Unbalance and Resonance Elimination on General Rotors with Active Bearings

Rotating machinery has a subtle, but profound impact on contemporary societies. Many modern achievements owe their existence to these machines, ranging from electrical power, cars, airplanes, to rockets. In these machines, rotor unbalances cause vibrations and stresses, decreasing their lifetime and leading to noise pollution. For decades, balancing and damping were the only methods to reduce these vibrations. The introduction of active magnetic bearings enabled new possibilities for rotor vibration reduction. Sophisticated control algorithms do not only allow for a reduction, but for a complete elimination of bearing forces caused by unbalances. Still, the existing methods suffer from drawbacks, including unclear behavior in rotor resonances, and poor stability. The invention of active bearings based on piezoactuators complicated the situation further: depending on the researcher’s background, contradicting methods are used for vibration reduction, resulting in an unclear and fragmented problem understanding. This work strives to resolve the apparent contradictions and drawbacks of the currently available methods to eliminate unbalances, generating a unified Problem solution for different active bearing technologies. After a careful Revision of the JEFFCOTT rotor, a new control approach is suggested. The latter does not only eliminate the rotor’s unbalance forces, but also the rotor’s resonance. The approach is extended to cover rotors with arbitrary mass, stiffness, damping and gyroscopic properties. A general, analytic solution indicates that the proposed control algorithm allows for a complete elimination of bearing forces and two rotor resonances. This is possible even when the rotor is attached to an arbitrary, flexible structure. The theoretical considerations allow for a derivation of control strategies for different actuator principles, technologies and arrangements, resulting in a consistent problem treatment and understanding. Actuator dimensioning Guidelines enable an effortless practical realization. This work introduces a new stability theorem for arbitrary mechanical Systems with collocated controllers. The theorem is subsequently applied to proof the controller’s superior stability properties, resulting in unconditional stability for general rotors