TITLE:
Finite Element Method Applied to the Eigenvalue Analysis of Flexible Rotors Supported by Journal Bearings
AUTHORS:
Wéderley M. Miranda, Marco Tulio C. Faria
KEYWORDS:
Flexible Rotors; Fluid Film Bearings; Rotor-Bearing Systems; Finite Element; Eigenvalue Problem
JOURNAL NAME:
Engineering,
Vol.6 No.3,
March
7,
2014
ABSTRACT:
This work deals with a finite element
procedure developed to perform the eigenvalue analysis of damped gyroscopic
systems, represented by flexible rotors supported on fluid film journal bearings.
The rotor finite element model is based on the Timoshenko beam theory,
accounting for the shaft rotary inertia and
gyroscopic moments. The governing equations for the hydrodynamic journal
bearing are obtained through the Galerkin weighted residual method applied to
the classical Reynolds equation. A perturbation scheme on the fluid film
governing equation permits to obtain the zero-th and first order lubrication
equations for the bearings, which allow the computation of the dynamic force
coefficients associated with the bearing stiffness and damping. The
rotor-bearing system equation, which consists of a case of damped gyroscopic
equation, is rewritten on state form to compute the complex eigenvalues. The
natural frequencies at several operating conditions are obtained and compared
to the technical literature data. The influence of the effective damping on the
eigenvalue real part sign is analyzed for some examples of rotor-bearing
systems, showing how the stability conditions can be predicted by the
eigenvalue analysis. The procedure implemented in this work can provide useful
guidelines and technical data about the selection of the more appropriate set of bearing parameters for
rotating machines operating at stringent conditions.