Unbalance-induced whirl of a rotor supported by oil-film bearings

Radhouane Sghir

doi:10.5802/crmeca.83

Abstract

This paper presents a nonlinear stability analysis of an unbalanced rotor-bearing system using the numerical continuation method and the numerical integration method. In this study, the effect of unbalance on journal motion is highlighted and a relationship is established between the bifurcation diagram of a balanced rotor and that of an unbalanced rotor. The results show that the stable operating speed range, the shaft motion type, the whirl speed and the chaotic motion occurrence depend on the unbalance level, the bearing geometry, the oil viscosity, and the speed range of unstable limit cycles existence.

Highlights

The unbalance force can generate several perturbations on the nonlinear phenomena within the hydrodynamic bearing and it can cause remarkable changes in the stability threshold compared to the balanced rotor
The bifurcation diagrams are determined using the numerical continuation as explained in detail in [7] and [8]
Bifurcation diagrams for a balanced rotor are determined by numerical continuation while the bifurcation diagrams of an unbalanced rotor are determined by numerical integrations

Summary

Introduction

The unbalance force can generate several perturbations on the nonlinear phenomena within the hydrodynamic bearing and it can cause remarkable changes in the stability threshold compared to the balanced rotor. Several investigations have focussed on the nonlinear dynamic analysis of rotating machines supported by hydrodynamic bearings [1,2,3,4,5,6,7,8] These studies have shown several phenomena that cannot be predicted and explained by linear analysis. The studies reported in [1,2,3,4] used the Hopf bifurcation theory to consider periodic oscillations in the vicinity of the critical stability speed for a rotor supported by two plain bearings These studies have shown that the Hopf point (the linear stability threshold) can bifurcate into stable limit cycles or unstable limit cycles. The bifurcation of the latter is produced at speeds above the stability threshold speed, while the bifurcation of unstable limit cycles occurs at speeds below the stability threshold speed

Results

Discussion

Conclusion