acetabular cup. Simple finite-element bone models were developed to simulate the contact between the articulating surfaces of the femoral head and the acetabular cup. The stresses within the bone structure were also studied. It was shown that a decrease in the clearance between the acetabular cup and femoral head had the largest effect on reducing the predicted contact-pressure distribution among all the factors considered in this study. It was found that as the clearance was reduced, the influence of the underlying materials, such as bone and cement, became increasingly important. Stress shielding was determined to occur in the bone tissue surrounding the hip resurfacing prosthesis considered in this study. However, the stress-shielding effects predicted were less than those observed in conventional total hip replacements. Both the effects of bone quality (reduction in elastic modulus) and the fixation condition between the cup and the bone were found to have a negligible effect on the predicted contact mechanics at the bearing surface. The loading was found to have a relatively small effect on the predicted maximum contact pressure at the bearing surface; this was attributed to an increase in contact area as the load was increased.     

Wear resistance of coating materials under the frictional heating conditions

The problem of the wear of an elastic coating due to a rigid body sliding over the coating surface and heating due to contact friction has been considered. The solution of the quasi-static problem has been constructed in the form of a series over eigenvalues. The area of unstable solutions of the problem, where the thermoelastic instability of a sliding contact takes place, has been determined in the dimensionless parameter space. The wear resistance of a coating has been studied for different kinds of materials depending on the following parameters: the relative sliding velocity of contact surfaces, the mode of the contact interaction of the friction surfaces, the coating thickness, etc. taking into account the temperature and stresses developing at the contact interface.     

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.     

考虑表面粗糙度的面齿轮齿面接触应力分析

根据齿轮啮合原理,得出了面齿轮的齿面方程,求得面齿轮齿面曲率。结合赫兹接触理论,推导了点接触面齿轮传动接触点的接触应力及应力沿齿面的分布规律,从齿根到齿顶,齿面接触应力先增大后减小,在靠近齿面中点处达到最大值。由粗糙表面接触理论,分析了面齿轮齿面微观弹塑性变形时的接触面积,并得到粗糙齿面接触时面齿轮齿面接触应力及其分布。对比分析了几种不同粗糙度条件下面齿轮齿面接触应力的变化规律,结果表明:齿面接触应力随表面粗糙度的增大而增大,与齿根处相比,齿顶接触应力受表面粗糙度影响更大。文中的分析可为面齿轮磨损及润滑机理的研究提供依据。     

Some microscopic aspects of the mild wear of steel*

The paper reviews the experimental classifications of the unlubricated sliding wear of metals, together with some of the suggested relationships between the wear rates, the real area of contact, the load, the hardnesses of the metals and the probability of producing wear particles at the real areas of contact. The microscopic nature of the interactions between sliding surfaces is discussed, with special emphasis on the advantages (and limitations) of using electron microscopy for studying these interactions, and the importance of using X-ray diffraction techniques to complementthe electron microscopy. Examples are then given of how the use of electron microscopy has revealed many facets of the mild wear of steel which would not otherwise have been suspected. For instance, the areas of contact between sliding steel surfaces are comparatively large and few in number, in contradistinction to the situation occurring in stationary contact. These large contact areas crack in a characteristic fashion reminiscent of fatigue failure or brittle fracture. They then flake off at a critical thickness (～ 10^?4cm) to provide the source for the wear debris. The wear debris collects initially in the rough regions which are left behind when the flakes become detached. In this position, the wear debris probably acts in an abrasive fashion. Eventually, the wear debris is thrown clear of the contact area. Analysis of this debris using X-ray diffraction techniques has shown that there is a strong correlation between the presence of certain oxides in the wear debris and the severity or mildness of the wear. It has also been used to estimate the temperatures occurring between the areas in sliding contact. This estimate is consistent with previously published dynamic thermocouple measurements. It also gives rise to consistent values of the activation energy required for oxidation during wear.     

ANALYSIS OF THERMAL-ELASTIC STRESS OF WHEEL-RAIL IN ROLLING-SLIDING CONTACT

A coupling thermo-mechanical model of wheel/rail in rolling-sliding contact is put forward using finite element method. The normal contact pressure is idealized as the Hertzian distribution, and the tangential force presented by Carter is used. In order to obtain thermal-elastic stress, the ther-mal-elastic plane stress problem is transformed to an elastic plane stress problem with equivalent fictitious thermal body force and fictitious boundary distributed force. The temperature rise and ther-mal-elastic stress of wheel and rail in rolling-sliding are analyzed. The non-steady state heat transfer between the contact surfaces of wheel and rail, heat-convection and radiation between the wheel/rail and the ambient are taken into consideration. The influences of the wheel rolling speed and wear rate on friction temperature and thermal-elastic stress are investigated. The results show the following: ① For rolling-sliding case, the thermal stress in the thin layer near the contact patch due to the friction temperature rise is severe. The higher rolling speed leads to the lower friction temperature rise and thermal stress in the wheel; ② For sliding case, the friction temperature and thermal stress of the wheel rise quickly in the initial sliding stage, and then get into a steady state gradually. The expansion of the contact patch, due to material wear, can affect the friction temperature rise and the thermal stress during wear process. The higher wear rate generates lower stress. The results can help under-stand the influence of friction temperature and thermal-elastic stress on wheel and rail damage.     

Contact and wear of paper-based friction materials for oil-immersed clutches—wear model for composite materials

Paper-based friction materials are widely used for oil-immersed clutches in automatic transmissions for passenger cars. It is known that repetition of engagements of the clutches causes wear of the friction materials leading to running-in with an increase in contact area. Observation of the contact of a typical paper-based friction material has been made by contact microscopy using the reflection of polarized light. The results have shown that contact is made at the top of its particulate and fibrous constituents, and comparison with the results of laser microscopy has revealed that the contact area observed by the contact microscopy is the contour contact area. An analysis has been made to describe this behavior by employing a mechanical model in which spherical and columnar asperities are supported by an elastic halfspace and wear under the loads they support. Analytical results describe the observed change in the contour contact area and demonstrate applicability of the model to wear of composite materials.     

The experimental and numerical analysis of quasi-steady wear processes for a sliding spherical indenter

The wear process on a frictional interface in a relative sliding motion of a punch on a substrate induces shape evolution of contact interface. For fixed contact zone the process tends to a steady state with fixed contact stress and strain distribution. Such steady state wear regimes were analyzed in the previous papers [1], [2], [3], [4], [5] by applying the principle of minimum wear dissipation rate. However, when the contact zone evolves in time due to wear process, as in the case of sliding spherical indenter, a quasi-steady state is reached with stress intensity dependent on the contact size parameter. On the other hand, the contact pressure distribution satisfies the condition of steady state. The simplified numerical analysis of wear process is presented by applying the quasi-steady conditions. The numerical predictions are confronted with experimental test results for two specific cases of soft and hard substrates. The quantitative specification of wear parameters is provided, first assuming constant values throughout the whole wear process, next assuming linearly or exponentially varying during the initial period and tending to constant values.     

Determining local wear equation based on friction and wear testing using a pin-on-disk scheme

Based on pin-on-disk friction and wear testing, the parameters of the wear rate as a function of sliding velocity and pressure with account for their distribution over the contact spot are computed. The parameters are compared to those obtained assuming a uniform distribution of velocities and pressures. It is assumed in the work that the contact spot does not vary, the disk does not wear out, and the study is carried out under steady-state wear conditions.     

杯形砂轮磨削高硬度球面砂轮磨损的研究

采用分块杯形砂轮磨削高硬度球面,磨削过程中砂轮磨损不仅影响砂轮磨削性能,而且造成工件和砂轮实际接触面积不断产生变化,影响磨削力和磨削质量。为此,基于展成法磨削原理研究砂轮块磨损后的形状变化,分析了分块砂轮的磨损形式,揭示了进给过程中砂轮块磨损形状的变化规律,推导了砂轮磨损量和砂轮工件接触面积的计算公式,分析了砂轮磨损速度的变化趋势及其影响因素,试验最后研究了砂轮磨损量的变化规律,并验证了砂轮磨损量的计算模型。     

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.