Dynamic behaviour of three-dimensional planetary geared rotor systems

Abstract

A six degrees of freedom dynamic model of a planetary geared rotor system with equally spaced planets is developed by considering gyroscopic effects. The dynamic model is created using a lumped parameter model of the planetary gearbox and a finite element model of the rotating shafts using Timoshenko beams. The gears and carrier in the planetary gearbox are assumed to be rigid, and the gear teeth contacts and bearing elements are assumed to be flexible. The modal analysis results show that torsional and axial vibrations on the shafts are coupled in the helical gearing configuration due to the gear helix angle whereas these vibrations become uncoupled for spur gearing. Mainly, the vibration modes are classified as coupled torsional-axial, lateral and gearbox for the helical gear configuration, and torsional, axial, lateral and gearbox for the spur gear configuration. Modal energy analysis is used to quantify the coupling level between the shafts and the planetary gearbox, highlighting the impact of the gearbox on certain mode families. Gyroscopic effects of the planetary gearbox are found to be of great importance in the gearbox dominated modes.