Transverse Vibration of Rotor Systems Integrated with Active Magnetic Bearings

In previous chapters, we studied analyses, measurements, identification, and condition monitoring in rotor-bearing systems. However, the recent trend is to have a control system integrated into the rotor system itself. This not only acts as a bearing to support the static load but also acts as an active control to keep the vibration level at a minimum so that undue stresses that could cause catastrophic failures are not developed. Moreover, it can be used as an exciter for condition monitoring of machinery; in fact, in smart condition monitoring, the controlling force (with vibration and current information) can also be used for finding the health of the machine. Such active magnetic bearings (AMBs) work on the concept that the rotor floats on the air and no metal-to-metal contacts exist. It also avoids lubrications and sealing systems to maintain a clean environment. In this concluding chapter, the important topic of AMBs (more toward the rotordynamic aspect of it) is covered so that readers are acquainted with recent developments in this area. It covers an introduction to the basic principles of AMBs, basic theories required in electromagnetism, and controls, especially those applied to rotors. Additionally, the classification of AMBs and their application areas are covered. Transfer functions (TFs) are developed for simple single-degree-of-freedom (single-DOF) and two-degree-of-freedom (two-DOF) rotor systems with AMBs for analyzing the stability of the system, which can be extended to multi-degree-of-freedom (multi-DOF). For illustration purposes, only the simple proportional-differential (PD) and proportional-integral-derivative (PID) controllers are considered. Subsequently, a simple procedure for the tuning of control parameters of these controllers is described. The performance of AMBs is obtained by controlling steady-state unbalance responses for various cases of rotor systems (e.g., single-DOF, two-DOFs, and four-DOFs) while considering the rotor rigid and for n -DOFs while considering flexible rotors. Stability analysis through Nyquist plots is given in detail for a two-DOF system. In the modeling of the n -DOF rotor system, the versatile finite element method analysis is used, which will enable the basic concepts introduced here to be applied to more practical rotor-bearing systems.