• CN:11-2187/TH
  • ISSN:0577-6686

›› 2008, Vol. 44 ›› Issue (6): 54-60.

• 论文 • 上一篇    下一篇

基于矩阵变换的多刚体系统振动分析符号建模

姜伟;陈学东;严天宏   

  1. 华中科技大学数字制造装备与技术国家重点实验室
  • 发布日期:2008-06-15

Symbolic Formulation of Rigid Multibody Systems for Vibration Analysis Based on Matrix Transformation

JIANG Wei;CHEN Xuedong;YAN Tianhong   

  1. State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science and Technology
  • Published:2008-06-15

摘要: 针对复杂多刚体系统振动分析问题,提出一种基于矩阵变换的符号建模方法。采用矩阵和矢量对刚体质量惯量、弹簧-阻尼连接参数、约束和空间运动状态进行整体定义,使符号推导简捷明了。将振动状态下刚体小位移线性化,通过线性变换描述不同点相对于不同坐标系位移之间的关系。分别针对无约束和开环约束多刚体系统采用拉格朗日方法导出适于作控制和振动分析的线性常微分方程,揭示了两组方程与表征系统约束拓扑信息的系统约束坐标变换矩阵之间的关系。进一步阐述一般开环约束系统中系统约束坐标变换矩阵的构造方法。数值仿真和试验结果验证了该方法的正确性和有效性。

关键词: 常微分方程, 多刚体系统, 符号建模, 矩阵, 振动分析

Abstract: A new symbolic formulation based on matrix transformation is presented for vibration analysis of rigid multibody systems. The basic elements such as mass and inertia of body, coefficients of spring and damper, joint and spatial motion status, are defined in form of matrix or vector so as to keep structural integrity and get clear notation. The small displacements of bodies under vibration status are linearized, and the relationship between displacements at different points with respect to different reference frames is formulated by linear transformation. Linearized ordinary differential equations for unconstrained and open-loop constrained rigid multibody systems are derived respectively by using Lagrangian method, and the resulting equations are suitable for control and vibration analysis. The relationship between the two sets of equations is revealed by systematic coordinates transformation matrix. The rule of formulating the systematic transformation matrix for an open-loop constrained system is finally presented. The correctness and effectiveness of the proposed algorithm are proved by the result of numerical simulation and experiment.

Key words: Matrix, Ordinary differential equations, Rigid multibody systems, Symbolic formulation, Vibration analysis

中图分类号: