FULLY SYMBOLIC GENERATION OF COMPLEX MULTIBODY MODELS*

Abstract

In this paper, a quasistatic finite element model of a spur gear pair is developed. A node-to-target contact formulation is given, where calculations of initial gaps are based upon the actual geometry of the gear flanks rather than upon a contact node and a facet or a line segment. By using a special contact search algorithm, profile modifications and mounting errors are easily incorporated in the analysis. The problem, which also includes friction, is solved by using a nonsmooth Newton method. The static transmission error can be calculated with accuracy with a relatively small number of nodes along the gear flanks. Several examples are given in order to demonstrate the model.     

Kinematic analysis of a novel pin-wheel joint

In this paper an innovative joint for the transmission of motion between parallel and incident axes is presented. It is made up of two frontal pin-wheels with cylindrical pins. The kinematics in case of parallel axes is discussed in detail. It is shown that, quite surprisingly, it may behave in many different ways, depending on the value of the center distance between the two axes. A systematic way to analyze the joint kinematics is provided.     

抗干涉齿轮集机构最优归一化编码的理论与方法

抗干涉齿轮集(CMG, Counter-Meshing Gears)机构是一种可用于确保要害系统安全性的机械组合锁的密码鉴别机构。对于N个A和N个B任意组合的二元解锁符号序列,如何用最小、固定的齿轮层数C和齿轮分度数D实现相应CMG机构密码鉴别齿牙的二元装定编码,是具有重要实用背景的CMG机构最优归一化编码问题。借助此前报道的CMG机构分类方法、二维迷宫映射图、关键陷阱格点(CTG, Critical Route Grid)的三色循环着色编码方法等工具,系统论述了CMG机构最优归一化编码的理论与方法。给出了两种可选的编码方法,及每种方法最小编码空间需求(用CD表征)和编码算法。根据编码空间和解锁符号序列的字长,定义了表征CMG机构编码效率的优值。利用这个物理概念清晰的优值比较两种可选的最优归一化编码方法,得到编码空间为C=3,D=N+2的第一类CMG机构是首选方法的结论。对于第一类CMG机构,最优归一化编码与先前报道的最少齿轮层数的优化编码并无不同,两者都需要最小C=3,D=N+2的编码空间,且CTG三色循环着色编码方法同样适用。应用CTG三色循环着色编码方法会在校验二维迷宫映射图中留下一个显著的指纹特征,全部CTG会被循环有规律地分配到仅三个颜色集上,也即设定的用于误码锁定的A-B复合齿轮之间的干涉将交替发生在仅三层密码齿轮上。     

EPSI validation for cylindrical gears

Shape deviations of spur gears obtained by using Electronic Speckle Pattern Interferometry are compared with the results of numerical simulation. The dual illumination method produces a speckle pattern by simultaneous illumination of a sample by two laser waves symmetrically in the direction of observation. Two images obtained, respectively, before and after deformation are subtracted to obtain the field of displacement. Furthermore, a study of meshing stiffness was performed for different types of setting for an internal gear.     

Application of a Special Yield Stress Strain Rate Law to Structural Impulse Problems

ABSTRACT

This paper presents approximate solutions to the dynamic response of three impulsively loaded structures: a wire with an impulsively loaded end mass, an impulsively loaded circular ring, and a cantilever beam with a tip mass subjected to an impulsive load at its tip. The material is assumed to be rigid, perfectly plastic with strain rate sensitivity. A proposed power law form of yield stress strain rate relationship is used to simplify the theoretical development. Numerical solutions are presented for mild steel and are compared with previously published results. Elastic effects and wave propogations are ignored.     

第二类抗干涉齿轮集机构复合齿轮的最小层数

抗干涉齿轮集(CMG)机构是一种精巧的密码鉴别机构,可用于确保要害系统保证性的机械组合锁中。CMG机构的密码鉴别功能取决于两个配对的、多层密码齿轮固定堆叠而成的编码复合齿轮。复合齿轮层数的最小化有利于工程应用优化;对复合齿轮最小层数问题的认识,也是基于CMG机构的机械组合锁的关键科学问题之一。此前已证明第一类CMG机构复合齿轮的最小层数为3;对于有一个独特的指纹特征的第二类CMG机构,其最小层数的问题更为复杂。由于任意一个NA+NB的解锁符号序列都可以简并为MAB(MN)的形式且保持编码二维迷宫映射图中关键陷阱格点(CTG)的色数不变,且CTG互斥约束关系随着MAB持续增/减任意数量的3AB呈现出周期性,因此首先应用二维迷宫映射变换和CTG互斥的十字叉判据,将第二类CMG机构3AB(或6AB),4AB和5AB三种基本模式中复合齿轮最小层数的证明过程转换为求解无向图G(V, E)顶点着色的色数,得到其色数分别为3,5和6。进一步得到最终结论,第二类CMG机构必须细分为与简并解锁符号序列对应的三种模式(3n)AB,(3n+1)AB和(3n+2)AB(n是自然数1, 2, ),最小齿轮层数分别为3,5和6。这意味着第二类CMG机构复合齿轮的最小层数受控于解锁符号序列结构的周期性。最后还给出了最小层数第二类CMG机构快捷编码的三模板着色方法。