The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

On the Relation of Load to Average Gap in the Contact Between Surfaces with Longitudinal Roughness

A computer simulation model for the contact between longitudinally-oriented rough surfaces has been formulated. This model closely duplicates the actual surf ace contact deformation behavior by taking into account the elastic interactions between the asperities. There were no assumptions made about the shapes, or any deformation behavior of the asperities, except for their obeying the laws of elasticity. The plastic deformations on the high asperity peaks were taken into account by setting a ceiling on their contact pressures at the material hardness value. The simulations used real surface profiles which were digitized from unworn circumferentially ground steel surfaces. Each pair of these profiles was mathematically combined to form an equivalent rough profile pressing against an infinitely rigid flat and having the appropriately adjusted elastic modulus. A total of 28 different pairs of profiles were used in the simulations. Each contacting pair was subjected to 30 different load levels and the local contact pressures and deformations were calculated. The contact simulations yielded some important mathematical relationships between parameters, such as the real area of contact, average gap, and average asperity load through statistical curve fitting. Two analytical functions were generated to relate the average load to average gap and the real area of contact to load.     

A micro-model for elasto-plastic adhesive–contact in micro-switches: Application to cyclic loading

Stiction is a major failure mode in micro-electromechanical systems. In previous works, a statistical rough surfaces interaction model, for which only elastic adhesive–contact has been considered, was developed for multiscale analyzes.However, during the impact between rough surfaces, plastic deformations of asperities cannot always be neglected. In the present work, the adhesion between rough surfaces is studied considering the elasto-plastic deformations of the asperities, and a model predicting the resulting micro-adhesive–contact forces is derived.For illustration purpose, an electrostatic-structural analysis is performed on a micro-switch. To determine the degree of plasticity involved, the impact energy of the movable electrode at pull-in is estimated. Thus the maximal adhesive force evolution during cyclic loading is predicted using the developed model.     

Analysis of mechanical properties of large particles in contact process and their impact on powder lubrication

Abstract

Impurities or wear particles are almost impossible to avoid during powder lubrication. This condition causes three-body contact with rough surfaces in the condition of mixed in large particles. The mechanical properties of large particles in the process of powder lubrication are analysed in this study by combining the caulking effect, covering effect and three-body elastic contact model. The relationship and influencing factor between load and the contact area and the separation between the two surfaces in the presence of a third body are determined. Furthermore, the impact of large particles on the lubricating effect is analysed. Experiments are conducted to observe the destruction of the powder layer of friction, the impact of large particles and specific forms of damage.     

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.     

Modelling of static friction in rubber–metal contact

A static friction model for contact between rough rubber and metal surfaces is developed. This model is based on the contact of a viscoelastic–rigid asperity couple. Single asperity contact is modelled in such a way that the asperities stick together in a central region and slip over an annulus at the edge of the contact. The slip area increases with increasing tangential load. Consequently, the static friction force is the force when the slip area is equal to the contact area. Using the model, the traction distributions, contact area, tangential and normal displacement of two contacting asperities are calculated. The single asperity model is then extended to multi-asperity contact, suitable for rough surfaces. This model allows calculation of the above-mentioned parameters for two rough surfaces (a rubber and a metal one) subjected to normal and tangential loads. A parametric study will be presented. The results are qualitatively in good agreement with those found in literature.     

Transient Rolling Contact Phenomena

Two cylinders of identical purely elastic materials are pressed together with parallel axes under the action of a normal force so that a contact strip forms. The cylinders are then shifted with respect to each other, which, under the influence of dry friction, gives rise to Cattaneo's (2) traction distribution with two slip areas. Subsequently they are rolled under the influence of a constant couple, reaching eventually Carter's (3) steady state with one slip area.

The question arises how the former traction distribution passes into the latter as a function of time. It is answered in the framework of a more general rolling contact problem.

The problem is solved numerically under the assumption of vanishing inertial effects, and results are presented. In the problem mentioned above it is found that Carter's (3) distribution is virtually attained when one to two contact widths have been traversed.     

TRIBOS: A Performance Evaluation Tool for Traction-Transmitting Partial EHD Contacts

The details are given of a computer model for performing a state-of-the-art tribological assessment of the performance of a lubricated concentrated rolling/sliding/spinning/contact comprising general anisotropic rough surfaces. The name chosen for this program is TRIBOS.

It computes: 1. The contact ellipse dimensions and area

2. The elastohydrodynamic (EHD) film thickness both at the plateau and at the constriction that forms at the rear of a lubricated concentrated contact under fully flooded (un-starved) and isothermal lubricant inlet conditions

3. The apportionment of the applied load between the asperities and the lubricant film

4. The magnitude and direction of the tractive force transmitted between the contacting bodies by the combined effects of (a) shearing of the fluid film and (b) coulomb friction between contacting asperities

5. The mean number of asperity contacts and the real contact area, i.e. the total contact area of the elastically deformed asperities

6. A film thickness correction factor accounting for lubricant starvation in the contact inlet

7. A film thickness correction factor accounting for a viscosity decrease of the inlet oil due to fluid heating

8. An index of surface fatigue behavior

The program is a synthesis of computational tools from the current literature for the computation of fluid film thickness and traction, and a general asperity simulation model for the elastic contact of anisotropic rough surfaces. In the example given, it is used to perform a comparative evaluation of the performance of 18 combinations of 9 surface roughnesses and 2 lubricants in a traction drive contact.     

粗糙表面微凸体对液黏传动的影响

为研究液黏传动过程中粗糙表面的承载特性,将分形理论引入到两粗糙表面摩擦过程之中,分析传动过程中混合摩擦和边界摩擦两阶段的微凸体承载过程,考虑微凸体弹塑性变形,对M-B模型进行修正,建立修正的微凸体承载模型。建立基于修正M-B模型的微凸体承载模型。通过数值仿真得到有效面积系数、分形参数对液黏调速离合器传动过程的影响规律;对修正的微凸体承载模型的计算结果与M-B模型的计算结果进行对比分析。结果表明:微凸体接触载荷和传递转矩随着面积比的增大而增大,当有效面积系数与尺度系数增大时,接触载荷与传递转矩均有所增大;分形维数为1.5时,微凸体接触载荷与传递转矩最小且随面积比的变化最为缓慢;在整个接触区域内,弹性变形区域的面积、接触载荷以及传递转矩最大,其次是弹塑性变形区域,塑性变形区域最小;考虑弹塑性变形时,微凸体接触载荷与传递转矩均有所下降;修正M-B模型和M-B模型间的修正系数范围在25%以内,修正系数随着有效面积系数、尺度系数的增大而增大,随着分形维数的增大而减小。     

两接触粗糙表面的椭圆弹塑性模型

视两单峰的接触区为椭圆,给出了两接触相糙表面的椭圆弹性通解.根据两单峰塑性接触时单个相糙峰的椭圆抛物面体积守恒推导了椭圆塑性通解.临界弹性干涉量随有效半径比增加而减小.塑性指数越小,临界弹性干涉量减小量越大.临界弹性干涉量随表面粗糙度增加、材料硬度减小而减小.椭圆、GW模型的临界弹性干涉量之比随有效半径比增加而减小.GW模型高估了临界弹性干涉量.椭圆、GW模型的塑性指数之比随有效半径比增加而增加.GW模型低估了塑性指数.有效半径比越大,偏差量越大.     

Contact stiffness of machine tool joints

The paper deals with the elasto-plastic deformation of the surface asperities in contact. The theoretical analysis has been carried out to estimate normal deformation of the interface of the joint and rotation of the joint axis, when the joint is subjected to normal and bending loads. The efforts have been made to estimate value of constant, m, which is useful for finding out elastic deformation of the contacting surfaces. The experiment was carried out to study the validity of the analytical approach. Conclusions are drawn on the basis of work done.     

Pressure distribution and deformations of machined components in contact

The paper presents a general method for calculating the pressure distribution at contacting machined surfaces and the resulting deformations of components subjected to external loads. It is well known that when machined surfaces are compressed one against the other then due to the deformation of the asperities the approach of the surfaces is related to the interface pressure by a non-linear function. Another effect that must be taken into account is that the actual area of contact is not known previously and is, of course, different from the apparent area. For the method presented, the contact or connexion between the components is simulated with finite elements, springs or plates defined as a function of the surface roughness and surface deformations. The system so established is solved in an iterative way using the finite element method and this enables the pressure distribution at the contact and the resulting deformations of the whole component to be determined. Finally, examples of some problems solved by different methods are given and the results compared with the experimental data.     

Limits of applicability of elastic contact models of rough surfaces

Recent stochastic models for analyzing the contact of rough surfaces assume that the asperities are microhertzian, i.e. that they can be approximated as second-order surfaces in the vicinity of contact points, and that the asperities deform elastically. Using a plane strain solution from the literature for a sinusoidally corrugated half-space, the range of validity of these assumptions is shown to be related to the mean square surface slope and the macrocontact pressure. By extension to random surfaces characterized by a one-dimensional spectral density function an interval on the surface spatial frequency is found over which the asperities deform elastically but without completely flattening. A numerical example is given.     

A numerical investigation of the sinusoidal model for elastic layers in line contact

Distributions of normal stresses and surface deformations, induced when an elastic layer of finite thickness is indented by a frictionless rough rigid flat or cylindrical indenter, are calculated numerically. It is assumed that the punch has a sinusoidal roughness superimposed on its nominal profile. Two cases will be examined, namely when the elastic layer is either bonded to a rigid backing or resting on a frictionless rigid backing (unbonded). Chebyshev polynomials of the first kind T_n(x) are utilized to model both the unknown pressure and the given deformation over the contact area. The governing elasticity equation is thereby reduced to a finite set of linear equations and hence a complete solution is found. The present numerical method is simple, accurate and valid in the full range of Poisson's ratio 0 v 0.5. Moreover, a set of semi-analytical solutions for the contact pressure is obtained for both thin unbonded and bonded elastic layers. The numerical results compared favourably with the asymptotic solutions. The effects of the layer thickness, layer compressibility and roughness amplitude parameters on the contact stresses and deformations are considered.     

An Engineering Model for Three-Dimensional Elastic-Plastic Rolling Contact Analyses

Fatigue life of heavily loaded rolling bearings is strongly dependent on elastic-plastic material properties. For bearing steels these elastic-plastic properties can be accurately obtained by performing monotonic or half-compressive tests. A three-dimensional strain deformation analysis based on the incremental theory of plasticity and the use of Prandtl-Reuss relations in conjunction with the von Mises yield criterion was developed in order to evaluate the permanent deformation in dry contacts loaded above the elastic limit in case of normal loading. The Ramberg-Osgood stress-strain relation for two martensitically hardened variants of SAE 52100 bearing steel considered the nonlinear kinematic and/or isotropic material behavior. Parameters describing the influence of retained austenite are modeled by using a nonlinear isotropic law. Pressure distribution and contact surface displacements during incremental loading are evaluated by using a conjugate gradient method and the internal stress field is derived by using the superposition principle. Further, a fast analysis of smooth surfaces in elastic-plastic static and rolling contact is developed based on analytical relations for the internal stress field. Cyclic evaluation of plastic strains and residual stresses is carried out until shakedown. In order to verify the theoretical model, rolling contact tests under high normal load were performed. Residual stresses and residual profiles measurements show excellent agreement between numerical and measured cyclic values.     

Mathematical slip-line field solutions for ploughing a hard particle over a softer material

Wear mechanisms and friction in metals can be investigated by the analysis of the unit event represented by the interaction of a hard particle or asperity with a softer surface. Effective friction is the result of the interaction of many such asperities which constitute the roughness of the harder of the solid surfaces. Three types of plastic deformation at the metal surface can be identified: ploughing, edge formation and chip formation. Each mode of plastic deformation can be analysed using the slip-line field plasticity theory which requires as inputs the geometry of the hard particle and some information on the interface between the harder and the softer surfaces. The classical and the recent chord solution by Oxley assumes a sharp edge sliding against a metal surface but does not consider a curved roughness profile. However, the profiles of real asperities are more like waves with rounded summits. In the present work a new model for the asperities interaction is shown, using the slip-line field theory to calculate the friction forces, depth of sheared layer, average contact pressure and friction coefficient for a cylindrical hard particle sliding over a softer surface. The theoretical results are presented as friction graphs and maps in which the regions of elastic deformations are shown using the Hertz theory while the region of plastic strains is obtained from the present analysis. Present model results are in good agreement with experimental data obtained by Busquet et al. and are quite different from the Oxley chord model for sliding a circular particle.     

Measurement of Pressure Distribution in EHL—Development of Method and Application to Dry Static Contacts

The development and application of a new technique to measure the pressure distribution in an elastohydrodynamic contact is described. The method uses optical interferometry to measure the local compression of a thin elastic layer sandwiched between the loaded surfaces. The elastic-layer thickness is mapped as a line profile across the contact and the measured compression is calibrated to give a pressure distribution. The data are acquired through a single triggered image rather than a scanning system so that transient pressures can be measured. The current study is limited to static contacts, and pressure profiles are presented for a number of contact conditions. These include smooth and textured surfaces and entrained debris. The results are compared to theoretical predictions for smooth surfaces.     

Role of Head Parameters on Head-Disc Interface

The effect of a nanoslider's crown, camber, twist and suspension load are parametrically studied and compared from a tribological standpoint. In this paper, stiction, friction, and contact start-slop (hereafter CSS) were performed on a modified disc drive equipped with a special strain gauge. For convex (positive crowned and cambered) sliders, up to five to six times reduction in rest stiction can be easily attained compared to flat sliders. This also applies to drives which have been turned off and turned on after one week.

Flat sliders with much of the air bearing surfaces etched away are, also studied. The patterned sliders did not reduce stiction when tested on a lightly textured disc coated with a lube system consisting of mobile and bonded phases.

The normal suspension force and weight of the slider when bonded together determine the apparent slider contact between the disc surface asperities. The reduction in contact area from six to four grams suspension load on the asperities is about 24 percent.

The effect of convex slider improves the disc durability during CSS. It is believed the geometry allows the convex-shaped magnetic slider to take off from the disc surface sooner than flat ones. That was observed by Lee and Bolasna. The concave slider will reduce stiction also because of smaller contact area. However, its inability to take off early results in catastrophic disc wear. Once in flight, the sliders are insensitive to the convex or concave effect.     

Effect of surface roughness on contact between solid surfaces

The analysis of the mechanism of contact between two solids was carried out considering the distribution of the radii of curvature of asperity peaks. The analytical results show that the mean radius of curvature of asperity peaks has a considerable effect on the nature of the deformation of contact asperities, i.e. whether the contact is plastic or elastic, and more effect on the real area of contact than the variation of the distribution of the radii of curvature.The radii of curvature at the asperity peaks and the real area of contact between two smooth surfaces were measured for comparison with the theoretical results. The results for isotropic surfaces produced by buffing and sandpaper agree with the theory; the real area of contact increases with decreasing surface roughness.     

A Numerical Model for the Dry Sliding Contact of Layered Elastic Bodies with Rough Surfaces

A numerical model for the two-dimensional dry sliding contact of two elastic bodies with real rough surfaces has been developed, where an elastic body contacts with a multi-layer surface under both normal and tangential forces. The model uses surface profile data directly recorded with a stylus measuring instrument and it is suitable for use on a microcomputer. Green's function for a unit normal load and a unit tangential load for the generalized plane strain problem are derived. Verification of the accuracy of the model by reproduction of test case results is presented. Contact pressure distribution for layers of varying coefficient of friction, thickness and elastic modulus is analyzed.