Abstract
This article aimed to investigate the dynamical behaviours of a controlled asymmetric rotating shaft system when the rub-impact forces between the rotor and stator occur. A nonlinear position-velocity controller is proposed to control the system's lateral vibrations. The suggested control algorithm is integrated into the shaft system via four electromagnetic poles that are fixed on a fixed frame and act as active actuators. The dynamics of the asymmetric shaft, the electromagnetic coupling between the magnetic poles and the rotating shaft, and the rub-impact forces between the rotating shaft and the stator are included in the studied model. The derived dynamical model is firstly analyzed as a continuous nonlinear dynamical system utilizing the asymptotic analysis while neglecting the rub-impact forces. Different response curves are plotted to predict the conditions under which the rotating shaft may suffer from the rub-impact forces. Secondly, the whole system model is analyzed numerically as a discontinuous nonlinear dynamical system utilizing the bifurcation diagram, Poincaré map, and frequency spectrum. The main obtained results illustrated that the rub-impact forces occurrence between the uncontrolled rotating shaft and the stator induces unbounded oscillation that can destruct the rotating shaft. However, the suggested control algorithm has improved the vibratory behaviours of the considered system via minimizing the oscillation amplitudes and preventing the rub-impact forces for a wide range of the disk eccentricities. Moreover, it was found that the rotating shaft can whirl in a full annular rub mode with bounded oscillations if the proposed controller fails to prevent the rub-impact forces occurrence due to either the large disk eccentricity or the large asymmetric stiffness coefficients.