A Simple (1-Flexible Rotor) Model That Shows Bull Gear Runout As a Source of Subsynchronous, Lateral, Vibration in Integrally Geared Compressor (IGC) Pinions

Abstract

A new flexible-pinion-shaft rotor model is presented to predict the response of the pinion shaft of an integrally geared compressor (IGC). The motion of the pinion shaft is driven by: (1) its own imbalance and (2) the axial reaction force developed by relative axial motion at the thrust collar (TC) that connects it to the pinion. The axial reaction force at the TC arises because of the relative axial motion between the pinion shaft and the bull gear (BG) at the overlapping area of the TC. The relative axial motion arises because of: (1) absolute axial motion of the pinion (assumed to be a rigid body), (2) pitch and yaw motion of the pinion at the TC, and (3) absolute axial motion of the BG at the TC overlap area. Because the axial reaction force acts at a radial distance from the mass center of the TC disk, it creates moments that couple the relative axial motion of the pinion and BG shafts to the radial motion of the pinion. The present model includes the local flexural stiffness of the BG. Excitation for the model is provided by: (1) runout from the BG at its running speed, Ω, acting through the axial reaction force of the TC, (2) runout from the pinion at its running speed, ω, acting through the axial reaction force of the TC, and (3) pinion TC mass imbalance at ω. Measured axial runouts of the BG and TC were taken from a test rig at the authors’ laboratory. Predictions for the TC oil-film axial stiffness and damping come from a proprietary Reynolds equation solution to the TC oil-film. The local axial stiffness of the BG at the overlap area was obtained from a finite element analysis of the authors’ test rig. The base rotordynamic model for the pinion was provided for a production IGC pinion by an IGC manufacturer including the bearings and structural dynamics model. Waterfall plots are presented from the model’s predictions of radial motion at the IGC’s Stage 1 compressor impeller. The response is dominated by synchronous response at the pinion speed, ω, and tracking subsynchronous response at the BG speed, Ω. The response at ω comes from the pinion’s imbalance, not the pinion runout at the TC. The response at Ω comes from the BG runout acting across the TC. The IGC manufacturer’s representatives state that predictions from the model are consistent with measurements from real IGCs, particularly in regard to the presence (and amplitudes) of tracking subsynchronous response amplitudes at the BG frequency. Obviously, more detailed models can be developed for the rotordynamics of IGCs, but the authors feel that this relatively simple, one-rotor model, is adequate to predict the observed tracking phenomena in IGCs. The analysis can be produced by modifying an existing rotor code or by simply downloading the rotor’s [M], [K], and [C] matrices over a range of speeds and then using MATLAB or similar codes.