An adhesive wear model of fractal surfaces in normal contact

A generalized adhesive wear analysis that takes into account the effect of interfacial adhesion on the total load was developed for three-dimensional fractal surfaces in normal contact. A wear criterion based on the critical contact area for fully-plastic deformation of the asperity contacts was used to model the removal of material from the contact interface. The fraction of fully-plastic asperity contacts, wear rate, and wear coefficient are expressed in terms of the total normal load (global interference), fractal (topography) parameters, elastic–plastic material properties, surface energy, material compatibility, and interfacial adhesion characteristics controlled by the environment of the interacting surfaces. Numerical results are presented for representative ceramic–ceramic, ceramic–metallic, and metal–metal contact systems to illustrate the dependence of asperity plastic deformation, wear rate, and wear coefficient on global interference, surface roughness, material properties, and work of adhesion (affected by the material compatibility and the environment of the contacting surfaces). The analysis yields insight into the effects of surface material properties and interfacial adhesion on the adhesive wear of rough surfaces in normal contact.     

Optimal shapes of contact interfaces due to sliding wear in the steady relative motion

The transient wear process at contact frictional interface of two elastic bodies in relative steady motion induces evolution of shape of the interface. A steady wear state may be reached with uniform wear rate and fixed contact surface shape. In this paper, the optimal contact shape is studied by formulating several classes of shape optimization problems, namely minimization of generalized wear volume rate, friction dissipation power and wear dissipation rate occurring in two bodies. The wear rule was assumed as a nonlinear dependence of wear rate on friction traction and relative sliding velocity, similar to the Archard rule. The wear parameters of two bodies may be different. It was demonstrated that different optimal contact shapes are generated depending on objective functional and wear parameters. When the uniform wear rate is generated at contact sliding surfaces, the steady state is reached. It was shown that in the steady state the wear parameters of two bodies cannot be independent of each other. The solution of nonlinear programming problem was provided by the iterative numerical procedure. It was assumed that the relative sliding velocity between contacting bodies results from translation and rotation of two bodies. In general, both regular and singular regimes of wear rate and pressure distribution may occur. The illustrative examples of drum brake, translating punch and rotating annular punch (disc brake) provide the distribution of contact pressure and wear rate for regular and singular cases associated with the optimality conditions. It is shown that minimization of the generalized wear dissipation rate provides solutions assuring existence of steady wear states.     

Application of BEM and optimization technique to wear problems

In this paper a new method for solving wear problems, using the Boundary Element Method (BEM) is proposed. The proposed method uses a shape optimization technique for rapid calculation of the maximum wear depth and the final geometry of the bodies in contact after a specified service period. The optimization method solves the wear problem directly, without using increments of the sliding distance as in the classical methods. The BEM is used for modelling both bodies in contact, treating the problem as a multi-region problem. The material loss is presented in terms of the applied load and the sliding distance, and is modelled using a linear wear model. The proposed method is shown to be robust as it requires only few iterations to achieve a converged solution. The reduction in computational effort, as compared to the classical incremental method, becomes more significant as the sliding distance increases.     

A thermodynamical approach to contact wear as application of moving discontinuities

The propagation of a moving surface inside a body is analysed within the framework of thermomechanical couplings when the moving surface is associated with an irreversible change in mechanical properties. The moving surface is a surface of heat sources and of entropy production whose intensities are related to particular energy release rates defined in terms of Hamiltonian gradients. For example, we analyse the wear process. Wear phenomena due to contact and relative motion between two solids depend on the loading conditions and material mechanical properties. Friction between contacting bodies induces damage of materials, producing surface and subsurface cracks. Particles are detached from sound solids when some local criteria are satisfied at the boundary. As wear occurs, geometrical changes take place and contact conditions are modified, and the particle induces a specific layer with particular properties. Then the interface between the bodies is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. We propose to describe the evolution of the interface using a framework developed earlier for inducing the general form of a wear law.     

Analytical solution of the contact problem for a system of bodies under collective wear

The contact problem is considered for a system of bodies subject to wear on a common base. The deformation properties of the bodies and the base are described by the Winkler model. The problem is reduced to a system of ordinary differential equations and an integral equation of hereditary type with difference kernel. The solution of the problem is constructed with the use of the Laplace transform. The asymptotics of the solution at large times is studied. The continuity conditions for the contact of each of the bodies with the base are derived.     

Numerical study of sliding wear caused by a loaded pin on a rotating disc

A computational approach is proposed to predict the sliding wear caused by a loaded spherical pin contacting a rotating disc, a condition typical of the so-called pin-on-disc test widely used in tribological studies. The proposed framework relies on the understanding that, when the pin contacts and slides on the disc, a predominantly plane strain region exists at the centre of the disc wear track. The wear rate in this plane strain region can therefore be determined from a two dimensional idealisation of the contact problem, reducing the need for computationally expensive three dimensional contact analyses. Periodic unit cell techniques are used in conjunction with a ratchetting-based failure criterion to predict the wear rate in the central plane strain region. The overall three dimensional wear rate of the disc is then determined by scaling the plane strain wear rate with a conversion factor related to the predicted shape of the wear track. The approach is used to predict pin-on-disc test data from an Al-Si coating using a tungsten carbide pin. The predicted results are found to be consistent with measured data.     

柔性对多体系统中铰接副磨损的影响

通过集成柔性多体动力学与磨损计算程序,提出了一种用于对柔性多体系统中间隙铰接副部位的磨损进行了预测的方法.基于绝对节点坐标方法(ANCF)建立了柔性部件的多体动力学模型,引入Lankanrani和Nikravesh提出的连续接触力模型计算间隙铰接副部分的法向接触力,采用Lu Gre摩擦模型计算切向摩擦力,并利用基于Archard模型的迭代计算程序计算磨损.为了提高计算效率,引入了并行计算策略.最后,通过对一个含柔性连杆的曲柄滑块机构机构进行仿真计算,发现当考虑部件的柔性时,得到的间隙处的冲击力会大幅降低,预测的磨损量也随之降低,并且随着机构柔性的增强,这种效果更为明显.     

Optimization of travelling wave ultrasonic motors using a three-dimensional analysis of the contact mechanism at the stator–rotor interface

The present paper investigates optimization rules and new design methodologies dealing with the contact mechanics in rotative travelling wave ultrasonic motors (TWUM). The proposed approaches focus on the design of the rotor, including the friction layer that is usually deposited onto its lower surface, while the stator is supposed to be preliminary designed. Contact aspects such as the transmission of mechanical power as well as the wear mechanism of the friction layer are investigated, according to the analysis of the stator–rotor contact mechanics in both hoop and radial directions. Considering a classical wear criterion in a preliminary step, a contact ratio, that allows the mechanical power to be optimized, is pointed out in the hoop direction. In a further step, the contact conditions in the radial direction are improved through the elastic fitting of the stator and rotor radial deflexions, therefore allowing the material's wear to be decreased. Some experimental tests, that have been recently performed, give a comparison of wear marks, which occur onto optimal and non-optimal rotor geometries. A first mechanism synthesis is finally proposed in such a way to allow the mechanical architecture of the rotor (including the friction layer) to be automatically designed according to a given set of mechanical constraints.     

A boundary element formulation for wear modeling on 3D contact and rolling-contact problems

The present work shows a new numerical treatment for wear simulation on 3D contact and rolling-contact problems. This formulation is based on the boundary element method (BEM) for computing the elastic influence coefficients and on projection functions over the augmented Lagrangian for contact restrictions fulfillment. The constitutive equations of the potential contact zone are Signorini’s contact conditions, Coulomb’s law of friction and Holm–Archard’s law of wear. The proposed methodology is applied to predict wear on different contact and rolling-contact problems. Results are validated with numerical solutions and semi-analytical models presented in the literature. The BEM considers only the degrees of freedom involved on these kind of problems (those on the solids surfaces), reducing the number of unknowns and obtaining a very good approximation on contact tractions using a low number of elements. Together with the formulation, an acceleration strategy is presented allowing to reduce the times of resolution.     

柔性多体系统中间隙铰接副的磨损预测

通过集成磨损计算与柔性多体动力学,对柔性系统中间隙铰接副部位的磨损进行了预测.基于绝对节点坐标方法（ANCF）建立了柔性部件的多体动力学模型,引入连续接触力模型计算间隙铰接副部分的接触力,并采用Archard磨损模型的迭代磨损计算程序预测磨损.为了得到在不同接触情况下的磨损系数,本文中采用了径向基神经网络处理试验数据.通过对含柔性连杆的曲柄滑块机构进行仿真计算,发现当考虑部件的柔性时,得到的间隙处的冲击力大幅降低,且预测的磨损量也略有降低,这种区别会随着仿真时间的增加而变得更加明显.     

摩擦信号分形维数与载荷和速度的关系研究

在立式万能摩擦磨损试验机上对GCr15/45#钢摩擦副进行不同接触载荷和滑动速度下的摩擦磨损试验,对初始滑动距离1 000 m内的摩擦系数信号进行数据采集,运用结构函数测度方法对摩擦系数信号进行分形表征,计算不同载荷和速度下的分形维数,研究摩擦信号的分形维数随载荷和速度的变化规律.结果表明,摩擦系数信号具有显著的分形特征,其分形维数随载荷和速度而变化.在相同载荷下,分形维数随滑动速度增加而增大;在相同速度下,分形维数随着接触载荷增加而增大.磨损率与摩擦系数信号的分形维数正相关.     

Third body modeling in fretting using the combined finite-discrete element method

A new approach was developed for modeling the effect of the third body on fretting. This was accomplished using the combined finite-discrete element method (FDEM) in which the third body is analyzed as discrete elements while the first bodies are modeled using finite elements. This approach provides a link between large scale models which treat the mass of wear debris as a single or small number of bodies and small scale models which only study a control volume. The FDEM was used to analyze the behavior of third body particles between flat sliding surfaces. When the third body mass is composed of unconnected particles, it behaves as a Newtonian fluid, but this behavior ceases when the particles are connected into platelets. The FDEM was also used to study the behavior of third body particles inside a Hertzian line contact. As the number of particles and platelet size increase the load carried by the worn slip zone grows larger in relationship to the unworn stick zone.     

Application of the angular superposition method to the contact problem on the compression of an elastic cylinder

The angular superposition method is used to construct an approximate solution of the contact problem on the compression of an elastic cylinder by two rigid plates. The solution thus obtained has a closed-form analytic expression and can be used in the entire domain of the cylinder cross-section. We analyze the absolute error, which takes the largest value near the points of contact between the plates and the cylinder, where the boundary conditions are discontinuous. According to the von Mises criterion, when moving into the depth of the cylinder from the contact site along the symmetry axis, the second invariant J ₂ of the stress deviator tensor first decreases and then, after attaining a minimum, increases and attains the largest value at a small depth, which agrees with Johnson’s photoelastic experiments and Dinnik’s computations. We present the graphs of the displacement and normal stress distributions over the contact site, the dependence of the compressing force on the displacements of rigid plates, and the dependence of the invariant J ₂ on the coordinate along the symmetry axis. If 640 computation points are chosen on the cylinder boundary and the Hertz law for the normal pressure on the contact site is used, then the error in the approximate solution near the endpoint of the contact site is approximately 55%, and if the proposed two-parameter normal law is used, then the error is of the order of 4%. On the free lateral surface of the cylinder boundary, we find the critical pointM*, which separates the cylinder contraction and extension parts.The contact problems are the most difficult problems, and their solution is complicated by the discontinuous boundary conditions [1–5]. In [6], the contact problem is solved by the Fourier method, which can be used only for bodies of classical shapes. In such cases, the problem can be reduced to solving coupled integral equations [7]. The interaction between the bandage and a cylindrical body is considered in [2, 6, 7]. In [8], the possibility of using the finite element method is investigated in the case of contact problems for a differential wheel with roughness of the contacting surfaces taken into account. In [9, 10], the method of homogeneous solutions is used to consider contact problems for a finite-dimensional elastic cylinder loaded on its end surfaces. Note that only error estimates are given in the literature cited above; the absolute error over the entire domain of the elastic body is not studied, although this is one of the important characteristics of the obtained approximate solution. A sufficiently complete survey of the literature in the field of contact interactions of elastic bodies is given in [3–5].In what follows, we propose to solve contact problems by the angular superposition method [11]. This method can be used for bodies of nonclassical shapes, which can be multiply connected, and the friction on the contact site can be taken into account. In the present paper, as a first example of applied character, we show how this method can be used in the simplest case. The multiple connectedness and the curvilinearity of the shape of the body, as well as taking into account the friction on the boundary, do not create new essential difficulties in this method.     

钢球检测用展开轮表面微结构增摩降磨特性分析

针对钢球缺陷检测过程中,镜面钢球打滑引起的滑动摩擦导致展开轮磨损这一问题,以实现展开轮增摩降磨为目标,提出将微结构应用于钢球展开轮表面的方法.首先,应用激光微造型技术在T10A试件表面加工不同特征参数凹坑微结构,采用单因素法在MMW-1立式万能磨擦试验机上进行点接触干滑动摩擦试验;在综合考虑局部激光硬化和几何参数对磨损性能影响的基础上,结合试验数据建立基于Archard理论的微结构磨损模型;最后通过仿真技术及磨损试验验证磨损模型的正确性,进而对微结构特征参数进行优选.结果表明:在点接触干滑动摩擦工况下,提出的三种微结构表面均可以实现增摩降磨;建立的磨损模型能准确地计算磨损系数用以分析实际工况的磨损特性;优选了凹坑面积在S_2~S_4范围内的菱形微结构.提出的方法为钢球表面缺陷检测设备提供了技术支持,所建的磨损模型为干摩擦状态下凹坑微结构表面磨损程度的预测提供了理论参考.     

磨损加疲劳载荷下的协同疲劳行为

自行研制的摩擦磨损装置与轴向疲劳试验机相互配合,实现GDL-1钢试样在疲劳应力(240~280 MPa)及接触载荷(30 N)作用下摩擦磨损疲劳试验.通过对磨损层厚度的分析,研究试样承受摩擦磨损载荷及拉压疲劳载荷双重作用下的疲劳寿命变化,用SEM扫描电镜观察分析次表层内疲劳裂纹扩展的演变过程,并采用Hertz线弹性理论和Smith接触理论计算分析摩擦表面以下切应力值.结果表明:在磨损疲劳载荷作用下,形变层的流变作用将显著影响疲劳小裂纹扩展方向,渐趋于切应力方向,从而提高试样疲劳寿命.在此基础上,建立了在摩擦磨损疲劳载荷下疲劳裂纹扩展模型.此外,计算可知在距表层深度0.03 mm处切应力最大,0.18 mm以内材料产生塑性变形,导致形变层的形成.     

接触应力对FCB车轮钢组织演变与性能的影响

利用双盘滚动摩擦磨损试验机进行了贝氏体车轮钢的滚动磨损试验,采用扫描电子显微镜(SEM)、电子背散射衍射(EBSD)分析不同接触应力条件下贝氏体车轮钢次表层微观组织演变. 结果表明:在滚动磨损条件下,磨损机制由黏着磨损转变为疲劳磨损,增大接触应力对黏着磨损阶段的磨损量影响不大,但会显著增加疲劳磨损阶段的磨损量;贝氏体车轮钢在塑性变形的过程中,贝氏体铁素板条中位错逐渐增值、先累积形成小角度晶界,而后形成大角度晶界,使贝氏体铁素体发生细化;接触应力的大小影响表层组织的演变,当接触应力增至1 150 MPa时,晶粒细化为超细等轴晶,继续增加接触应力,组织变化并不明显. 接触应力大小会影响贝氏体车轮钢的表面硬度. 接触应力增加使贝氏体车轮钢的表面硬度增高,硬化层深度增大.      

Enhanced model of load distribution along the line of contact for non-standard involute external gears

The presence of undercut at the tooth root, non-equal addendum on pinion and wheel, non-standard tooth height or non-standard center distance may have decisive influence on the load distribution along the line of contact of spur and helical gear teeth. The curve of variation of the meshing stiffness along the path of contact, quite symmetric respect the midpoint of the interval of contact, loses its symmetry for non-standard geometries and operating conditions. As a consequence, the critical contact points for bending and wear calculations may be shifted from their locations for standard gears. In this paper, a non-uniform model of load distribution along the line of contact of standard spur and helical gears, obtained from the minimum elastic potential criterion, has been enhanced to fit with the meshing conditions of the above mentioned non-standard cylindrical gear pairs. The same analytical formulation of the initial model may be used for the non-standard gears by considering appropriate values of a virtual contact ratio, which are also presented in the paper.     

Simulation of spatial multibody systems with friction

A formulation for modeling and simulation of friction effects in spatial multibody systems is presented. Constraint reaction forces on rigid bodies that are connected by joints that support friction are derived as functions of Lagrange multipliers, using D’Alembert’s principle. Friction forces acting on bodies are calculated as a function of joint geometry, constraint reaction forces that are functions of Lagrange multipliers, and relative velocities at constraint contact points that are determined by system kinematics. Friction forces are implemented in index 0 differential-algebraic equations of motion that are solved numerically using explicit and implicit numerical integration methods. Spatial examples are presented, yielding accurate results and demonstrating that the systems are not stiff, even in the presence of friction and stiction.     

高速与重载铁路的疲劳磨损对比研究

滚动接触疲劳和磨损是铁路钢轨损伤的主要问题.研究根据赫兹接触理论在JD-1型轮轨模拟试验机上通过改变车速和轴重来模拟高速和重载铁路的滚动接触,并用光镜和扫描电镜研究磨损表面,分析高速和重载条件下钢轨的磨损与疲劳机理.结果表明:随车速增加,钢轨磨损量减小,但出现大量斜裂纹,接触疲劳加剧.而随着轴重增加,塑性变形明显,磨损量迅速增加,但由于部分刚萌生的微裂纹被磨去,疲劳损伤较为轻微.     

Exact formulae for determination of the mean temperature and wear during braking

This paper deals with the one-dimensional transient heat conductivity contact problem of a sliding two semi-spaces, which induces effects of friction, heat generation and water during braking. In the present temperature analysis the capacity of the frictional source on the contact plane dependent on the time of braking. The problem solved exactly using the Laplace transform technique. Numerical results for the temperature are obtained for the different values of the input parameter, which characterise the duration of the increase of the contact pressure during braking from zero to the maximum value. An analytical formulae for the abrasive wear of the contact plane is obtained in the assumption, that the wear coefficient is the linear function of the contact temperature. Received on 8 September 1998