薄膜粗糙表面有摩擦接触问题的数值计算研究

采用ANSYS的APDL语言编程通过参数化变量方式实现了薄膜粗糙表面有摩擦接触问题的整个建模与分析过程,其中包括参数化生成满足高斯分布的随机粗糙表面与计及摩擦因数和薄膜/基体弹性模量比变化情况下的自动有限元分析过程。计算结果表明:当摩擦因数一定时,随着薄膜/基体弹性模量比的增大,应力分布逐渐向基体深处扩展,粗糙表面上各点接触压力一致减小,接触压力峰值减小的最大幅度为9.0%;当弹性模量比一定时,摩擦因数的变化对基体部分应力分布的影响不大,然而随着摩擦因数的增加,粗糙表面上各点接触压力增大,接触压力峰值增加的最大幅度为13.2%,可见摩擦因数和弹性模量比对薄膜粗糙表面的接触应力有明显影响。     

Elastohydrodynamic lubrication analysis of a functionally graded layered bearing surface,with particular reference to 'cushion form bearings' for artificial knee joints

Elastohydrodynamic lubrication of a functionally graded layered (FGL) bearing surface, whose elastic modulus increases with depth from the bearing surface, was investigated in this study. The finite difference method was employed to solve the Reynolds equation, simultaneously with the elasticity equation of the bearing surface, under circular point contacts. The finite element method was adopted to solve the elasticity equation for the FGL bearing surface. The displacement coefficients thus obtained were used to calculate the elastic deformation of the bearing surface, required for the elastohydrodynamic lubrication analysis. Good agreement of the predicted film thickness and pressure distribution was obtained, between the present method and a previous study for a single layered bearing surface with a uniform elastic modulus. The general numerical methodology was then applied to an FGL bearing surface with both linear and exponential variations in elastic modulus, with particular reference to the 'cushion form bearing' for artificial knee joints. The predicted film thickness and pressure distribution were shown to be quite close to those obtained for a single layer under typical operating conditions representative of artificial knee joints, provided that the elastic modulus of the single layer was chosen to be the average elastic modulus of the graded layer.     

Influence of Poisson's ratio variation on lateral spring constant of atomic force microscopy cantilevers

Atomic force microscopy (AFM) can be used to measure the surface morphologies and the mechanical properties of nanostructures. The force acting on the AFM cantilever can be obtained by multiplying the spring constant of AFM cantilever and the corresponding deformation. To improve the accuracy of force experiments, the spring constant of AFM cantilever must be calibrated carefully. Many methods, such as theoretical equations, the finite element method, and the use of reference cantilever, were reported to obtain the spring constant of AFM cantilevers. For the cantilever made of single crystal, the Poisson's ratio varies with different cantilever-crystal angles. In this paper, the influences of Poisson's ratio variation on the lateral spring constant and axial spring constant of rectangular and V-shaped AFM cantilevers, with different tilt angles and normal forces, were investigated by the finite element analysis. When the cantilever's tilt angle is 20 degrees and the Poisson's ratio varies from 0.02 to 0.4, the finite element results show that the lateral spring constants decrease 11.75% for the rectangular cantilever with 1muN landing force and decrease 18.60% for the V-shaped cantilever with 50nN landing force, respectively. The influence of Poisson's ratio variation on axial spring constant is less than 3% for both rectangular and V-shaped cantilevers. As the tilt angle increases, the axial spring constants for rectangular and V-shaped cantilevers decrease substantially. The results obtained can be used to improve the accuracy of the lateral force measurement when using atomic force microscopy.     

负泊松比可变弧角曲边内凹蜂窝结构的力学性能

在环形蜂窝结构的基础上,提出了一种具有负泊松比效应的可变弧角曲边内凹蜂窝结构。分析了刚架结构的弯曲内力,利用能量法给出了曲边内凹蜂窝结构的横/纵向等效弹性模量和等效泊松比的解析公式。当弧角为180°时,所提出的曲边内凹蜂窝结构可退化为已有的环形蜂窝结构。所得解析解、已有理论解和有限元结果三者有较好的吻合度,表明了所提出方法的有效性。基于所得解析解讨论了微结构几何参数对等效弹性模量和等效泊松比的影响,研究结果表明：等效弹性模量受弧角的影响显著;等效泊松比受弧角、竖直壁板长度和两竖直壁板间宽度的影响较为明显,而受连接部分长度的影响不明显。     

UHMWPE基水润滑尾轴承润滑特性仿真及试验研究

针对UHMWPE基高分子复合材料水润滑轴承的润滑特性开展研究。采用双向流固耦合算法研究弹性模量和泊松比等材料参数以及转速、负载等工况参数对水润滑轴承偏心率、最大水膜压力、轴承最大变形量、最小水膜厚度、摩擦因数等润滑特性的影响。基于改性UHMWPE高分子复合材料轴承的试验,验证了仿真方法的正确性。研究表明:计入弹性变形的流固耦合算法在研究高分子复合材料轴承性能方面具有更高的精度;随轴瓦材料弹性模量和泊松比的增大,轴承承载力逐渐增大、弹性变形量逐渐减小;随负载增大,轴承最大水膜压力和最大变形量基本呈线性增长;随转速增大,轴承最大水膜压力和轴承最大变形量显著减小;对于高分子复合材料轴承,低速、重载工况下不计入弹性变形的算法误差更大。     

A morphological elastic model of general hexagonal columnar structures

A general three-dimensional (3D) anisotropic hexagonal model of columnar structure with non-uniform strut morphology is developed. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square honeycombs, and 3D hexagonal and rhombic cellular materials of rod-like columnar structure. The effective elastic constants are determined taking account of bending, axial, and shear deformations of the struts. Unlike the theoretical work of other investigators for 2D honeycombs, considering bending, axial and shearing deformations of struts, the present model not only produces transverse isotropy for regular hexagonal columnar structure but also provides a consistent Poisson's ratio when applied to a square honeycomb. The effect of tapered strut morphology on the elastic properties of cellular structures is investigated. For the general hexagonal columnar structures, the bending compliance is the dominant function for the in-plane elastic constants of 2D and 3D structures (excluding the in-plane shear modulus of rhombic structures) and the out-of-plane shear moduli of 3D structures, but the axial compliance is dominant for the in-plane shear modulus of 2D and 3D rhombic structures and the out-of-plane Young's modulus of 3D structures. For cellular materials with the same relative density, the presence of taper increases values of the effective Young's and shear moduli for which the bending compliance is dominant, but decreases those for which the axial compliance is dominant. It is found that the effective elastic properties of cellular materials are dependent not only on the relative density but also on strut morphology both in cross-section geometry and its variation along the strut length which the present model takes account of. These results illustrate the importance of the strut morphology in calculating the effective elastic properties of cellular materials.     

颗粒增强复合材料有效弹性模量的预报

用细观力学的方法对陶瓷颗粒增强金属基复合材料进行研究,把材料简化为三相模型,陶瓷粒子和基体壳简化为椭球形二相胞元,用Mori-Tanaka法建立二相胞元的刚度预报模型.结果表明,二相胞元为横观各向同性,具有5个独立的弹性常数.据二相胞元方位的随机性,由应力应变换轴公式和物理方程确定复合材料的平均应变,进而得到复合材料的等效弹性模量和等效泊松比以及等效刚度模量的理论计算公式,并通过对所建模型的分析,确定各参量与陶瓷颗粒含量之间的关系.     

基于三类单胞模型的开、闭孔泡沫材料弹性性能的有限元分析

在对发泡过程进行假设的基础上,根据泡沫材料微结构的特点,建立开孔和闭孔泡沫材料的简单立方、面心立方和体心立方单胞模型,导出相对密度和胞体结构参数的定量关系.由这三类单胞模型描述的泡沫材料均具有周期性的特点,且单胞还具有结构对称性.文中利用有限元方法,在适当的边界条件下计算整个密度范围内泡沫材料的弹性模量和泊松比,数值拟合模量计算公式.通过与已有的实验资料和理论预测结果的比较,说明有限元数值计算的有效性.     

纳米金属材料宏观弹性模量的数值模拟研究

将分子动力学模拟方法与连续体的有限元模拟技术相结合,进行"复合有限元"方法的探索与研究.首先,将纳米金属材料看作由晶粒、晶界、三叉晶界组成的复合材料,基体是具有不规则原子结构的界面相,夹杂是具有理想晶格的晶粒相,用有限元源程序自动生成系统fepg软件模拟材料的宏观弹性模量,并进一步调整晶粒尺寸,研究晶粒尺寸对材料宏观弹性模量的影响.研究结果表明,随着晶粒尺寸的减小,晶界、孔洞等所占的体积比增大,材料的弹性模量也随之下降.     

Atomic-scale finite-element model of tension in nanoscale thin film

In this paper, a 2D atomic-scale finite-element model of tension in nanoscale thin film is developed in which Morse’s potential energy function is used to model the interactive forces between atoms. The model is fed into the finite-element package LS-DYNA and both a single integration point and an explicit solution method are used for solving the tension process rapidly to investigate the size effect of different film thicknesses and the effect of different atomic vacancy ratios on nanoscale thin film under tension. The results show that since the applied displacement is exerted at both ends for different thickness of a perfect crystal, a neutral line is formed at the middle of the material. The material slides along the easiest slip direction to cause a “necking” feature on both sides. The stress initially increases with the gradual increase of strain and thicker film shows a larger tensile stress. After the film experiences the peak stress, the stress then decreases with the gradual increase of strain. While the applied displacement is applied at both ends for different vacancies, a neutral line is formed at the middle of material, but this is not apparent due to the random scattered vacancies. The material slides along the easiest slip direction from left to right, and the stress concentration areas near the constrained ends form “necking” features. Stresses are not zero at zero strain. Tension tests for different vacancy ratios show different maximum stresses. Film with a larger vacancy ratio shows a lower stress at the same strain. As the vacancy ratio of the film under tension increases, the strength and elastic modulus reduces.     

轴表面矩形微螺旋槽织构对唇形油封密封性能的影响

基于唇形油封的反向泵送作用密封原理,提出了一种轴表面矩形微螺旋槽织构,以提升油封密封性能;建立了油封唇口稳态的符合质量守恒的流体润滑理论模型,考虑了油封唇口表面粗糙形貌和弹性变形的影响,采用有限元法求解流体压力控制方程,获得了泵送率和摩擦扭矩等性能参数,研究了矩形微螺旋槽织构参数和轴转速对油封密封性能的影响规律。结果表明：泵送率具有随微螺旋槽角度的增大而呈先缓慢增大后逐渐减小,且螺旋角最佳值约25°,随微螺旋槽深度、线数和轴转速的增大而增大等变化规律;摩擦扭矩具有随微螺旋槽角度、深度的增大而减小,随微螺旋槽线数的增大而增大,随轴转速的增大而呈先增大后减小以至趋于稳定等变化规律。研究结果为轴表面微槽织构提高油封密封性能的设计与应用提供了参考。     

单晶硅力学性能及尺寸效应的离散元模拟

通过建立紧密连接且随机分布在指定区域内的圆盘形颗粒离散单元的力学模型来研究单晶硅的力学性能,并采用不同尺寸的离散元模型研究力学性能尺寸效应。结果表明:泊松比、单轴抗压强度、弹性模量以及断裂韧性的尺寸效应不明显,弯曲强度则随着模型尺寸的增大而减小。建立了连续体经典断裂力学有限宽板条单边直裂纹的离散元力学模型,改变初始裂纹长度进行模拟得到的结果与单边切口梁模拟结果及文献报道的试验值一致。     

负泊松比蜂窝芯非线性等效弹性模量研究

设计并加工了一种负泊松比蜂窝结构,采用柔性悬臂梁模型,对蜂窝壁板大变形条件下的弯曲变形进行分析,给出了蜂窝芯面内等效弹性模量理论计算公式。通过有限元仿真和力学实验的对比分析,验证了非线性理论计算公式的正确性。得出了等效弹性模量的非线性特性及相同方向和不同方向弹性模量的变化特性。研究结果为柔性蜂窝芯层的工程实用化提供了参考。     

注塑成型短玻纤增强复合材料各向异性弹性常数预测方法

针对注塑成型短玻纤增强复合材料,研究二阶纤维取向张量与纤维取向角度之间的连续函数关系,建立纤维均质化RVE模型。基于Taguchi正交试验设计方法,利用DIGIMAT软件对短玻纤增强复合材料RVE模型进行仿真试验,定量分析纤维质量分数（A）、纤维长径比（B）和纤维取向张量（C）对短玻纤增强复合材料力学性能的影响规律。考虑注塑成型过程中的纤维分层效应,提出了夹芯分层模型并进行铺层设计。基于灰箱理论和反求工程,选取纤维长径比、表层厚度比和芯层厚度比、表层纤维取向张量、纤维取向矢量旋转角四个影响因素,反演预测短玻纤增强复合材料PA66（GF50）正交各向异性弹性常数,与材料拉伸弹性模量E₃₃、泊松比u₃₁和泊松比u₃₂的试验结果对比,相对误差分别为0.80%、0.29%和1.35%。     

基于十四面体模型的开孔泡沫材料弹性模量的有限元分析

利用十四面体模型描述开孔泡沫材料的胞体结构，并用有限元方法确定开孔泡沫材料的弹性模量。计算中使用相同尺寸的十四面体胞体模型，并考虑两种不同支柱截面（圆截面和Plateau截面）形状对弹性模量计算的影响。此外，通过数值方法研究开孔泡沫材料的弹性模量随模型尺寸的变化规律。同时，讨论边界条件处理对开孔泡沫材料弹性模量计算的影响。结果表明，支柱为Plateau截面形状的模型，其弹性模量明显高十具有圆截面支柱模型的结果。且两种模型的弹性模量均随模型尺度的增加而增加，最终趋于一个稳定值，并与Warren和Kraynik的理论预测较为一致。此外，边界条件对模型刚度的影响随着模型尺度的增加而逐渐减小。     

晶粒相对尺寸对FCC多晶体板材单向拉伸流动应力的影响

采用动力显式有限元方法和速率相关的多晶体弹性-粘塑性有限元分析模型模拟退火FCC多晶体和6111-T4铝板的单向拉伸过程。考察了板厚与晶粒尺寸之比变化时由于晶界约束变化而导致板材流动应力变化的规律，得出的结论表明，晶粒的相对尺寸增大时，相邻晶粒之间晶界的约束作用也随之增大，从而导致多晶体材料流动应力增大，该结论与实验结果相吻合。     

微观织构配流副热-流-固耦合润滑特性

通过建立轴向柱塞泵配流副的几何模型,利用雷诺方程推导了配流副的油膜压力方程,采用有限差分法和松弛迭代法求解雷诺方程。利用FORTRAN语言编程求解,利用MATLAB语言对油膜厚度、压力、温度分布进行了仿真研究。结合油膜厚度方程、雷诺方程、能量方程、弹性变形方程、黏温黏压方程和密度温压方程,仿真微观织构配流副的热弹流润滑特性。研究表明：配流副油膜厚度增大,最大油膜压力减小,最高温度值减小;配流副的热-流-固耦合效果随油膜间隙收敛逐渐明显,在最小油膜厚度处达到最大,并且,油膜压力值达到最大;加工微观织构可以显著改变配流副的油膜压力和温度分布。     

Elastohydrodynamic lubrication analysis of ultra-high molecular weight polyethylene hip joint replacements under squeeze-film motion

Elastohydrodynamic lubrication was analysed under squeeze-film or normal approach motion for artificial hip joint replacements consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup and a metallic or ceramic femoral head. A simple ball-in-socket configuration was adopted to represent the hip prosthesis for the lubrication analysis. Both the Reynolds equation and the elasticity equations were solved simultaneously for the lubricant film thickness and hydrodynamic pressure distribution as a function of the squeeze-film time was solved using the Newton-Raphson method. The elastic deformation of the UHMWPE cup was calculated by both the finite element method and a simple equation based upon the constrained column model. Good agreement of the predicted film thickness and pressure distribution was found between these two methods. A simple analytical method based upon the Grubin-Ertel-type approximation developed by Higginson in 1978 [1] was also applied to the present squeeze-film lubrication problem. The predicted squeeze-film thickness from this simple method was found to be remarkably close to that from the full numerical solution. The main design parameters were the femoral head radius, the radial clearance between the femoral head and the acetabular cup, and the thickness and elastic modulus for the UHMWPE cup; the effects of these parameters on the squeeze-film thickness generated in current hip prostheses were investigated.     

铀表面铝镀层热应力的有限元分析

对铀表面磁控溅射沉积铝镀层的热应力进行了热弹塑性有限元分析。结果表明：镀层内的热应力较大,达到铝的屈服强度,镀层界面两侧存在明显应力梯度,试样侧边存在由于边缘效应引起的应力分布不均匀性,至侧边约4倍镀层厚度处,应力分布不均匀性逐渐消失；沉积温度升高,界面塑性应变明显增大,镀层弹性模量和泊松比对镀层界面热应力和塑性应变的影响较小,而屈服强度的影响较大,减薄镀层厚度有利于改善镀层界面的热应力和塑性应变。     

浮环弹性变形对浮环动静压轴承润滑特性的影响

浮环轴承在高速工况下运行时,浮环表面在油膜压力作用下会发生弹性变形,影响轴承润滑性能。针对带有深浅腔的浮环动静压轴承,采用有限元法和有限差分法耦合求解油膜Reynolds方程、能量方程和温黏关系式,采用变形矩阵法求解弹性变形方程,计算浮环弹性变形分布;在浮环平衡的基础上,分析浮环变形对环速比、油膜承载力、端泄流量等润滑特性参数的影响。结果表明：浮环弹性变形分布与油膜压力分布呈现一致性,转速越高,偏心越大,变形越明显;考虑浮环弹性变形,浮环达到平衡状态时,内膜偏心率增加,环速比减小,轴承承载力与摩擦力矩均有所增加;由于浮环变形对内、外膜间隙及流动液阻的不同影响,使得内膜端泄流量增加,外膜端泄流量减少。