A model of the forced vibrations of a flexible, asymmetric, and unbalanced shaft, supported by two magnetic bearings, is derived to simulate the effect of different schemes of active control on shaft dynamic behavior. Simulation results were compared for several cases of single and multi-access bearing controls, rigid-body mode only and rigid with flexible mode control, and linear and nonlinear bearing responses. It is shown that the multi-access bearing response, calculated from the known equation of the stable ROCL (Reduced Order Closed Loop) and based on the direct velocity-displacement feedback, provided the most precise shift in critical frequencies and also reasonable suppression of shaft vibration amplitudes. The nonlinear bearing design was also briefly discussed. The stability analysis showed that stability limits were influenced by more parameters in this case, but no particular advantages were observed in suppression of the vibration amplitudes as compared to the linear case.

Issue Section:
Gas Turbines: Structures and Dynamics
Topics:
Displacement, Feedback, Magnetic bearings, Vibration, Bearings, Stability, Bearing design, Simulation results
1.
Allaire, P. E., Humphris, R. R., and Kelm, R. D., “Dynamics of Flexible Rotor in Magnetic Bearings,” Proc. of Rotordyn. Instability Problems in High-Performance Turbomach., NASA Conference Publication 2443, 1986.
2.
Allaire, P. E., Humphris, R. R., and Kelm, R. D., “Magnetic Bearings for Vibration Reduction and Failure Prevention,” Proc. of the 45th Meeting of Mech. Failure Prevention Group, NBS, Gaithersburg, MD, Apr. 16–18, 1985.
3.
Allaire, P. E., Lewis, D. W., and Jain, V. K., “Feedback Control of a Single Mass Rotor on Rigid Supports,” J. of the Franklin Institute, Vol. 312, No. 1, July 1981.
4.
Allaire, P. E., Lewis, D. W., and Knight, J. D., “Active Vibration Control of a Single Mass Rotor on Flexible Supports,” J. of the Franklin Institute, Vol. 315, No. 3, Mar. 1983.
5.
Baruch, H., “A Recursive Pole Displacement Method for Large Flexible Structures,” presented at the 1987 ASME Design Technology Conferences—11th Biennial Conference on Mechanical Vibration and Noise, Boston, MA, Sept. 1987.
6.
Firoozian, S. R., “Modeling and Control of Turbomachinery Vibrations,” presented at the 1987 ASME Design Technology Conf., Boston, MA, Sept. 1987.
7.
Humphris, R. R., Allaire, P. E., and Lewis, D. W., “Design and Testing of Magnetic Bearings for Vibration Reduction,” Proc. of the 41st Meeting of Mech. Failure Prevention Group, Maryland, Oct. 1986.
8.
Humphris, R. R., Allaire, P. E., Lewis, D. W., and Barret, L. E., “Diagnostic and Control With Magnetic Bearing,” Proceedings of the 24th Intersociety Energy Conversion Eng. Conf., 1989.
9.
Humphris, R. R., Kelm, R. D., Lewis, D. W., and Allaire, P. E., “Effect of Control Algorithms on Magnetic Journal Bearing Properties,” ASME JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER, Vol. 108, Oct. 1986.
10.
Joshi, S. M., and Groom, N. J., “Design of Reduced-Order Controllers for Large Flexible Structures,” presented at the XVIth Annual Allerton Conf. on Communication, Control and Computing, Allerton House, Monticello, IL, 1978.
11.
Kasarda, M., Allaire, P. E., Humphris, R. R., and Barret, L. E., “A Magnetic Damper for First Mode Vibration Reduction in Multimass Flexible Rotors,” ASME JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER, Vol. 112, Oct. 1990.
12.
Lewis, D. W., Moore, J. W., Bradley, P. L., and Allaire, P. E., “Vibration Limiting of Rotors by Feedback Control,” Proceedings of NASA/ARO Workshop on Rotor Dynamic Instability, 1982.
13.
Levine, W. S., and Athans, M., “On the Determination of the Optimal Constant Output Feedback Gains for Linear Multivariable Systems,” IEEE Trans. on Automatic Control, Vol. AC-15, No. 1, Feb. 1970.
14.
Lin, J. G., “Closed-Loop Asymptotic Stability and Robustness Conditions for Large Space Systems With Reduced Order Controllers,” presented at the 20th IEEE Conf. on Decision and Control, San Diego, IEEE Control Systems Society, 1981.
15.
Lin, J. G., Lin, Y. H., and Preston, R. B., “Stability Augmentation for Large Space Structures by Modal Dashpots and Modal Springs,” presented at the VPI-SU/AIAA Symp., Dynamics and Control of Large Flexible Spacecraft, Blacksburg, VA, 1981.
16.
Lin, J. G., Hegg, D. R., Lin, Y. H., and Keat, J. E., “Output Feedback Control of Large Space Structures: An Investigation of Four Design Methods,” presented at the Sec. VPI-SU/AIAA Symp., Dynamics and Control of Large Flexible Spacecraft, Blacksburg, VA, 1979.
17.
Muszynska, A., “Whirl and Whip-Rotor/Bearing Stability Problems,” ASME Journal of Sound and Vibration, Vol. 110, No. 3, 1986.
18.
Muszynska, A., “Improvements in Lightly Loaded Rotor/Bearing and Rotor/Seal Models,” Rotating Machinery Dynamics, Vol. 1, ASME, New York, 1987.
19.
Nonami, K., “Vibration Control of Rotor Shaft Systems by Active Control Bearings,” NASA Technical Memorandum 87053, 1985.
20.
Salm, J., and Schweitzer, G., “Modelling and Control of a Flexible Rotor With Magnetic Bearings,” Inst. of Mech. Engrs., York, United Kingdom, 1984.
21.
Schweitzer, G., “Magnetic Bearings,” Rotordynamics 2. Problems in Turbomachinery, Springer-Verlag, 1988.
22.
Schweitzer, G., and Ulbrich, H., “Magnetic Bearings—A Novel Type of Suspension,” presented at the Sec. Int. Conf. on Vibrations in Rotating Mechinary, Institution of Mechanical Engineers, London-Cambridge, 1980.
23.
Schweitzer, G., “Characteristics of a Magnetic Rotor Bearing for Active Vibration Control,” Inst. Mech. Engrs., Vol. C239, 1976.
24.
Salm, J., “Eine aktive magnetische Lagerung eines elastichen Rotors als Beispiel ordungsreduzierter Regelung grosser elasticher Systeme,” VDI-Verlag GmbH, Dusseldorf, 1988.
25.
Stanway, R., and O’Reilly, J., “State-Variable Feedback Control of Rotor-Bearing Suspension Systems,” IMechE, C274, 1984.
26.
Strunce, R. R., et al., “Active Control of Space Structures,” Final Technical Report No. RADC-TR-81-289, C. S. Draoer Laboratory, Inc., Cambridge, MA, 1981.
27.
Ulbrich, H., and Anton, E., “Theory and Application of Magnetic Bearings With Integrated Displacement and Velocity Sensors,” Inst. Mech. Engrs., Vol. C299, 1984.
28.
Proceedings of the Second Int. Symposium on Magnetic Bearings, Tokyo, Japan, July 12–14, 1990.
29.
“Magnetic Bearings,” Proceedings of the First Int. Symposium ETH Zurich, G. Schweitzer, ed., Switzerland, June 6–8, 1988.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.