Nonlinear Vibration Analysis for a Jeffcott Rotor with Seal and Air-Film Bearing Excitations

Yuefang Wang,Xiaoyan Wang

doi:10.1155/2010/657361

Abstract

The nonlinear coupling vibration and bifurcation of a high-speed centrifugal compressor with a labyrinth seal and two air-film journal bearings are presented in this paper. The rotary shaft and disk are modeled as a rigid Jeffcott rotor. Muszynska's model is used to express the seal force with multiple parameters. For air-film journal bearings, the model proposed by Zhang et al. is adopted to express unsteady bearing forces. The Runge-Kutta method is used to numerically determine the vibration responses of the disk center and the bearings. Bifurcation diagrams for transverse motion of the rotor are presented with parameters of rotation speed and pressure drop of the seal. Multiple subharmonic, periodic, and quasiperiodic motions are presented with two seal-pressure drops. The bifurcation characteristics show inherent interactions between forces of the air-film bearings and the seal, presenting more complicated rotor dynamics than the one with either of the forces alone. Bifurcation diagrams are obtained with parameters of pressure drop and seal length determined for the sake of operation safety.

Highlights

The motion stability of high-speed rotor systems has drawn extensive attention throughout the past several decades
The nonlinear coupling vibration excited by a labyrinth seal and two air-film journal bearing is investigated through numerical simulations for high-speed centrifugal compressors
The results obtained with various rotation speeds and seal pressure drops show complexity of nonlinear vibration and bifurcation behavior in the displacements of the rotor system

Summary

Introduction

The motion stability of high-speed rotor systems has drawn extensive attention throughout the past several decades. Various studies of the oil-film forces were carried out to present nonlinear vibrations, for example, super- and subharmonic motions, of the rotor system related to the bearing dynamics 10–12. An effective model was proposed by Muszynska to express nonlinear seal forces based on experimental results 13, This model was later adopted by Ding et al in their study on the Hopf bifurcation of a symmetric rotor-seal system and by Hua et al who numerically obtain the nonlinear vibration and bifurcation characteristics of an unbalanced rotor-seal system. It is worth emphasizing that the interaction between the seal and bearing excitations should not be ignored since complicated, large-amplitude motions can be developed for rotors of compressors and turbines. The oil-film force proposed by Zhang et al 18, 19 is used to model the nonlinear, unsteady air-film excitation in the current study. The intricacy in the motion’s bifurcation presents complicated dynamics of the system in contrast to the rotors with either of bearing forces or of the seal excitations

Problem Modeling

Subharmonic Motions and Bifurcation Behavior

Conclusions