運用非線性疊代法於多體系統之動力學分析

Using Nonlinear Recursive Formulation on Dynamic Analysis of Multi-body Systems

朱德日(Chu Duc Nhat)

指導教授 ： 黃運琳

國立虎尾科技大學/工程學院/機械與機電工程研究所/碩士(2012年)

摘要

使用多体系统的动态分析非线性递归制定方法。第一部分是用于一组相互关联的变形机构组成的开环机械系统的动态分析。第二部分是用于闭环灵活运动的机械系统动态分析。起初，身体的每个系统配置确定使用的参考和弹性的协调耦合。儿童机构在开环系统的绝对速度和加速度的绝对速度和加速度的上级机构和机构之间的关节相对统筹的时间导数表示。动态的运动微分方程为每个链接使用な?牛顿 - 欧拉方程。实际的联合反应和结合的运动关系和な?牛顿 - 欧拉方程的な?力之间的关系是用来建立一个松散的耦合方程组，其中有一个稀疏矩阵结构的系统。使用矩阵分区和递归投影技术的基础上最佳的块分解，有效的解?方案为系统加速和联合反应部队。它还允许一个去耦联合和弹性加速度的系统程序。其次，运动和力模型开发使用绝对引用，相对合资，弹性坐标以及联合反应部队。这种非线性的递推导致运动方程松散耦合系统。在一个闭环运动链，削?在选定的辅助关节，以形成生成树结构。毗邻的开环机械系统方程的相容性条件和辅助关节反作用力的关系，以形成闭环的动态方程。使用这些方程和事实与松紧度的自由相关的联合反应部队，并不代表独立变量的稀疏矩阵结构，解耦联合和弹性加速度的方法。不同于现有递归配方，此方法不需要大的非线性矩阵的逆或分解。它会导致方程的尺寸的松紧程度的自由，独立的小系统。在这项研究中还讨论了应用在闭环变形多体系统的动态分析的动态解耦方法。在这项研究中的几个数值例子说明了利用发达国家在这次调查中的数值算法。

关键词：非线性递归公式，开环的变形多体，な?牛顿 - 欧拉方程，闭环，小学联合，共同辅助。

關鍵字

非线性递归制定的 ； 开环变形多体 ； 闭环

並列摘要

Using nonlinear recursive formulation method for the dynamic analysis of multi-body systems is presented. The first part is used for the dynamic analysis of open-loop mechanical systems that consist of a set of interconnected deformable bodies. The second part is used for the dynamic analysis of a closed-loop flexible kinematic mechanical system. At first, the configuration of each body in the system is identified using a coupled set of reference and elastic co-ordinates. The absolute velocities and accelerations of child bodies in the open-loop system are expressed in terms of the absolute velocities and accelerations of the parent bodies and the time derivatives of the relative co-ordinates of the joints between the bodies. The dynamic differential equations of motion are developed for each link using the generalized Newton-Euler equations. The relationship between the actual joint reaction and the generalized forces combined with the kinematic relationship and the generalized Newton-Euler equations are used to develop a system of loosely coupled equations which has a sparse matrix structure. Using matrix partitioning and recursive projection techniques based on optimal block factorization, an efficient solution for the system acceleration and joint reaction forces is obtained. It also allows a systematic procedure for decoupling the joint and elastic accelerations. Secondly, the kinematic and force models are developed using absolute reference, joint relative, and elastic coordinates as well as joint reaction forces. This nonlinear recursive formulation leads to a system of loosely coupled equations of motion. In a closed-loop kinematic chain, cuts are made at selected auxiliary joints in order to form spanning tree structures. Compatibility conditions and reaction force relationships at the auxiliary joints are adjoined to the equations of open-loop mechanical systems in order to form closed-loop dynamic equations. Using the sparse matrix structure of these equations and the fact that the joint reaction forces associated with elastic degrees of freedom do not represent independent variables, a method for decoupling the joint and elastic accelerations is developed. Unlike existing recursive formulations, this method does not require inverse or factorization of large nonlinear matrices. It leads to small systems of equations whose dimensions are independent of the number of elastic degrees of freedom. The application of dynamic decoupling method in dynamic analysis of closed-loop deformable multi-body systems is also discussed in this study. The use of the numerical algorithm developed in this investigation is illustrated by several numerical examples in this study.

Keywords: Nonlinear recursive formulation, Open-loop deformable multibody, Generalize Newton-Euler equations, Closed-loop, Primary joint, Auxiliary joint.

並列關鍵字

Nonlinear recursive formulation ； Open-loop deformable multibody ； Closed-loop

參考文獻

[1] K. Changizi and A. A. Shabana, ‘A recursive formulation for the dynamic analysis of open loop deformable multibody systems’, ASME J. Appl. Mech., 55,687-693 (1988).

[2] H. Goldstein, Classical Mechanical, Addision-Wesley, Reading, MA, 1980.

[4] S. S. Kim and M. J. Vanderploeg, ‘A general and efficient method for dynamic analysis of mechanical systems using velocity transformation’, ASME J. Mechanisms Trans, Automat. Des., 108, 176-189 (1986).

[5] J. E. Keat, ‘Multibody system order n dynamics formulation based on velocity transform method’, AIAA J. Guidance control and Dynamics, 13, 207-212 (1990).

[6] S. S. Kim and E. J. Haug, ‘A recursive formation for flexible multibody dynamics, Part I: open-loop systems’, Comp. Method Appl. Mech. Eng., 71, 293-314 (1988).