Multi-harmonic adaptive vibration control of AMB-driveline systems with non-constant velocity flexible couplings

Active Magnetic Bearings (AMB) have been proposed by many researchers and engineers as an alternative to replace traditional contact bearings in rotors and driveshafts. Such active, non-contact bearings do not have frictional wear and can be used to suppress vibration in sub- and supercritical rotor dynamic applications. One important issue that has not yet been addressed in previous AMB driveline control studies is the effect of non-constant velocity (NCV) flexible couplings, such as U-Joint or disk-type couplings. The NCV effects introduce periodic parametric and forcing actions that are functions of shaft speed, driveline misalignment and load-torque. Previous research has found that NCV couplings can greatly impact stability and cause significant harmonic excitation at integer multiples of the shaft speed. Thus, to ensure closed-loop stability and acceptable performance of any AMB-driveline with NCV couplings, these effects must be accounted for in the control law design. In this paper, a hybrid control law consisting of an analog PD feedback controller augmented with a slowly updating, multiple harmonic adaptive vibration control (MHAVC) is developed for a U-joint-driveline system supported by AMBs. The function of the PD controller is to ensure closed-loop stability and convergence of the MHAVC, while the MHAVC suppresses the steady-state vibration. Closed-loop stability, convergence, and performance are investigated over a range of shaft speeds for various misalignment and load-torque levels. It is found that there is an optimal range of P and D feedback gains that ensures both convergence of the MHAVC and maximizes the robust stability of the closed-loop system, with respect to NCV effects. Furthermore, it is demonstrated that the MHAVC can effectively suppress the multi-harmonic vibration induced by shaft imbalance and NCV coupling effects without knowledge of the disturbance input distribution.