Hopf bifurcation of a magnetic bearing system with time delay

Ji, JC; Hansen, CH

Hopf bifurcation of a magnetic bearing system with time delay

Ji, JC

Hansen, CH

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Publication Type:: Journal Article
Citation:: Journal of Vibration and Acoustics, Transactions of the ASME, 2005, 127 (4), pp. 362 - 369
Issue Date:: 2005-08-01

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Field	Value	Language
dc.contributor.author	Ji, JC https://orcid.org/0000-0003-3280-5463	en_US
dc.contributor.author	Hansen, CH	en_US
dc.date.issued	2005-08-01	en_US
dc.identifier.citation	Journal of Vibration and Acoustics, Transactions of the ASME, 2005, 127 (4), pp. 362 - 369	en_US
dc.identifier.issn	1048-9002	en_US
dc.identifier.uri	http://hdl.handle.net/10453/15435
dc.description.abstract	This paper is concerned with a study of the influence of a time delay occurring in a PD feedback control on the dynamic stability of a rotor suspended by magnetic bearings. In the presence of geometric coordinate coupling and time delay, the equations of motion governing the response of the rotor are a set of two-degree-of-freedom nonlinear differential equations with time delay coupling in nonlinear terms. It is found that as the time delay increases beyond a critical value, the equilibrium position of the rotor motion becomes unstable and may bifurcate into two qualitatively different kinds of periodic motion. The resultant Hopf bifurcation is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. Based on the reduction of the infinite dimensional problem to the flow on a four-dimensional center manifold, the bifurcating periodic solutions are investigated using a perturbation method. Copyright © 2005 by ASME.	en_US
dc.relation.ispartof	Journal of Vibration and Acoustics, Transactions of the ASME	en_US
dc.relation.isbasedon	10.1115/1.1924644	en_US
dc.subject.classification	Acoustics	en_US
dc.title	Hopf bifurcation of a magnetic bearing system with time delay	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	127	en_US
utslib.for	091304 Dynamics, Vibration and Vibration Control	en_US
utslib.for	0905 Civil Engineering	en_US
utslib.for	0913 Mechanical Engineering	en_US
utslib.for	0915 Interdisciplinary Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	127	en_US

Abstract:

This paper is concerned with a study of the influence of a time delay occurring in a PD feedback control on the dynamic stability of a rotor suspended by magnetic bearings. In the presence of geometric coordinate coupling and time delay, the equations of motion governing the response of the rotor are a set of two-degree-of-freedom nonlinear differential equations with time delay coupling in nonlinear terms. It is found that as the time delay increases beyond a critical value, the equilibrium position of the rotor motion becomes unstable and may bifurcate into two qualitatively different kinds of periodic motion. The resultant Hopf bifurcation is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. Based on the reduction of the infinite dimensional problem to the flow on a four-dimensional center manifold, the bifurcating periodic solutions are investigated using a perturbation method. Copyright © 2005 by ASME.

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http://hdl.handle.net/10453/15435