Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

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.     

Elasto-Plastic Contact of Rough Surfaces

An isothermal elasto-plastic asperity contact model is developed and presented in this paper, which deals with micro plastic flows of materials and the influence of the elasto-plastic deformation of materials on the behavior of contacting surfaces. The model is solved with the incremental form of a simplex-type algorithm. The von Mises yield criterion is used to determine the onset of the plastic deformation. The effectiveness and validity of the model are studied through analyzing a Hertzian contact problem. Substrate stresses are calculated and differences are observed. Furthermore, the contact pressure, real area of contact, and average gap of real rough surfaces under the elastic, elastic-perfectly-plastic, and the elasto-plastic contact conditions are numerically investigated and the results are compared.     

Experimental and theoretical investigation of running-in

In this paper, the running-in and steady-state wear in the mixed-EHL line contact problem are analytically and experimentally studied. An experimental apparatus is designed and built to investigate the transient wear process during the initial stage of contact of two rollers with fresh surfaces as well as the contact of broken-in surfaces, when wear rate becomes steady. Seven experiments are conducted with five running-in experiments on fresh rollers and two steady-state experiments on the run-in rollers. The results of experimental tests and a series of simulations of an analytical model that uses the load-sharing concept and accounts for plastic deformation of asperities during the running-in stage are presented. The comparison of experimentally measured wear weight, wear depth, surface roughness, friction coefficient, and surface temperature of these seven experiments are shown to be in good agreement with the simulation results.     

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.     

A new roughness parameter to evaluate the near-surface deformation in dry rolling/sliding contact

Within this work, a two-dimensional finite element model for rolling contact of a wheel on a rail is presented that accounts for the roughness of the contact surfaces. The rail material is modeled with elastic–plastic behavior. The maximum of the plastic shear strain is concentrated close to the surface of the rail and is mainly influenced by the surface roughness. A concept is proposed that demonstrates one crucial parameter of the roughness determines surface deformation (based on results of a sinusoidal roughness model). This roughness parameter depicts the ratio between asperity height and width. Numerical validation is achieved for predicting plastic shear strains in rough surfaces. The plastic shear strain is associated with surface damage, such as cracks and wear.     

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。     

Numerical Study of the Effect of Tribofilm Kinetics and Its Hardness on the Roughness Evolution of the Substrate in Boundary Lubrication Regime

Abstract

A tribochemical modeling framework that considers the growth of a tribofilm on the contacting surfaces has been used in this work. The model couples a fast contact mechanics model with the thermodynamics of interfaces and captures the growth of the tribofilm on the asperities. The model was shown to be able to capture the dynamics of a tribosystem and the evolution of surface topography. The model considers the effect of plastic deformation and wear in modifying the surface geometries. In a recent work by the authors (Ghanbarzadeh et al., Wear, 362–363, 2016), the same numerical model was validated against experiments in a micropitting rig (MPR) and the wear, topography, and tribofilm thickness results were compared. In this work, validation of the model is presented and the effect of tribofilm kinetics and its hardness have been numerically studied to assess the evolution of surface roughness in a rolling sliding contact. Results suggest that the kinetics of the tribofilm growth significantly influence the roughness evolution with higher kinetics resulting in a rougher interface. Similarly, the tribofilm hardness affects the roughness evolution and is more influential in the later stages of roughness evolution.     

An unsteady mixed soft EHL model, with application to a rotary lip seal

A rotary lip seal usually operates with full-film lubrication. However at low speeds, such as those encountered during startup and shutdown, mixed lubrication occurs and asperities on the lip contact the shaft. To simulate this condition, a mixed soft EHL model has been constructed. The fluid mechanics of the lubricating film is described by a Reynolds equation that can handle interasperity cavitation. The bulk deformation of the lip is computed using influence coefficients, while the junctions between the asperities and the shaft are modeled as Hertzian contacts. Since the shaft is rough, the flow is unsteady and an unsteady analysis is required. The model shows how the shaft roughness affects such seal characteristics as load support, contact load ratio, contact area ratio, cavitation area ratio, reverse pumping rate and average film thickness.     

Elastic–Plastic Spherical Contact Modeling Including Roughness Effects

The effect of material properties and surface roughness on the contribution of asperities and sphere bulk displacements to the total displacement of a rough spherical contact is investigated. A dimensionless transition load, above which the contribution of the bulk displacement exceeds the contribution of the asperities displacement, is found as a function of the plasticity index and dimensionless critical interference of the sphere bulk. A criterion is proposed for evaluating the importance of surface roughness in calculating the displacement of a rough spherical contact. Some experimental results with a spherical micro-contact are presented to verify the model.     

Analyzing Elastic-Plastic Real Rough Surface Contact in Running-in

A numerical method is presented for evaluating the elastic-elastic contact of real rough surface contacts during running-in. For the surface contact, an elastic-plastic model based on the variational method is applied to analyze the pressure distribution and contact area of worn surfaces during running-in. In conjunction with the classical statistic model of Greenwood and Williamson, the numerical result showed that the plasticity index Ψ was decreased to one in the elastic range as running-in proceeded. In comparison with the Hertzian solution, the influence of the asperities is very significant on the pressure distribution, thereafter causing a higher peak value of contact pressure. For the subsurface, the interior stress from the von Mises criterion was calculated to evaluate the subsurface stress field subject to both normal and tangential forces. In the calculated of the interior stress, the total stress is decomposed into a fluctuating component and a smooth component. The fluctuating part is solved by using FFT from the concept of the convolution theorem while the smooth part is obtained directly by analytical solution. Calculations of contact area and subsurface stress on experimentally produced surfaces whose topography has been determined using an atomic force microscope and friction coefficient front sliding have been carried out. The results showed that asperities and friction coefficient gave rise to stress increase in the near-surface stress field and produced a high stress zone towards the surface. As a result, transverse asperity cracking was produced. The calculations and supporting experimental evidence clearly confirmed that the reduction of peak pressure during running-in decreased the plastic deformation of contact.     

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.     

Theoretical and Experimental Study of a Thermal Contact Conductance Model for Elastic,Elastoplastic and Plastic Deformation of Rough Surfaces

This study developed a thermal contact conductance model that takes into account surface asperities with elastic, elastoplastic and plastic deformation. The surface asperity model considers the continuity and smoothness of variables across different modes of deformation. Experiments were also conducted to measure thermal contact conductance for samples with different surface roughness when the contact pressure was increased or decreased. The trend of the test data supports the theoretical results.     

Effect of ratio of hardnesses,load, and roughness parameters on approach in elastoplastic contact of rough surfaces of flat parts

The effect of various factors, such as the roughness parameters, the ratio of the hardnesses of materials of the parts, the average pressure, and the curvature radius of asperities, on the approach in the elastoplastic contact of the flat rough surfaces of two materials with similar hardnesses has been considered. In this case, asperities on the rough surface simultaneously undergo plastic deformation and penetrate into the counterface.     

Effects of Surface Roughness on Point Contact EHL

The effects of orientation of surface roughness, entrainment (rolling) velocity, and slide/roll ratio on micro-elastohydrodynamic lubrication (micro-EHL) are investigated under pointcontact conditions using the optical interferometry technique. Long bumps with constant height and wavelength produced artificially on the surface of a highly polished steel ball are used as a model roughness. It is shown that the asperities are elastically deformed and the magnitude depends on the film factor A, defined by the ratio of the central film thickness based on smooth surfaces to the composite surface roughness, as well as the surface kinematic conditions and the orientation of the asperities. It is also found that a thin or thick oil film formed at the inlet of the contact by a moving rough surface travels through the contact region at a speed very close to the average speed of the contacting surfaces. The possible mechanism is discussed.     

Real area of contact and boundary friction in metal forming

Upper-bound models for asperity flattening on a workpiece surface undergoing bulk plastic deformation are developed. It is found that the effective hardness of the surface can be greatly reduced by the presence of underlying plastic flow. Theoretical predictions of the variation of real area of contact with strain show excellent agreement with experiments using model asperities in rolling. Friction models which allow for the reduction in effective hardness are developed for cases in which roughness is concentrated on either the workpiece or tooling.     

The Effect of Asperity Flattening During Cyclic Normal Loading of a Rough Spherical Contact

The effect of asperity flattening of a rough spherical contact during cyclic loading is investigated experimentally. Two types of surfaces are examined; the first is an “as-manufactured” isotropic surface and the second a smooth “laser-polished” surface. Both the surfaces exhibit a large amount of hysteresis of the load–displacement curve during the first load–unload cycles. This hysteresis is found to decrease as a function of the number of load cycles. A comparison of the experimental results with results obtained from a numerical model for a rough spherical contact shows good correlation. The model shows that for rough surfaces the total displacement is a function of the contacting asperities while for smooth surfaces the main contribution comes from the bulk displacement.     

Microscopic asperity contact and deformation of ultrahigh molecular weight polyethylene bearing surfaces

The effect of the roughness and topography of ultrahigh molecular weight polyethylene (UHMWPE) bearing surfaces on the microscopic contact mechanics with a metallic counterface was investigated in the present study. Both simple sinusoidal roughness forms, with a wide range of amplitudes and wavelengths, and real surface topographies, measured before and after wear testing in a simple pin-on-plate machine, were considered in the theoretical analysis. The finite difference method was used to solve the microscopic contact between the rough UHMWPE bearing surface and a smooth hard counterface. The fast Fourier transform (FFT) was used to cope with the large number of mesh points required to represent the surface topography of the UHMWPE bearing surface. It was found that only isolated asperity contacts occurred under physiological loading, and the real contact area was only a small fraction of the nominal contact area. Consequently, the average contact pressure experienced at the articulating surfaces was significantly higher than the nominal contact pressure. Furthermore, it was shown that the majority of asperities on the worn UHMWPE pin were deformed in the elastic region, and consideration of the plastic deformation only resulted in a negligible increase in the predicted asperity contact area. Microscopic asperity contact and deformation mechanisms may play an important role in the understanding of the wear mechanisms of UHMWPE bearing surfaces.     

热力耦合下微接触点塑性应变沿深度变化分析

在考虑粗糙实体弹塑性变形、热力耦合、微凸体间相互作用和摩擦热流耦合等影响下,运用有限元法数值模拟具有三维分形特性的粗糙面与刚性平面间滑动摩擦过程,分析了粗糙实体接触凸点塑性变形随深度变化情况。发现：在速度的突变和闪点温度形成时,摩擦接触表层等效塑性应变增大明显;在这一摩擦表层,过不同接触点的纵向剖面塑性应变沿深度分布不同：有的是接触表面塑性变形最大,有的是在接触微凸体表面下某一深度塑性变形最严重,而接触凸点表面的塑性应变稍小些。这与相关文献用SEM研究干摩擦后金属摩擦表层变形照片后发现的结果一致。滑动摩擦过程中,金属粗糙摩擦接触表层塑性变形的不断累积,将会导致材料表层中的夹杂或微观缺陷周围萌生微孔和裂纹源。     

Effect of asperity interactions on rough surface elastic contact behavior: Hard film on soft substrate

An improved elastic micro-contact model of rough surfaces accounting for asperity interactions is proposed. The contact behavior of a single asperity system is composed of a stiffer hemi-spherical asperity deformation and bellowing softer substrate deformation, which is then extended to rough surface contact including asperity interactions. Using the solution of substrate deformation, normal positions of individual asperities are adjusted during quasi-static contact, from which surface interactive forces are obtained. Analytical simulations are performed using the proposed rough surface contact model, whose results are compared to Greenwood-Williamson-based models and with experimental measurements.