Active Magnetic Bearings for High Speed Spindle Design With Nonlinear Time-Frequency Control

Abstract

A novel concept applicable to the control of spindles at high speed is developed by using active magnetic bearings (AMBs) that are non-contact and of low vibration. Though former studies are abundant and demonstrating promising potentials, however, two major issues hamper the broader application of AMBs. The first is the disregard for the gyroscopic effect and geometry coupling that influence the magnitude as well as distribution of the electromagnetic force in AMBs. Not considering the two has a significant implication for the proper control of AMBs. This paper considers the gyroscopic effect and explores the geometry coupling of the electromagnetic actuators to the formulation of a comprehensive nonlinear AMB-rotor model. The model provides the basis for the creation of a novel time-frequency control algorithm whose derivation requires no linearization or mathematical simplification of any kind, thus allowing the model system to retain its true fundamental characteristics. Unlike proportional-integral-derivative (PID) controllers that are dominant in most if not all AMB configurations, the controller developed for the research is inspired by the wavelet-based nonlinear time-frequency control methodology that incorporates the basic notions of online system identification and adaptive control. Due to the fact that dynamic instability is characterized by time-varying frequency and non-stationary spectrum, the control of AMBs needs be executed in the time and frequency-domain concurrently to ensure stability and performance at high speed. Wavelet filter banks and filtered-x least-mean-square (LMS) algorithm are two of the major salient physical features of the controller design, with the former providing concurrent temporal and spectral resolutions needed for identifying the nonlinear state of motion and the latter ensuring the dynamic stability of the AMB-rotor system at extremely high speed. It is shown that the vibration of the rotor is unconditionally controlled by maintaining a mandatory 0.55 mm air gap at 187,500 rpm subject to a tight spatial constraint (tolerance) of the order of 0.1375mm, which is the 25% of the air gap.