On the steady-state forward and backward whirling motion of asymmetric nonlinear rotor system

Abstract

Nonlinear lateral vibrations and the corresponding whirling motions of asymmetric horizontally supported rotor system are investigated within this article. The rotating shaft is modeled as a two-degree-of-freedom nonlinear Jeffcott-rotor system. The nonlinear restoring force of the rotating shaft, asymmetry in both the linear and nonlinear stiffness coefficients, the disk weight, the disk eccentricity, and the eccentricity orientation angle are included in the studied model. The asymptotic analysis is utilized to derive the autonomous amplitude-phase modulating equations that govern the system lateral vibrations in the horizontal and vertical directions. Bifurcation diagrams of both the system vibration amplitudes and the corresponding phase angles are obtained. The main acquired results revealed that the existence of the asymmetry in the rotating shaft stiffness coefficients widens the spinning speed interval at which the system may have more than one stable solution. In addition, increasing the linear asymmetrical stiffness coefficient can eliminate the system backward whirling motion. Finally, numerical confirmations for the obtained analytical results are performed that illustrated their accuracy in the prediction of the system vibration amplitudes and the whirling direction whether forward, backward, or along a straight line.