Stability and coupling dynamic behavior of nonlinear journal active electromagnetic bearing rotor system

Abstract

The stability and coupling dynamic behavior of a journal active electromagnetic bearing rotor system are analyzed. The gyroscopic effect is considered in the rotor model. The system equations are formulated by combining equations for rotor motion and decentralized proportional integral differential (PID) controllers. A method combining the predictor-corrector mechanism and the Netwon-Raphson method is presented to calculate the critical speed at the corresponding Hopf bifurcation point of the system. For periodic motions, a continuation method combining the predictor-corrector mechanism and shooting method is presented. Nonlinear unbalanced periodic motions and their stability margins are obtained using the shooting method and established continuation method for periodic motions. With the change of control parameters, the system local stability and bifurcation behaviors are obtained using the Floquet theory. The numerical examples show that the schemes not only significantly save computing cost, but also have high precision.

References

1. Nonami K Yamanaka T Tominaga M Vibration and control of a flexible rotor supported bymagnetic bearings (control-system analysis and experiments withoutgyroscopic effects)JSME International JournalSeries III 1990 33(4)475482
2. Antkowiak B M Nelson F C Rotordynamic modeling of anactively controlled magnetic bearing gas turbine engineASME Journal of Engineering for Gas Turbines andPower 1998 120(3)621625. doi:10.1115/1.2818191
3. Ho Y S Yu L Liu H Rotor dynamic coefficients of a thrust active magneticbearing considering runner tiltProc InstnMech Engrs Part J, Journal of Engineering Tribology 1999 213451462. doi:10.1243/1350650991542802
4. Shiau T N Sheu G J Yang C D Vibration and control of a flexible rotor in magnetic bearingsusing hybrid method and H^∞ controltheoryASME Journal of Engineering for GasTurbines and Power 1997 119(1)178185. doi:10.1115/1.2815545
5. Virgin L N Walsh T F Knight J D Nonlinear behavior of a magnetic bearing systemASME Journal of Engineering for Gas Turbines andPower 1995 117(7)582588. doi:10.1115/1.2814135
6. Chinta M Palazzolo A B Stability and bifurcation ofrotor motion in a magnetic bearingJournalof Sound and Vibration 1998 214(5)793803. doi:10.1006/jsvi.1998.1549
7. Mohamed A Fawzi P Nonlinear oscillations in magneticbearing systemIEEE Transactions on AutomaticControl 1993 38(8)12421245. doi:10.1109/9.233159
8. Sundararajan P Noah S T Dynamics of forced nonlinearsystems using shooting/arc length continuation method–applicationto rotor systemASME, Journal of Vibrationand Acoustics 1997 119(1)1020. doi:10.1115/1.2889694
9. Ho Y S Liu H Yu L Stability and bifurcation of a rigid rotor-magnetic bearingsystem equipped with thrust magnetic bearingProc Instn Mech Engrs Part J, Journal of Engineering Tribology 2001 215457470. doi:10.1243/1350650011543691
10. Lu Yanjun Yu Lie Liu Heng Stability and bifurcation of nonlinear bearing-rotor systemChinese Journal of Mechanical Engineering 2004 40(10)6267(in Chinese)