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A time-varying stiffness rotor active magnetic bearings under combined resonance
Faculty
Science
Year:
2008
Type of Publication:
Article
Pages:
Authors:
Amer, Y. A, Eissa, M. H, Hegazy, U. H
DOI:
10.1115/1.2755118
Journal:
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME ASME-AMER SOC MECHANICAL ENG
Volume:
75
Research Area:
Mechanics
ISSN
ISI:000255132400011
Keywords :
active magnetic bearings, combined resonance, periodic time-varying stiffness
Abstract:
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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