A Nonlinear Model of Rotor-Bearing-Seal System Associated With Leakage Through the Labyrinth Seal

Abstract

A nonlinear mathematical model for the rotordynamics of the rotor under the influence of the leakage air flow through a labyrinth seal was established in the present study. An interlocking seal was chosen for study. The rotor-bearing-seal system with four degrees of freedom was modeled as Jeffcot rotor subject to the aerodynamic force induced by the leakage flow through the interlocking seal and the oil-film force induced by the oil flow in the journal bearing. Particular attention was placed on the spatio-temporal variation of the aerodynamic force on the rotor surface in the coverage of the seal clearance and the cavity volume, which was specifically delineated by using Muzynska model and the perturbation analysis, respectively. The governing equation of the rotordynamics, into which the aerodynamic force integrated over all seal clearances and cavity volumes was incorporated together with the oil-film force, was solved by using the fourth-order Runge-Kutta method to obtain the orbit of the whirling rotor. Stability of the rotating rotor was inspected by using the orbital motions and the phase trajectories. The influence of the leakage air flow through the interlocking seal on the whirling rotor was described in terms of the rotating speed and the seal clearance. The results convincingly demonstrate that the destabilization of the rotor-bearing-seal system was reduced due to the aerodynamic force induced by the leakage air flow through the interlocking seal.