弹性状态下粗糙表面法向接触刚度的研究

粗糙表面接触问题是一类重要和具有实用价值的实际工程问题。采用Ｈｅｒｔｚ理论和粗糙表面随机接触模型, 研究弹性状态下粗糙表面法向接触刚度,推导出在不同接触体的法向接触刚度公式。由推导的理论公式可知,粗糙表面 在随机接触模型中接触刚度跟载荷成正比,与表面粗糙度均方值成反比     

弹性状态下粗糙表面的法向接触刚度

粗糙表面接触问题是一类重要和具有实用价值的实际工程问题。采用Hertz理论和粗糙表面随机接触模型,研究弹性状态下粗糙表面法向接触刚度,推导出在不同接触体的法向接触刚度公式。由推导的理论公式可知,粗糙表面在随机接触模型中接触刚度跟载荷成正比,与表面粗糙度均方值成反比。     

高速轮轨粗糙表面法向和切向接触刚度研究

为准确计算高速轮轨粗糙表面法向和切向接触刚度,基于W-M函数分形理论建立高速轮轨表面粗糙度三维数值模型;分析轮轨法向和切向接触刚度理论,运用有限元法离散轮轨接触面建立轮轨粗糙表面接触有限元简化模型;基于罚函数的面-面接触算法定义轮轨接触,加载位移载荷计算轮轨法向和切向接触刚度。计算结果表明:接触载荷作用下考虑轮轨表面粗糙度可更为准确地计算法向和切向接触刚度;轮轨法向接触刚度受法向载荷影响较大,且随着法向载荷的增加而增加,而摩擦因数对法向接触刚度的影响甚微;轮轨切向接触刚度随着法向载荷和摩擦因数的增加而增加,随着切向载荷的增加而减小。     

粗糙平面接触刚度的研究

从材料表面微观特征的分析着手，采用弹性接触理论和概率分析方法，对两个粗糙平面间的接触刚度问题进行了研究，提出了一种表面接触刚度的理论计算方法，给出了相应算例，计算结果表明，本文提出的方法是有效的。     

数控机床滚动导轨结合面接触静刚度分析

以数控机床滚动导轨为研究对象,利用接触力学及弹性力学中的接触理论,分析计算滚动导轨结合面的接触刚度,建立了结合面的接触刚度的求解公式,得到接触刚度的理论模型。基于有限元分析软件,对结合面建立有限元模型,然后,对滚动导轨结合面进行加载求解,得到应力云图,通过excel拟合相应载荷与变形量的关系曲线,把得到处理后的结果与理论计算结果相对比,验证了此有限元分析方法可行。为进一步研究滚动导轨结合面的接触刚度奠定基础。     

三维真实粗糙表面弹性接触的全域数值解

本文提出了三维真实粗糙表面弹性接触问题的全域数值求解方法。这种方法采用网格规则划分和局部柔度矩阵存储解决了计算机存储问题;采用求解域收缩和逐次低松弛迭代解决了接触方程求解问题。运用这种方法可以获得真实粗糙表面弹性接触时全接触域内的压力分布与总载荷、接触图象及其实接触面积、接触变形与接触刚度等参数。计算结果与实测结果符合得较好。     

混合润滑下粗糙表面的接触刚度研究*

针对润滑状态下结合面的接触刚度问题,建立一种混合润滑状态下粗糙表面接触刚度等效薄层模型,将接触界面的总刚度等效为固体接触刚度和润滑剂接触刚度之和,研究不同实际接触面积下的表面形貌和润滑剂类型对法向接触刚度的影响,并讨论固体刚度和润滑剂刚度占总法向刚度的比例。结果表明：粗糙界面的法向接触刚度随法向载荷的增加而增加,且混合润滑状态下的接触刚度大于干接触条件下的接触刚度;在初始接触时,法向接触刚度敏感地依赖于润滑性能;随着实际接触面积的增大,表面形貌对接触刚度的影响变得更加明显。     

基于接触分形理论的机械结合面法向接触刚度模型

为能够从理论上建立起具有尺度独立性的机械结合面法向接触刚度的理论模型,从而解决以往研究 荼存在的缺陷与不足,在一定的假设下,基于球体与平面的赫兹接触理论和接触分形理论,首次从理论上给出了具有尺度独立性的机械结合面法向接触刚度分形模型,并取得了与实验一致的数字仿真研究结果。     

机械结合面法向接触刚度分形理论模型

基于分形理论同时考虑微凸体的弹性、第一弹塑性、第二弹塑性、完全塑性四个阶段的变形状态,得出单个微凸体在各变形阶段的接触刚度模型,从而得出影响单个微凸体法向接触刚度的相关参数。引入频率指数并得出各变形阶段频率指数的临界值,推导出频率指数值处于不同区间时结合面的接触刚度模型。模型仿真结果表明,分形维数D取1. 1～1. 9时,随着D值的增大,无量纲法向接触刚度的值单调增大;微凸体频率指数处于各个区间时无量纲法向接触刚度的值随法向实际接触面积的增大均增大。     

拉杆转子轮盘结合面法向接触刚度试验

用功率谱法分析了拉杆转子轮盘接触面表面粗糙度与分形参数之间的关系,结合分形接触理论,建立了轮盘结合面法向接触刚度模型,通过轮盘表面材料参数、法向载荷及轮盘表面的分形参数来计算轮盘结合面的法向接触刚度,并通过试验进行验证。研究表明:轮盘结合面理论计算刚度与试验测试刚度趋势一致;分形接触理论在定性上是正确的,但分形理论适用范围有限,仅适用于粗糙度较小、法向接触载荷较大的场合,与试验刚度测试结果存在一定的偏差。     

Assessment of tangential and normal stiffness of contact between rough surfaces using ultrasonic method

The acoustic model of contact, previously proposed for longitudinal ultrasonic waves, was adopted for shear waves. It was found that the measurements of the phase shift of coefficient of reflection from the contact interface, taken both for shear and longitudinal ultrasonic waves of the same frequency, allows us to find the tangential to normal contact stiffness ratio for the contact tested.

However, an analysis based on the Greenwood-Williamson model and the Hertz-Mindlin theory revealed that for a contact between rough surfaces with spherical asperities, the ratio of the tangential to the normal contact stiffness is independent of surface height distribution and is, moreover, equal to that ratio for an elementary contact.

In order to verify the theoretical predictions, measurements of the phase shift of longitudinal and shear ultrasonic waves of frequency 10 MHz were carried out for the loaded contact (up to 300 MPa) between ground quartz samples. It appeared that the value of the tangential to normal contact stiffness ratio resulting from the ultrasonic measurements is fairly close to that predicted by the Hertz-Mindlin theory.     

The normal approach between rough flat surfaces in contact

The relationship between the normal approach and load for a variety of rough flat surfaces has been considered experimentally and theoretically. The experimental values of normal approach measured by a capacitance technique correlate well with the theoretical values based on the measured surface parameters. For smooth surfaces the texture deformation is essentially elastic whilst the rough surfaces behave plastically. Linearity between the normal approach and the surface roughness at any given load is established and is thereby in agreement with theoretical expectation.     

Contact analysis of three-dimensional rough surfaces under frictionless and frictional contact

A methodology for surface and sub-surface stress calculation of nominally flat on flat rough surface contact has been developed. This methodology is applicable for both large area contact (Hertzian contact) and small area of asperity contact (point load contact) with and without surface friction. A total of nine rough surfaces are generated by the computer with specified standard deviation of surface heights, σ, of 0.3, 1.0 and 3.0 nm, and correlation length, β^*, of 0.1, 0.5 and 0.9 μm. Under the typical applied load at the magnetic head slider-disk interface, small numbers of contact points are obtained and the deformation is purely elastic. Since these contact points are scattered and isolated, asperity contact behaves like point load contact. As β^* becomes larger, more adjacent points will be in contact at a certain contact spot and this is especially true at small σ. All the cases of flat on flat rough surface contact yield maximum von Mises stress on and near the surface at both frictionless and frictional contacts; no local maximum occurs in the sub-surface. In general, the friction effect in the vicinity of contact point is to increase the stress magnitude, while outside this region it also alters the stress distribution. For a surface of small β^* and large σ at high load of 1000 times of the nominal pressure at the head-disk interface, the contact pressure reaches the hardness at a few contact points and plastic deformation takes place in the near surface.     

A finite element-based model of normal contact between rough surfaces

Engineering surfaces can be characterized as more or less randomly rough. Contact between engineering surfaces is thus discontinuous and the real area of contact is a small fraction of the nominal contact area. The stiffness of a rough surface layer thus influences the contact state as well as the behavior of the surrounding system. A contact model that takes the properties of engineering surfaces into account has been developed and implemented using finite element software. The results obtained with the model have been verified by comparison with results from an independent numerical method. The results show that the height distribution of the topography has a significant influence on the contact stiffness but that the curvature of the roughness is of minor importance. The contact model that was developed for determining the apparent contact area and the distribution of the mean contact pressure could thus be based on a limited set of height parameters that describe the surface topography. By operating on the calculated apparent pressure distribution with a transformation function that is based on both height and curvature parameters, the real contact area can be estimated when the apparent contact state is known. The model presented is also valid for cases with local plastic flow in the bulk material.     

Frictionally-excited thermoelastic contact of rough surfaces

Frictional sliding contact between two elastically similar half-planes, one of which has a sinusoidally wavy surface, is studied in the full-contact regime. The steady-state regime is evaluated, within the limits imposed by the well-known phenomenon of thermo-elastic instability (TEI). TEI gives a critical speed whose value depends on the wavelength of the perturbation, and above which the perturbation itself grows arbitrarily with time. It is found that the TEI critical speed, V_cr, is clearly identified by the steady-state solution only in the special and limiting case when the flat half-plane is non-conductor; in that case, V_cr is the speed for which the steady-state predicts infinite amplification. In all other cases, V_cr (appropriate to the wavelength of the profile) does not correspond to infinite amplification, nor to the maximum one, V_M. In the limiting case of thermoelastically similar materials, not only the system is unconditionally stable (V_cr=∞) for f H₁<0.5, where f is the friction coefficient and H₁ a certain thermoelastic constant, but the regime at the maximum amplification is also always stable, and arbitrarily large amplification is obtained for f H₁ tending to infinity. However, it is found that in most practical cases of braking systems, V_crV_M, and so the limiting conditions are reached at V_cr. At this speed, the amplification is typically not extremely high.     

Measurements of pressure and area dependent tangential contact stiffness between rough surfaces using digital image correlation

The present paper describes an experimental technique to accurately measure the tangential contact stiffness between two rough contacting surfaces manufactured from the titanium alloy Ti-6Al-4V. The digital image correlation method is employed to measure the local displacement field. The effect of normal contact pressure, nominal contact area and fretting wear on tangential contact stiffness is investigated. The experiments indicate that the tangential contact stiffness is approximately proportional to the nominal contact area and the normal pressure raised to the power of 0.64. Multiple experiments with the same parameters show good repeatability given the number of variables involved.     

粗糙表面滑动摩擦接触模型研究的进展

对近年来国内外粗糙表面模型的进展进行了概述,根据粗糙表面模型类型的不同,分为粗糙表面和平面接触模型以及双粗糙表面接触模型,在各自模型中按照静载和滑动接触类型的研究进展进行表述,并提出了一些目前研究中遇到的热力耦合的问题以及将来双粗糙分形表面模型的发展.     

Computer simulation of the contact of rough surfaces

A program for the computer simulation of the contact of two rough surfaces has been developed, which makes it possible to determine the real area of contact and the penetration of microasperities at specified parameters of microgeometry under specified loads for friction pairs with fairly soft coatings or without coatings. The model has been tested using a comparison of the results of numerical simulation with the experimental data, which has shown their good agreement. The results can be used to simulate the contact of the rough surfaces, including the case when one of these surfaces is covered with a solid-lubricating or other functional coating.     

Computer simulation of the contact of rough surfaces

Rough contact was simulated by adding height measurements of a number of pairs of real surfaces, both isotropic and anisotropic, by computer and analyzing the resulting contour maps. The number of contours per unit area was computed for various separations, where a contour may enclose either a contact or a void. Measurements of the contour density agreed well with theory. Voids begin to appear at a separation of about $\text{1}\text{1}\text{2}$ times the roughness, and it is suggested that they may act as lubricant traps. The size distribution of contacts was also investigated and was found to be log-normal.     

Simulation and experiment of secondary contact stiffness of rough surface

Machined surfaces usually need to be loaded several times during assembly. The surface morphology after the simulation loading may be quite different from the physical loading, which subsequently causes differences between the contact stiffness after secondary simulation loading and secondary physical loading results. The fractal theory was used to reconstruct the measured surface morphology, followed by contact stiffness simulation and test. The results show that contact stiffness of new morphology obtained by the first simulated loading using the elastic-plastic deformation theory are smaller than the first loading test results, with an average error of −9.71 %. Contact stiffness of used morphology obtained by the first simulated loading using the pure elastic deformation theory are in good agreements with the second loading test results, with an average error of 4.71 %. However, the average contact stiffness of new morphology obtained by the second simulated loading using the elastic-plastic deformation theory, which is traditionally used for contact analysis, are 2.15 times larger than the second loading test result. These research results demonstrate a feasible finite element method (FEM) for solving the contact problem of rough surfaces that need to be assembled multiple times.