京沪高铁弓网系统动态接触仿真及预紧力优化

弓网接触状态直接影响电气化列车的受流性能,良好的弓网接触是高速列车安全运行的重要保证.采用Marc有限元软件及其子程序实现吊弦刚度的非线性特性模拟,并建立弓网动态接触的有限元模型,通过合理的单元类型的选用以及边界条件的定义进行仿真、分析和计算.对时速350 km/h列车和3组预紧力下的弓网接触关系进行仿真和分析,仿真计算得出较优的预紧力合理值.     

基于非线性力反馈模型的软组织变形仿真

虚拟手术仿真研究中反馈力一般采用线性模型,但软组织的反馈力往往呈现出非线性的特点.通过对软组织生物力学特性的分析,将非线性性质应用到软组织力反馈模型的研究.在保持原线性反馈力方向不变的前提下,加入非线性扰动,建立了反馈力的非线性模型,从而使反馈力更加真实.首先构建了人体肝脏物理模型,然后给出了非线性力反馈模型方程,并对人体肝脏物理模型变形和反馈力进行了仿真.为了减小计算量采用了整体刚度矩阵缩减算法.仿真结果表明该模型有较好的非线性和可调节性.     

扭转激励下螺纹连接结构动力学行为

根据真实螺纹的几何参数,运用Abaqus建立螺纹连接结构的精确有限元模型,采用扭矩法施加预紧力,分析在扭转载荷作用下螺纹连接结构的动力学行为。结果表明：当螺钉与被连接件之间的摩擦力矩小于螺纹接触界面的摩擦力矩时,连接结构在扭转交变载荷作用下容易发生松动;当螺钉与被连接件和内外螺纹2组接触副之间的摩擦因数增大时,螺纹连接结构的摩擦耗散能变化较小,而当被连接件之间的摩擦因数增大时,连接结构的摩擦耗散能呈线性增加;根据三阶修正Iwan模型得到的响应曲线与有限元分析结果吻合。     

轴承预紧力对转子系统静动态特性的影响

轴承预紧力的大小直接影响到滚动轴承-转子系统的静动态特性. 综合考虑离心力和陀螺力矩效应,在Romax软件中建立了5自由度轴承-转子系统动力学模型,分析了预紧力对轴承刚度、工作接触角以及工作寿命的影响,并搭建了轴承 转子系统试验台做验证试验. 在不同轴承预紧力下,分别研究了轴承刚度、工作接触角、工作寿命、静载荷作用下轴承 转子系统的静变形以及动不平衡载荷作用下主轴系统的振动响应等,并在轴承-转子试验台上进行试验验证,得到了轴承预紧力与这些因素的关系曲线. 在此基础上,研究了预紧力对转子系统固有频率的影响,结果表明加大预紧力有助于提高系统的固有频率. 研究结果可为轴承-转子系统的设计与分析提供理论参考.     

发电机挡块组件有限元分析

为分析抽水蓄能发电机挡块组件的von Mises应力（以下简称应力）分布情况,在MSC Marc中建立有限元模型,分别采用截面法和渗透接触法对螺栓施加预紧力,通过对发电机挡块组件处于稳定转速、抽水启动、抽水停机、发电启动、发电停机和甩负荷等工况的非线性接触分析,得到各工况下该发电机挡块组件的应力分布.结果表明,2种螺栓预紧力的施加方法是等效的;各工况下最大应力均发生在螺栓圆角处;转速大小对应力分布起决定性作用.该结果可为抽水蓄能发电机挡块组件结构的分析设计提供参考.     

基于接触非线性的螺钉标准件的优化设计方法

针对压力容器如何安全、可靠、经济地选择螺钉标准联接件的问题,通过一元回归分析拟合出不同规格的螺钉标准件,从而将离散变量转化成连续变量,并运用ANSYS参数化语言APDL建立了螺钉及容器模型,考虑了压力容器在工作状态下的非线性接触,并在此基础上以螺钉成本为目标函数,以螺钉强度为约束条件,对螺钉的个数和尺寸进行分析,得到优化结果;并对变量进行敏度分析,为螺钉标准件的进一步选择提供了方向,解决了工程问题.结果表明这种方法为以后螺钉标准件的建立以及基于接触非线性的优化设计提供了一条可行的路径,对相关的工程应用具有借鉴意义.     

销钉连接叶片固有特性分析有限元模型研究

计算销钉连接转子叶片动频需采用有限元接触技术,而非线性接触分析难度和计算量都较大,因此提出两种线性简化工程模型,将求解非线性问题转换为求解线性问题,从而大大降低了分析难度和计算量.经检验其计算结果精度可满足工程分析要求.同时对简化柔度矩阵法及面约束简化模型有限元法计算的动频结果进行了分析,对发动机叶片固有振动特性分析有帮助.     

不同载荷工况下机床主轴预紧力选取的数值分析方法

为研究预紧力对机床主轴的影响,提出在不同载荷工况下机床主轴预紧力选取的数值分析方法.计算得到预紧力与轴承刚度的关系,在轴系结构有限元模型中设置不同预紧力下的轴承刚度值,通过静力学分析求解轴系变形和刚度;计算得到预紧力与轴承发热量的关系,在轴系热分析有限元模型中设置轴承热源,通过传热分析求解主轴温升.计算结果表明,该方法...     

小口径离轴抛物面反射镜挠性支撑设计分析

关于反射镜支撑稳定性优化设计问题,离轴抛物面反射镜作为空间光学遥感器的重要光学元件,面形精度直接影响遥感器性能。针对反射镜所处环境,组件一阶频率要求高,设计了一种反射镜背部中心单点挠性支撑结构,并利用拓扑优化技术对反射镜进行了轻量化设计。为了结构设计的合理性,采用有限元技术对反射镜组件进行了模态分析、结构强度分析、谐响应分析及热环境分析。分析结果表明:反射镜在重力作用下最大面形误差RMS=1.16nm;在±10℃温度载荷作用下最大面形误差RMS=11.46nm;反射镜组件一阶频率为574.19Hz。使挠性支撑结构具有良好的静、动态特性和热尺寸稳定性,满足反射镜面形要求。     

弹性预紧约束非线性对结构振动的影响

针对大型空间可展开结构中存在的关节非线性间隙约束问题,研究弹性预紧约束非线性对结构动态特性的影响.首先,基于轴向拉伸力学模型,构造了轴向拉伸关节三维梁单元.其次,使用Kelvin-Voigt接触及Coulomb摩擦模型,建立了粘弹性预紧约束下整体结构非线性动力学方程,继而分析了不同预紧约束下关节对结构非线性振动的影响.结果表明,在关节非线性约束下,结构振动传递特性的高频响应增加,低阶振动能量传递到高阶振动上.     

A finite element procedure to time dependent contact analysis

The subject of this paper is a finite element approach to solve contact problems involving contact-time dependence and interactions and frictional conditions. The procedure finds application in elastic or inelastic analysis of structural systems with two or more parts separated by small gaps and subjected to cyclic static loadings, as encountered, e.g. in nuclear reactor core components.The procedure is based on the load increment method and the introduction of orthotropic gap elements. Their stiffnesses both in the directions normal and tangential to the opposing surfaces assume an infinitesimal or a finite value according to the open or close configuration and to the frictional conditions. At every time step the locations of the contacts are at first identified through the non-positive values of the Jakobian in the gap elements. Then the new global stiffness is determined with the contribution of the stiff elements at the contact regions limited to the present time step to account for the preceding free relative motion.Two elementary illustrative analyses show the validity of the procedure in determining the time points of the gap closure and opening and in accounting for contact interactions. Finally an application to a real contact problem in the reflector subassembly of a nuclear reactor core is given.     

A mathematical framework for rigid contact detection between quadric and superquadric surfaces

The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C² continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton–Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C² continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super) ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.     

A method for shell contact analysis

A relatively general and computationally efficient method of shell contact analysis using the discrete Fourier transform is developed for linear and certain types of nonlinear problems. The method predicts the contact boundary and the interfacial pressure distribution. It is illustrated by calculating the road contact pressure predicted by a finite element toroidal shell model of a pneumatic tire.     

Determination of wheel–rail contact points with semianalytic methods

The multibody simulation of railway vehicle dynamics needs a reliable and efficient method to determine the location of the contact points between wheel and rail that represent the application points of the contact forces and influence their directions and intensities. In this work, two semi-analytic procedures for the detection of the wheel–rail contact points (named the DIST and the DIFF methods) are presented. Both the methods consider the wheel and the rail as two surfaces whose analytic expressions are known. The first method is based on the idea that the contact points are located in the point in which the distance between the contact surfaces has local maxima, and is equivalent to solve an algebraic 4D-system. The second method is based on the idea that in the contact points the difference between the surfaces has local minima and is equivalent to solve an algebraic 2D-system. In both cases, the original problem can be reduced analytically to a simple 1D-problem that can be easily solved numerically.     

On Clamping Planning in Workpiece-Fixture Systems

Deformations of contacts between the workpiece and locators/clamps resulting from large contact forces cause overall workpiece displacement, and affect the localization accuracy of the workpiece. An important characteristic of a workpiece-fixture system is that locators are passive elements and can only react to clamping forces and external loads, whereas clamps are active elements and apply a predetermined normal load to the surface of workpiece to prevent it from losing contact with the locators. Clamping forces play an important role in determining the final workpiece quality. This paper presents a general method for determining the optimal clamping forces including their magnitudes and positions. First, we derive a set of “compatibility” equations that describe the relationship between the displacement of the workpiece and the deformations at contacts. Further, we develop a locally elastic contact model to characterize the nonlinear coupling between the contact force and elastic deformation at the individual contact. We define the minimum norm of the elastic deformations at contacts as the objective function, then formulate the problem of determining the optimal clamping forces as a constrained nonlinear programming problem which guarantees that the fixturing of the workpiece is force closure. Using the exterior penalty function method, we transform the constrained nonlinear programming into an unconstrained nonlinear programming which is, in fact, the nonlinear least square. Consequently, the optimal magnitudes and positions of clamping forces are obtained by using the Levenberg–Marquardt method which is globally convergent. The proposed planning method of optimal clamping forces, which may also have an application to other passive, indeterminate problems such as power grasps in robotics, is illustrated with numerical example.      

A Dirichlet–Neumann type algorithm for contact problems with friction

Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We introduce a new algorithm for the numerical solution of a nonlinear contact problem with Coulomb friction between linear elastic bodies. The discretization of the nonlinear problem is based on mortar techniques. We use a dual basis Lagrange multiplier space for the coupling of the different bodies. The boundary data transfer at the contact zone is essential for the algorithm. It is realized by a scaled mass matrix which results from the mortar discretization on non-matching triangulations. We apply a nonlinear block Gauss–Seidel method as iterative solver which can be interpreted as a Dirichlet–Neumann algorithm for the nonlinear problem. In each iteration step, we have to solve a linear Neumann problem and a nonlinear Signorini problem. The solution of the Signorini problem is realized in terms of monotone multigrid methods. Numerical results illustrate the performance of our approach in 2D and 3D. Received: 20 March 2001 / Accepted: 1 February 2002 Communicated by P. Deuflhard     

Designing an assembly line for modular products

To respond to the challenge of agile manufacturing, companies are striving to provide a large variety of products at low cost. Product modularity has become an important issue. It allows to produce different products through combination of standard components. One of the characteristics of modular products is that they share the same assembly structure for many assembly operations. The special structure of modular products provides challenges and opportunities for operational design of assembly lines. In this paper, an approach for design of assembly lines for modular products is proposed. This approach divides the assembly line into two subassembly lines: a subassembly line for basic assembly operations and a subassembly line for variant assembly operations. The design of the subassembly line for basic operations can be viewed as a single product assembly line balancing problem and be solved by existing line balancing methods. The subassembly line for the variant operations is designed as a two-station flowshop line and is balanced by a two-machine flowshop scheduling method. A three-station flowshop line for a special structure of modular products is proposed and illustrated with an example.     

利用点面提取的任意多面体快速靠接

文章主要讨论沿直线运动的多面体靠接问题.根据多面体的几何特性，通过一系列的筛选和变换将多面体的靠接问题转化成为计算少量点与平面多边形的距离问题，从而大大地提高了任意空间多面体靠接的计算速度.该算法可广泛地用于以多面体为数学模型的计算机图形学、机器人、多媒体和CAD/CAM等众多领域的系统中.     

A nonsmooth nonlinear conjugate gradient method for interactive contact force problems

Interactive rigid body simulation is important for robot simulation and virtual design. A vital part of the simulation is the computation of contact forces. This paper addresses the contact force problem, as used in interactive simulation. The contact force problem can be formulated in the form of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better.