Abstract
This article aimed to control the lateral vibrations of an asymmetric vertically supported nonlinear rotating shaft system. The system is molded as a two-degree-of-freedom nonlinear system having external and multi-parametric excitations. A combination of both the linear and nonlinear proportional-derivative controller is proposed to control the system dynamics. Four poles active magnetic bearing system is utilized as an active actuator through which controllable magnetic forces are applied to stabilize the considered system. The mathematical model that governing the whole system dynamics is derived. Applying the asymptotic analysis, the slow flow equations of motions are obtained. The system oscillatory behaviors before and after control are explored. The main acquired results showed that the asymmetric rotating shaft system without control could exhibit large vibration amplitudes even for very small eccentricity because asymmetry induced parametric excitations. Moreover, the system may have a single-stable solution, bi-stable solutions, tri-stable solution, or quadri-stable solutions at the same spinning-speed depend on the shaft angular velocity (Ω). Besides, the system asymmetry is resulting in the appearance of backward whirling motion besides the forward whirling one. However, the proposed nonlinear controller showed its capability of eliminating the all mentioned undesired phenomena, where the controlled system responded as a linear one with very small forward whirling motion only. Finally, the conditions to prevent the occurrence of rub/impact force between the rotating shaft and the electromagnetic pole legs are discussed.
•The nonlinear lateral vibration of the asymmetric rotating shaft is controlled using a nonlinear PD-controller.•The best control method is a combination of both a linear proportional-derivative and cubic-velocity feedback controller.•The proposed controller can force the system to respond as a linear one with a single periodic attractor.•The designed control system can operate properly as long the shaft eccentricity is lower than the critical value.