基于拟蒙特卡罗方法的测量不确定度评定

测量不确定度是表征测量结果可靠性的一个重要参数.针对蒙特卡罗方法在测量不确定度评定时存在的收敛速度较慢以及仿真结果不稳定的不足,利用拟蒙特卡罗方法进行测苗不确定度的评定.拟蒙特卡罗方法使用拟随机数进行仿真计算.在测量不确定度的评定中,先基于Halton序列产生分布较为均匀的随机数,再利用数学变换转换成服从相应概率分布的随机数进行仿真评定计算.对圆柱体积测量不确定度的模拟评定结果表明,拟蒙特卡罗方法收敛速度快,计算结果较为稳定,可以简单高效地用于测量不确定度的评定.     

基于佳点集的装配公差分析方法

为提高传统的蒙特卡罗模拟方法进行公差数值分析时计算结果的收敛速度,基于数论中的佳点集理论构造出一种新的准蒙特卡罗法(quasi-Monte Carlo method)。在此基础上建立了基于确定性定位分析的白车身翼子板装配三维偏差模型,分别采用传统的蒙特卡罗伪随机数序列和基于佳点集的准蒙特卡罗法序列对该模型进行公差数值分析。在理论分析基础上的结果表明,在进行高精度复杂机械产品的装配公差分析过程中,与传统的蒙特卡罗模拟方法相比,所提出的方法的计算结果所需要的统计样本较少并且精度较高。     

静态MC方法在公差分析中的三种用法

蒙特卡罗(Monte Carlo,MC)方法是一种用于仿真计算的随机模拟方法,静态蒙特卡罗方法简单易用,比较适合于用计算机模拟来解决公差分析这样的随机问题。论述计算机辅助公差分析中应用静态蒙特卡罗模拟的三种用法,即以样本矩的估计来计算闭环公差,以样本频率的估计来计算装配成功率,以样本次序统计量的估计来计算满足装配成功率要求的闭环公差,并给出具体的计算示例,说明用静态蒙特卡罗方法解决公差分析问题的可行性。     

基于旋量参数的三维公差累积的运动学模型

研究了三维公差累积的运动学模型及其在计算机辅助公差设计中的应用，基于机器人学中的运动学分析方法研究了自参考和互参考公差域的旋量参数及其约束不等式，给出三维公差累积的运动学模型的一般表示式；研究了此模型在公差优化设计中的应用，一个齿轮泵的实例验证了此模型的有效性。     

基于特征几何变动的三维公差综合建模方法研究

针对计算机辅助公差设计中的三维公差综合问题,研究并建立了基于特征几何变动的三维公差综合方法和模型。在机械产品的装配中,将各零件配合几何特征视为刚体,利用刚体在三维空间中六个自由度方向上的微小几何变动所形成的区域来描述三维公差,在此基础上,采用机器人运动学中的齐次坐标变换方法获得各个特征几何变动量的累积关系等式,并通过工程计算中常用的广义逆求解得到装配功能要求与各配合几何特征自由度变动量间的关系,由此建立三维公差综合模型。最后,将本文阐述的方法运用于齿轮泵装配体实例,得到了轮齿侧向间隙要求与各配合特征几何变动量间的三维公差综合模型,从而验证了本文所提方法的实用性和有效性。     

雅可比-旋量模型在三维统计公差再设计中的应用研究

在确定产品功能要求(Functional Requirement,FR)和相应尺寸链的功能要素(Functional Element,FE)副之后,可以推导雅可比-旋量模型的数学表达式。蒙特卡罗模拟使用大量随机数值作为输入来反复运行该模型,使这个确定性的公差分析模型能执行三维统计公差分析。为了实现三维统计公差再设计,提出了在统计条件下雅可比-旋量模型中每个FE对总FR的贡献百分率的计算方法,以帮助设计者确定哪些公差需要收紧或是放松。经过几轮的公差再设计,直到计算出的FR值满足产品所要求的FR,三维统计公差的再设计得以实现。将该方法应用于活塞式发动机装配的曲柄连杆机构以验证其有效性,并通过与确定性公差设计方法比较表明,这里方法能显著降低所需的精度,从而大大降低产品生产和检验成本。     

基于变动几何约束网络的公差设计研究

在阐述和完善变动几何约束的定义和分类,变动几何约束网络的生成及其运动学模型的基础上,研究了计算机辅助公差类型的生成规则、方法,公差网络的表示方法,以及公差大小的最优分配方法。给出了基于三维CAD系统的计算机辅助尺寸公差和形位公差综合设计的总体框架和原型系统。实例分析验证了此系统的有效性。     

旋量理论与矢量积法相结合求解雅可比矩阵

雅可比矩阵是描述机器人特征的重要参数之一。基于旋量理论和矢量积法,本文提出了求解雅可比矩阵的改进方法。该方法继承了旋量理论用于机器人操作的优越性,避免了采用传统DH参数法来建立局部坐标系,简化了机器人运动学、动力学的分析方法。本文针对一种三分支机器人进行了计算机仿真,结果证实了所提方法的正确性与实用性。     

基于配合约束的几何公差分配方法

当公差原则为相关原则时，如何建立相关尺寸公差到几何公差的定量转换关系，实现几何公差的精准分配，是该领域亟待解决的问题。通过几何公差自顶向下分配的定性分析与定量计算，提出一种基于配合约束的几何公差分配方法。根据配合公差、互参照公差和自参照公差之间的约束，构建了基于配合约束的公差关联模型；基于上述关联，构建了与产品结构同步的几何公差设计过程模型；将装配接点作为配合公差传递的基本载体，根据装配接点的顺序和表面类型，提出了相关配合表面旋量矩阵的分析方法，并基于旋量矩阵生成相关表面的几何公差约束；以基于旋量矩阵的公差约束、加工精度约束和互参照公差对自参照公差的约束为约束条件，以最小总公差成本为目标函数，利用遗传算法实现了几何公差数值的优化。最后，以曲轴活塞机构为实例进行了几何公差的分配，经与经验法对比，验证了该方法的经济性与有效性。     

基于三维图样的公差优化分配方法研究

提出了基于模型定义技术及动态同构树数据框架的三维图样实现方法,为数控机床公差优化分配过程提供优质数据源。基于雅可比旋量法构建了公差分析模型,对公差传递链各个环节进行了敏感度分析。在满足设计要求的条件下,以成本最小为原则,对各环节公差进行最优配置。以某龙门导轨磨床磨头为例,建立了各零部件的三维图样,并在系统中完成了其公差优化分配过程。验证了基于三维图样的公差优化分配方法的可行性。     

基于特征的公差分析及其非线性问题研究

基于特征的公差分析方法在计算机辅助公差设计中有着广泛的应用.通过对具体案例的公差分析研究了蒙特卡洛模拟法和线性化方法的计算精度,并提出一种处理特征尺寸非正态分布的方案.     

Computer simulation machining a 3D free surface by using a 3-RPRU parallel machine tool

A novel computer aided geometric approach is proposed to machine a 3D free surface by adopting a 3-RPRU parallel machine tool. Based on the geometry constraint and dimension-driving technique, a 3-RPRU parallel simulation mechanism is first created. Next, a 3D free surface and a guiding plane of tool path are constituted. Finally, the 3-RPRU parallel simulation mechanism, the 3D free surface, and the guiding plane of the tool path are combined together, and a novel 3-RPRU simulation parallel machine tool is created for machining a 3D free surface. In the light of two specified tool paths, the extension of the three driving rods and the position of the moving platform are solved and visualized dynamically. Based on the computer simulation results, some analytic formulas are derived to solve the extension of driving rods of the 3-RPRU parallel machine tool in a reverse solving process. From the simulation and analytic results, it is proven that the computer simulation machine tool approach is equivalent to the analytic approach to machine 3D free surfaces. The computer simulation machine tool approach is straightforward without compiling computer programs, and is also advantageous from the viewpoint of accuracy and repeatability. This project is supported by NSFC 50575198.     

Quasi Ellipsoid Gear Surface Reconstruction Based on Meshless Local Petrov-Galerkin Method and Transmission Characteristic

Special transmission 3D model simulation must be based on surface discretization and reconstruction,but special transmission usually has complicated tooth shape and movement,so present software can't provide technical support for special transmission 3D model simulation.Currently,theoretical calculation and experimental method are difficult to exactly solve special transmission contact analysis problem.How to reduce calculation and computer memories consume and meet calculation precision is key to resolve special transmission contact analysis problem.According to 3D model simulation and surface reconstruction of quasi ellipsoid gear is difficulty,this paper employes meshless local Petrov-Galerkin(MLPG) method.In order to reduce calculation and computer memories consume,we disperse tooth mesh into finite points-sparseness points cloud or grid mesh,and then we do interpolation reconstruction in some necessary place of the 3D surface model during analysis.Moving least square method(MLSM) is employed for tooth mesh interpolation reconstruction,there are some advantages to do interpolation by means of MLSM,such as high precision,good flexibility and no require of tooth mesh discretization into units.We input the quasi ellipsoid gear reconstruction model into simulation software,we complete tooth meshing simulation.Simulation transmission ratio during meshing period was obtained,compared with theoretical transmission ratio,the result inosculate preferably.The method using curve reconstruction realizes surface reconstruction,reduce simulation calculation enormously,so special gears simulation can be realized by minitype computer.The method provides a novel solution for special transmission 3D model simulation analysis and contact analysis.     

4-DOF并联机器人型综合与分析的计算机辅助几何法

提出运用计算机辅助几何法来研究新型4自由度并联机器人的型综合问题，利用在CAD软件草图环境下建立的并联机器人模拟机构，基于并联机器人的模拟机构，综合出多种新型4自由度机构，并用计算机模拟法，分析了动平台的运动特性。模拟结果表明，计算机辅助几何法的应用，不但大大简化了并联机器人机构型综合的难度，而且快捷直观，值得推广。     

计算机辅助三维公差设计的研究现状

三维公差设计是计算机辅助公差设计的重点。总结了国内外学者对于计算机辅助三维公差设计的研究现状,分析了常见的三维公差表示模型及其设计方法,对三维公差设计的发展前景进行了展望。     

Tolerance effects on natural frequencies of multibody systems undergoing constant rotational motion

A general multi-body formulation to analyze the tolerance effects on the statistical property variations of natural frequencies of multi-body systems undergoing constant rotational motion is proposed in this paper. To obtain the tolerance effects, Monte-Carlo simulation method is conventionally employed. However, the Monte-Carlo simulation has serious drawbacks; spending too much computation time for the simulation and achieving very slow convergence around some dynamically unstable regions. To resolve such problems, a method employing analytical sensitivity information is suggested in this paper. To obtain the sensitivities of natural frequencies the eigenvalue problem should be differentiated with respect to a design variable. The sensitivities of mass and stiffness matrices should be calculated at the dynamic equilibrium. By employing the sensitivities of natural frequencies along with the tolerance of the design variable, the statistical property variations of the natural frequencies can be calculated. This paper was recommended for publication in revised form by Associate Editor Seockhyun Kim Seung Man Eom graduated from the Department of Mechanical Engineering at Incheon University in 2005 and received his master degree from the Department of Mechanical Engineering at Hanyang University in 2007. He is currently working as a Researcher of Aircraft Development Team in KIAT(Korea Institute of Aerospace Technology, Koreanair), DaejeonDeajeon, Korea. Bum Suk Kim graduated from the School of Mechanical Engineering at Hanyang University in 2006 and received his master degree from the same department in 2008. He is currently working as a Ph.D. student in the School of Mechanical Engineering in Hanyang University, Seoul, Korea. Hong Hee Yoo graduated from the Department of Mechanical Design and Production Engineering at Seoul National University in 1980 and received his master degree from the same department in 1982. He received his Ph.D. degree in 1989 from the Department of Mechanical Engineering and Applied Mechanics in the University of Michigan at Ann Arbor, U.S.A. He is currently working as a professor in the School of Mechanical Engineering in Hanyang University, Seoul, Korea.     

数论方法在统计公差分析中的应用

Monte-Carlo仿真方法通常用于复杂装配组件的公差分析,其主要缺点是计算量大、效率低.对此,提出以基于数论方法产生的伪随机数代替由Monte-Carlo方法所产生的随机数进行仿真.与随机数相比,伪随机数的分布更为均匀.算例结果表明基于伪随机数的公差分析具有Monte-Carlo方法简单实用的优点,同时计算量小,在计算精度相同的情况下计算效率可以提高10～20倍.     

随机平面桁架动力特性蒙特卡罗法的节俭研究

考虑平面桁架所有结构参数的随机性，通过随机因子法和对随机参数间相关性的研究，对结构的质量矩阵和刚度矩阵的随机性提出了两种近似处理方法。第1种方法能获得结构动力特性均方根上限，第2种方法能获得结构动力特性随机性的近似解，这两种方法都能显著节俭Monte—Carlo数值模拟法求解的计算量。算例表明，该方法不但节省了数值模拟的时间，且具有较好的精度。     

Optimal tolerance design for mechanical assembly considering thermal impact

In this paper, a cost–tolerance model based on neural network methods is proposed in order to provide product designers and process planners with an accurate basis for estimating the manufacturing cost. Tolerance allocation among the assembly components is carried out to ensure that the functionality and design quality are satisfied considering the effect of dimensional and geometric tolerance of various components of the assembly by developing a parametric computer aided design (CAD) model. In addition, deformations of various components of mechanical assembly due to inertia and temperature effects are determined and the same is integrated with tolerance design. The benefits of integrating the results of finite element simulation in the early stages of tolerance design are discussed. The proposed method is explained with an application example of motor assembly, where variations due to both dimensional and geometric tolerances are studied. The results show that the proposed methods are much effective, cost, and time saving than the ones considered in literature.