Analysis and identification of the additive and multiplicative fault parameters in a cracked-bowed-unbalanced rotor system integrated with an auxiliary active magnetic bearing

Abstract

The present work brings out a novel model based analysis and identification of the additive and multiplicative fault parameters in an active magnetic bearing (AMB) controlled rotor system. In mathematical modeling, the unbalance is considered as an additive fault, whereas the effect of shaft residual bow on crack are considered as multiplicative faults. In equations of motion (EOMs), the multiplicative fault parameters appear in a product form, which is much more challenging to handle as well of the practical importance for its analysis and identification. EOMs have been developed considering the influences of the external as well as internal (rotating) damping, and the gyroscopic effect due to axially offset disc on the rotor-AMB system. The shaft has a transverse fatigue crack (breathing model) and an initial shaft bow. The proposed rotor-AMB model uses a PID (proportional-integral-derivative) controller to regulate the supply currents to the AMB to actively control the vibration of the system due to inherent faults. In the response analysis, the effects of rotor faults on the rotor displacements and AMB control currents are shown in full spectrum. Furthermore, an identification methodology has been developed from complex frequency domain EOMs to facilitate the estimation of the additive and multiplicative fault parameters in a cracked bowed rotor system. To comply with the practical aspects, different measurement noises and modeling errors have been added to test the robustness of the proposed algorithm.