北京航空航天大学学报 ›› 2009, Vol. 35 ›› Issue (2): 236-240.

• 论文 • 上一篇    下一篇

温度场中柔性臂超谐共振及复杂运动分析

贠 超1, 崔一辉1, 王 伟1, 汤 青2   

  1. 1. 北京航空航天大学 机械工程及自动化学院, 北京 100191;
    2. 廊坊市智通机器人系统有限公司, 廊坊 065001
  • 收稿日期:2008-07-20 出版日期:2009-02-28 发布日期:2010-09-16
  • 作者简介:贠 超(1952- ),男,陕西三原人,教授,cyun18@vip.sina.com.
  • 基金资助:

    国家863计划资助项目(2007AA04Z231266)

Super-harmonic resonance and complex movement analysis of flexible manipulator in temperature field

Yun Chao1, Cui Yihui1, Wang Wei1, Tang Qing2   

  1. 1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. Langfang InterSmart Robotic Systems Co., Ltd., Langfang 065001, China
  • Received:2008-07-20 Online:2009-02-28 Published:2010-09-16

摘要: 通过Garlerkin方法建立了考虑阻尼、材料非线性、温度变化和轴向激励的柔性臂系统动力学微分方程.分析了系统存在同、异宿轨道及周期轨道的充分必要条件,通过Hamilton函数得到了对应的参数方程表达式.根据非线性振动的多尺度法,得到了系统在3次超谐共振情况下的一次近似解及其定常解,揭示了系统内各参数之间的关系.对得到的微分方程进行数值计算,分析柔性臂系统参数对纵向振动响应曲线的影响.结果表明,材料非线性和温度变化对系统纵向振动的影响不可忽略;在一定参数条件下,系统有发生复杂非线性运动的可能.为了有效的控制柔性臂的振动,应合理选取系统的物理参数,避免其处于混沌运动状态.

Abstract: In order to study on nonlinear vibration of flexible manipulator, a mathematical model of mechanical system considering damping, material nonlinearity, temperature variation and axial excitation was established using the Garlerkin method. Furthermore, the adequate and essential conditions for homoclinic orbits, hetroclinic orbits and period orbits were obtained by Hamilton functions of the system, and the corresponding specific analytic expressions of different orbits were deduced. Based on the multiple scales method for nonlinear vibration analysis, the first approximation solutions and corresponding to steady state solutions of the 3 super-harmonic resonances were studied. The relations between different parameters were revealed clearly. Numerical analysis results show that material nonlinearity and temperature variation are critical factors influencing the vibration, which should not be neglected. In some conditions, the movement such as chaotic motion can be found in the system. In order to control the flexible manipulator effectively, parameters should be designed correctly to avoid the chaotic movement.

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