Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system  

作　　者：刘爽 赵双双 孙宝平 张文明 

机构地区：[1]Key Laboratory of Industrial Computer Control Engineering of Hebei Province,Yanshan University [2]National Engineering Research Center for Equipment and Technology of Cold Strip Rolling,Yanshan University

出　　处：《Chinese Physics B》2014年第9期271-277,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.61104040);the Natural Science Foundation of Hebei Province,China(Grant No.E2012203090)

摘　　要：Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.

关 键 词：relative rotation electromechanical coupling Hopf bifurcation CHAOS 

分 类 号：O415.5[理学—理论物理]