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

doi:10.1088/1674-1056/23/9/094501

›› 2014, Vol. 23 ›› Issue (9): 94501-094501.doi: 10.1088/1674-1056/23/9/094501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

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

刘爽^{a b}, 赵双双^a, 孙宝平^a, 张文明^{a b}

a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China

收稿日期:2014-01-16 修回日期:2014-02-25 出版日期:2014-09-15 发布日期:2014-09-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61104040) and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090).

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

Liu Shuang (刘爽)^{a b}, Zhao Shuang-Shuang (赵双双)^a, Sun Bao-Ping (孙宝平)^a, Zhang Wen-Ming (张文明)^{a b}

a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China

Received:2014-01-16 Revised:2014-02-25 Online:2014-09-15 Published:2014-09-15
Contact: Zhang Wen-Ming E-mail:hudiezhaoshuang@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61104040) and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090).

摘要/Abstract

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.

关键词: relative rotation, electromechanical coupling, Hopf bifurcation, chaos

Abstract: 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.

Key words: relative rotation, electromechanical coupling, Hopf bifurcation, chaos

中图分类号: (Rotational dynamics)

45.20.dc

05.45.-a (Nonlinear dynamics and chaos)

刘爽, 赵双双, 孙宝平, 张文明. Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system[J]. , 2014, 23(9): 94501-094501.

Liu Shuang (刘爽), Zhao Shuang-Shuang (赵双双), Sun Bao-Ping (孙宝平), Zhang Wen-Ming (张文明). Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system[J]. Chin. Phys. B, 2014, 23(9): 94501-094501.

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

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

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