A simplified elliptic model of rough surface contact

Nayak's analysis of isotropic surface roughness as a random field has been extended to show that most summits are only mildly ell, the most common ratio of principal summit curvatures being near 2:1. Also from Nayak's theory, the distribution of the geometric-mean summit curvature with height has been obtained. By using an approximate solution for elliptical Hertzian contacts based on the geometric-mean summit curvature, the full elliptical solution of Bush, Gibson and Thomas can be reproduced more conveniently. Their values for the area of contact are accurately reproduced, and it is argued that the present values for load and contact pressure are more plausible: unlike the original numerical values, the present values converge smoothly to the BGT asymptote . Once again, it is found that elastic contact models can explain the proportionality between contact area and load, although at realistic loads the proportionality is merely very good, not exact. The model shows that a plasticity index ψm≡(E^*/H)σm (closely related to Mikic's index) can be used to predict the behaviour of surfaces in contact.     

A stiffness model of a joint surface with inclination based on fractal theory

Under long-term uneven loading, joint surfaces between the components of heavy-duty machine tools become inclined owing to both external loads as well as the heavy weight of the machinery itself. In this study, to reconstruct the real contact parameters at certain angles of inclination, the macro contact angle was first converted into a micro contact angle based on the stress characteristics and the deformation of asperities were considered. The real contact surface area was then calculated using piecewise integration according to three stages deformation: elastic, elastoplastic, and completely plastic. A stiffness model of the joint surface was derived according to classification theory. Finally, an experimental system with inclinations between the joint surfaces was built and used to validate the model by comparing theoretical and experimental mode values. The present paper analyzes the influence of different fractal parameters, inclination values, and other important parameters on the characteristics of the joint surface using the proposed fractal model and provides a theoretical basis for improving the design and precision of heavy-duty CNC machine tools.     

工程粗糙表面接触摩擦热力学研究进展

对近年国内外工程粗糙表面微观热力学的数值模拟的进展作了综述,介绍了工程粗糙表面的表征、接触模型、表面温升的计算模型与方法的研究现状,并提出了当前相关研究中所遇到的问题及今后研究发展方向.     

The elastic contact of a rough surface

The elastic contact of an isotropically rough surface with a plane is treated by approximating the summits of a random process model by paraboloids with the same principal curvatures and applying the classical Hertzian solution for their deformation. The errors in this approximation are computed in terms of the separation and of a bandwidth parameter α. Load and real contact area are derived as functions of separation. For large separation the fractional area of real contact is found to be half the bearing area fraction and the separation may be eliminated to give direct porportionality between load and area. For all separations the load is approximately proportional to the contact area. The constant of proportionality depends only on the Hertzian elastic modulus and the profile absolute mean slope. Experimental measurements of the latter and of α for a variety of surfaces show little variation in either, and the measured values of α are within the range of applicability of the model. The theory is critically compared with existing theories.     

基于分形和高斯滤波的维修件粗糙表面重构与基准提取

通过维修件粗糙表面轮廓的功率谱探讨了维修件粗糙表面的分形特征,利用W_M函数建立二维和三维粗糙表面分形模型,对维修件粗糙表面轮廓进行了二维和三维重构。并采用高斯函数,对利用分形模型所重构的粗糙表面进行滤波,分别提取了维修件粗糙表面分形模型的评定基准线和评定基准面。论文把分形理论和高斯滤波相结合,应用于维修件的粗糙表面的重构和评定,最后编写MATLAB程序,进行了实验仿真,为研究维修件表面微观几何形貌对结合面摩擦、密封等装配后的连接性能提供了基础。     

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.     

基于粗糙集理论的多属性评估方法的研究

传统的模糊综合评价方法利用模糊数学理论来描述评价过程中涉及的一些模糊因素,取得了一定效果。但这种方法存在的隶属度参数调整的主观性、网络结构不易确定、模糊规则的选取等问题不易解决。本文提出结合粗糙集理论（RS）和模糊神经网络（FNN）的一种网络评估模型。使得网络的结构容易确定,并利用Rosetta软件轻松提取模糊规则。是一种具有通用性的网络评估模型。     

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.     

Simulation and experiment of secondary contact stiffness of rough surface

Machined surfaces usually need to be loaded several times during assembly. The surface morphology after the simulation loading may be quite different from the physical loading, which subsequently causes differences between the contact stiffness after secondary simulation loading and secondary physical loading results. The fractal theory was used to reconstruct the measured surface morphology, followed by contact stiffness simulation and test. The results show that contact stiffness of new morphology obtained by the first simulated loading using the elastic-plastic deformation theory are smaller than the first loading test results, with an average error of −9.71 %. Contact stiffness of used morphology obtained by the first simulated loading using the pure elastic deformation theory are in good agreements with the second loading test results, with an average error of 4.71 %. However, the average contact stiffness of new morphology obtained by the second simulated loading using the elastic-plastic deformation theory, which is traditionally used for contact analysis, are 2.15 times larger than the second loading test result. These research results demonstrate a feasible finite element method (FEM) for solving the contact problem of rough surfaces that need to be assembled multiple times.

     

Application of spherical indentation mechanics to reversible and irreversible contact between rough surfaces

A probabilistic model for the deformation mechanics of the interface between randomly rough metal surfaces, which is geometrically and mechanically more realistic than previous models, is derived and numerically evaluated. The model is based on the premise that the contact of two nominally plane engineering surfaces is in general equivalent to loading their sum against a smooth plane. The “sum surface” is assumed to be Gaussian and isotropic; thus the height and curvature of its peaks are correlated random variables. By using an idealized peak shape which is paraboloidal only at its vertex, the surface height distribution of the population of peaks is also made Gaussian. The upper load limit of the model is estimated, beyond which the microcontacts can no longer be assumed to be geometrically discrete and mechanically independent. Each microcontact is assumed to grow by mutual spherical indentation, thus enabling the entire deformation range, from Hertzian elastic to fully plastic, to be described by previously determined empirical functions. A two-stage linear/power law stress-strain curve is assumed. By summing over all microcontacts the total contact area and load are obtained as functions of the separation of the mean surfaces. For elastic deformation both normal loading and sliding friction are treated. For plastic flow two cases are considered: (1) identical materials; (2) one surface remains elastic. The mechanics of unloading are also investigated. After enough microcontacts have yielded to cause significant deviation from totally elastic behavior, the contact mechanics depend principally on the strain hardening exponent, the ratio of the yield stress to the Young's modulus, and the measurable ratio of the mean peak radius to the r.m.s. height of the sum surface.     

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.     

Random process model of rough surfaces in plastic contact

The plastic contact of a rough surface and a hard, smooth flat is analyzed by modeling the rough surface as an isotropic, Gaussian, random process. The applicability of this model to the contact of two rough surfaces is discussed, and it is shown that the model is appropriate.It is not necessary to analyze interactions of asperity pairs, with the attendant questions of their misalignment, the shape of their caps, etc. Instead, a model involving the interaction of the continuous surfaces is developed, which implicitly takes into account these geometrical factors, as well as allowing for the possibility of the coalescence of microcontacts as the normal pressure is increased.Approximate relations between the density of finite contact patches, their mean area and mean circumference, and the normal pressure/hardness ratio are derived. These relations depend not only on the density and height distribution of maxima, but also on the shape of the Power Spectral Density of the surface. Many surfaces of interest are likely to give rise to multiply-connected contact patches at all except very high separations. The density of holes appearing within the contact patches as well as their area is estimated.Results are derived for surfaces that may be partitioned into two components, one with a large r.m.s. value and a narrow roughness spectrum, and the other with a small r.m.s. value and an arbitrary spectrum. For these surfaces, the density of holes at small separations becomes equal to the density of finite contact patches; the area of the holes remains small, however. It is conjectured that for surfaces that may not be partitioned in this manner, conventional models of contact are inapplicable. Specifically, the contact patches are likely to be perforated by holes at all separations, the hole area being a significant fraction of the contact area. Unit events such as the contact or collision of asperities also appear to become meaningless     

The effect of surface films on the static contact of rough flat surfaces

The study of contact phenomena of solid surfaces, such as the electrical and thermal conductance across interfaces, friction and wear, fluid leakage through seals and the stiffness of joints, is of vital importance in many engineering applications. The effect of surface films, such as oxides of the metal, oils and grease, on the behaviour of two surfaces in contact under a normal load has been studied. The contact behaviour has been quantitatively assessed by measuring the normal approach of two surfaces in contact; a capacitance technique was employed for the measurement of displacements. Theoretical analyses are presented for determining the normal approach as a function of load. The various statistical parameters of surfaces relevant to such analyses are also presented. It has been demonstrated that the presence of surface films enhances the stiffness of deformable surfaces.     

The plastic contact between a rough and a flat surface

Experimental results are presented for the real contact area between two solids. Qualitative agreement is found with Williamson's theory of plastic contact but better quantitative expressions are presented. The hypothesis of uniform rise of the non-contacting parts of the surface is examined.     

Film-forming capability in rough surface EHL investigated using contact resistance

Highly loaded machine elements such as gears and cams have a non-smooth surface topography that is created during manufacturing. It is well known that the film-building properties of such surfaces may be different from those that are perfectly smooth. The capability to form a separating film may also be altered in time due to run-in phenomena. In this study, a smooth steel ball was loaded against rough steel discs and run under pure rolling as well as sliding conditions. Several different steel surfaces were tested under nominal EHL conditions, where the contact was monitored by means of its electrical resistance and capacitance. Each surface was first run in for 15 min, followed by a sweep-in speed determining the lift-off curve. Electrical contact measurements were continuously conducted during run in as well as lift-off. Fully formulated gear oil and its base fluid were used as test lubricants. Results show that run in of a surface seems to be a competition between conformation of surface topography and tribofilm formation. At the tested conditions, the formation of a tribofilm is dependent on the initial surface topography and is created rapidly causing less metal–metal contact. This film also seems to effectively prohibit changes in surface topography causing less structural run in than expected.     

基于粗糙集理论的系统建模与故障诊断

应用粗糙集理论,可以从原始的数据中提取有用的知识或规则.依据这一思想,本文建立了一个实际非线性系统的粗糙集模型.在建模过程中,首先用系统输入输出的采样数据构成原始信息表,然后离散化,再利用粗糙集算法得到系统粗糙集模型的不完备规则集,通过实验和线性插补法实现规则集完备化,最后完成模型的设计和校验.校验结果表明所建的粗糙集模型是有效的,并利用该模型实现了系统的一种故障诊断.     

基于粗糙集的改进重要度绩效分析法

为处理属性绩效值和总体顾客满意度间的非线性关系,以及属性绩效值和属性重要度间的依赖关系,提出基于粗糙集的改进重要度绩效分析法.通过挖掘绩效值和总体顾客满意度间的数据关系,获得潜在的属性重要度.由于粗糙集无法处理连续属性,结合模糊c均值聚类算法对数据进行离散化处理.该方法克服了传统重要度绩效分析法难以准确描述绩效值、重要度和总体顾客满意度间的关系,且重要度的确定主观性强的缺陷.以水平定向钻机的维修服务为例,验证了所提方法的可行性与有效性.     

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.