Dynamic modeling and nonlinear analysis for lateral-torsional coupling vibration in an unbalanced rotor system

Imbalance is a common problem in rotating machinery. In addition to the unbalanced force, lateral-torsional coupling vibration can also be induced by the mass imbalance. However, the related nonlinear behaviors and coupling mechanism are still not well understood, especially when lateral-angular motion is incorporated in a model. In this paper, a model for coupling lateral and torsional vibrations of an unbalanced rotor is developed by Lagrangian dynamics, in which the coupling of lateral-angular and torsional motions is first considered. Based on the model, the lateral responses, torsional responses, coupling excitation characteristics and coupling mechanisms are investigated in detail. The results show that mass imbalance can lead to nonlinear timevarying characteristics in the dynamic equations. When the imbalance is small, the lateral vibration can be degraded to a traditional imbalance problem. Meantime, very small transient torsional vibration with torsional natural frequency ft in frequency domain can be observed at the beginning. The coupling excitation applying on the torsional DOF caused by the lateral synchronous whirling is demonstrated to behave the feature of static torque, consequently, there actually exists no steady-state torsional vibration in small unbalanced rotor. Under largely unbalanced conditions, both resonant and unstable behavior can be observed in the lateral and torsional responses. The combined resonance is induced by the lateral translational-torsional coupling, while the instability is caused by lateral angular-torsional coupling. By increasing the lateral damping, the instability phenomenon can be suppressed, and the lateral amplitude in the resonance region can be effectively reduced.