Nonlinear Analysis of Rotor-AMB System with Current Saturation Effect

Authors

  • Xiaoshen Zhang 1 Institute of Nuclear and New Energy Technology 2 Collaborative Innovation Center of Advanced Nuclear Energy Technology 3 Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University, Beijing, 100084, China
  • Tianpeng Fan 1 Institute of Nuclear and New Energy Technology 2 Collaborative Innovation Center of Advanced Nuclear Energy Technology 3 Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University, Beijing, 100084, China
  • Zhe Sun 1 Institute of Nuclear and New Energy Technology 2 Collaborative Innovation Center of Advanced Nuclear Energy Technology 3 Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University, Beijing, 100084, China
  • Lei Zhao 1 Institute of Nuclear and New Energy Technology 2 Collaborative Innovation Center of Advanced Nuclear Energy Technology 3 Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University, Beijing, 100084, China
  • Xunshi Yan 1 Institute of Nuclear and New Energy Technology 2 Collaborative Innovation Center of Advanced Nuclear Energy Technology 3 Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University, Beijing, 100084, China
  • Jingjing Zhao 1 Institute of Nuclear and New Energy Technology 2 Collaborative Innovation Center of Advanced Nuclear Energy Technology 3 Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University, Beijing, 100084, China
  • Zhengang Shi 1 Institute of Nuclear and New Energy Technology 2 Collaborative Innovation Center of Advanced Nuclear Energy Technology 3 Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University, Beijing, 100084, China

Keywords:

Current saturation, nonlinear analysis, numerical integration, pitchfork bifurcation

Abstract

The analysis on nonlinear dynamics of a rotor-AMB system is conducted in this paper. The nonlinearity of electromagnetic force and current saturation effect are taken into account. The nonlinear model of the rotor-AMB system is built and the nonlinear dynamic behaviors of the system in both resonance region and non-resonance region are investigated through numerical integration method. This paper shows that the rotor-AMB system can exhibit some complicated nonlinear dynamic behaviors, such as soft spring characteristic of the amplitude-frequency response curve, the jump phenomenon, and pitchfork bifurcation. And the effects of exciting force and current saturation on these nonlinear dynamic behaviors of the system are discussed.

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References

G. Schweitzer and E. H. Maslen, Magnetic Bearings: Theory, Design, and Application to Rotating Machinery. Springer, 2009.

Z. Sun, J. Zhao, Z. Shi, and S. Yu, “Identification of Flexible Rotor Suspended by Magnetic Bearings,” Proceeding of 21st International Conference on Nuclear Engineering, 2013.

Z. Sun, Y. He, J. Zhao, Z. Shi, L. Zhao, and S. Yu, “Identification of active magnetic bearing system with a flexible rotor,” Mechanical Systems & Signal Processing, vol. 49, no. 1-2, pp. 302-316, 2014.

N. A. Saeed, M. Eissa, and W. A. El-Ganini, “Nonlinear oscillations of rotor active magnetic bearings system,” Nonlinear Dynamics, vol. 74, no. 1-2, pp. 1-20, 2013.

J. Ji and C. H. Hansen, “Non-linear oscillations of a rotor in active magnetic bearings,” Journal of Sound & Vibration, vol. 240, no. 4, pp. 599-612, 2001.

A. Hu, L. Hou, and L. Xiang, “Dynamic simulation and experimental study of an asymmetric doubledisk rotor-bearing system with rub-impact and oilfilm instability,” Nonlinear Dynamics, vol. 84, no. 2, pp. 1-19, 2015.

L. Xiang, X. Gao, and A. Hu, “Nonlinear dynamics of an asymmetric rotor-bearing system with coupling faults of crack and rub-impact under oilfilm forces,” Nonlinear Dynamics, vol. 86, no. 2, pp. 1-11,2016.

T. Inoue, Y. Sugawara, and M. Sugiyama, “Modeling and nonlinear vibration analysis of a rigid rotor system supported by the magnetic bearing (effects of delays of both electric current and magnetic flux),” Neuroimage, vol. 13, no. 13, pp. 1203-1203, 2010.

J. Ji, “Stability and Hopf bifurcation of a magnetic bearing system with time delays,” Journal of Sound & Vibration, vol. 259, no. 4, pp. 845-856, 2013.

K. Kang and A. Palazzolo, “Homopolar magnetic bearing saturation effects on rotating machinery vibration,” IEEE Transactions on Magnetics, vol. 48, no. 6, pp. 1984-1994, 2012.

W. Zhang and X. Zhan, “Periodic and chaotic motions of a rotor-active magnetic bearing with quadratic and cubic terms and time-varying stiffness,” Nonlinear Dynamics, vol. 41, no. 4, pp. 331- 359, 2005.

M. J. Jang and C. K. Chen, “Bifurcation analysis in flexible rotor supported by active magnetic bearing,” International Journal of Bifurcation & Chaos, vol. 11, no. 08, pp. 2163-2178, 2001.

J. I. Inayat-Hussain, “Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings,” Chaos Solitons & Fractals, vol. 41, no. 5, pp. 2664-2671, 2009.

J. I. Inayat-Hussain, “Nonlinear dynamics of a statically misaligned flexible rotor in active magnetic bearings,” Communications in Nonlinear Science & Numerical Simulation, vol. 15, no. 3, pp. 764- 777, 2010.

W. Zhang, M. Yao, and X. Zhan, “Multi-pulse chaotic motions of a rotor-active magnetic bearing system with time-varying stiffness,” Chaos Solitons & Fractals, vol. 27, no. 1, pp. 175-186, 2006.

F. Sorge, “Stability analysis of rotor whirl under nonlinear internal friction by a general averaging approach,” Journal of Vibration & Control, vol. 16, no. 4, pp. 301, 2015.

F. Sorge, “Approach to rotor-shaft hysteretic whirl using Krylov-Bogoliubov techniques,” Journal of Vibration & Control, vol. 21, no. 5, pp. 883-895, 2013.

T. Inoue, Y. Ishida, and S. Murakami, “Theoretical analysis and experiments of the nonlinear vibration in a vertical rigid rotor supported by the magnetic bearing system,” Journal of System Design & Dynamics, vol. 1981, no. 1, pp. 295-306, 2007.

M. Kamel and H. S. Bauomy, “Nonlinear study of a rotor–AMB system under simultaneous primaryinternal resonance,” Applied Mathematical Modelling, vol. 34, no. 10, pp. 2763-2777, 2010.

Z. Sun, X. Zhang, T. Fan, X. Yan, J. Zhao, L. Zhao, and Z. Shi, “Nonlinear dynamic characteristics analysis of active magnetic bearing system based on cell mapping method with a case study,” Mechanical Systems & Signal Processing, vol. 117, pp. 116-137, 2019.

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” Journal of Computational & Applied Mathematics, vol. 6, no. 1, pp. 19-26, 1980.

B. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics. Cambridge University Press, 2004.

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Published

2019-04-01

How to Cite

[1]
Xiaoshen Zhang, “Nonlinear Analysis of Rotor-AMB System with Current Saturation Effect”, ACES Journal, vol. 34, no. 04, pp. 557–566, Apr. 2019.

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