A finite element-based model of normal contact between rough surfaces

Engineering surfaces can be characterized as more or less randomly rough. Contact between engineering surfaces is thus discontinuous and the real area of contact is a small fraction of the nominal contact area. The stiffness of a rough surface layer thus influences the contact state as well as the behavior of the surrounding system. A contact model that takes the properties of engineering surfaces into account has been developed and implemented using finite element software. The results obtained with the model have been verified by comparison with results from an independent numerical method. The results show that the height distribution of the topography has a significant influence on the contact stiffness but that the curvature of the roughness is of minor importance. The contact model that was developed for determining the apparent contact area and the distribution of the mean contact pressure could thus be based on a limited set of height parameters that describe the surface topography. By operating on the calculated apparent pressure distribution with a transformation function that is based on both height and curvature parameters, the real contact area can be estimated when the apparent contact state is known. The model presented is also valid for cases with local plastic flow in the bulk material.     

Prediction of contact temperature rise between rough sliding bodies: An artificial neural network approach

Prediction of contact temperature rise between sliding bodies is difficult due to the large number of parameters that affect the contact phenomenon. It is far more complex if the instantaneous roughness of the sliding pair is taken into consideration since the roughness may change significantly during sliding. It was felt that a multilayer feedforward neural network might be a convenient method to predict the change in surface roughness and the instantaneous maximum temperature rise at the contact between rough sliding bodies. The model accepts initial surface roughness of the mating surfaces, their material properties and the operating parameters as input variables and predicts the final surface roughness and the corresponding maximum contact temperature after a specified sliding time.     

Validation of a simplified numerical contact model

Surface roughness tends to have a significant effect on how loads are transmitted at the contact interface between solid bodies. Most numerical contact models for analyzing rough surface contacts are computational demanding and more computationally efficient contact models are required. Depending on the purpose of the simulation, simplified and less accurate models can be preferable to more accurate, but also more complex, models. This paper discusses a simplified contact model called the elastic foundation model and its applicability to rough surfaces. The advantage of the model is that it is fast to evaluate, but its disadvantage is that it only gives an approximate solution to the contact problem. It is studied how surface roughness influences the errors in the elastic foundation solution in terms of predicted pressure distribution, real contact area, and normal and tangential contact stiffness. The results can be used to estimate the extent of error in the elastic foundation model, depending on the degree of surface roughness. The conclusion is that the elastic foundation model is not accurate enough to give a correct prediction of the actual contact stresses and contact areas, but it might be good enough for simulations where contact stiffness are of interest.     

A model of thermal contact conductance at high real contact area fractions

Thermal contact conductance (TCC) is studied in the whole range of real contact area fractions between zero and unity. For this purpose, a two-scale model is developed in which the effective (macroscopic) TCC coefficient is obtained from the solution of the heat conduction problem at the scale of asperities. Additional thermal resistance at the real contact spots is included in the model. The model is applied for several real 3D roughness topographies for which the effective TCC coefficient is determined as a function of the real contact area fraction and the local TCC coefficient at real contact spots. An analytical function is found which approximates this relationship in the whole range of parameters, and a characteristic length-scale parameter is introduced which characterizes the effective TCC properties of a rough surface.     

Surface separation and contact resistance considering sinusoidal elastic–plastic multi-scale rough surface contact

The current work considers the multi-scale nature of surface roughness in a new model that predicts the real area of contact and surface separation as functions of load. This work is based upon a previous rough surface multi-scale contact model which used stacked elastic–plastic spheres to model the multiple scales of roughness. Instead, this work uses stacked 3D sinusoids to represent the asperities in contact at each scale of the surface. By summing the distance between the two surfaces at all scales, a model of surface separation as a function of dimensionless load is obtained. Since the model makes predictions for the real area of contact, it is also able to make predictions for thermal and electrical contact resistance. In accordance with concerns in previous works that the iterative calculation of the real contact area in multi-scale methods does not converge, this work not only tests but also gives conditions required for convergence in these techniques. The results are also compared to other existing rough surface contact models.     

Computer simulation of the contact of rough surfaces

A program for the computer simulation of the contact of two rough surfaces has been developed, which makes it possible to determine the real area of contact and the penetration of microasperities at specified parameters of microgeometry under specified loads for friction pairs with fairly soft coatings or without coatings. The model has been tested using a comparison of the results of numerical simulation with the experimental data, which has shown their good agreement. The results can be used to simulate the contact of the rough surfaces, including the case when one of these surfaces is covered with a solid-lubricating or other functional coating.     

On the Modeling of Elastic Contact between Rough Surfaces

The contact force and the real contact area between rough surfaces are important in the prediction of friction, wear, adhesion, and electrical and thermal contact resistance. Over the last four decades various mathematical models have been developed. Built on very different assumptions and underlying mathematical frameworks, model agreement or effectiveness has never been thoroughly investigated. This work uses several measured profiles of real surfaces having vastly different roughness characteristics to predict contact areas and forces from various elastic contact models and contrast them to a deterministic fast Fourier transform (FFT)-based contact model. The latter is considered “exact” because surfaces are analyzed as they are measured, accounting for all peaks and valleys without compromise. Though measurement uncertainties and resolution issues prevail, the same surfaces are kept constant (i.e., are identical) for all models considered. Nonetheless, the effect of the data resolution of measured surface profiles will be investigated as well. An exact closed-form solution is offered for the widely used Greenwood and Williamson (GW) model (Greenwood and Williamson, Proceedings of the Royal Society of London A, vol. 295, pp. 300–319), along with an alternative definition of the plasticity index that is based on a multiscale approach. The results reveal that several of the theoretical models show good quantitative and qualitative agreement among themselves, but though most models produce a nominally linear relationship between the real contact area and load, the deterministic model suggests otherwise in some cases. Regardless, all of the said models reduce the complicated surface profiles to only a few key parameters and it is therefore unrealistic to expect them to make precise predictions for all cases.     

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.     

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.     

Normal contact between rough surfaces by the Discrete Element Method

This paper presents the study of nonadhesive, frictionless contact between elastic solids realized by the Discrete Element Method. This numerical method dedicated to multi-contact problems is applied to the field of tribology by studying the normal contact between a rigid rough surface and an elastic body modeled by spheres. A specific interparticle stiffnesses derived from homogenization techniques is implemented. From numerical tests carried out on spheres packings, we observe that the desired main macroscopic elastic constants are correctly modeled. Concerning the study of normal contact between rough surfaces, the obtained results are in accordance to existing theoretical models and numerical results from the literature, thereby demonstrating the potential of the Discrete Element Method to study the normal contact between contacting elastic bodies with rough surfaces. In particular, we recover the linear dependence of the real contact area with the normal load. In addition, we show that decreasing the surface roughness increases the average contact pressure.     

Contact and thermal analysis of transfer film covered real composite-steel surfaces in sliding contact

For composite-steel surfaces in sliding contact an anisotropic numerical contact algorithm has been developed to study the ‘layer type’ problems. An FE contact analysis was applied to evaluate the contact parameters (real contact area, contact pressure distribution and normal approach). The contact temperature rise was determined by using both a numerical thermal algorithm for stationary and a FE transient thermal technique for ‘fast sliding’ problems.The effect of a continuous transfer film layer (TFL), that had built up during wear of the PEEK matrix material on the steel counterpart, was considered. Its thickness was assumed to be t=1 μm, and its material properties were that of PEEK at room temperature or, in the case of frictional heating, at a temperature of 150°C (i.e. above the glass transition temperature of the polymer matrix).Results are presented for a spherical steel asperity, with/without TFL, sliding over composite surfaces of different fibre orientation, and in addition, for real composite-steel surfaces (based on measured surface roughness data) in sliding contact. The TFL has an effect on the contact parameters especially at higher operating temperatures (i.e. 150°C); it results in the production of a larger contact area and a lower contact pressure distribution. The contact temperature rise is clearly higher if a TFL is present. Due to the low thermal conductivity of PEEK, the TFL is close to the melting state or it even gets molten within a small vicinity of the contact area.     

密封结构中粗糙表面特征对其气密性的影响

基于Gauss分布函数和指数自相关函数关系建立三维粗糙表面的数学模型,获得密封面的数值粗糙表面。进而在三维数值粗糙表面的基础上,采用流动数值分析方法,对金属垫片密封结构的气密性进行了研究,分析表面粗糙度、应力以及材料力学特性等相关参数对泄露率的影响。为构建泄漏率表达式,引入流量因子表征现有模型泄漏率与平行圆板模型的差异,流量因子是膜厚比的函数。该工作实现了静接触密封结构泄漏特性定量评估的数值分析方法,对各种硬密封结构的高精度设计有着重要指导意义。     

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.     

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Elastic contact of rough surfaces: A simple criterion to make 2D isotropic roughness equivalent to 1D one

We analyze the periodic contact between an elastic half-space and two types of rough substrates: (i) a perfect isotropically rough rigid substrate (2D isotropic roughness), and (ii) a perfect anisotropically rough rigid substrate, i.e. a substrate with roughness in only one direction (1D roughness). The analysis is carried out with the aid of proprietary codes, that we have developed (both in real and Fourier space) to deal with this type of contacts. Of course, 1D contacts differ from 2D isotropic contacts. However, our results and theoretical arguments suggest a possible criterion to make 2D contacts equivalent to 1D ones from the point of view of contact area and separation calculations. The rule consists in replacing the 2D power spectral density (PSD) of the isotropic surface into an equivalent 1D PSD. Interestingly the transformation rule does not depend on the statistical properties of the surface roughness, hence seems to have a universal character for isotropic surfaces.     

A statistical model of elasto-plastic asperity contact between rough surfaces

This work models statistically elasto-plastic contact between two rough surfaces using the results of a previous finite element analysis of an elasto-plastic sphere in contact with a rigid flat. The individual asperity contact model used accounts for a varying geometrical hardness effect that has recently been documented in previous works (where geometrical hardness is defined as the uniform pressure found during fully plastic contact). The contact between real surfaces with known material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. The asperity is modeled as an elastic-perfectly plastic material. The model produces predictions for contact area, contact force, and surface separation. The results of this model are compared to other existing models of asperity contact. Agreement exists in some cases and in other cases it corrects flaws, especially at large deformations. The model developed by Chang, Etsion and Bogy is also shown to have serious flaws when compared to the others. This work also identifies significant limitations of the statistical models (including that of Greenwood and Williamson).     

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.     

Numerical and finite element contact temperature analysis of real composite-steel surfaces in sliding contact

Numerical techniques have been developed and used to evaluate the contact temperature distribution between real composite-steel surfaces in sliding contact. To characterise the contact temperature problem of composite materials new definitions for composite Peclet numbers have been introduced. In case of `slow sliding' problems a stationary numerical technique was applied, whereas for `intermediate and fast sliding' problems transient finite element (FE) solutions were preferred. At first sliding contacts of a single steel asperity over polyetheretherketone (PEEK) or carbon fibre (CF)/PEEK composite surfaces were modelled in order to study the contact temperature development on a microscopic level. It was followed by contact temperature results for real composite-steel sliding surfaces; the latter helped to provide information about the actual stress conditions, which are necessary to model the wear process of this pair of materials in future works.     

基于分形几何的表面微观形貌模拟及粘着弹性接触计算研究

基于Ausloos和Berman提出的推广的W-M函数对具有分形特征的粗糙表面进行仿真模拟,分析了函数中与尺度无关的特征参数对表面微观形貌的物理意义。同时,基于Yan和Maugis的理论研究,用模拟的分形表面建立了考虑表面效应的弹性接触模型,通过数值方法对整个过程进行迭代求解,得到了两接触面在不同的接触条件下各个接触斑点上的载荷分布和真实接触面积以及接触斑点的数量和尺寸。由于真实接触面积的尺寸敏感地反应表面微观几何形貌的变化,因此该方法为研究粘着机制和减小微尺度粘着效应提供了思路。     

Deformation due to contact between a rough surface and a smooth ball

Theoretical and experimental results are presented to evaluate the deformation behavior of the contact between a real rough flat surface and a smooth ball. There are three deformation responses: plastic deformation of the asperities only, plastic deformation of the bulk only and combined plastic deformation of both the asperities and the bulk. The effects of the surface roughness and the Hertzian contact parameters on the effective contact pressure are presented. The experimental results confirmed the theoretical prediction very well. For a given Hertzian contact situation the surface roughness plays an important role in controlling the deformation behavior of the contacting surfaces. A criterion is presented to predict the deformation behavior of contacting engineering surfaces.