Dynamics of a Jeffcott rotor-magnetic bearing system with time delays

International Journal of Non-Linear Mechanics

Volumn 38, Issue 9, 2003, Pages 1387-1401

  Ji, J C ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Hopf bifurcation; Jeffcott rotor; Magnetic bearing; Primary resonance; Stability; Time delay

Indexed keywords

BIFURCATION (MATHEMATICS); DELAY CIRCUITS; DIGITAL CONTROL SYSTEMS; EQUATIONS OF MOTION; ROTORS;

CONTROL GAINS;

MAGNETIC BEARINGS;

EID: 0037412242     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(02)00078-1     Document Type: Article

References (20)

1. G. Genta, S. Carabelli, Noncolocation effects on rigid body rotordynamics of rotors on AMB, Proceedings of the Seventh International Symposium on Magnetic Bearings, ETH Zurich, August 2000, pp. 63-68.
2. Ji J.C., Hansen C.H. Non-linear oscillations of a rotor in active magnetic bearings. J. Sound Vibration. 240:2001;599-612.
3. Virgin L., Walsh T.F., Knight J.D. Nonlinear behavior of a magnetic bearing system. ASME J. Eng. Gas Turbines Power. 117:1995;582-588.
4. D. Laier, R. Markert, Nonlinear oscillations of magnetically suspended rotors, Proceedings of the Second European Nonlinear Oscillation Conference, Prague, 1996, pp. 239-242.
5. Hale J.K. Theory of Functional Differential Equations. 1977;Springer, New York.
6. Kuang Y. Delay Differential Equations with Applications to Population Dynamics. 1993;Academic Press, New York.
7. Wischert W., Wunderlin A., Pelster A. Delay-induced instabilities in nonlinear feedback systems. Phys. Rev. E. 49:1994;203-219.
8. G. Schweitzer, H. Bleuler, A. Traxler, Active Magnetic Bearings, basics, properties and applications of active magnetic bearings, Verlag der Fachvereine(vdf), ETH-Zurich, 1994.
9. Maslen E.H., Allaire P.E. Magnetic bearing sizing for flexible rotors. ASME J. Tribol. 114(2):1992;223-229.
10. Maslen E.H., Bielk J.R. A stability model for flexible rotors with magnetic bearings. ASME J. Dyn. Syst. Meas. Control. 114(1):1992;172-175.
11. Kolmanovskii V.B., Nosov V.R. Stability of Functional Differential Equations. 1986;Academic Press, London.
12. Campbell S.A., Belair J. Resonant condimension two bifurcation in the harmonic oscillator with delayed forcing. Canad. Appl. Math. Quart. 7:1999;217-238.
13. Campbell S.A. Stability and bifurcations in the harmonic oscillator with multiple, delayed feedback loops. Dyn. Continuous Discrete Impulsive Syst. 5:1999;225-235.
14. Guckenheimer J., Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. 2nd Edition:1986;Springer, New York.
15. Plaut R.H., Hsieh J.C. Chaos in a mechanism with time delays under parametric and external excitation. J. Sound Vibration. 114:1987;73-90.
16. Plaut R.H., Hsieh J.C. Non-linear structural vibrations involving a time delay in damping. J. Sound Vibration. 117:1987;497-510.
17. Nayfeh A.H., Mook D.T. Nonlinear Oscillations. 1979;Wiley, New York.
18. Hagedorn P. Nonlinear Oscillation. English Edition:1982;Clarendon Press, Oxford.
19. Hale J.K. Oscillations in Nonlinear Systems. 1971;McGraw-Hill, London.
20. D. Laier, Nichtlinearitaeten Magnetgelagerter Rotorsysteme, Fortschritte-Berichte VDI Verlag, Duesseldorf, 1999, p. 86.