基于分形的三维粗糙表面弹塑性接触力学模型与试验验证

基于分形几何理论,利用双变量的Weierstrass-Mandelbrot函数模拟三维分形粗糙表面,建立了三维分形粗糙表面弹塑性接触模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定了粗糙表面上各等级微凸体的面积分布密度函数,获得了总接触载荷和真实接触面积之间的关系式。计算结果表明:单个微凸体的临界接触面积与其尺寸相关,随着微凸体等级的增大,微凸体的高度和峰顶曲率半径减小。微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形,与经典的赫兹模型保持一致。粗糙表面的力学性能仅与最小等级及后续的6个等级微凸体相关,其余微凸体基本上对整个粗糙表面的力学性能影响很小。最后对粗糙表面的接触力学性能进行了试验测试,验证了该模型的合理性与正确性。     

考虑表面张力的机械结合面特性建模研究

表面张力是物质表面层分子间存在的力,它对机械结合面的接触特性有着重要的影响。为此,采用Nayak随机过程模型表征各向同性表面上微凸体的高度与曲率分布,建立考虑表面张力的单个微凸体接触模型,通过高斯-切比雪夫求积公式求解验证了模型的正确性;基于统计学理论将单个微凸体的计算模型扩展到整个粗糙表面上,建立了新的结合面接触模型,揭示了表面张力对结合面接触载荷、真实接触面积以及接触刚度的影响规律。结果表明:当两表面间平均距离相同时,与传统不考虑表面张力的模型相比,新模型具有较大的接触载荷和接触刚度,较小的真实接触面积;当接触载荷增大时,真实接触面积增大的速率随着表面张力的增大而减小;接触刚度随着接触载荷或真实接触面积的增大而增大,且表面张力越大,递增速率越快。     

含硬涂层结构的表面微观接触新模型

为研究含有硬涂层的粗糙表面中微凸体和基体变形对表面微观接触特性的影响规律,利用Hertz接触理论分别求出微凸体和基体的接触刚度,利用不动点迭代法确定微凸体变形量,建立关于微凸体接触变形量的刚度模型,通过并联关系耦合接触刚度,建立新的接触表面微观接触模型。为验证新模型对含有硬涂层的粗糙表面接触特性描述的正确性,建立了不同大小和不同材料的单微凸体有限元模型,通过与Hertz模型、有限元分析结果比较,发现当基体材料和微凸体材料不同时,微凸体/基体系统的应力分布会不均匀,微凸体表面的接触力比材料相同时的接触力小,最大应力比材料相同时的最大应力大;在变形量很小的时候,Hertz模型解和新模型解都很好地与有限元分析结果相吻合,随着变形量的变大,有限元分析解和新模型解开始同时偏离Hertz模型解,但新模型解一直趋近于有限元分析解。     

基于粗糙表面分形表征新方法的结合面法向接触刚度模型

如何有效预测结合面的接触刚度,是机械结构设计研究的一个重要课题。结合面接触刚度模型主要分为基于统计学特征参数的和基于分形参数的两类。前者依赖于粗糙表面形貌的测量尺度,后者与测量尺度无关。然而,多数研究者在利用分形理论进行建模时,以对应于微凸体接触面积a的尺寸l=a~(1/2)作为微凸体基底尺寸描述微凸体初始轮廓,给出了错误的微凸体变形机制和结合面接触刚度模型。提出了一种基于D,G和最大微凸体高度的粗糙表面轮廓分形表征新方法,探讨了微凸体接触变形机制,建立了与测量尺度无关的粗糙表面接触力学分形模型,揭示了接触刚度的变化规律。研究表明:接触载荷可用表达式F_c=F(E,D,G,h,a_L)描述;当结合面上的接触压力小于其屈服强度时,无论微凸体发生何种变形,结合面均因存在有弹性变形的接触点而具有一定的法向接触刚度。     

粗糙表面微凸体模型构建与接触特性分析

基于粗糙表面形貌测量试验，提出一种采用二次函数回转体等效微凸体的办法，建立微凸体接触半径与接触变形的解析关系，弥补了半球体模型单一曲率半径的缺陷；然后根据几何模型，重新推导出单个微凸体在弹性、弹塑性和完全塑性三种变形阶段的接触表达式，并应用接触力学理论和概率统计方法，建立粗糙表面的微观接触模型；最后将所建模型与CEB模型、ZMC模型以及KE模型的仿真结果进行了对比，验证了所建模型的有效性，并揭示了塑性指数、微凸体尺寸参数对接触特性的影响规律。研究表明：相比于半球体模型，二次函数模型对微凸体轮廓的拟合效果更好，能够在载荷较大的情况下，更加精确地进行结合面接触特性分析；塑性指数是影响接触刚度的主要因素，塑性指数越大，其接触面积越小，抵抗变形的能力越弱；微凸体尺寸参数对接触刚度的影响较小，微凸体直径与高度的比值越大，接触面积和接触刚度越大。     

粗糙表面的分形表征

最近的研究表明，随机粗糙表面是自仿射的多尺度的，因而表面轮廓的高度分布方差，叙率和曲率的方差不再是唯一的。本文基于分形几何理论提出了一种新的粗糙表面表征方法。使用Ｗｅｉｅｒｓｔｒａｓｓ－Ｍａｎｄｅｌｂｒｏｔ函数得到粗糙表面的分形参数－－“固有”参数，而这些参数可以提供任何长度尺度的粗糙度结构信息。     

结合面静态接触参数的统计模型研究

基于对粗糙表面形貌统计分析的基础上,综合考虑微凸体的完全弹性、弹-塑性和完全塑性三种变形机制,建立了结合面的接触面积、接触载荷及接触刚度的统计模型。该模型揭示了结合面接触参数与材料性能参数及粗糙表面形貌参数之间复杂的非线性关系。在不同的微凸体高度随机分布及塑性指数条件下,对接触参数进行预估和对比研究。结果表明,修正的指数分布对高斯分布有着较好的近似,而简单的指数分布与高斯分布之间的误差较大,且相差1至3个数量级;接触表面间距减小时,接触参数值均呈现增大的趋势;塑性指数增大时,接触载荷和接触刚度都随之增大,而接触面积的变化较小。     

结合面微观接触面积分布数值仿真分析方法

机械系统中结合面的接触状态会显著影响装配体动力学特性,结合面接触面积是描述接触状态的关键参数。分形接触模型是结合面分析中的常用方法,经典MB接触模型将结合面简化为刚性平面与粗糙面接触,以W-M分形函数描述粗糙面轮廓曲线,利用岛屿面积分布规律描述接触点面积分布,但以往研究并未分析该分布是否符合分形函数描述的粗糙面。因此提出求解W-M函数所描述轮廓的接触面积分布规律的数值仿真方法。根据粗糙表面形貌分形特征的有限性,将粗糙轮廓描述为连续可导的曲线,利用曲线与直线相交模拟粗糙面与平面的接触。利用梯度上升算法求出所有极值并计算各微凸体截线长度,进而获得面积的离散分布,分别以Majumdar与Komvopoulos提出的面积分布函数形式拟合离散点。结果表明前述分布规律符合数值仿真法求得的接触点面积分布,但存在更准确的分布函数形式。同时,该方法有望用于求解两粗糙面接触模型的面积分布,为进一步研究两粗糙面间的接触状态提供思路。     

结合面切向接触刚度的概率统计模型

该文考虑结合面上微凸体接触为椭圆形接触, 运用弹性力学空间半无限体受载荷变形理论, 并根据椭圆形接触面上压力分布的Hertz理论, 推导出椭圆形接触面的长、短半轴计算式和单个微凸体接触时的切向接触刚度表达式. 建立了结合面上微凸体椭圆形接触面的长、短半轴呈二维正态分布、高度呈正态分布情况下的宏观切向接触刚度模型, 得到了相应的宏观切向接触刚度表达式. 通过数值计算给出了切向接触刚度随结合面的法向载荷、切向载荷、椭圆微凸体的离心率、微凸体分布的相关系数、微凸体测量高度和微凸体分布的标准方差等各影响因素的变化情况, 增大法向载荷可以提高结合面的切向接触刚度, 而切向载荷的增大会导致切向接触刚度的 减小.     

基于分形理论的两粗糙表面接触的黏滑摩擦模型EI北大核心CSCD

两粗糙表面的接触本质上是大量微凸体的接触,具有复杂的力学行为,连接界面的力学建模是重要的科学问题。从微观角度出发,对单个微凸体进行接触分析,并考虑了微凸体相互作用造成的基底面的下降,根据分形理论积分,建立了整个接触面的法向接触模型。利用该模型,可确定在给定法向预紧载荷下微接触截面积的概率密度函数;根据Mindlin模型、Masing准则和分形理论,建立了两粗糙表面接触的切向载荷与切向位移的关系,并研究了不同参数对系统能量耗散的影响。数值仿真结果表明,能量耗散随分形维数D增大而增大,随分形粗糙度参数G及法向预紧力增大而降低。     

Experimental Investigation of Thermal Contact Conductance: Variations of Surface Microhardness and Roughness

Surface roughness parameters were measured using nine different sampling intervals. The results showed that the roughness of profile was nearly a constant at all sampling intervals; the slope, peak curvature and density of the profile decreased with increasing sampling interval; and the distribution of the peak height was different from the profile height distribution and was not Gaussian. It was found that the surface microhardness value, under small loads, varied with the indentation size and the surface preparation procedure. A model was developed which used a discretization method to obtain the contact radius and area in each section of the surface summit height distribution curve. This model eliminated some of the assumptions made by previous models and can be used to predict the thermal contact conductance without assuming the asperity deformation mode and surface summit height distribution. The predicted thermal contact conductance values were in good agreement with experimental results.     

Thermal contact conductance of pressed contacts at low temperatures

The influence of variations of interface temperature in the range 50-300 K on the thermal contact conductance between aluminium and stainless steel joints was determined. Predictions were done by modeling the deformation at the interface for different values of surface finish and contact pressure over the range of interface temperatures. Both elastic and plastic deformation was considered. Experiments were carried out in a closed loop cryostat and the results were shown to compare well with the predictions. A reduction of the interface temperature resulted in a smaller value of thermal contact conductance. Interfacial pressure variation had much lower influence at the smaller value of temperatures. The role of surface roughness at the contact was also seen to be less significant at lower interface temperatures and the zone of hysteresis was smaller. A correlation was developed for estimating thermal contact conductance at joints over this temperature range. An explicit dependence of contact conductance on temperature was not seen to be necessary as long as the changes in the hardness and thermal conductivity of the material with temperature are incorporated in the correlation.     

A Study on Thermal Contact Resistance at the Interface of Two Solids

In this paper, numerical simulations and measurements of the thermal contact conductance (TCC) at the interface between the plane ends of two cylinders in contact are carried out. The random model of surface roughness is developed, and the non-dimensional basic equations are solved based on a grid system with equi-peripheral intervals in the azimuthal direction that can express reasonably the real contact spot distribution. The effects of the contact pressure, the thermal conductivity of the interstitial medium, and the mean absolute slope of the rough surface on the TCC were clarified by using a network method. In the experiments, four pairs of brass cylinders, each of which has similar surface topology, are used for the TCC measurements. The hysteretic nature of TCC versus contact pressure was observed in the first loading cycle. The present numerical results show that the TCC increases linearly with the mean absolute slope of the surfaces even at the same mean roughness. Such a tendency agrees well with the measurements.     

基于红外热成像的印刷橡皮布应变测试

目的采用红外热成像系统对压印接触区域橡皮布的动态应变进行测试。方法建立压印接触区域几何模型,结合热弹性效应与热辐射理论分析温度与应变之间的函数关系,并采用红外热像系统测得压印接触区域橡皮布的温度分布情况,最后通过有限元仿真得到橡皮布压痕处的应变云图。结果沿轴线方向,压印接触区域橡皮布温度、应变均呈不均匀分布,轴端温度高于中间区域温度;轴端应力集中,节点位移大,变形量大,中间区域节点位移小,变形量小,中间区域应变量低于轴端区域应变量。结论采用红外热成像技术测试印刷过程中橡皮布动态应变的方法是可行的。     

Evaluation of thermal contact conductance using a new experimental-numerical method in fin-tube heat exchangers

In a fin-tube heat exchanger the contact between fin collar and tube surface is obtained through mechanical expansion of tubes. Since the interfaces between the tubes and fins consist partially of metal-to-metal contact and partially of air, the features of heat transfer through the contact interfaces have not been fully investigated. The present study aims at the development of a new tool including an experiment and a numerical calculation for the estimation of the thermal contact conductance between the fin collar and tube surface, and pursues the evaluation of the factors affecting the thermal contact conductance in a fin-tube heat exchanger. Heat exchangers fabricated for the current study have been put to the test for heat balance in a vacuum chamber with water as an internal fluid. And a finite difference numerical scheme has been used for the data reduction of the experimental data to evaluate the thermal contact conductance. Fin-tube heat exchangers employed in the current research are of tube diameter of 7 mm with different tube expansion ratios, fin spacings, and fin types. The results of the present study imply that these parameters as well as hydrophilic fin coating have a significant effect on the thermal contact conductance. It has been discovered that the portion of the thermal contact resistance is not negligible compared with the total thermal resistance in a fin-tube heat exchanger, and this means that in order to reduce the thermal contact resistance thoughtful care should be taken in fabricating heat exchangers.     

干气密封动静环摩擦界面热弹法向接触刚度分形模型

基于分形理论,根据重新建立的微凸体接触模型,并考虑微凸体弹性变形以及热应力变形,建立了干气密封两摩擦界面热弹性法向接触刚度计算模型,并对其影响因素进行了数值分析。研究结果表明:热法向接触刚度、弹性法向接触刚度均随无量纲真实接触面积、分形维数增大而增大,而随特征尺寸增大而减小,其中分形维数、特征尺寸对弹性法向接触刚度影响较为显著;摩擦因数对热法向接触刚度和弹性法向接触刚度的影响相反,摩擦因数增大,热法向接触刚度变大,而弹性法向接触刚度变小;热法向接触刚度随着转速以线性方式增大。摩擦界面热弹法向接触刚度分形模型的建立与分析,将为研究考虑热效应的干气密封摩擦振动奠定一定基础。     

Conductance histogram evolution of an EC-MCBJ fabricated Au atomic point contact

This work presents a study of Au conductance quantization based on a combined electrochemical deposition and mechanically controllable break junction (MCBJ) method. We describe the microfabrication process and discuss improved features of our microchip structure compared to the previous one. The improved structure prolongs the available life of the microchip and also increases the success rate of the MCBJ experiment. Stepwise changes in the current were observed at the last stage of atomic point contact breakdown and conductance histograms were constructed. The evolution of 1G0 peak height in conductance histograms was used to investigate the probability of formation of an atomic point contact. It has been shown that the success rate in forming an atomic point contact can be improved by decreasing the stretching speed and the degree that the two electrodes are brought into contact. The repeated breakdown and formation over thousands of cycles led to a distinctive increase of 1G0 peak height in the conductance histograms, and this increased probability of forming a single atomic point contact is discussed.     

Stochastic modulation in molecular electronic transport junctions: molecular dynamics coupled with charge transport calculations

The experimental variation in conductance that can be expected through dynamically evolving Au-molecule-Au junctions is approximated using molecular dynamics to model thermal fluctuations and a nonequilibrium Green's function code (Hückel-IV 2.0) to calculate the charge transport. This generates a statistical set of conductance data that can be used to compare directly with experimental results. Experimental measurements on Au-single molecule junctions show a large variation in conductance values between different identically prepared junctions. Our computational results indicate that the Au-Au and the Au-molecule fluctuations provide extensive geometric freedom and an associated broad distribution in calculated conductance values. Our results show agreement with experimental measurements of the low bias voltage conductance and conductance distribution for both thiol-Au and amine-Au linker structures. -     

MT300/KH420碳纤维/聚酰亚胺树脂复合材料层合圆柱壳高温承载性能

基于Donnell-Mushtali近似理论及热弹性理论,考虑结构热变形和材料高温性能衰减等温度影响因素,对MT300/KH420碳纤维/聚酰亚胺树脂复合材料圆柱壳在常温、420℃及周向210~420℃不均匀温度场等热载工况下的承载性能进行了理论分析。并引入一阶屈曲模态缺陷作为几何初始扰动,利用ABAQUS,采用非线性显式动力学方法完成对MT300/KH420复合材料圆柱壳在以上热载工况下的轴压稳定性有限元仿真计算,计算结果与理论分析较为一致。设计并开展MT300/KH420复合材料圆柱壳力-热载荷联合轴压试验,获得圆柱壳在以上热载工况下的破坏载荷和破坏模式。研究表明:高温工况下,力学性能衰减和温场不均匀引起的结构热变形是影响MT300/KH420复合材料圆柱壳轴向失稳载荷的主要因素。