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.     

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。     

粗糙表面接触模型的研究进展

实际工程中的接触表面都不是绝对光滑的,当两物体相互接触时,真实表面的接触实际上是微凸体间的接触.粗糙表面间的接触行为对摩擦、磨损、润滑、密封和传热等有着重要的影响,是摩擦学研究的主要课题之一.介绍了Hertz弹性接触模型、统计学接触模型和分形接触模型,对粗糙表面接触模型的研究现状和进展作了分析和评述.由Hertz模型只能求解一些几何形状比较规则的物体,应用范围非常有限;各种统计学模型都是经过简化的理想模型,这些简化究竟能导致多大误差目前还没有精确的分析;分形模型利用了包含全部表面粗糙度信息的分形参数D和G,其对粗糙表面接触性质的预测不受仪器分辨率和取样长度的影响,使预测具有惟一性或确定性.     

二维自适应粗糙表面弹塑性接触模型

提出一种基于自适应粗糙表面描述的弹塑性接触模型。根据某一给定阈值,去除粗糙表面上对接触力学行为影响较小的结点以减少计算时间。采用在计算区域划分及结点排布上较为灵活性的无网格伽辽金—有限元耦合方法求解自适应粗糙表面弹塑性接触模型。算例表明,当接触压力相对误差约为5%时,自适应接触模型的计算时间相对于非自适应接触计算可减少约50%。分析不同阈值对接触压力分布、接触间隙及接触体弹塑性应力分布的影响。     

粗糙表面分形接触模型的研究进展

工程表面具有分形特征,利用分形参数对表面形貌进行表征不受仪器分辨率和取样长度的影响。2个粗糙表面之间的接触行为对摩擦、磨损、润滑、密封和传热等均有着重要的影响,因而一直是摩擦学研究的重要课题之一。基于表面的分形特性而建立的接触模型,可使表面接触的分析结果具有确定性和唯一性。介绍分形表面形貌的Weierstrass-Mandelbrot函数生成方法并给出利用MATLAB程序生成的分形曲线和曲面,分析和评述近二十年来分形接触模型中单个微凸体的接触行为、接触面积分布与真实接触面积、接触变形方式与接触载荷以及总的真实接触面积与接触载荷之间的关系等方面的研究情况,并简单列举分形接触模型在机械学科中的应用情况。指出结合分形理论对表面接触行为进行研究是接触理论发展的必然趋势,为摩擦学研究提供新的思路。     

渗氮钢粗糙表面的弹塑性接触研究

利用弹塑性有限元和单纯形法求解弹塑性接触模型，分别模拟了屈服强度呈梯度变化的渗氮钢、未经处理的匀质材料和硬涂层材料粗糙表面的弹塑性接触行为。与未经处理的匀质材料相比，渗氮钢可承受更大接触载荷。在相同载荷作用下，渗氮钢表面粗糙峰接触面积较小，平均间距较大，接触体内材料不易发生屈服，从而显著提高接触性能。和硬涂层材料相比，渗氮钢接触体内等效von Mises应力分布平缓，没有应力突变。最后讨论了渗氮层和硬涂层的厚度对粗糙表面接触特性的影响。     

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。     

平面磨削粗糙表面的微观接触模型

通过拟合实测平面磨削表面单个微凸体的轮廓数据,提出一种采用半周期余弦曲线回转体等效微凸体的方法。通过对实测表面轮廓的峰谷标记处理,获得了等效微凸体轮廓的尺寸参数。结合高斯分布,建立了能够更加准确表征平面磨削表面形貌特征的模拟表面。在模拟表面的基础上,基于接触力学理论与统计学理论,重新解算了微凸体在弹塑性变形区间的临界压入深度。推导出接触区域内接触参数与接触压力的解析关系,进而建立起一种针对平面磨削表面的微观接触模型。最后将实测平面磨削表面的统计参数作为接触模型数据仿真的初始值,将本文模型与CEB模型以及KE模型就平均距离和真实接触面积的预测结果进行了对比分析。结果显示,在相同接触压力的条件下,该模型相比CEB模型与KE模型所得到的平均距离与真实接触面积的预测值更大,并且三者之间的差值随着接触压力的增加而逐渐增大。结合不同微凸体轮廓假设对平面磨削表面微凸体轮廓数据的拟合结果来看,该模型对于平面磨削表面接触参数的预测结果更加准确且合理。     

车削真实粗糙表面的弹塑性接触有限元分析

目前表面模型主要以统计数学方法和分形方法居多,不能真实的反应表面特征.通过Wyko NT1100形貌测量仪获得车削表面的形貌数据,利用最小二乘法对Bad点和噪声点进行拟合插值处理,然后通过逆向建模得到真实粗糙表面模型,运用有限元方法,研究了弹性阶段和弹塑性阶段无量纲化接触面积和位移随无量纲化载荷的变化关系.结果表明:利用测量数据格式与CATIA V5之间联系,可以建立真实粗糙表面的模型;在弹性接触阶段,无量纲化接触面积和位移与无量纲化载荷之间近似成线性关系;而在弹塑性接触阶段,当弹塑性切向模量Et较大时,无量纲化接触面积和位移与无量纲化载荷之间才近似成线性关系.当载荷一定时,Et越小,接触面积和位移越大,对于一定接触面积和位移的载荷也越大.     

粗糙表面热弹塑性接触问题的无网格法

建立可考虑屈服应力温度相关的粗糙表面热弹塑性接触无网格法数值计算模型.研究摩擦力和不同热输入情况下圆柱体与弹塑性平面的接触力学特性,探讨摩擦热效应对表面温升、接触压力和接触面积的影响.结果表明在考虑剪切摩擦力作用后,弹塑性接触压力分布不再关于接触区域中轴线对称而出现了"塌陷"现象.通过无网格法解与有限元法解比较发现不恰当的有限元网格划分会造成接触压力的数值震荡,而无网格法可避免这一现象的发生.发现忽略温度相关效应将高估最大接触压力而低估相应外载荷下产生的接触面积.     

两弹塑性接触粗糙表面的严格解析解

GW干接触模型存在5个缺陷。当相糙峰高度的概率密度为Gauss分布时,给出了数学期望接触点数、总接触面积、总载荷、总电导的严格解析解,采用软件Maple计算了抛物柱面函数。实例计算表明接触点数与载荷近似成凸弧形直线正比例关系;量纲一的间距是联系接触点数、总接触面积、总载荷、总电导的纽带,它依赖名义压应力,但对名义压应力的变化不敏感;接触面积与载荷很接近直线正比例关系,在弹性接触条件下存在一个准弹性接触硬度,接触压应力等于准弹性接触硬度,名义面积对接触面积几乎无影响。     

两弹塑性接触粗糙表面的静密封流量

当峰高的概率密度为指数分布时,利用泰勒公式推导了弹性载荷的近似解析解,给出了塑性载荷的严格解析解,导出了静密封流量的经验表达式。通过密封表面的泄漏量与表高标准差的3次方成正比。在塑性接触状态,存在一个临界塑性指数,当塑性指数大于临界塑性指数时,总载荷与塑性指数、粗糙度参数皆无关,量纲一的塑性泄漏量与较软材料的硬度有关,与两接触粗糙表面的复合弹性模量无关。     

Modification of the elastic-plastic model for the contact of rough surfaces

An analysis of some drawbacks of the elastic-plastic model for the contact interaction of rough surfaces of metal pieces is reported. Computational and experimental techniques are used to derive a new expression for the plastic load as a function of the interference for an asperity.     

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.     

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.     

A model for the liquid-mediated collapse of 2-D rough surfaces

Small-scale devices are particularly vulnerable to adverse effects of adhesion because of large surface area to volume ratios. Additionally, small gaps can be easily bridged at high humidity or when there are other contaminant liquids present. The bridging of a portion of an interface by a liquid droplet of given volume tends to pull surfaces in closer proximity due to the sub-ambient pressures that arise. In turn, the area spanned by the bridge will increase and lead to a greater adhesive force. A previous study considering a liquid bridge between two elastic half-spaces initially separated by a uniform gap demonstrated that, under certain conditions, an instability will arise whereby the surfaces come into full contact. Owing to the regularity of the geometry considered, the problem was amenable to a semi-analytical treatment and the stability condition was expressible analytically in terms of a single dimensionless group. In the present work, we develop a model to include the effects of surface roughness. The influence of asperities on the surface is treated by means of a recently developed multi-scale model that considers the full range of wavelengths comprising the surface profile. In the simulations, two nominally flat rough surfaces are brought together under a prescribed load and a liquid bridge of given volume is introduced in the contact, the initial areal coverage being determined by the initial mean surface separation. The interface configuration is then iterated until a configuration is found that satisfies the equations of elasticity and capillarity for the given liquid volume. As a result of the simulation, critical values are found for combinations of parameters that delineate stable and unstable conditions.     

Simplified stiffness model for spherical rough contacts

Abstract

Obtaining a surface with negligible roughness is very expensive, time consuming and unnecessary. The influence of surface roughness on the contact stiffness is of great importance. The extra cost associated with unnecessary surface finish can be limited by eliminating the unnecessary machining operations beyond the required surface finish. In this article, a simplified solution is presented to calculate the stiffness of rough contact between the workpiece and spherical locator; also, the effect of surface roughness on the stiffness and deformation of rough spherical contact is studied for different applied loads to find an ‘economic roughness’ under machining forces.     

A thermal creep model for the contact of nominally flat surfaces: Jeffreys' linear visco-elastic model

This work considers the mechanics of contact of thermo-visco-elastic materials. In particular the creep behavior of a nominally flat rough surface in contact with a rigid half space is studied. The rough surface is modeled using fractal geometry. A synthesized profile, a Cantor structure, is utilized to model the surface. Such a profile has two scaling parameters and different heights for each generation of asperities. The effect of temperature will be included through the concept of activation energy using the Arrhenius equation.The objective of this model is to study the normal creep approach of the surface (punch) as a function of the applied creep load, time, and temperature. The material of the punch is assumed to behave according to Jeffreys' model. Such a model is an arrangement of springs and dashpots in parallel and/or in series.The creep approach of linearly visco-elastic materials is explored using elastic-visco-elastic correspondence analysis. An asymptotic power law is obtained, which relates the force and the bulk temperature acting on the punch to its approach. This model is valid only when the approach between the punch and the half space is in the range of the roughness size. The proposed model admits an analytical solution for the case when the deformation is linear thermo-visco-elastic. The obtained model shows a good agreement when compared with experimental results from literature.     

A numerical investigation of the sinusoidal model for elastic layers in line contact

Distributions of normal stresses and surface deformations, induced when an elastic layer of finite thickness is indented by a frictionless rough rigid flat or cylindrical indenter, are calculated numerically. It is assumed that the punch has a sinusoidal roughness superimposed on its nominal profile. Two cases will be examined, namely when the elastic layer is either bonded to a rigid backing or resting on a frictionless rigid backing (unbonded). Chebyshev polynomials of the first kind T_n(x) are utilized to model both the unknown pressure and the given deformation over the contact area. The governing elasticity equation is thereby reduced to a finite set of linear equations and hence a complete solution is found. The present numerical method is simple, accurate and valid in the full range of Poisson's ratio 0 v 0.5. Moreover, a set of semi-analytical solutions for the contact pressure is obtained for both thin unbonded and bonded elastic layers. The numerical results compared favourably with the asymptotic solutions. The effects of the layer thickness, layer compressibility and roughness amplitude parameters on the contact stresses and deformations are considered.     

变齿厚斜齿轮传动齿面接触数学模型的建立

变齿厚斜齿轮传动综合了斜齿轮和变位齿轮传动的优点,为保证平行轴变齿厚斜齿轮接触良好,传动可靠,应对设计的齿轮对进行齿面接触分析.根据设计的待加工齿轮参数,确定小、大齿轮的齿面方程,建立其接触的数学模型,进而对标准安装以及存在安装误差的齿面接触情况进行研究,为接触有限元分析及制造加工奠定理论基础.