弹性接触中的表面微滑问题及数值求解

研究法向载荷和切向载荷耦合作用下的三维弹性点接触问题.当切向载荷不足使接触体发生整体滑动时,接触面产生微滑区域.对于异质物体的接触,即使仅有法向载荷作用,由于变形的不协调,接触面同样会产生微滑区域.运用半解析的方法求解微滑接触问题,影响系数通过Green函数得到解析解,压力和切应力的求解基于共轭梯度法和快速傅里叶变换法.算法仅在关心的接触区域划分网格,缩短计算时间.通过对比光滑同质物体接触的数值解和解析解来验证算法.分析正弦异质表面接触的压力分布、切应力分布、粘着区域.结果显示,由于粗糙峰的存在,粘着区域为多个不连通的区域.随着切向力的增加,压力分布沿着切向力相反的方向倾斜,切应力τx逐步变为正值,粘着区域沿着切向力相反的方向移动并逐渐变小.     

非高斯粗糙表面的弹性微滑接触问题研究

研究的是粗糙表面微滑接触问题。分析在不同参数下的非高斯粗糙表面对最大接触压力和最大切向应力的影响。使用共轭梯度法(CGM)来求解切向应力和接触压力,通过解析法得到影响系数(ICs),由此计算表面弹性变形或位移,并采用快速傅里叶变换方法(FFT)加速表面变形计算。结果表明:偏态参数的变化对最大接触压力和最大切向应力的影响较大,但是峰度参数的变化对最大切向应力影响较小;在相同的偏态和峰度条件下,各项同性和各项异性粗糙表面的最大切向应力和最大接触压力比较接近。     

微动接触中分形粗糙表面的接触应力研究

表面粗糙度对微动状态下接触面的接触压力和剪切摩擦力有着显著影响.在这项研究中,创建Python脚本将Matlab中利用Weierstrass-Mandelbrot函数构造的分形表面轮廓坐标导入ABAQUS中,并使用样条曲线拟合轮廓坐标,从而构建包含粗糙表面的二维柱面/平面接触模型.采用有限元方法研究考虑粗糙表面接触的接触压力和剪切摩擦力分布,并讨论材料弹性、弹-塑性和载荷幅值对剪切摩擦力的影响.结果表明,粗糙表面的存在导致接触压力分布为非光滑曲线,局部应力集中程度高;当表面粗糙度较大时,接触面上接触压力的分布是离散的.同时发现,不同材料接触副下,剪切摩擦力沿粗糙表面的分布差异明显.     

基于分形理论的结合面微观接触特性分析

为了研究结合面微观接触特性,基于分形理论,建立粗糙表面轮廓模型,进行结合面接触趋近耦合研究。通过二维粗糙表面与光滑表面微观接触趋近过程的仿真分析,研究分形维数、表面粗糙度、位移载荷对结合面接触状态的影响机理。提出利用激光声表面波检测粗糙结合面接触的方法,并进行了实验验证。研究结果表明,粗糙表面微凸体形貌是决定材料接触性能的关键因素;微凸体接触形成的真实接触面积远小于名义接触面积。工程问题中,通过名义接触面积计算出的载荷与材料表面实际承受的载荷存在较大差异。     

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。     

点接触混合润滑闪温分析

基于统一的Reynold方程系统,数值分析点接触混合润滑固体表面温度分布。采用瞬态移动点热源积分方法计算闪温,通过两表面温度平衡方程迭代确定热流分配系数,研究在不同卷吸速度和滑滚比情况下,光滑表面和非高斯随机粗糙表面点接触混合润滑的温度分布。结果表明:数值模拟得出的两表面温差很小,符合实际情况;非高斯随机粗糙表面与光滑表面最大温升都在出口区,非高斯随机粗糙表面比光滑表面温升更高;滑滚比一定时,卷吸速度越大两表面温升越大;卷吸速度一定时,滑滚比越大两表面温升越大。     

一种结合部法向刚度的预估方法

提出一种结合部法向刚度的预估方法.通过表面形貌测量仪获取粗糙表面的轮廓数据,拟合生成粗糙表面轮廓曲线,在此基础上建立考虑摩擦的二维粗糙表面的有限元弹塑性接触模型,用罚函数法计算压力在0～0.8 MPa的加载过程中接触层的应力、位移和接触面积.计算结果表明,粗糙表面真实的接触面积在低载荷下快速增大,高载荷下的增大速度很缓...     

基于JKR模型的粗糙圆柱表面线黏着接触分析*

利用粗糙平面接触模型,假定表面单个微凸体的接触采用JKR黏着接触模型,同时考虑圆柱体表面的整体变形,建立了粗糙圆柱表面线黏着接触模型,推导出表面等效压力分布方程。把压力方程量纲一化,采用修正Newton-Raphson法对方程进行迭代求解,计算出粗糙圆柱表面存在表面力作用下的等效压力分布曲线。结果表明外载荷不小于零时,接触中心压力为正,微凸体被压缩;而接触边缘处压力为负,微凸体被拉伸,表明黏着区域主要分布在接触边缘。同时计算出接触半宽随外载荷的变化曲线,当外载荷为拉伸力并大于某一临界值时,表面分开。并且与经典的接触模型进行了对比,发现低载时模型之间的差别较大,而载荷比较大时趋于一致。     

不同滑动速度下干接触体瞬态温度场计算

工程实际中,由于摩擦力的存在,接触副的运动将导致接触区内产生大量的摩擦热,使接触副温度升高;由此产生的瞬时高温会使接触副更易发生弹塑性变形、引起表层下裂纹的萌生及扩展,甚至使接触副表面发生化学变化。建立了不同滑动速度下干接触体的滑动接触模型,利用快速傅立叶变换,通过求解拉普拉斯热传导方程,获得光滑及粗糙表面接触副的瞬时温升以及接触体内部各离散点的温度分布,即半无限体干接触的温度场。结果表明,相同载荷及摩擦因数条件下,相对滑动速度对接触体的温升及其温度分布有重要影响;粗糙峰表面接触处的瞬时温升远高于光滑表面接触处的瞬时温升。     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

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.     

微动接触应力的有限元分析

以方足微动桥,试样接触几何条件为研究对象,应用ANSYS有限元分析软件对其接触面上的应力分布进行弹性有限元分析,验证用ANSYS所建计算模型的正确性,分别计算不同名义接触压力和不同摩擦因数条件下接触状态（粘着区、滑动区、张开区）和接触面应力分布,选取不同水平的循环载荷进行计算,研究接触状态和应力分布随循环载荷的变化情况。结果表明,微动疲劳过程中接触表面拉应力与剪应力在接触面的粘,滑交界区存在突变,微动疲劳裂纹正是在这一区域内萌生并扩展,计算结果与实验结果吻合很好。     

A Numerical Model for the Dry Sliding Contact of Layered Elastic Bodies with Rough Surfaces

A numerical model for the two-dimensional dry sliding contact of two elastic bodies with real rough surfaces has been developed, where an elastic body contacts with a multi-layer surface under both normal and tangential forces. The model uses surface profile data directly recorded with a stylus measuring instrument and it is suitable for use on a microcomputer. Green's function for a unit normal load and a unit tangential load for the generalized plane strain problem are derived. Verification of the accuracy of the model by reproduction of test case results is presented. Contact pressure distribution for layers of varying coefficient of friction, thickness and elastic modulus is analyzed.     

Analyzing Elastic-Plastic Real Rough Surface Contact in Running-in

A numerical method is presented for evaluating the elastic-elastic contact of real rough surface contacts during running-in. For the surface contact, an elastic-plastic model based on the variational method is applied to analyze the pressure distribution and contact area of worn surfaces during running-in. In conjunction with the classical statistic model of Greenwood and Williamson, the numerical result showed that the plasticity index Ψ was decreased to one in the elastic range as running-in proceeded. In comparison with the Hertzian solution, the influence of the asperities is very significant on the pressure distribution, thereafter causing a higher peak value of contact pressure. For the subsurface, the interior stress from the von Mises criterion was calculated to evaluate the subsurface stress field subject to both normal and tangential forces. In the calculated of the interior stress, the total stress is decomposed into a fluctuating component and a smooth component. The fluctuating part is solved by using FFT from the concept of the convolution theorem while the smooth part is obtained directly by analytical solution. Calculations of contact area and subsurface stress on experimentally produced surfaces whose topography has been determined using an atomic force microscope and friction coefficient front sliding have been carried out. The results showed that asperities and friction coefficient gave rise to stress increase in the near-surface stress field and produced a high stress zone towards the surface. As a result, transverse asperity cracking was produced. The calculations and supporting experimental evidence clearly confirmed that the reduction of peak pressure during running-in decreased the plastic deformation of contact.     

The Subsurface Stress Field Created by Three-Dimensionally Rough Bodies in Contact with Traction

A numerical simulation technique for calculating the complete subsurface stress field for three-dimensionally rough bodies in sliding contact is described. The stresses are calculated using real digitized three-dimensional surface profiles. The effects of the surface roughness and the sliding friction are presented. Using an existing contact simulation code, the digitized surfaces are mathematically pressed together and the real areas of contact and the asperity pressures are calculated. The surfaces are assumed to remain elastic throughout the contact simulation process. The shear forces at the asperity contact interfaces are assumed to be proportional to their calculated normal pressures. The subsurface stresses are then determined with these known normal and tangential forces at the surface.     

Fretting fatigue crack initiation lifetime predictor tool: Using damage mechanics approach

Fretting fatigue is a combination of two complex mechanical phenomena. Fretting appears between components that are subjected to small relative oscillatory motions. Once these connected components undergo cyclic fatigue load, fretting fatigue occurs. In general, fretting fatigue failure process can be divided into two main portions, namely crack initiation and crack propagation. Fretting fatigue crack initiation characteristics are very difficult to detect because damages such as micro-cracks are always hidden between two contact surfaces.In this paper Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Analyses (FEA) is used to find a predictor tool for fretting fatigue crack initiation lifetime. For this purpose an uncoupled damage evolution law is developed to model fretting fatigue crack initiation lifetime at various fretting condition such as contact geometry, axial stress, normal load and tangential load. The predicted results are validated with published experimental data from literature.     

Basic principles of rough surface contact analysis using numerical methods

A detailed account of the principles involved in using numerical elastic contact techniques on digitized measurements from rough surfaces is presented in relation to two- and three-dimensional topography data. The main results of such analyses are shown to include the detailed interface geometry and the subsequent contact pressure distribution involved. Methods of defining the resulting sub-surface stresses created by this contact pressure distribution are also presented for static normal loading, and for the case of a normal load in the presence of a frictional surface shear. The problems posed in dealing with plastic asperity contacts are also discussed, together with an outline of how the numerical methods described have been modified further to allow analysis of rough layered bodies of dissimilar materials, thus offering a very useful design tool for surface coatings.     

The contact behavior of elastic/plastic non-Gaussian rough surfaces

A three-dimensional contact analysis was conducted to investigate the contact behavior of elastic--perfectly plastic solids with non-Gaussian rough surfaces. The effect of skewness, kurtosis and hardness on contact statistics and the effect of skewness and kurtosis on subsurface stress are studied. Non-Gaussian rough surfaces are generated by the computer with skewness, Sk, of −0.3, 0.0 and 0.3, and kurtosis, K, of 2.0, 3.0 and 4.0. Contact pressures and subsurface stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and patch solutions. Variation of fractional elastic/plastic contact area, maximum contact pressure and interplanar separation as a function of applied load were studied at different values of skewness and kurtosis. Contact pressure profiles, von Mises stresses, tensile and shear stress contours as a function of friction coefficient were also calculated for surfaces with different skewness and kurtosis. In this study, it is observed that surfaces with Sk = 0.3 and K = 4 in the six surfaces considered have a minimum contact area and maximum interplanar separation, which may provide low friction and stiction. The critical material hardness is defined as the hardness at which severe level of plastic asperity deformation corresponding to the Greenwood and Williamson’s cut-off A _plastic/A _real = 0.02 occurs for a given surface and load condition. The critical material hardness of surfaces with Sk = 0.3 and K = 4 is higher than that of other surfaces considered.     

A numerical model of friction between rough surfaces

This paper describes a computational method to calculate the friction force between two rough surfaces. In the model used, friction results from forces developed during elastic deformation and shear resistance of adhesive junctions at the contact areas. Contacts occur between asperities and have arbitrary orientations with respect to the surfaces. The size and slope of each contact area depend on external loads, mechanical properties and topographies of surfaces. Contact force distribution is computed by iterating the relationship between contact parameters, external loads, and surface topographies until the sum of normal components of contact forces equals the normal load. The corresponding sum of tangential components of contact forces constitutes the friction force. To calculate elastic deformation in three dimensions, we use the method of influence coefficients and its adaptation to shear forces to account for sliding friction. Analysis presented in Appendix A gives approximate limits within which influence coefficients developed for flat elastic half-space can apply to rough surfaces. Use of the method of residual correction and a successive grid refinement helped rectify the periodicity error introduced by the FFT technique that was used to solve for asperity pressures. The proposed method, when applied to the classical problem of a sphere on a half-space as a benchmark, showed good agreement with previous results. Calculations show how friction changes with surface roughness and also demonstrate the method's efficiency.