反向回转双机驱动振动系统的自同步理论.pdfVIP

第 45 卷第 9 期 机 械 工 程 学 报 Vol.45 No.9 2009 年 9 月 JOURNAL OF MECHANICAL ENGINEERING Sep. 2009 DOI ：10.3901/JME.2009.09.024 反向回转双机驱动振动系统的自同步理论* 赵春雨 刘 戡 叶小芬 王得刚 闻邦椿 (东北大学机械工程与自动化学院 沈阳 110004) 摘要：利用异步电动机电压同步坐标系，得出电动机稳态运行时电磁转矩与转速的关系。运用动力学理论分析反向回转双机 驱动振动系统的动力学特性，建立系统频率俘获的方程，得到实现频率俘获的条件及俘获频率和两偏心转子相位差的理论计 算方程。利用非线性动力学理论，建立了频率俘获的稳定方程。利用 Routh-Hurwitz 准则获得系统稳定性条件。 关键词：频率俘获 机电耦合 非线性动力学 自同步 振动系统 中图分类号：TH113 Self-synchronization Theory of a Vibrating System with Two-motor Drives Rotating in Opposite Directions ZHAO Chunyu LIU Kan YE Xiaofen WANG Degang WEN Bangchun (School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004) Abstract ：The relation between the electromagnetic torque and the rotor speed of an induction motor is derived in the synchronous frame of the stator voltage. The dynamic characteristic of a vibrating system with two-motor drives rotating in opposite directions is analyzed by using the dynamic theory and the equations of frequency capture are established. The conditions for implementing frequency capture and the equations of calculating capturing frequency and the phase difference are obtained. The stable equations of implementing frequency capture in the system are deduced by using nonlinear dynamics theory and the condition for system stability is obtained by using Routh-Hurwitz criterion. Key words ：Frequency capture Electric-mechanic coupling Non-linear dynamics Self-synchronization Vibrating system 在某些非线性系统中，不仅实现 3 倍频同步，而且 * 0 前言 可以实现各次谐波的倍频同步，即 2 倍频、3 倍频 和 n 倍频同步。实际上，多个旋转体或多个更加通 最早发现机械系统的振动同步现象或自同步 用的旋转机械结