Hopf bifurcation of a magnetic bearing system with time delay

Journal of Vibration and Acoustics

Volumn 127, Issue 4, 2005, Pages 362-369

  Ji, J C ^a   Hansen, Colin H ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF MOTION; FEEDBACK CONTROL; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; ROTORS; SYSTEM STABILITY; TWO TERM CONTROL SYSTEMS;

COMPLEX CONJUGATE EIGENVALUES; HOPF BIFURCATION; TIME DELAY;

MAGNETIC BEARINGS;

EID: 24644511267     PISSN: 10489002     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1924644     Document Type: Article

References (23)

1. Laier, D., and Markert, R., 1996, "Nonlinear Oscillations of Magnetically Suspended Rotors," Proc. of Second European Nonlinear Oscillations Conference, Academy of Science of the Czech Republic, Prague, Vol, I, pp. 239-242.
2. Steinschaden, N., and Springer, H., 1999, "Some Nonlinear Effects of Magnetic Bearings," Proc. of 1999 ASME Design Engineering Technical Conference, Las Vegas, Sept. 12-16, ASME, New York, ASME Paper No. DEC99/VIB-8063.
3. Virgin, L. N., Walsh, T. F., and Knight, J. D., 1995, "Nonlinear Behaviour of a Magnetic Bearing System," ASME J. Eng. Gas Turbines Power, 117, pp. 582-588.
4. Chinta, M., and Palazzolo, A. B., 1998, "Stability and Bifurcation of Rotor Motion in a Magnetic Bearings" J. Sound Vib., 214(5), pp. 793-803.
5. Lawen, J. L., and Flowers, G. T., 1997, "Synchronous Dynamics of a Coupled Shaft Bearing Housing System With Auxiliary Support From a Clearance Bearing: Analysis and Experiment," ASME J, Eng. Gas Turbines Power, 119(2), pp. 430-435.
6. Wang, X., and Noah, S., 1998, "Nonlinear Dynamics of a Magnetically Supported Rotor on Safety Auxiliary Bearings," ASME J. Vibr. Acoust., 120(2), pp. 596-606.
7. Xie, H., Flowers, G. T., Feng, L., and Lawrence, C., 1999, "Steady-State Dynamic Behaviour of a Flexible Rotor With Auxiliary Support From a Clearance Bearing," ASME J. Vibr. Acoust., 121(1), pp. 78-83.
8. Kirk, R. G., 1999, "Evaluation of AMB Turbomachinery Auxiliary Bearings," ASME J. Vibr. Acoust., 121(2), pp. 156-161.
9. Chinta M., Palazzolo, A. B., and Kascak, A., 1996, "Quasi-Periodic Vibration of a Rotor in Magnetic Bearing With Geometric Coupling," Proc. of Fifth International Symposium on Magnetic Bearings, Kanazawa University, Kanazawa, pp. 147-152.
10. Knight, J. D., Xia, Z., and McCaul, E. B., 1992, "Forces in Magnetic Journal Bearings: Nonlinear Computation and Experimental Measurement," Proc. of Third Int. Symp. on Magnetic Bearings, Alexandria, VA, Technomic Pub Co, Lancaster, pp. 441-450.
11. Schweitzer, G., Bleuler, H., and Traxler, A., 1994, Active Magnetic Bearings, Basics, Properties and Application of Active Magnetic Bearings, Verlag der Fachvereine (vdf), ETH-Zurich.
12. Bajaj, A. K., 1982, "Bifurcating Periodic Solutions in Rotationally Symmetric Systems," SIAM J. Appl. Math., 42(5), pp. 1078-1098.
13. Haasard, B. D., Kazarinoff, N. D., and Wan, Y. H., 1981, Theory and Applications of Hopf Bifurcations, Cambridge University Press, Cambridge.
14. Hale, J., 1977, Theory of Functional Differential Equations, Springer-Verlag, New York.
15. Hale, J. K., and Verduyn Lunel, S. M., 1993, Introduction to Functional Differential Equations, Springer-Verlag, New York.
16. Halanay, A., 1966, Differential Equations, Stability, Oscillations, Time Lags, Academic Press, New York.
17. Kalmar-Nagy, T., Stepan, G., and Moon, F. C., 2001, "Subcritical Hopf bifurcations in the Delay Equation Model for Machine Tool Vibrations," Nonlinear Dyn., 26, pp. 121-142.
18. Gilsinn, D., 2002, "Estimating Critical Hopf Bifurcation Parameters for a Second-Order Delay Differential Equation With Application to Machine Tool Chatter," Nonlinear Dyn., 30, pp. 103-154.
19. Campbell, S. A., Belair, J., Ohira, T., and Milton, J., 1995, "Limit, Cycles, Tori, and Complex Dynamics in a Second-Order Differential Equation With Delayed Negative Feedback," J. Dyn. Differ. Equ., 7 (1), pp. 213-236.
20. Fofana, M. S., and Ryba, P. B., 2004, "Parametric Stability of Nonlinear Time Delay Equations," Int. J. Non-Linear Mech., 39, pp. 79-91.
21. Buono, P.-L., and LeBlanc, V. G., 2003, "Versal Unfoldings for Linear Retarded Functional Differential Equations," Diff. Eq., 193, pp. 307-342.
22. Yu, P., 1998, "Computation of Normal Forms Via a Perturbation Technique," J. Sound Vib., 211(1), pp. 19-38.
23. Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley, New York.