轧机主传动机电耦联扭振系统的动态分岔研究  

Dynamical Bifurcation Study on Electromechanical Coupling Vibration in Rolling Mill’s Drive System

作　　者：刘爽[1,2] 张业宽[2] 刘彬[2] 

机构地区：[1]燕山大学工业计算机控制工程河北省重点实验室,秦皇岛066004 [2]燕山大学电气工程学院,秦皇岛066004

出　　处：《机械工程学报》2010年第3期83-89,共7页Journal of Mechanical Engineering

基　　金：国家十一五重大科技攻关(2007BAF02B10);河北省自然科学基金(F2008000882);河北省教育厅科学重点研究(ZH2007102)资助项目

摘　　要：针对交流电机驱动的轧机主传动系统存在的低频扭振失稳问题,依据拉格朗日—麦克斯韦原理建立交流电机电磁能与传动系统机械能耦联作用的轧机主传动非线性系统的动力学方程,并运用动态分岔理论研究该类高维非线性自治系统的振动特性。对定子与转子电阻随温度变化导致主传动系统出现非双曲奇点时系统中产生的高余维动态分岔现象,采用多尺度和谐波平衡法求解非线性微分方程组的近似解析解,不经中心流形直接求得原系统的三阶规范形,研究系统的Hopf分岔情况、二维环面分岔情况,甚至三维环面分岔情况,运用Hurwitz判据分析分岔发生时系统周期解和概周期解的稳定性,给出稳定域边界条件,数值仿真验正结论的正确性,为轧机主传动系统的平稳运行提拱理论依据。In order to solve the problem of low frequency vibration in rolling mill drive system driven by AC motor, the nonlinear dynamics equations of rolling mill drive system with coupling action of electromagnetic energy and mechanical energy are established on the basis of Lagrange-Maxwell theory, and the vibration characteristic of this kind of multidimensional nonlinear autonomous system is studied by using the theory of dynamical bifurcation. Considering the high dimensional bifurcation caused by the nonhyperbolic fixed points when the resistances in stator and rotor change, the nonlinear differential equations’ approximate analytical solutions are solved with the aid of multiple time scales and harmonic balance, and the third-order normal form is obtained directly without application of center manifold theory. According to the normal form, the double Hopf bifurcations, 2D tori and 3D tori bifurcations are studied, and the stability of periodic and quasi-periodic solutions is analyzed by using Hurwitz criterion, and the boundary conditions of stable regions are given for each solution. The numerical simulation verifies the correctness of the conclusions, thereby providing a theoretical basis for smooth running of the rolling mill drive system.

关 键 词：轧机主传动系统 机电耦联 动态分岔 稳定性 

分 类 号：TH113.1[机械工程—机械设计及理论]