Effect of a Planetary Gearbox on the Dynamics of a Rotor System

Abstract

The dynamic analysis of rotors with bladed disks has been investigated in detail over many decades and is reasonably well understood today. In contrast, the dynamic behaviour of two rotors that are coupled via a planetary gearbox is much less well understood. The planetary gearbox adds inertia, mass, stiffness, damping and gyroscopic moments to the system and can strongly affect the modal properties and the dynamic behaviour of the global rotating system. The main objective of this paper is to create a six degrees of freedom numerical model of a rotor system with a planetary gearbox and to investigate its effect on the coupled rotor system. The analysis is based on the newly developed finite element software “GEAROT” which provides axial, torsional and lateral deflections of the two shafts at different speeds via Timoshenko beam elements and also takes gyroscopic effects into account. The disks are currently considered as rigid and the bearings are modelled with isotropic stiffness elements in the translational and rotational directions. A novel planetary gearbox model has been developed, which takes the translational and rotational stiffness and the damping of the gearbox, as well as the masses and inertias of the sun gear, ring gear, planet gears and carrier into account. A rotating system with a planetary gearbox has been investigated with GEAROT. The gearbox mass and stiffness parameters are identified as having a significant effect on the modal behaviour of the rotor system, affecting its natural frequencies and mode shapes. The higher frequency modes are found to be more sensitive to the parameter changes as well as the modes which have a higher deflection at the location of the gearbox on the rotor system. Compared with a single shaft system, the presence of a gearbox introduces new global modes to the rotor system and decouples the mode shapes of the two shafts. The introduction of a planetary gearbox may also lead to an increase or a reduction of the frequency response of the rotor system based on gear parameter values.

Dynamic behaviour of three-dimensional planetary geared rotor systems

“…Moreover, making the helix angle zero cancels the coupling term between the axial and torsional directions, resulting in uncoupled torsional, axial and lateral modes. In the case of helical gears, axial thrust forces can create unexpected torsional excitations on the shaft, which can be of great significance for geared turbofan engines where planetary gearboxes are commonly used [56].…”

“…Among these studies, the finite element method has become a popular tool for the dynamic analyses [41,42,44,45,48,49]. Although the dynamic behaviours of spur and helical geared rotor systems are well understood today, less research has been carried out to understand the dynamic behaviour of planetary geared rotor systems [50][51][52][53][54][55][56][57] . So far, one DOF torsional [50][51][52], five DOF lateral-torsional [53] and six DOF lateral-torsional-axial [54][55][56][57] models of planetary geared rotor systems have been investigated for wind turbine and geared turbofan engine applications.…”

“…Although the dynamic behaviours of spur and helical geared rotor systems are well understood today, less research has been carried out to understand the dynamic behaviour of planetary geared rotor systems [50][51][52][53][54][55][56][57] . So far, one DOF torsional [50][51][52], five DOF lateral-torsional [53] and six DOF lateral-torsional-axial [54][55][56][57] models of planetary geared rotor systems have been investigated for wind turbine and geared turbofan engine applications. From this research, only two of the six DOF models have taken gyroscopic effects into account for geared turbofan engine applications [56,57].…”

“…So far, one DOF torsional [50][51][52], five DOF lateral-torsional [53] and six DOF lateral-torsional-axial [54][55][56][57] models of planetary geared rotor systems have been investigated for wind turbine and geared turbofan engine applications. From this research, only two of the six DOF models have taken gyroscopic effects into account for geared turbofan engine applications [56,57]. Wei et al [57] considered the forced vibration analysis of a geared turbofan engine due to loss of a blade creating rotating imbalance.…”

“…Wei et al [57] considered the forced vibration analysis of a geared turbofan engine due to loss of a blade creating rotating imbalance. Tatar and Schwingshackl [56] used a low fidelity model of the planetary gearbox, including uncoupled gearbox stiffness, to investigate the planetary gearbox impact on the dynamics of the rotor system. The modal behaviour of planetary geared rotor systems is still only partially understood, and more work is needed to provide a full understanding of the dynamic behaviour of such systems.…”