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.     

Frictionally-excited thermoelastic contact of rough surfaces

Frictional sliding contact between two elastically similar half-planes, one of which has a sinusoidally wavy surface, is studied in the full-contact regime. The steady-state regime is evaluated, within the limits imposed by the well-known phenomenon of thermo-elastic instability (TEI). TEI gives a critical speed whose value depends on the wavelength of the perturbation, and above which the perturbation itself grows arbitrarily with time. It is found that the TEI critical speed, V_cr, is clearly identified by the steady-state solution only in the special and limiting case when the flat half-plane is non-conductor; in that case, V_cr is the speed for which the steady-state predicts infinite amplification. In all other cases, V_cr (appropriate to the wavelength of the profile) does not correspond to infinite amplification, nor to the maximum one, V_M. In the limiting case of thermoelastically similar materials, not only the system is unconditionally stable (V_cr=∞) for f H₁<0.5, where f is the friction coefficient and H₁ a certain thermoelastic constant, but the regime at the maximum amplification is also always stable, and arbitrarily large amplification is obtained for f H₁ tending to infinity. However, it is found that in most practical cases of braking systems, V_crV_M, and so the limiting conditions are reached at V_cr. At this speed, the amplification is typically not extremely high.     

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 numerical-analytical approach to determining the real contact area of rough surface contact

ABSTRACT

The objective of this study is to improve the accuracy of the real contact area calculated by the semi-analytical method (SAM). Two types of surface pairs are investigated: an analytically generated sinusoidal wavy surface against a rigid flat, and a pair of real rough surfaces. The results suggest that the real contact area calculated by the SAM is extremely sensitive to the resolution of input, i.e. the grid size. The SAM results of the real contact areas show poor convergence, especially in the case of the real rough surfaces. The main reason for this difference is the ‘over-covering’ effect when SAM calculates the real contact area. An exponential extrapolation technique is proposed to predict the real contact area values when further refinement of the grid resolution is unfeasible.     

A simplified thermoelastohydrodynamic model for a parallel surface slider

The present paper presents an original, quasi-analytical, thermoelastohydrodynamic (TEHD) model for a fluid film, parallel surface, elastic slider. Temperature variation along the slider is included in a simplified manner, based on Tipei assumption (viscosity variation along the pad is proportional to film thickness variation) [Tipei N. Theory of lubrication. Stanford, CA: Stanford University; 1962]. The elastic deformation of the slider, due to film pressure, is estimated using a simplified 1D elastic beam model. A simple, closed-form equation is proposed for load capacity–film thickness relationship. Parametric analysis performed with this quasi-analytical model shows optimal values for the most important design parameters. It is shown that suitable pad geometry can generate important load-carrying effects.     

On the elastic contact of rough surfaces: Numerical experiments and comparisons with recent theories

Some numerical experiments are conducted for studying the decrease of the elastic contact area in the elastic contact of fractal random surfaces when adding components of roughness of progressively smaller wavelengths. In particular, Fourier and Weierstrass random series are used, and a recent accurate and efficient method developed by the authors is used, involving superpositions of overlapping triangles. Some comparisons are made using two recent theories, that of Ciavarella et al. published in 2000 on the deterministic Weierstrass fractal profile, and that of Persson published in 2001 on random generic contact. We show that both theories tend to underpredict the contact area by a significant (and similar) factor in these representative cases in the region of light loads (partial contact), where the non-linearities of the contact mechanics are not included in neither of the formulations. In Persson's theory case, the discrepancy is particularly large at high fractal dimensions of the profile, where in theory the numerical experiments should be more closely reproducing a true Gaussian process. The Ciavarella et al. “Archard-like” theory, is only accurate when the parameter γ (the ratio of successive wavelengths) is unrealistically large. However, we only tested the Ciavarella et al. theory in the simplified “Hertzian approximation” form assuming partial contact at the peaks of contact, although we don’t expect the full version to improve dramatically the results.     

Basic principles of rough surface contact analysis using numerical methods

A detailed account of the principles involved in using numerical elastic contact techniques on digitized measurements from rough surfaces is presented in relation to two- and three-dimensional topography data. The main results of such analyses are shown to include the detailed interface geometry and the subsequent contact pressure distribution involved. Methods of defining the resulting sub-surface stresses created by this contact pressure distribution are also presented for static normal loading, and for the case of a normal load in the presence of a frictional surface shear. The problems posed in dealing with plastic asperity contacts are also discussed, together with an outline of how the numerical methods described have been modified further to allow analysis of rough layered bodies of dissimilar materials, thus offering a very useful design tool for surface coatings.     

A new diagnostic technique for asperity contact

Investigations into high frequency gear vibration have given a diagnostic technique which shows asperity interactions. Smith shocks are generated at the contacts and can be detected using high frequency accelerometers to give a measure of the number and intensity of the contacts.     

Elastic/plastic contact of surfaces considering ellipsoidal asperities of work-hardening multi-phase materials

The importance of the plasticity index for defining the degree of elastic and plastic deformation of surface asperities is described. Some experimental validation of the argument is provided and the method is extended to cover the case of ellipsoidal asperity contacts and the effect of work-hardening for a general asperity height probability distribution. It is also shown how the model may be applied to study the behaviour of multi-phase composites. The arguments are based on Hertzian contacts without tractions but may be used with reasonable confidence for contacts where the coefficient of friction is less than 0.1.     

Multi-asperity elliptical JKR model for adhesion of a surface with non-axially symmetric asperities

Surfaces can present high levels of topographic asymmetry and, therefore, theories based on the assumption of symmetry cannot be effectively employed.A new multi-asperity adhesion model that assumes that asperities are not perfectly hemispherical is presented here, this model is based on the elliptical JKR model for a single asperity. The adhesion between a soft tissue with asperities greatly asymmetric and a polymer was modelled, the predicted adhesion forces were successfully validated against experimentally obtained data. Moreover, simulations with a simpler model, which assumes symmetrical asperities, have been also carried out; these results were significantly different from those obtained, using both the newly developed model and those determined experimentally. This highlights the importance of the model presented in this work.     

A comparison of multiaxial fatigue criteria as applied to rolling contact fatigue

Under rolling contact fatigue (RCF) existing multiaxial fatigue criteria are not well validated and predict significantly different results. Results for simple typical Hertzian RCF pure rolling are shown as previously remarked by the authors, the Dang Van criterion applied to RCF gives over-optimistic fatigue limits, due to the large influence of the hydrostatic component of the stress, particularly under some conditions. It is here shown that the “simpler” Crossland criterion gives a more realistic fatigue limit of Hertzian peak pressure, and the more “elaborate” Papadopoulos criterion gives an even more conservative value, of about 3-3.5 times higher than the fatigue limit under pure shear. It is suggested that the multiaxial criteria per se do not give a reliable estimate of the fatigue limit, and perhaps an integration within Weibull-like theories should be attempted in the future, as well as a more “unified” approach and mix of criteria taken from gears design, rolling contact in railways, and in rolling bearings.     

Fractal prediction model of thermal contact conductance of rough surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces,which has been widely studied since last few decades,and for predicting which many theoretical models have been established.However,the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity.In this paper,a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes:elastic,elastoplastic and fully plastic.Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model.The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area.The larger the fractal dimension,or the smaller the fractal roughness,the larger the thermal contact conductance is.The thermal contact conductance increases with decreasing the ratio of Young’s elastic modulus to the microhardness.The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface,which provide certain reference to the further study on the issue of heat transfer between contact surfaces.     

Contact between rough wavy surfaces allowing for the mutual effect of the asperities

The paper proposes a model of contact interaction between wavy rough surfaces allowing for the mutual effect of microasperities. The model is intended to calculate the contact parameters under heavy loadings and, correspondingly, at large contour areas. The model in question assumes that the contact waves deform elastically and the asperities deform plastically.     

Hardness of a surface containing uniformly spaced pyramidal asperities

Pyramidal asperities of different apical angle were machined on a flat copper surface. Hardness was estimated from the load–displacement graphs obtained by pressing a spherical rigid indenter onto the asperities. The variation of hardness with apical angle and pitch was recorded with a view to contributing to the development of a general framework for relating measured hardness to the surface roughness. This revised version was published online in July 2006 with corrections to the Cover Date.     

A molecular dynamics simulation of 3D rough lubricated contact

In this paper, a molecular dynamics simulation of three dimensional rough surface contact under different lubricated conditions was carried out. At atomic scale, mixed lubrication involves nano-asperity contact where the load is supported not only by asperities but also by a sufficient amount of confined lubricant. The contact area and pressure distribution of various lubricated conditions, e.g. dry, partially lubricated and fully lubricated, were presented. It has been found that cavities were formed between upper and lower surfaces under the load, and confined lubricant molecules were able to fill the cavity and support the load, resulting in the decrease of contact area and thus the protection of surface topography.     

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.     

A simplified analysis for the surface texture of rough engineering surfaces

Based on a simple triangular model of the asperity in the profile of a rough engineering surface, an analysis is developed which shows that the cumulative frequency distribution of asperity peaks and valleys with depth normal to the nominal plane of the surface may define the surface texture completely.Experimental verification of the analysis is presented for surfaces having a wide range of roughness characteristics.     

Contact of surface asperities in wear

Stresses have been examined under the elliptical Hertzian contact area, which appear during a real contact between two asperities in the process of sliding friction. The stresses are found according to the Mises-Hencky criterion and characterize the ability of the material to change its shape. Relationships have been found of such a maximum stress under the surface of the contact area depending on the geometric parameters of the contact area, on the friction coefficient and the maximum pressure in the centre of contact area. The processing of the calculation data was conducted according to a special program on a computer and yielded an approximate relationship to calculate the maximum reduced stress. The distribution of dangerous stresses under the contact surface has been shown. The most critical points may be both within the surface layer of the material and on the contact area itself.     

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.