On the sliding instabilities at rough surfaces

In this paper, the onset of sliding between two elastic half-spaces in contact, subjected to a tangential force, is studied within the framework of critical phenomena. First, it is shown that the contact domain between two rough surfaces is a lacunar set and that the distribution of contact stresses is multifractal. By applying an increasing tangential force, under constant normal load, the so-called regime of partial-slip comes into play. However, the continuous and smooth transition to full sliding, predicted by the classical Cattaneo-Mindlin theory, is not confirmed by the experiments, which show marked frictional instabilities. A numerical multi-scale procedure is proposed, taking into account the redistribution of stress, consequent to partial-slip, among the contact areas at all scales. It is shown that the lacunarity of the contact domain delays the onset of instability, when compared to compact Euclidean domains. Independently of the assumptions made for the frictional behaviour at the scale of the asperities (Coulomb friction for meso-scale asperities, adhesion for micro-scales), renormalization permits the critical value of the tangential force which provides the instability to be found. Moreover, the multifractal analysis of the domains where the shear resistance is activated captures the size-scale effects on the friction coefficient, currently evidenced by the experiments.     

干气密封滑动摩擦界面切向接触刚度分形模型

为揭示干气密封滑动摩擦界面高频微幅自激摩擦振动规律,用分形参数表征摩擦界面形貌特性,根据重新建立的微凸体接触变形方式,以及对非协调弹性体在切向力作用下初始滑动问题的研究,建立了干气密封滑动摩擦界面切向接触刚度分形模型. 通过数值对切向接触刚度的影响因素进行了分析,研究结果表明:切向接触刚度随分形维数、真实接触面积和材料特性系数的增大而增大;切向接触刚度随特征尺度、摩擦系数的增大逐渐减小. 相比于分形维数、特征尺度和材料特性系数对切向接触刚度的影响,摩擦系数的影响相对较小. 这些研究结果为进一步研究干气密封高频微幅自激摩擦振动奠定了基础.      

三方程线性弹性-阻尼DEM模型及碰撞参数确定

建立了一种考虑法向接触力、切向接触力(含静滑动摩擦力及动滑动摩擦力)和力矩(含由切向力产生的力矩及静滚动摩擦力矩和动滚动摩擦力矩)的三方程线性弹性-阻尼离散单元模型,并将该模型应用到颗粒物料的三维数值模拟中,讨论了模型中几个重要碰撞参数--刚性系数、阻尼系数及摩擦系数的选择及其对计算结果的影响,同时也探讨了时间步长等计算参数对模拟结果的影响.为了验证算法和参数选择的正确性,本文对几个有代表性的颗粒系统进行了数值试验研究,并对计算结果进行了细致的分析,验证了新模型和参数选择的正确性.     

Friction force model and rolling dynamics for a ball on a rough surface with presliding displacement taken into account

A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz’s theory for the “ball-rough horizontal surface” tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters.     

Axi-symmetric bodies of equal material in contact under torsion or shift

Summary Two axi-symmetric bodies are pressed together, so that their axes of symmetry coincide with the contact normal and the normal force is held constant. A small torque about the contact normal or a small tangential force is applied. For bodies of equal material, the normal and tangential stress states are uncoupled, and can solved separately. The surfaces of the bodies are thought as a superposition of infinitesimal rigid flat-ended punches. Consequently, the normal stress distribution can be calculated as a summation of differential flat punch solutions. A formula results, which is identical with the solution of Green and Collins. After application of a torque an annular sliding area forms at the border of the contact area. For reasons of symmetry, the common displacement of the inner stick area must be a rigid body rotation. Similarly to the normal problem, the solution can be thought as a superposition of rigid punch rotations. The tangential solution can be derived analogically, in form of a superposition of rigid punch displacements. The present method also solves the problem of simultanous normal and torsional or tangential loading with complete adhesion. As an example, Steuermann's problem for polynomial surfaces of the formA _2nr²ⁿis solved. The solutions for constant normal forces can be used as basic functions for loading histories with varying normal and tangential forces.     

微/纳尺度粘着滑动接触的多尺度分析

采用分子动力学与有限元耦合的多尺度方法,求解二维刚性圆柱表面压头与弹性平面的微/纳尺度粘着滑动接触问题,通过与全分子动力学模拟结果的比较验证了多尺度方法的有效性。对压头半径、滑动速度、下压深度以及是否考虑粘着效应等对滑动接触性能的影响进行了全面研究,通过不同条件下摩擦力及接触力分布的比较,揭示了上述各参数对粘着滑动接触...     

Multi-scale modeling of grouted sand behavior

The mechanical properties of sand: stiffness, cohesion and, to a less extent, friction angle can be increased through the process of grouting. A constitutive model adapted for cohesive-frictional materials from a homogenization technique which allowed us to integrate constitutive relations at the grain level has been developed to obtain constitutive equations for the equivalent continuous granular medium. A representative volume was obtained by mobilizing particle contacts in all orientations. Thus, the stress–strain relationship could be derived as an average of the behavior of these local contact planes. The local behavior was assumed to obey a stress-dependent elastic law and Mohr–Coulomb’s plastic law. The influence of the cement grout was modeled by means of adhesive forces between grains in contact, which were added to the contact forces created by an external load. The intensity of these adhesive forces is a function of nature and amount of grout present inside the material and can be reduced due to a damage mechanism at the grain contact during loading. In this paper, we present several examples of simulation which show that the model can reproduce with sufficient accuracy the mechanical improvement induced by grouting as well as the damage of the grain cementation during loading.     

Probability density functions of contact forces for cohesionless frictional granular materials

A theory is developed for the probability density functions of contact forces for cohesionless, frictional granular materials in quasi-static equilibrium. This theory is based on a maximum information entropy principle, with an expression for information entropy that is appropriate for granular materials. Entropy is maximized under the constraints of a prescribed stress and that the normal component of the contact force is compressive and that the tangential component of the contact force is limited by Coulomb friction. The theory results in a dependence of the probability density function for the tangential contact forces on the friction coefficient. The theoretical predictions are compared with results from discrete element simulations on isotropic, two-dimensional assemblies under hydrostatic stress. Good qualitative agreement is found for means and standard deviations of contact forces and the shape of the probability density functions, while the quantitative agreement is fairly good. Discrepancies between theory and simulations, such as the difference in shape of the probability density function for the normal force and the observed dependence on elastic properties of the exponential decay rate of tangential forces, are attributed to the fact that the method does not take into account any kinematics, which are essential in relation to elastic effects.     

Modeling of friction at different scale levels

We construct a model for studying the common influence of the imperfect elasticity of actual bodies, the microgeometry of their surfaces, and their adhesive interaction on the contact characteristics (the contact pressure distribution, the region of actual contact) and on the sliding friction force. The model is based on the solution of a plane contact problem of sliding of a rigid body with a regular relief on the boundary of a viscoelastic foundation with surface molecular attraction in the gap between the surfaces taken into account. We analyze the influence of the surface microgeometry parameters at different scale levels on the character of the surface interaction (the saturated or discrete contact) and the friction force for different sliding velocities of the contacting bodies.     

Mechanics of thermophoretic and thermally induced edge forces in carbon nanotube nanodevices

A double walled carbon nanotube thermal actuator consisting of a short outer tube sliding along a long inner tube under a temperature gradient is used as a model system to investigate the mechanics of thermophoretic and thermally induced edge forces in nanoscale contact based on the theory of lattice dynamics. It is shown that the total thermophoretic force has two components: a gradient force due to the change in van der Waals energy in the direction of temperature gradient and an unbalanced edge force due to the temperature difference between the two tube ends. Closed-form analytical expressions are derived for the gradient and unbalanced edge forces, with results in excellent agreement with molecular dynamics simulations. This study represents a first analytical study of thermophoretic and thermally induced edge forces between two solid bodies, and may have far reaching implications on thermomechanical nanodevices and nanoscale contact.     

Micro-plasticity of surface steps under adhesive contact: Part II—Multiple-dislocation mediated contact hardening

The study of micro-plastic behavior of rough surface contacts is the critical link towards a fundamental understanding of contact, friction, adhesion, and surface failures at small length scales. In the companion paper (Yu, H.H., Shrotriya, P., Gao, Y.F., Kim, K.-S., 2007. Micro-plasticity of surface steps under adhesive contact. Part I. Surface yielding controlled by single-dislocation nucleation. J. Mech. Phys. Solids 55, 489–516), we have studied the onset of surface yielding due to single-dislocation nucleation from a stepped surface under adhesive contact. Here we analyze the contact hardening behavior due to multiple dislocations in a two-dimensional dislocation model. Continuum micro-mechanical analyses are used to derive the configurational force on the dislocation, while a modified Rice–Thomson criterion is used to model dislocation nucleation. Dislocations nucleated from the surface step are stabilized and pile up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The dislocation pileup will exert a strong back stress to prevent further dislocation nucleation and thus lead to the contact hardening behavior, the degree of which depends on the slip-plane orientation. Particularly, we find that dislocation interactions between two slip planes can make the contact loading order-of-magnitude easy to nucleate multiple dislocations, which is thus named “latent softening”. A mechanistic explanation shows that the latent softening is closely related to the stress-concentration mode mixity at the surface step. Dislocation nucleation will modify the geometric characteristics of the surface step, so that the contact-induced stress state near the step, as described by the mode mixity, changes, which influences the subsequent dislocation nucleation. Our calculations show that the dislocation pileup on one slip plane can even cause the spontaneous dislocation nucleation on the other slip plane without further increase of the contact load. Furthermore, it is found that rough surface contacts at small length scale can lead to the dislocation segregation and the formation of a surface tensile sub-layer. The discrete-dislocation model presented here and in the companion paper provides novel insights in bridging the atomistic simulations and continuum plastic flow analysis of surface asperity contact.     

On indentation of a pair of rigid punches connected by an elastic beam into an elastic half-plane with regard to the friction and adhesion forces in the contact region

The contact problem of indentation of a pair of rigid punches with plane bases connected by an elastic beam into the boundary of an elastic half-plane is considered under the conditions of plane strain state. The external load is generated by lumped forces applied to the punches and a uniformly distributed normal load acting on the beam.It is assumed that the contact between the punch and the elastic half-plane can be described by L. A. Galin’s statement, i.e., it is assumed that the adhesion acts in the interior part of each of the contact regions and the tangential stresses obeying the Coulomb law act on their boundaries.With the symmetry taken into account, the problem is stated only for a single punch, and solving this problem is reduced to a system of four singular integral equations for the tangential and normal stresses in the adhesion region and the contact pressure in the sliding zones. The solution of the constitutive system together with three conditions of equilibrium of the system of punches connected by a beam is constructed by direct numerical integration by the method of mechanical quadratures.As a result of the numerical analysis, the contact stress distribution functions were constructed and the values of the sliding zones and the punch rotation angle were determined for various values of the geometric, elastic, and force characteristics.     

The bouncing motion appearing in a robotic system with unilateral constraint

The hopping or bouncing motion can be observed when robotic manipulators are sliding on a rough surface. Making clear the reason of generating such phenomenon is important for the control and dynamical analysis for mechanical systems. In particular, such phenomenon may be related to the problem of Painlevé paradox. By using LCP theory, a general criterion for identifying the bouncing motion appearing in a planar multibody system subject to single unilateral constraint is established, and found its application to a two-link robotic manipulator that comes in contact with a rough constantly moving belt. The admissible set in state space that can assure the manipulator keeping contact with the rough surface is investigated, and found which is influenced by the value of the friction coefficient and the configuration of the system. Painlevé paradox can cause either multiple solutions or non-existence of solutions in calculating contact force. Developing some methods to fill in the flaw is also important for perfecting the theory of rigid-body dynamics. The properties of the tangential impact relating to the inconsistent case of Painlevé paradox have been discovered in this paper, and a jump rule for determining the post-states after the tangential impact finishes is developed. Finally, the comprehensively numerical simulation for the two-link robotic manipulator is carried out, and its dynamical behaviors such as stick-slip, the bouncing motion due to the tangential impact at contact point or the external forces, are exhibited.     

粘着摩擦系数的分形几何研究

计及作用于接触斑点上的切向力，通过比较作用于接触斑点上的法向弹性载荷与法向塑性载荷，确定了区分弹性接触与塑性接触区域的临界接触斑点面积．总的粘着摩擦系数被表示为弹性接触区与塑性接触区的粘着摩擦系数的组合．假设屈服压力及局部粘着摩擦系数不依赖于接触斑点且等于塑性接触区中的平均值，则总的粘着摩擦系数可用简单的表达式描述．分形几何参数及归一接触面积对于粘着摩擦系数的效应已通过算例表明，研究中，分别考虑了忽略与计及接触斑点的微粒间的相互作用，两种情况的结果完全不同．     

Sliding of a spherical indenter on a viscoelastic foundation with the forces of molecular attraction taken into account

The problem of sliding of a spherical indenter on a viscoelastic foundation is solved in a quasistatic formulation taking account the forces of adhesive attraction which are considered different at the entrance to and exit from the contact region due to changes in the surface properties during the interaction. It is found that the contact characteristics and the frictional force due to the imperfect elasticity of the foundation depend on the surface and bulk properties of the materials of the interacting bodies and the interaction conditions (load, velocity, etc.).     

Painlevé paradox during oblique impact with friction

In analyses using non-smooth dynamics, oblique impact of rough bodies in an unsymmetrical configuration can result in self-locking or “jam” at the sliding contact if the coefficient of friction is sufficiently large; this has been termed, Painlevé’s paradox. In the range of configurations and coefficients of friction where Painlevé’s paradox occurs, analyses based on rigid body dynamics give results indicating that either there are multiple solutions or the solution is nonexistent. This conundrum has been resolved by considering that the contact has small normal and tangential compliance which is representative of deformability in a local region around the contact point. An analysis using a hybrid model which includes local compliance of the contact region has calculated the time-dependent changes in relative motion of colliding bodies for a range of incident angles of obliquity, tan^?1[?V₁(0)/V₃(0)] where V₁(0)and V₃(0) are the incident tangential and normal relative velocities at the contact point, respectively. The paradox is shown to result from a negative relative acceleration of the contact points during an initial period of sliding – a negative acceleration that is inconsistent with the assumption of rigid-body contact.     

A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations

A minimal two degree of freedom model is used to clarify from an intuitive perspective the physical mechanisms underlying the mode-coupling instability of self-excited friction induced oscillations. It is shown that simultaneous out-of-phase oscillations of friction force and displacement tangential to the friction force may lead to energy transfer from the frictional system to vibrational energy. Also it is shown that the friction force acts like a cross-coupling force linking motion normal to the contact surface to motion parallel to it and that a necessary condition for the onset of instability is that these friction-induced cross-coupling forces balance the corresponding structural cross-coupling forces of the system. Finally the origin and the role of phase shifts between oscillations normal and parallel to the contact surface is clarified with respect to the mode-coupling instability. It may be expected that the intuitive picture gained will be of considerable help for practical design purposes.     

Contact force and mechanical loss of multistage cable under tension and bending

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first-and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theo-retical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is compli-cated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads.     

基于神经网络的间隙机构运动副磨损预测

应用BP神经网络建立了磨损率与接触应力、滑动速度和材料硬度之间的非线性关系模型,并对该网络模型进行了验证和测试,结果表明,训练良好的神经网络模型能够准确反映样本所蕴含的内在磨损规律,且具有较好的预测效果。基于非线性弹簧阻尼模型和修正的Coulomb摩擦力模型对含间隙曲柄滑块机构进行数值仿真分析,获得间隙机构运动副的接触应力和相对滑动速度,利用训练好的神经网络磨损模型对轴套的磨损进行迭代磨损预测分析,发现随着曲柄转数的增加,轴套表面一些特定位置处的磨损越来越严重,最终导致轴套表面出现非均匀磨损现象,其原因是间隙机构运转过程在一些特定位置处产生了较大接触应力和碰撞力。     

Complex variable formulation for non-slipping plane strain contact of two elastic solids in the presence of interface mismatch eigenstrain

In this paper, the problems of non-slipping contact, non-slipping adhesive contact, and non-slipping adhesive contact with a stretched substrate are sequentially studied under the plane strain theory. The main results are obtained as follows:(i) The explicit solutions for a kind of singular integrals frequently encountered in contact mechanics (and fracture mechanics) are derived, which enables a comprehensive analysis of non-slipping contacts. (ii) The non-slipping contact problems are formulated in terms of the Kolosov–Muskhelishvili complex potential formulae and their exact solutions are obtained in closed or explicit forms. The relative tangential displacement within a non-slipping contact is found in a compact form. (iii) The spatial derivative of this relative displacement will be referred to in this study as the interface mismatch eigenstrain. Taking into account the interface mismatch eigenstrain, a new non-slipping adhesive contact model is proposed and its solution is obtained. It is shown that the pull-off force and the half-width of the non-slipping adhesive contact are smaller than the corresponding solutions of the JKR model (Johnson et al., 1971). The maximum difference can reach 9% for pull-off force and 17% for pull-off width, respectively. In contrast, the new model may be more accurate in modeling the non-slipping adhesion. (iv) The non-slipping adhesions with a stretch strain (S-strain) imposed to one of contact counterparts are re-examined and the analytical solutions are obtained. The accurate analysis shows that under small values of the S-strain both the natural adhesive contact half-width and the pull-off force may be augmented, but for the larger S-strain values they are always reduced. It is also found that Dundurs’ parameter β may exert a considerable effect on the solution of the pull-off problem under the S-strain.These solutions may be used to study contacts at macro-, micro-, and nano-scales.