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.
Magnetic Bearing Control of Flexible Shaft Vibrations Based on Multi-access Velocity-Displacement Feedback
Petela, G., and Botros, K. K. (January 1, 1995). "Magnetic Bearing Control of Flexible Shaft Vibrations Based on Multi-access Velocity-Displacement Feedback." ASME. J. Eng. Gas Turbines Power. January 1995; 117(1): 188–197. https://doi.org/10.1115/1.2812771
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