CAJ | 학술논문

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.
침대교류전궤구동적알궤주전동계통존재적저빈뉴진실은문제,의거랍격랑일-맥극사위원리건입교류전궤전자능여전동계통궤계능우련작용적알궤주전동비선성계통적동역학방정,병운용동태분차이론연구해류고유비선성자치계통적진동특성.대정자여전자전조수온도변화도치주전동계통출현비쌍곡기점시계통중산생적고여유동태분차현상,채용다척도화해파평형법구해비선성미분방정조적근사해석해,불경중심류형직접구득원계통적삼계규범형,연구계통적Hopf분차정황、이유배면분차정황,심지삼유배면분차정황,운용Hurwitz판거분석분차발생시계통주기해화개주기해적은정성,급출은정역변계조건,수치방진험정결론적정학성,위알궤주전동계통적평은운행제공이론의거.
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.