AMOS: Analytical Methods for Optimal Vibration Reduction on General Rotors

主动磁轴承的引入导致了描述和理解转子主动控制的巨大努力。尽管有大量不同的控制策略，如何设计最优控制器的一般性陈述很少。其原因是，当代控制策略的基础上，信号理论，只有很少关注的结构特性的柔性转子。此外，当前控制策略的复杂数学背景妨碍了对潜在转子动态现象的透彻分析，并且无法给出控制策略是否是最优的线索。在过去的几年里，机械工程机电系统研究所在主动压电轴承的描述方面取得了重大进展。用解析方法，可以从理论和实践两方面证明一般转子的不平衡力可以与环境完全隔离。此外，不同的主动轴承技术的一般性描述已经发现，然而，分析研究表明，即使没有力，大的转子偏转可能会发生在附近的自由转子共振。该项目同样侧重于转子的隔离，但还考虑了转子的变形。这是通过包括转子弯曲能量来实现的。因此，可以在每个操作点保持转子位移受限并消除所有共振。然而，轴承力和弯曲能量的独立最小化是不可能的。一个控制目标的性能的改善降低了另一个。这是一个Pareto问题。本项目提出的方法能够达到两个控制目标的极限情况，并可以执行两者的加权组合。这是通过最小化系统的弹性能量来实现的，弹性能量包括弯曲能量和轴承内的弹性能量，其与轴承力成比例。弹性能量的计算是使用通用刚度矩阵来执行的，该刚度矩阵应用弯曲能量和支承力的加权。这种方法的优点在于，仅需要一个控制器来达到两个控制目标，这使得能够在操作期间容易地改变权重。该方法不同于其中减振、使转子围绕其几何轴线旋转以及振动隔离被组合的方法，因为弯曲能量与旋转轴线的空间定位无关。建议的方法将进行测试，数值和真实的世界条件下的转子试验台。所获得的知识将使一般性的陈述的结构动力学的工作原理的主动压电轴承。

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.