AMOS: Analytical Methods for Optimal Vibration Reduction on General Rotors

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The introduction of Active Magnetic Bearings resulted in strong efforts to describe and understand the active control of rotors. Despite of the large amount of different control strategies, general statements how to design optimal controllers are scarce. The reason is that contemporary control strategies base on signal theory and have only little focus on the structural properties of flexible rotors. Furthermore, the complex mathematical background of current control strategies prevents a thorough analysis of the underlying rotor dynamic phenomena and gives no clues whether or not a control strategy is optimal. In the last years, the Institute for Mechatronic Systems in Mechanical Engineering significantly progressed in the description of active piezoelectric bearings. With analytical methods, it was possible to prove both analytically and practically that unbalance forces of general rotors can be completely isolated from the environment. Furthermore, a generalized description for different active bearing technologies has been found. However, the analytical investigation revealed that even without forces, large rotor deflections may occur in the vicinity of a free rotor resonance. This project likewise focuses on the isolation of rotors but additionally considers the deformation of the rotor. This is achieved by including the rotor bending energy. Thus, it is possible to keep the rotor displacements limited in every operating point and eliminate all resonances. An independent minimization of the bearing forces and the bending energy is, however, not possible. The improvement of the performance of one control objective reduces the other one. Thus, this is a Pareto problem. The proposed approach of this project is capable to reach both control objectives as limit cases and can perform a weighted combination of both. This is achieved by minimizing the elastic energy of the system, comprised of the bending energy and the elastic energy within the bearings, which is proportional to the bearing forces. The calculation of the elastic energy is performed using a general stiffness matrix, which applies the weighting of the bending energy and the bearing forces. The advantage of this approach is that only one controller is required to reach both control objectives, which enables an easy change of the weighting during operation. This approach differs from an approach where vibration reduction, spinning the rotor around its geometrical axis, and vibration isolation are combined because the bending energy is independent of the spatial positioning of the axis of rotation. The suggested approach will be tested numerically and under real world conditions on a rotor test-rig. The gained knowledge will enable general statements on the structural dynamics working principle of active piezoelectric bearings.