Active magnetic bearing(AMB) is an electromagnetic device to suspend a rotor without any mechanical contact and lubrication by using attractive electromagnetic forces controlled by electronic control system. Mechanical non-contact provides the possibility of high circumferential speed and no friction and wear in the magnetic bearing. In particular, no lubrication considerably reduces routine maintenance, eliminates sealing requirements, and make it possible to operate in severe environment such as vacuum, steam, cryogenics, sterile and corrosive atmosphere. It can be compensated for tool wear, control shaft position, and adjust stiffness and damping during operation of the machinery by electronic control. AMBs have been increasingly utilized for many industrial applications because of their excellent advantages over conventional mechanical bearings.
The AMB requires more accurate design and prediction of dynamic behavior to improve its performance, reliability and stability as a component of overall rotor bearing system with industrial application growth. However AMB systems often show discrepancies between the predicted and the measured dynamic behaviors due to the inaccurate and complicated modeling associated with the frequency characteristics of power amplifiers and electromagnets, and magnet flux loss and delay such as eddy current, leakage and fringing effects. Therefore accurate system parameter identification becomes a crucial factor when it is necessary to improve the system performance and stability making some prediction on the system. The identification of AMB system is mainly concerned with the dynamic characteristic analysis of the controlled system, the use of magnetic bearings as exciters, and the development of algorithm for parameter identification. But most studies on system identification in the past are confined to parameter identification fore controller design without considering dynamic characteristics of the rotating machinery or simple comparison of the experimental and theoretical results. An unbalance on a rotor in the rotating machinery causes alternating forces of the bearings and synchronous whirl motions of the shaft. So far many studies for unbalance response control have been mainly performed in two ways. One is to suppress the unbalance response of the shaft. Another is to block the synchronous vibration from feedback by adding a band-reject filter circuit in the feedback loop or to generate a rotating magnetic force to counteract the unbalance force. The latter may bring about the instability of system or requires the accurate estimation of unbalance.
In this work, the in-situ identification of a four-axis AMB system in laboratory is performed by using magnetic bearings as exciters and the unbalanc e response of the system is controlled by optimal control with frequency-shaped cost functional. An AMB system is developed, which is equipped with two sets of piezoelectric type force transducers so that in-plane forces generated by a pair of magnetic bearings can be measured. The rotor is excited by in-plane forces generated by each radial magnetic bearing, and the excitation signals are downloaded by the host PC. In the test, magnetic bearings are used as exciter as well as actuators for feedback control. The parameters of power amplifier and electromagnet unit are identified from the relation between input voltage and output current of power amplifier. The current and position stiffnesses of magnetic actuators are accurately estimated from magnetic force, current and displacement signals measured by built-in force transducers, current sensors and eddy current type proximity probe respectively. In particular, the physical properties of the AMB system are identified from directional frequency response functions(dFRFs) obtained by complex modal testing, using magnetic bearings as exciters while the system is in operation. It has been well known that, whereas both forward and backward modes in the classical FRFs appear over one-sided frequency region, resulting in overlapping of the otherwise physically well separated modes and they are completely separated in the dFRFs for isotropic rotor system. Here the bearing parameters of the AMB system are directly extracted by solving a nonlinear regression problem based on an output error formulation between the measured and theoretically computed directional frequency response matrices(dFRMs) with the inertia properties. The experimental results show that the dFRF is a powerful tool for the identification of bearing properties as well as modal parameters of the system. In addition, it is also shown that the presence of anisotropy and asymmetry can be clearly diagnosed by using dFRFs. The unbalance response of AMB system is controlled by optimal control with frequency-shaped cost functional. Because the cost functional of this control is expressed in the frequency domain with frequency dependent weighting matrix being penalized over specific range of frequencies, this control method provides the system with rotational speed dependent feedback gains, i.e., low feedback gains in high rotational speed and high feedback gains in low rotational speed. This control method does not require the accurate estimation of unbalance as well as not bring about the instability of the system. This control method is proved to be superior through numerical simulation and experiment.
