Paper Info
Title
Nonlinear Dynamic Behavior Of A Rotor Active Magnetic Bearing
Abstract
The nonlinear dynamic behavior of a rigid disc-rotor supported by active magnetic bearings (AMB) is investigated, without gyroscopic effects. The vibration of the rotor is modeled by a coupled second order nonlinear ordinary differential equations with quadratic and cubic nonlinearities. Their approximate solutions are sought applying the method of multiple scales in the case of primary resonance. The Newton-Raphson method and the pseudo-arclength path-following algorithm are used to obtain the frequency response curves. Choosing the Hopf bifurcations as the initial points and applying the shooting method and the pseudo-arclength path-following algorithm, the periodic solution branches are obtained. At the same time, the Floquet theory is used to determine the stability of the periodic solutions. A detailed bifurcation analysis of the dynamic (periodic and chaotic) solutions of the averaged equations is presented. The three types of primary Hopf bifurcations are found for the first time in the rotor-AMB system. It is shown that the limit cycles undergo cyclic fold, period doubling bifurcations, and intermittent chaotic attractor, whereas the chaotic attractors undergo explosive bifurcation and boundary crises. In the regime of multiple coexisting solutions, multiple stable equilibriums, periodic solutions and chaotic solutions are the most interesting phenomena observed.
Year
DOI
Venue
2010
10.1142/S0218127410028124
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Active magnetic bearings, primary Hopf bifurcation, chaos, crises, hysteresis
Journal
20
Issue
ISSN
Citations 
12
0218-1274
1
PageRank 
References 
Authors
0.70
1
2
Name
Order
Citations
PageRank
Hongkui Chen121.20
Usama H. Hegazy210.70