考虑摩擦切向力的弹塑性粗糙表面接触模型

基于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,提出一种综合考虑弹塑性变形以及摩擦切向力等因素的新型粗糙表面接触模型。通过分析不同塑性指数以及载荷条件下该模型与ZMC模型以及GW模型预测。结果发现:在低塑性指数、小法向接触载荷情况下,该模型预测的真实接触面积相比ZMC模型偏小,甚至比GW模型预测的真实接触面积偏小,但是随着法向接触载荷的增加,该模型预测的真实接触面积逐渐增大,并超过ZMC模型以及GW模型预测结果;在高塑性指数下,该模型预测的真实接触面积即使在小法向接触载荷情况下也相比ZMC模型以及GW模型预测的真实接触面积大,且随着载荷的增加,真实面积之间的差距也逐渐增大;随着塑性指数的增加,该模型预测的真实面积超过GW模型以及ZMC模型预测值的临界载荷逐渐减小。     

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。     

基于分形几何与接触力学理论的结合面法向接触刚度计算模型

基于分形几何理论和接触力学理论,用分形理论表征粗糙表面微凸体参数,考虑微凸体由弹性变形向弹塑性变形以至最终向完全塑性变形转化的过程,建立各变形阶段微凸体的接触刚度模型。在此基础上,提出机械结合面法向接触刚度计算模型,该模型揭示了在不同的塑性指数下,结合面法向接触载荷与法向接触刚度之间的关系。结果表明,在塑性指数较小时,微凸体的变形以弹性为主,法向接触载荷与接触刚度之间表现为近似线性关系;随着塑性指数的增加,微凸体变形主要以塑性为主,法向接触载荷与接触刚度之间表现为较强非线性关系。对已有的铣削加工和磨削加工情况下的结合面法向接触刚度试验结果,利用该模型进行数值计算、仿真和分析。结果表明:提出的模型更与试验曲线吻合。     

基于真应力-应变关系的粗糙表面法向接触模型

提出一种粗糙表面的法向弹塑性接触分析的建模方法。基于微凸体的弹塑性有限元接触模型,分别研究了40Cr、45和Q235三种钢材料的微凸体与刚性平面的法向接触特性。有限元模型中采用三种材料的真应力-应变关系,考察了不同强化特性对微凸体接触性质的影响。建立了微凸体在弹性、弹塑性、塑性变形阶段统一的接触变量变化规律的表达式。在此基础上应用概率统计理论建立粗糙表面法向弹塑性接触模型。所建立的接触模型中微凸体接触变量的变化规律完全基于弹塑性有限元模型的计算结果,无需将微凸体的变形过程区分为不同的变形阶段,避免了接触变量在各阶段采用不同函数表达式带来的连续性和光滑性问题,以及在弹塑性阶段采用插值函数的随意性问题。通过与其他接触模型的计算结果相比较,证明了所提出接触模型的合理性。     

计及弹塑性及硬度随表面深度变化的结合部单次加载模型

基于分形几何学理论和传统统计接触力学理论的无缝连接,考虑微凸体由弹性变形向弹塑性变形以致最终向塑性流动转化的过程,架构结合部单次加载模型。在此基础上,应用带一个随机相位的Weierstrass-Mandelbrot函数构建粗糙表面的微观几何学形貌。数值仿真曲线图显示,法向总接触载荷随着实际接触面积的增加而微凸弧式增加,在相同实际接触面积下,法向总接触载荷随着分形粗糙度的加大而变大;实际弹塑性接触面积占实际接触面积的百分率随着实际接触面积的增加而凹弧式减小;法向弹塑性接触载荷占法向总接触载荷的比例随着实际接触面积的增加而凹弧式减小,随着分形粗糙度的减小而变小;法向总接触载荷随着分形维数的加大经历首先增加然后减小,随后再增加最后再减小的2次循环过程;随着分形维数的增加,法向弹塑性接触载荷占法向总接触载荷的百分比先减小后增加;实际弹塑性接触面积占实际接触面积的比值随着分形维数的变大先减小后增加;忽略弹塑性变形的CEB模型会导致预测的法向接触力大于弹塑性模型,CEB模型法向接触力与弹塑性模型的相对误差为4.798%~56.58%。结合部单次加载模型可为粗糙表面弹塑性接触的精确求解提供一定的理论基础。     

微观随机粗糙表面接触有限元模型的构建与接触分析

基于相关文献提出粗糙表面模拟方法,通过软件工具在ANSYS中建立微观粗糙表面接触有限元模型,利用该模型分析载荷对弹塑性变形和接触面积的影响。结果表明:随着正压力的增大,粗糙表面上不断地有微凸峰与平面发生弹性接触变形,接触斑点(或接触斑点群)的数目逐渐增加,斑点中心区域的弹性变形很快达到最大,微凸峰负荷变形的同时也使斑点四周区域受到挤压;初始接触时,轮廓高度较大的微凸峰率先发生弹性变形,随着压力的增大,金属材料所受应力达到屈服极限同时粗糙表面的弹性变形和塑性变形的集中区域不断增加,真实接触面积不断增大;接触区数目的增多和接触区面积的增加都可以导致接触面上真实接触面积增加;随着压力的增大,真实接触面积的增大并不是由于接触区数目的增多,而是微观接触区面积的增大。     

具有连续光滑特性的结合面接触刚度模型

结合面接触刚度直接影响着机械系统的静、动态力学性能和精度保持性水平.基于微凸体在弹性、弹塑性以及完全塑性接触变形过程中,接触刚度具有连续、光滑特性的思想,首先提出利用Hermite多项式插值函数,来弥补单一微凸体接触刚度建模时存在的不连续等缺陷,建立了具有连续光滑特性的单一微凸体接触刚度新模型;然后基于统计学方法,建立了结合面的法向接触刚度模型;最后将所建模型与GW、ZMC、KE和BRAKE模型进行对比分析.结果表明:本文模型实现了单一微凸体接触刚度在不同接触状态之间连续且光滑地转变;对于光滑表面形貌,基于GW、ZMC、KE以及BRAKE模型预测的接触刚度与本文模型结果的差异较小,其中本文模型最接近于纯弹性的GW模型;当表面粗糙度增大时,GW模型与其他几种模型的差异逐渐增大,此时本文模型与考虑微凸体多种变形阶段的ZMC模型吻合较好;再次表明载荷与表面粗糙度是影响刚度的两个主要因素,即随着载荷的增大或表面粗糙度的减小,接触刚度递增.     

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。     

考虑多尺度接触状态的新接触模型

提出了一种接触模型,模型的建立基于经典的Hertz接触力学理论和现有的分形接触模型。研究了单个微凸体接触状态随尺度序数n的变化规律,考虑了不同尺度序数n的影响而引入线性因子对模型进行修正,采用了与以往分布函数计算方法不同的思路,在此基础上对微凸体面积分布函数积分求和,获得了接触表面真实接触载荷与接触面积的关系。结果表明:单个微凸体的临界参数对接触参数有影响;微凸体的变形顺序为弹性,弹塑性,塑性变形,与传统的接触模型一致;线性因子与特征系数G,分形维数D有一定的关系;新的分布函数和线性因子的引入提高了接触参数的精度;考虑多尺度特性的新模型相比经典的GW模型,MB模型与Bhushan试验数据更接近,尤其在接触载荷较大时;与现有的考虑尺度因素的接触模型做比较,计算精度有了更进一步的提高。     

螺栓结合面微观接触模型

针对螺栓结合面弹塑性区域内的接触机理难以确定问题,根据在变形状态转变的临界点处微凸体真实接触面积与接触载荷转化均满足连续和光滑条件,构造新的多项式函数来描述接触变形与接触面积之间的关系。利用统计学方法建立螺栓结合面真实接触面、接触载荷与接触刚度模型。理论计算结果表明:随着平均表面距离的减少,接触载荷、接触面积和接触刚度随之增加;接触面积和接触刚度,随着接触载荷的增加而增加,当接触载荷增加一定程度后接触刚度和接触面积值分别趋于理想接触刚度和名义接触面积值;当螺栓结合面处于弹性和弹塑性接触状态时,塑性指数越大,接触面积越大,而平均接触距离和接触刚度就越小,当处于完全塑性状态时,塑性指数越大,刚度和平均接触距离就越大,而真实接触面积影响较小。     

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.     

Elastic–plastic adhesive contact of rough surfaces based on plastic asperity concept

The paper describes an analysis of adhesive contact between rough surfaces with small-scale surface asperities using an elastic–plastic model of contact deformation based on fictitious plastic asperity concept developed by Abdo and Farhang [Int. J. Non-Linear Mech. 40 (2005) 495]. The model considers simultaneous occurrence of elastic and plastic behaviours for an asperity. The well-established elastic adhesion index and plasticity index are used to consider the different contact conditions that arise as a result of varying load and material parameters. The load-separation behaviour for different combinations of these parameters is obtained. Comparison with previous elastic–plastic model that was based on elastic-then-plastic assumption is made showing significant differences.     

The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

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.     

Elastic–plastic adhesive contact of rough surfaces with asymmetric distribution of asperity heights

The elastic–plastic adhesive contact of rough surfaces is extended to include asymmetric distribution of asperity heights using the Weibull distribution with skewness as the key parameter to characterize asymmetry. The well-established elastic adhesion index and plasticity index are used to consider the different conditions that arise as a result of varying load and material parameters. The loading and unloading behaviour for different combinations of adhesion index, plasticity index and skewness values are obtained as functions of mean separation between the surfaces. It is seen that surfaces with negative skewness experience higher adhesion compared to surfaces with positive or zero skewness.     

基于不同微观固体接触模型的轮轨表面变形特性分析

针对轮轨表面接触变形问题,采用不同的统计型微观固体接触模型,即Greenwood-Williamson （GW）模型,Chang-Etsion-Bogy （CEB）模型和Zhao-Maietta-Chang （ZMC）模型,研究轮轨接触表面变形特性。利用Newton-Raphson方法对微观固体接触模型公式进行求解,并同时求解间隙方程和载荷平衡方程。考虑不同粗糙度和不同塑性指数下各微观固体接触模型的压力分布情况,以及接触半径随载荷的变化情况。并将不同微观固体接触模型的结果和Hertz模型结果对比,结果表明弹塑性微观接触模型（CEB,ZMC）比弹性模型（GW）有着更小的接触压力以及更宽的接触半径,最大压力均小于最大Hertz接触压力,接触半径均大于Hertz接触半径。     

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.     

基于分形理论的滑动摩擦表面接触力学模型

依据分形理论,考虑微凸体变形特征及摩擦作用的影响建立滑动摩擦表面接触力学模型。采用一个三次多项式来表达弹塑性变形微凸体的接触压力与接触面积的关系,从而满足在变形状态转变临界点处的微凸体接触面积与接触压力转化皆是连续和光滑的条件。推导出滑动摩擦表面临界弹性变形微接触面积、临界塑性变形微接触面积、量纲一真实接触面积的数学表达式。理论计算结果表明,表面形貌一定时,真实接触面积随着载荷的增大而增大;载荷一定时,真实接触面积随着特征尺度系数的增大而减小,随着分形维数的增大先增大后减小;当表面较粗糙时,摩擦因数对真实接触面积的影响很小;随着表面光滑程度的增大,摩擦因数对真实接触面积的影响增大,真实接触面积随着摩擦因数的增大而增大,特别是当摩擦因数较大时,真实接触面积增大的幅度也较大。接触力学模型的建立,为研究滑动摩擦表面间的摩擦磨损性能提供了依据。