This paper is concerned with the nonlinear oscillations and dynamic behavior of a rigid disk-rotor supported by active magnetic bearings (AMB), without gyroscopic effects. The nonlinear equations of motion are derived considering a periodically time-varying stiffness. The method of multiple scales is applied to obtain four first-order differential equations that describe the modulation of the amplitudes and the phases of the vibrations in the horizontal and vertical directions. The stability and the steady-state response of the system at a combination resonance for various parameters are studied numerically, applying the frequency response function method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening, and softening nonlinearity. A numerical simulation using a fourth-order Runge-Kutta algorithm is carried out, where different effects of the system parameters on the nonlinear response of the rotor are reported and compared to the results from the multiple scale analysis. Results are compared to available published work.
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January 2008
Research Papers
A Time-Varying Stiffness Rotor Active Magnetic Bearings Under Combined Resonance
U. H. Hegazy,
U. H. Hegazy
Department of Mathematics, Faculty of Science,
e-mail: uhijazy@yahoo.com
Al-Azhar University
, Gaza, Palestine
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M. H. Eissa,
M. H. Eissa
Department of Engineering Mathematics,
Menoufia University
, Faculty of Electronic Engineering, Menouf 32952, Egypt
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Y. A. Amer
Y. A. Amer
Department of Mathematics, Faculty of Science,
Zagazig University
, Zagazig, Egypt
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U. H. Hegazy
Department of Mathematics, Faculty of Science,
Al-Azhar University
, Gaza, Palestinee-mail: uhijazy@yahoo.com
M. H. Eissa
Department of Engineering Mathematics,
Menoufia University
, Faculty of Electronic Engineering, Menouf 32952, Egypt
Y. A. Amer
Department of Mathematics, Faculty of Science,
Zagazig University
, Zagazig, EgyptJ. Appl. Mech. Jan 2008, 75(1): 011011 (12 pages)
Published Online: January 14, 2008
Article history
Received:
April 20, 2006
Revised:
June 6, 2007
Published:
January 14, 2008
Citation
Hegazy, U. H., Eissa, M. H., and Amer, Y. A. (January 14, 2008). "A Time-Varying Stiffness Rotor Active Magnetic Bearings Under Combined Resonance." ASME. J. Appl. Mech. January 2008; 75(1): 011011. https://doi.org/10.1115/1.2755118
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