微凸体分布计算方法对曲面接触预测的影响

为借助Greenwood-Williamson(GW)接触模型开展粗糙表面接触分析，基于微凸体识别的参数定义法和基于随机过程理论的谱矩法都被广泛用于微凸体分布参数计算。为厘清应用不同计算方法产生的接触求解差异，针对粗糙曲面接触，利用快速傅里叶变换重构获得不同统计分布下的粗糙表面随机样本，由三点定义法和谱矩法分别计算仿真样本的微凸体峰点分布参数，对样本开展GW接触分析，得到两种计算方法下接触预测结果，对结果进行了对比讨论，分析了样本表面统计分布参数、高通滤波常数、曲率半径和载荷的影响。最后，通过试验数据对谱矩法的计算偏差进行了检验，对微凸体分布参数计算给出了建议。     

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。     

粗糙体变形特性对接触过程的应力与应变的影响

运用W-M函数生成分形粗糙表面,建立一个新的双粗糙体接触模型,采用有限元方法模拟仿真了在粗糙体不同变形特性条件下的接触过程,并分析了接触表面的应力分布及不同接触位置的塑性应变随深度的变化规律．结果表明双粗糙接触表面的应力主要集中在个别的较高微凸体上,其应力最大值出现在微凸体肩部区域的位置;等效塑性应变在不同位置沿深度的变化,呈现出不同的规律,微凸体顶部区域沿深度方向的最大等效塑性应变均发生在次表层,材料表层下的塑性应变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,对比不同变形特性的模型,得出弹塑性一刚体模型的最大应力及应变值都大于弹塑性一弹塑性模型。     

一种点接触粗糙表面摩擦行为的预估方法研究

针对润滑状态下连接界面的接触问题,对流体动力油膜和粗糙表面的摩擦特性进行了研究,提出了一种点接触粗糙表面摩擦行为的预估方法。首先,基于载荷分配思想建立了粗糙表面摩擦模型,利用Hertz理论中的最大接触压力分别确定了微凸体高度分布服从高斯分布、指数分布以及三角分布时粗糙表面的接触载荷;然后,通过弹性流体动力润滑膜厚公式求解了流体动力油膜承担的载荷;最后,绘制了滑动速度-摩擦系数曲线,模拟了整个润滑过程中连接界面摩擦系数的变化。研究结果表明:仿真结果与试验数据具有一致性,且不同法向载荷、粗糙表面形貌、润滑剂粘度以及假设的微凸体高度分布对摩擦系数的影响程度不同;微凸体假设为高斯分布时,仿真结果更接近试验数据;该方法可以为机械结构的润滑状态预测提供理论基础。     

微系统粗糙表面的多峰黏着弹性接触分析

在微系统中,粗糙表面间的黏着力是影响微尺度对象能否成功装配的主要因素。为研究微尺度对象粗糙表面的接触机理,将Maugius理论和分子作用的Kim物理接触理论相结合,建立了微尺度对象的多峰黏着弹性接触模型,应用三维分形几何进行黏着力的求解,并对Kim物理接触黏附半径做近似计算,且将新建模型与不考虑分子作用力的Morrow模型进行比较。分析结果表明:微凸体两粗糙表面的物理接触距离越小,对黏着影响越大;分形维数增加,微凸体物理接触的黏着作用显著增加;随着分形粗糙度减小,Kim物理接触的微凸体数目明显增多,黏着力显著增加。     

新的粗糙表面弹塑性接触模型

提出一种新型的粗糙表面弹塑性微观接触模型.该模型的建立基于接触力学理论和接触微凸体由弹性变形向弹塑性变形及最终向完全塑性变形的转化皆是连续和光滑的假设.研究单个微凸体在载荷逐渐增加时的变形规律,并重点推出弹塑性变形区间的接触方程.在此基础上应用概率统计理论导出了粗糙表面的接触载荷、平均分离和实际接触面积之间的数学关系式.在不同的塑性指数和载荷条件下,该模型与GW弹性模型和CEB弹塑性模型就实际接触面积和法向距离的预测结果进行了对比.结果表明,在同样塑性指数和载荷条件下比GW模型预测的实际接触面积大但法向距离小,且两者的差距随塑性指数和载荷的增加而增大.因此该模型的预测结果更加符合人们的试验观察和直觉,能够更加科学和合理地描述两个粗糙表面的微观和宏观接触状态.     

基于域扩展因子和微凸体相互作用的结合面接触刚度模型研究

结合面接触刚度直接影响了机械设备的整机动态特性,为了建立更为准确的接触刚度模型,以分形几何理论为基础,利用单一微凸体承受局部载荷时的弹性变形特性,并基于域扩展因子引入微接触截面积分布函数,推导了考虑表面微凸体相互作用影响的结合面接触刚度分形模型。为了验证所提出模型的准确性,通过三维非接触式测量,获得了试验试样的表面轮廓数据,并根据结构函数法,计算了各个试样的表面分形参数,进而将理论接触刚度与试验结果对比分析,结果表明：法向接触刚度的增长速率与粗糙面表面临界接触面积有关,临界接触面积决定了结合面内的弹性变形占比。考虑微凸体相互作用后,所提出模型的预测曲线更加符合试验中法向载荷与接触刚度的关系。     

考虑蠕变特性的橡胶微凸体与金属表面接触特性分析

金属-橡胶接触广泛存在于密封结构中,密封接触表面上微凸体间的相互作用会直接影响整个密封界面的接触特性,进而影响其密封性能。基于粗糙密封界面的单个微凸体,考虑橡胶的蠕变特性,采用理论分析和仿真研究相结合的方式研究橡胶微凸体与金属表面的接触特性。通过橡胶蠕变特性的实验结果,构建橡胶蠕变计算模型;构建半球微凸体与金属平板间的有限元模型,进行考虑蠕变特性的仿真,分析其接触特性,并与Hertz接触理论的计算值进行对比。结果表明：在蠕变阶段,接触半径、法向变形量和最大等效蠕变应变均随蠕变时间的增加而增大,最大接触压力随蠕变时间增大而减小,这均可能导致密封性能的下降;随压力载荷的增大,接触半径、法向变形量、最大接触压力和最大等效蠕变应变均增大,但增大的趋势逐渐减小;橡胶微凸体与金属表面间的等效模量随蠕变时间的增加而减小,随压力载荷增大而增大。     

过盈配合接触界面的研究

通过W-M函数建立具有分形特征的等效粗糙表面与刚性平面的接触模型,模拟压缩机叶轮与轴过盈配合下界面的接触。将接触模型导入到有限元软件Ansys中,分析接触模型接触面积、接触压力、滑移面积、粘着面积与变载荷的关系和表面路径上的应力与变形。结果表明,接触时只有个别较高的微凸体发生接触,微凸体肩部区域的应力较大,微凸体中心位置变形量最大,接触界面在一定的法向载荷下接触面积减小,粘着面积增大,配合件发生了宏观的变形。     

基于分形理论的结合面微观接触特性分析

为了研究结合面微观接触特性,基于分形理论,建立粗糙表面轮廓模型,进行结合面接触趋近耦合研究。通过二维粗糙表面与光滑表面微观接触趋近过程的仿真分析,研究分形维数、表面粗糙度、位移载荷对结合面接触状态的影响机理。提出利用激光声表面波检测粗糙结合面接触的方法,并进行了实验验证。研究结果表明,粗糙表面微凸体形貌是决定材料接触性能的关键因素;微凸体接触形成的真实接触面积远小于名义接触面积。工程问题中,通过名义接触面积计算出的载荷与材料表面实际承受的载荷存在较大差异。     

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.     

A numerical model of friction between rough surfaces

This paper describes a computational method to calculate the friction force between two rough surfaces. In the model used, friction results from forces developed during elastic deformation and shear resistance of adhesive junctions at the contact areas. Contacts occur between asperities and have arbitrary orientations with respect to the surfaces. The size and slope of each contact area depend on external loads, mechanical properties and topographies of surfaces. Contact force distribution is computed by iterating the relationship between contact parameters, external loads, and surface topographies until the sum of normal components of contact forces equals the normal load. The corresponding sum of tangential components of contact forces constitutes the friction force. To calculate elastic deformation in three dimensions, we use the method of influence coefficients and its adaptation to shear forces to account for sliding friction. Analysis presented in Appendix A gives approximate limits within which influence coefficients developed for flat elastic half-space can apply to rough surfaces. Use of the method of residual correction and a successive grid refinement helped rectify the periodicity error introduced by the FFT technique that was used to solve for asperity pressures. The proposed method, when applied to the classical problem of a sphere on a half-space as a benchmark, showed good agreement with previous results. Calculations show how friction changes with surface roughness and also demonstrate the method's efficiency.     

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.     

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.     

A Numerical Contact Model Based on Real Surface Topography

A numerical finite element contact model is developed to make use of the high precision surface topography data obtained at the nanoscale by atomic force microscopy or other imaging techniques while minimizing computational complexity. The model uses degrees of freedom that are normal to the surface, and uses the Boussinesq solution to relate the normal load to the long-range surface displacement response. The model for contact between two rough surfaces is developed in a step-by-step manner, taking into account the far-field effects of the loads developed at asperities that have come to contact in previous steps. Method accuracy is verified by comparison to simple test cases with well-defined analytical solutions. Agreement was found to be within 1 % for a wide range of practical loads for the high precision models. Applicability of extrapolation from lower precision models is presented. The real contact area estimates for micrometer-size tribology test machine surfaces are calculated and convergence behavior with mesh refinement is investigated.     

Contact width and compliance between cylinders and rough plates

The contact mechanism between a cylinder and a rough plate is theoretically analysed for mixed, elastic and plastic contacts of asperities. The analysis leads to the result that the contact pressure, the contact width and the compliance between the cylinder and plate differ considerably from those calculated from the Hertz equation and the Lundberg equation when the surface roughness in contact is greater and the normal load is lower. It is also found that the difference between the calculated contact width and the compliance based on mixed asperity contacts and those based on elastic or plastic asperity contacts is small. To confirm the analysed results, the contact width between the cylinder and the rough steel or rough copper plate was measured by means of evaporated carbon and lamp black film coatings on the rough surfaces. The compliance between the surfaces was also measured using differential transformers. Little difference was found between the analysed results and the experimental results.     

Abrasive wear between rough surfaces in deep drawing

In tribology, many surface contact models are based on the assumption that surfaces are composed of a collection of small asperities of which the tips are equally sized and spherically shaped and have some kind of statistical height distribution. This approach was used in 1966 by Greenwood and Williamson and was successfully followed by many researchers during the following decades. The statistical representation of surface topography enables calculation of contact forces and asperity deformations with reasonable accuracy using well established equations. Although this approach has proven to be suitable for static contact situations, alternative representations of the surface topography are required when modelling abrasive wear. In the current work an elastoplastic contact model is developed in which a representation of the surface topography is obtained by best fit approximations of the micro-contacts, obtained from real, measured surface height data. In this deterministic surface representation, the tips of the contacting asperities are assumed to have an ellipsoidal shape. Given the material parameters and contact conditions, the load and deformation of a single asperity can be computed. Subsequently, the wear induced by each individual asperity is obtained by inserting its size and shape and the conditions into a “single asperity micro-abrasion model”. By summing the contributions of all individual asperities, the total abrasive wear volume is obtained. The results of the developed abrasive wear model are compared with results obtained using a statistical approach.     

Average flow model with elastic deformation for CMP

We present a three-dimensional (3D) average flow model considering elastic deformation of pad asperities for chemical mechanical planarization. To consider the contact deformation of pad asperities in the calculation of the flow factor, 3D contact analysis of a semi-infinite solid based on the use of influence functions is conducted for computer-generated rough surfaces. The average Reynolds equation and boundary conditions of both force and momentum balance are used to investigate the effects of pad roughness and external pressure conditions on a film thickness and wafer position angles. It is found that the position angles decrease with the increasing of the applied pressure and the roughest pad has the highest position angles at any given load. Comparing elastic and rigid pads, the minimum film thickness formed between the elastic pad and the wafer is thinner than that between the rigid pad and the wafer.     

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.