岩石节理(断裂)表面的多重分形性质

提出了新的投影覆盖法———ＰｒｏｊｅｃｔｉｖｅＣｏｖｅｒｉｎｇＭｅｔｈｏｄ（ＰＣＭ），并结合无接触激光表面测量技术直接测定出断裂表面分维值Ｄ∈［２，３）．建立了表面粗糙性投影覆盖概率函数，分析了节理（断裂）表面的多重分形性质．     

关于断裂表面分维估测的研究

本文利用回归分析理论对断裂表面的分维估测方法进行了研究.定量地描述了在双对数坐标系下利用线性回归计算分维的方法的可靠性,并引入了统计自相似度的概念.最后,利用残差分析法对分维估测的回归模型以及异常点问题进行了初步的研究,通过剔除异常点提高了分维估测算法的可靠性和计算结果的精确性.     

锡基巴氏合金磨损表面的分形与磨损率

利用结构函数分析法研究了滑动摩擦学系统中金属磨损表面轮廓线的分形特性。结果表明：磨损表面轮廓线在小于Ｓｍ的尺度上具有分形结构。采用结构函数法可以方便地确定粗糙表面轮廓线的分形参数，即垂直于滑动方向上磨损表面轮廓线的分维Ｄ可作为磨损表面分维的特征值，它与金属磨损率的变化有着密切的关系，最佳分维Ｄｏｐｔ值对应于材料的最低磨损率。     

粗糙表面上微液滴的数值模拟

本文使用VOF方法将微液滴在粗糙壁面上的接触现象转化为不可压缩两相流动问题,并对其进行三维数值模拟.选择具有柱形突起和槽道两种微结构的壁面进行模拟.计算了不同粗糙系数时液滴在突起结构表面的静止形态和接触角,计算结果和实验数据吻合得较好.和理论模型进行比较,分析了经典模型的适用范围.对于微槽道结构的壁面,计算给出不同方向测量得到的液滴接触角.实现了液滴在倾斜壁面上滑落过程的模拟.液滴沿斜面下滑时,前进角和后退角的变化存在周期性,这一周期性变化和表面粗糙结构密切相关.     

基于分子动力学-格林函数法的分形粗糙表面摩擦行为研究

任何物体间的表面摩擦均可看成是粗糙面间的摩擦,且大部分粗糙表面具有分形特征.为探究分形粗糙表面的摩擦行为,利用分子动力学-格林函数法(GFMD)建立微观分形粗糙表面模型,采用位移加载控制分形粗糙表面的接触和摩擦过程,并根据广度优先搜索算法识别接触团簇分布.之后分别计算原子尺度、接触团簇尺度和界面尺度下的最大摩擦系数与摩擦力,并利用影响矩阵法研究摩擦过程中接触团簇之间的相互作用,分析接触团簇之间的距离和面积对相互作用的影响.结果表明:在摩擦过程中,摩擦系数从小尺度到大尺度逐渐减小;摩擦力随位移呈现周期性波动,接触团簇并非同时达到最大摩擦力,而是发生局部滑移,整体滑移模型预测的摩擦力是分子模拟结果的上限值;所提出的影响矩阵法可以较好地模拟接触团簇之间的相互作用,利用影响矩阵计算得到的最大摩擦力与GFMD模型结果基本一致,而不考虑局部滑移影响计算得到的最大摩擦力比GFMD模型结果大20%,并且接触团簇之间的相互作用与距离成反比,与面积成正比.结果可为粗糙表面的界面分析和优化提供理论依据.     

粗糙表面法向接触刚度的分形模型

提出了以往有关粗糙表面法向接触刚度理论研究工作的缺陷与不足,并在一定的前提假设下,基于球体与平面的接触理论和粗糙表面的分形接触理论,从理论上给出了具有尺度独立性的粗糙表面法向接触刚度分形模型,并进行了数字仿真研究。     

点、线接触真实粗糙表面的弹流润滑研究

本文给出了点、线接触的真实粗糙表面的微弹流数值解。在给定随机粗糙表面样本后,求解大小不同的载荷和粗糙的弹流问题。从计算结果可以看出,由于Reynolds方程中速度项的作用,在表面对应粗糙的位置处引起了压力变化,从而因其产生的弹性变形使粗糙变得平滑。对此光滑表面解可以看出,因粗糙引起的压力和膜厚的变化在光滑解附近波动。载荷较大时,压力分节接近固体接触情况。     

MEMS动平板的切向静电阻力

由于微机械的表面积与体积之比远大于宏机械,所以微机械中的表面阻力难以忽略,为了改善MEMS器件的性能和可靠性,必须对其影响进行研究.基于能量守衡法,本文建立了光滑平板和正方形、四棱锥两种微凸体粗糙表面平板的切向静电阻力模型,讨论了微小尺度、表面形貌、外加电压以及因流片制造工艺而产生的微凸体、凹坑或孔对两个相对运动的带电平板间的切向静电阻力的影响.分析表明：当平板宽度与两平板之间的距离之比、表面形貌因数和外加电压增大时,切向静电阻力也将随之增加;表面形貌因数则与微凸体在平板的总投影面积与平板面积之比成正比,随相对表面粗糙度增加而非线性增加.     

扫描电镜下断口表面的三维重建及分形维数的测量

基于数字散斑相关方法,利用扫描电镜立体对技术和计算机视觉方法实现了物体表面的三维重建,讨论了影响其精度的原因,并且利用分形理论对表面的三维形貌进行了定量分析,由立方体覆盖法得到了三维形貌的分形维数.作为应用的实例,将该方法应用到岩石断口的三维重建中,得到了重建后的高度云图和分形维数.结果表明,利用扫描电镜立体对技术对断口表面进行三维重构并进行分形维数的计算是一种行之有效的断口定量分析方法.这为研究材料断裂的微观机理、断裂过程和断裂性质等问题提供了一种途径.     

粗糙薄层弹性体接触刚度分析

薄层弹性体功能结构表面在工程领域有着广泛的应用前景,薄层弹性体的接触特性分析对功能结构表面设计与应用非常重要.采用随机粗糙表面模拟生成技术和有限元分析技术建立了粗糙薄层弹性体表面的接触刚度确定性分析模型,研究了薄层弹性体的接触特性,对基于半数值确定性分析方法的粗糙层-基体层串联模型用于粗糙薄层弹性体接触刚度计算的适用性进行了讨论,进一步分析了粗糙薄层弹性体串联模型接触刚度的误差来源.研究结果表明:当薄层弹性体的基体层厚度小于10倍表面均方根粗糙度时,由传统粗糙层-基体层串联模型分析获得的粗糙薄层弹性体刚度误差将超过15%,误差主要来源于粗糙峰的大变形和基体层的局部变形不均匀的共同作用.     

基于基底长度的粗糙表面分形接触模型的构建与分析

为建立更为精确的粗糙表面接触模型,根据微凸体变形特征、分形理论以及摩擦的作用,从微观角度基于基底长度建立了粗糙表面分形接触模型.通过与其他粗糙表面接触模型和实验数据的比较,验证了本文模型的正确与合理,并由数值仿真分析了分形维数、接触载荷与真实接触面积之间的相互关系.分析结果表明:特征尺度一定时,要维持一定的真实接触面积,分形维数越大,所需要的力也越大;分形维数与特征尺度一定时,随着载荷的增加,接触面积也在增加;特征尺度与接触力一定时,随着分形维数的增大,真实接触面积在减小.该模型的建立为进一步研究粗糙表面的摩擦、磨损与润滑提供了理论依据.     

粗糙表面的分形特征与分形表达研究

得用触针轮廓仪和数据采集系统对磨削和车削表面的粗糙轮廓曲线进行了测量，并就粗糙表面的分形特征作了分析与讨论，同时还提出了粗糙表面的特征粗糙度概念及其定义，并将其用表面粗糙度水平的表述。     

Morphological covering based generalized dimension for gear fault diagnosis

This investigation presents a new generalized dimension estimation method based on morphological covering (MC) technique for characterizing the nonlinearity and complexity of vibration signals measured from gearbox. A synthetic fractal signal is employed to evaluate and compare the proposed MC technique with the traditional box-counting (BC) method and a similar approach developed in literature. Results revealed that the presented MC method is the one providing the most reliable generalized dimension estimation results. Furthermore, we applied this scheme to analyze the vibration signals from a gearbox with three operation states. The estimated general dimensions are used as the input feature vector for classifiers to the gear working states. Experimental results showed that our presented scheme achieves the best performance on discriminating the gear conditions. We also explore the calculational efficiency of the MC method. Results demonstrated that the MC method requires much less computational cost than BC method and seems to be more suitable for on-line condition monitoring of gearboxes.     

工程粗糙表面粘着磨损的分形学研究

建立了分形接触模型,并在Ａｒｃｈａｒｄ粘着磨损理论基础上,结合磨损过程中剪切应力对实际接触表面的影响,建立了弹、塑性接触条件下的粘着磨损分形模型,通过试验得出了磨损体积损失与分形参数的关系,为降低磨损与加工成本及确定表面最佳分形维数提供了实验依据．     

The influence of the statistical properties of self-affine surfaces in elastic contacts: A numerical investigation

In the last years, an increasing number of papers has been published in the field of contact mechanics between rough fractal surfaces. The increase in research is motivated by the wide variety of natural and industrial processes that involve formation of rough surfaces and interfaces, characterized by self-similarity or self-affine properties on multiple scales. In this paper, the contact between a linear elastic half-space and a rough self-affine fractal rigid surface is studied by employing a numerical method recently developed by the authors (Putignano et al., 2012). The paper aims at investigating the influence of surface parameters as fractal dimensions, mean square slope and mean square roughness on the relation between the contact area, the load and the average separation. The results show that, for relatively small loads, the real contact area–load relationship coefficient of proportionality $\kappa$ takes the universal value $\kappa =2$ independent of the statistical properties and fractal dimension D_f of the rough surface. This universal constant is just in between the two values predicted respectively by Bush et al. (1975) and Persson (2001). We also find that the average separation vs. load relation is affected by the fractal dimension D_f of the rough surface, as higher D_f lead to an increase of the average separation. Finally, in this work, we also study the behavior of the power spectral densities of the elastically deformed surface and of the distribution of local separations. We find that the trend of this quantities is in agreement with recent theoretical predictions.     

Three-dimensional vibration analysis of prisms with isosceles triangular cross-section

This paper studies the three-dimensional (3-D) free vibration of uniform prisms with isosceles triangular cross-section, based on the exact, linear and small strain elasticity theory. The actual triangular prismatic domain is first mapped onto a basic cubic domain. Then the Ritz method is applied to derive the eigenfrequency equation from the energy functional of the prism. A set of triplicate Chebyshev polynomial series, multiplied by a boundary function chosen to, a priori, satisfy the geometric boundary conditions of the prism is developed as the admissible functions of each displacement component. The convergence and comparison study demonstrates the high accuracy and numerical robustness of the present method. The effect of length-thickness ratio and apex angle on eigenfrequencies of the prisms is studied in detail and the results are compared with those obtained from the classical one-dimensional theory and the 3-D finite element method. Sets of valuable data known for the first time are reported, which can serve as benchmark values in applying various approximate beam and rod theories.     

考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析

为建立更完善和精确的结合面接触刚度模型,本文根据分形理论和摩擦学原理,从微观角度建立了考虑摩擦因素的结合面切向接触刚度分形预估模型.通过数值仿真分析研究了接触载荷、分形维数、摩擦系数和接触面积等因素对结合面切向接触刚度的影响.分析结果表明:结合面切向接触刚度随法向载荷和分形维数的增加而增大,而随分形尺度参数的增大而减小;摩擦系数对结合面切向接触刚度的影响较大,不同实际接触面积下的切向刚度相差较大;当分形维数较小时,摩擦系数对结合面切向刚度的影响将降低.这些研究对于进一步开展结合面的动力学特性研究具有重要意义.     

Study on stress wave propagation in fractured rocks with fractal joint surfaces

This paper presents the experimental and theoretical investigation of property of stress wave propagation in jointed rocks by means of SHPB technique and fractal geometry method. Our aim focuses on the influence of the rough joint surface configuration on stress wave propagation. The comparison of behavior of reflection and transmission waves, deformation and energy dissipation of a rough joint surface characterized by its fractal feature with that of a smooth plane joint has been carried out. It has shown that the rough joint surface distinctly affects the stress wave propagation and energy dissipation in the jointed rocks. The rougher the joint surface was, the more permanent deformation occurred and the more attenuation stress wave took place as well. A nonlinear relationship between the normalized energy dissipation ratio W_J/W_I of the jointed rock and the joint roughness in terms of the fractal dimension has been formulated. It seems that the ratio W_J/W_I, presenting how much energy has been dissipated in the joint, nonlinearly increased with the increment of the fractal dimension D of the jointed surface. The ratio W_J/W_I of a roughly jointed rock, however, tends to be the same as that of a smoothly jointed rock if the fractal dimension is less than a critical value D_c = 2.20. The energy dissipation ratio at the critical point D_c seem to be a constant, not dependent of rock type but fractal joint configuration.     

粗糙表面测量轮廓的分形插值模拟

引入粗糙表面的分形插值理论，提出用分形插值函数模拟粗糙表面轮廓的方法。并以车削，磨削及磨损表面为研究对象，对粗糙表面进行了分形插值模拟，系统地研究了影响其模拟模拟效果的因素和规律。发现可以采用分形插值理论来模拟或表征具有分形特征的粗糙表面。     

粗糙表面接触力学问题的重新分析

为了克服基于统计学参数的接触模型的尺度依赖性以及现有接触分形模型推导过程中初始轮廓表征受控于接触面积或取样长度的不足，基于粗糙表面轮廓分形维数$D$、尺度系数$G$ 和最大微凸体轮廓基底尺寸$l$，建立了新的粗糙表面接触分形模型，探讨了微凸体变形机制、粗糙表面的真实接触面积和接触载荷的关系，揭示了接触界面的孔隙率和真实接触面积随端面形貌、表面接触压力等参数变化的规律，给出了不同形貌界面被压实的最大变形量. 结果表明:微凸体变形从弹性变形开始，并随着平均接触压力$p_{\rm m}$ 的增大逐步向弹塑性变形和完全塑性变形转变；接触界面的初始孔隙率$\phi_{0}$ 随$D$ 的增大而增大，压实孔隙所需要的最大变形量$\delta $ 也随之增大；接触压力$p_{\rm c}$ 增大，孔隙率$\phi$ 减小，并随着$D$ 的增大和$G$ 减小，$\phi$ 快速减小，直至填实，变为零；$D$ 较小时，$G$ 的增大对真实接触面积的增大影响较小；$D$ 较大时，$G$ 的增大对真实接触面积的增大作用明显. 研究成果为端面摩擦副的润滑与密封设计提供了理论基础.