磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性,且表面电势和磁势是常数。微动接触依赖载荷的加载历史,所以首先求解单独的法向加载问题,然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区,其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换,磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组,然后数值离散为线性代数方程组,利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

刚性圆形压头作用下热电材料半平面的无摩擦接触问题

热电材料可以将热能转化为电能,反之亦然,这一优良的性质将有助于研发更具成本效益的设备和器件。本文研究了刚性圆形压头作用在热电材料半平面的无摩擦接触问题。假定压头为电导体、热导体,且压头压入深度及与材料的接触区域宽度未知。首先求解电场和温度场,利用傅里叶变换得到了电势函数、温度、电流密度和能量通量的解析表达式。然后求解弹性场,利用积分变换和边界条件,将该热弹性接触问题转化为第一类奇异积分方程并数值求解。数值结果讨论了压头半径和热电载荷对法向接触应力、电流强度因子和能量通量强度因子的影响。结果表明,对于圆压头,热电材料的法向电流密度、法向能量通量在接触边缘表现出奇异性,而表面法向接触应力在接触边缘为零。本文建立的研究模型有助于更深层次的了解热电材料的接触行为。     

具周期裂纹的半平面周期接触问题的奇异积分方程数值解法

运用Hilbert核的奇异积分方程的数值解法研究具任意形状裂纹的各向同性弹性半平面在周期压头作用下的周期接触问题,将所考虑问题转化为第一型或第二型的奇异积分方程组．最后给出带垂直裂纹的半平面在光滑平底压头作用下的数值结果．令α→∞时,就得到非周期经典结果．     

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的散射

本文研究一类粘着型界面裂纹的弹性波散射问题．文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组．采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组．最后本文给出裂纹尖端粘着区的大小和界面应力的数值结果．     

基于边界元法求解三维弹性摩擦接触问题

边界元法求解三维摩擦接触问题,其中一个关键点在于如何确定滑移方向。即当出现相对滑移时,滑移方向如何确定。当前常采用的方法是,粘结点利用切向面力得到滑移方向,滑移点利用切向相对位移得到滑移方向。不过该方法难以保证收敛性。针对这一问题,本文采用滑移方向预测技术得到滑移方向。即以后出现相对滑移时,滑移方向采用预测技术中得到的滑移方向。由于摩擦接触问题和历史加载相关,本文采用增量法求解。不同摩擦系数下的数值结果都证明了本文算法的有效性和收敛性及滑移方向预测技术的有效性。     

功能梯度材料涂层半空间的轴对称光滑接触问题

求解了功能梯度材料涂层半空间的轴对称光滑接触问题,其中梯度层剪切模量按照线性变化,利用Hankel积分变换方法求解微分方程,将问题化为具有Cauchy型奇异核的积分方程.数值方法求解表明:功能梯度材料涂层半空间在刚性柱形压头和球形压头作用下,接触表面分布应力,接触半径以及最大压痕受材料梯度效应的影响较大.     

微/纳尺度粘着滑动接触的多尺度分析

采用分子动力学与有限元耦合的多尺度方法,求解二维刚性圆柱表面压头与弹性平面的微/纳尺度粘着滑动接触问题,通过与全分子动力学模拟结果的比较验证了多尺度方法的有效性。对压头半径、滑动速度、下压深度以及是否考虑粘着效应等对滑动接触性能的影响进行了全面研究,通过不同条件下摩擦力及接触力分布的比较,揭示了上述各参数对粘着滑动接触...     

单侧摩擦梯度非均匀双半平面的反平面运动

研究了二个半平面的反平面运动，二个半平面都是剪切弹性模量与材料密度为梯度的非均匀介质，它们之间的界面是具有Coulomb摩擦的单侧界面. 当介质的梯度参数按二次幂规律变化时，求得了这一问题的解析解，给出了界面上粘着区与滑移区以及相应的界面剪应力与相对滑移量的分布. 通过抛物线脉冲入射下的数值计算发现：界面上的剪应力呈反双峰形分布，正、反滑移区出现在峰值点附近，其范围随界面上施加的外压力σ=fsp∞/μ0的增加而减小，当外压力达到某一数值时，滑移区消失，整个界面将完全粘着在一起.     

人股骨密质骨横断面的微动磨损特性研究

采用配置外加体液恒温循环装置的高精密微动试验台研究了天然活性股骨密质骨/纯钛的微动磨损行为,探讨了不同位移幅值下摩擦系数随循环次数变化的规律.结果表明,在90N法向载荷下,随位移幅值增加,股骨密质骨的微动运行状态从部分滑移向完全滑移状态转变.当位移幅值较小时,接触表面变形处于弹性协调状态,损伤轻微.随着位移幅值的增加,接触表面变形逐步向弹、塑性变形以及严重塑性变形和粘着转变,微动损伤加剧.与此同时,密质骨试件微动磨痕深度随位移幅值的增加而增大,并同摩擦系数存在良好的对应关系.为了提高密质骨抵抗微动损伤的能力,有必要控制植入体/骨界面的微动幅度和降低摩擦系数.     

Winkler地基模型上功能梯度材料涂层的摩擦接触问题

研究Winker地基模型上功能梯度材料涂层在一刚性圆柱形冲头作用下的摩擦接触问题。功能梯度材料涂层表面作用有法线向和切线向集中作用力。假设材料非均匀参数呈指数形式变化,泊松比为常量,利用Fourier积分变换技术将求解模型的接触问题转化为奇异积分方程组,再利用切比雪夫多项式对所得奇异积分方程组进行数值求解。最后,给出了功能梯度材料非均匀参数、摩擦系数、Winker地基模型刚度系数及冲头曲率半径对接触应力分布和接触区宽度的影响情况。     

Physics-based modeling for partial slip behavior of spherical contacts

A physics-based modeling approach for partial slip behavior of a spherical contact is proposed. In this approach, elastic and elastic–plastic normal preload and preload-dependent friction coefficient models are integrated into the Cattaneo–Mindlin partial slip solution. Partial slip responses to cyclic tangential loading (fretting loops) obtained by this approach are favorably compared with experiments and finite element results from the literature. In addition to load-deformation curves, tangential stiffness of the contact and energy dissipation per fretting cycle predictions of the models are also provided. Finally, the critical assumptions of elastically similar bodies, smooth contact surface and negligible adhesion, and limitations of this physics-based modeling approach are discussed.     

Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch

This paper focuses on the study of a frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid flat punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. An analytical closed-form solution is obtained for the normal contact stress, electric displacement and magnetic induction distributions. The main objective of this paper is to study the effect of the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat stamp profile.     

有限长滚子黏滑接触分析

有限长线接触在齿轮传动与滚子轴承中广泛存在，滚子端部的应力集中严重影响机械零件的疲劳寿命. 本文中基于矩阵法和重叠半空间模型方法建立了有限长滚子黏滑接触的数值计算模型，利用共轭梯度法和快速傅里叶变换方法对模型进行了求解；并且分析了滚子自由端面和不同切向力对滚子黏滑接触的影响. 结果表明:当两有限长滚子的自由端面完全重合时，切应力在端面不会出现应力集中现象，端面的黏着区域相比于中间截面的黏着区会缩小. 此外，随着切向力的增大，端面黏滑区域的切应力增大.      

New analytical and numerical results for two-dimensional contact profiles

Recently, a generalized Coulomb law for elastic bodies in contact has been developed by the author, which assumes that the tangential traction is the difference of the slip stress of the contact and the stick area, whereby each stick area corresponds to a smaller contact area. It holds for multiple contact regions also. Several applications for elastic half planes, half spaces, thin and thick layers and impact problems have been published. For plane contact of equal bodies with friction, it provides exact solutions, and the interior stress field can be expressed with analytical results in closed form. In this article, a singular superposition of flat punch solutions is outlined, in which the punches are aligned with an edge of the contact area. It is shown that this superposition satisfies Coulomb's inequalities directly, and new results for the Muskhelishvili potentials of several profiles are presented. It is illustrated how problems of singularity and multi-valuedness of complex functions can be solved in closed form, and the Chebyshev approximation used by earlier authors can be avoided. For comparison, some previous solutions for symmetric profiles are appended. Some results for the interior stress field, the pressure, the frictional traction and the surface displacements are compared with FEM solutions of an equivalent problem. The small differences between both methods show characteristic features of the FEM model and the theoretical assumptions, and are shortly explained. Further, this example can be used as benchmark test for FEM and BEM programs.     

Analytical solutions for inherently incremental,similar elastic contact problems with bulk stress

Analytical solutions are obtained for a class of inherently incremental, similar elastic half-plane frictional contact problems which involve simultaneous application of a changing, remote bulk-stress during oblique loading. The method is based on Abel Integral Equations. The spatial gradient of the slip function is obtained uniquely by the conditions determining the existence of a bounded solution to the shear traction Cauchy SIE and global shear equilibrium, provided there is stick at all points in the contact throughout the loading. Solutions are obtained for both the cylindrical indenter and the flat punch with rounded edges. The method also lends itself easily to generalization to non-linear load paths and a number of such problems are considered. Problems involving the development of slip zones within the contact may be solved in some special cases.     

Frictional moving contact over the surface between a rigid punch and piezomagnetic materials – Terfenol-D as example

A general theory of the frictional moving contact of piezomagnetic materials indented by a flat or cylindrical punch is set up. The rigid punch moves at a constant speed and the Coulomb friction law applies inside the contact region. Terfenol-D with high magnetostriction and coupling is chosen. Employing the Galilean transformation and Fourier transform, Cauchy integral equations of the second kind are obtained and solved exactly. Closed-form expressions of physical quantities on the surface in terms of elementary functions are given. Numerical analyses are conducted to reveal the effects of the friction coefficient and moving speed of the punch on various surface stresses and magnetic induction. The singularity, discontinuity and spike of the surface magnetic induction may be important factors to explain why surface damage occurs for piezomagnetic materials.     

柔性梁斜碰撞问题的非线性动力学建模和实验研究

本文研究柔性梁点面斜碰撞问题。用Hertz接触模型处理法向撞击力,分别用Hertz切向接触模型和Coulomb摩擦力模型处理粘滞状态和滑动状态的摩擦力。从精确的应变与位移的关系出发,用绝对节点坐标法建立了柔性梁的动力学方程。为了准确地处理斜碰撞切向运动的复杂状态,提出滑动-粘滞切换的准则,在此基础上,设计了斜碰撞实验,数值对比了法向撞击力和法向速度的时间历程的仿真计算结果与实验结果,验证了Hertz理论在斜碰撞情况下的正确性。另一方面切向速度的实验与理论的结果对照表明滑动-粘滞切换准则的有效性。     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

The evolution of the process zone when a complete contact is subject to cyclically varying loads

A rigid punch pressed against an incompressible half-plane by a constant normal load is subject to both a cyclically varying shearing force, and a synchronously varying underlying bulk tension. The evolution of the slip/stick distribution along the contact interface is found during a loading cycle. An asymptotic approach is subsequently used to determine the order of singularity, and hence spatial distribution of the local stress state. A generalised stress intensity factor is then defined to scale the corresponding asymptotic solution, and hence map out the evolution of the process zone. The analysis shows that there is a smooth transition in the form of the asymptotic solution in moving from an ‘adhered’ contact edge to a ‘slipping’ contact edge, and vice versa. The implications of the results to fretting fatigue are discussed.     

润滑油脂对钢丝微动磨损特性的影响

在自制的微动摩擦磨损试验机上,以矿用钢丝为研究对象,探讨润滑油脂对钢丝微动磨损特性的影响规律.结果表明:润滑油脂使钢丝微动运行区域中部分滑移区和混合区显著缩小,滑移区增大;摩擦系数和磨损量显著降低,跑合期延长;润滑油脂条件下,部分滑移区损伤轻微,环状区域较光滑,混合区和滑移区摩擦氧化减少,损伤以表面疲劳及磨粒磨损为主,磨痕表面较平滑,损伤程度明显小于干摩擦条件.