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.
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e-mail: jcji@mecheng.adelaide.edu.au
e-mail: chansen@mecheng.adelaide.edu.au
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August 2005
Technical Papers
Hopf Bifurcation of a Magnetic Bearing System with Time Delay
J. C. Ji,
J. C. Ji
School of Mechanical Engineering,
e-mail: jcji@mecheng.adelaide.edu.au
The University of Adelaide
, SA 5005, Australia
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Colin H. Hansen
Colin H. Hansen
School of Mechanical Engineering,
e-mail: chansen@mecheng.adelaide.edu.au
The University of Adelaide
, SA 5005, Australia
Search for other works by this author on:
J. C. Ji
School of Mechanical Engineering,
The University of Adelaide
, SA 5005, Australiae-mail: jcji@mecheng.adelaide.edu.au
Colin H. Hansen
School of Mechanical Engineering,
The University of Adelaide
, SA 5005, Australiae-mail: chansen@mecheng.adelaide.edu.au
J. Vib. Acoust. Aug 2005, 127(4): 362-369 (8 pages)
Published Online: December 16, 2004
Article history
Received:
March 14, 2004
Revised:
December 16, 2004
Citation
Ji, J. C., and Hansen, C. H. (December 16, 2004). "Hopf Bifurcation of a Magnetic Bearing System with Time Delay." ASME. J. Vib. Acoust. August 2005; 127(4): 362–369. https://doi.org/10.1115/1.1924644
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