Dynamic Behaviors of Geared Rotor System in Integrally Centrifugal Compressor

Abstract

In this paper, a five-shaft geared rotor system coming from a prototype of centrifugal compressor is taken to investigate the determination of its critical speeds and unbalance response analyses. And also its complicated dynamic characteristics due to the interaction of the multiple rotors in paralleled arrangement and coupled by different gears are studied. A finite element model of the geared rotor system is established, where the rotating beam elements (6 DOFs at each node) are used and the linear mesh stiffness of engaged helical gears is involved. Then, Campbell diagrams of the rotor system with different mesh stiffness are calculated using the image eigenvalues of the coefficient matrices based on the FE model. To improve the computational efficiency, an analytical model is derived to calculate the coupling dynamic response, and the effect of mesh coupling is analyzed. Finally, vibrations of shafts near the bearing are measured on test rig to verify the calculated vibration phenomena of the whole machine. Comparing with the results without the mesh effort, some new critical speed lines appear in the system’s Campbell diagram due to involving of gear mesh stiffness. In addition, significant coupling phenomenon shows in the Campbell diagram that the critical speed lines corresponding to different modes transform sharply from one to the other in some richly concentrated areas, where the lateral vibration, axial vibration, and the meshing vibration are mixed at the same time. The rotating frequency of any shaft can affect the vibration frequencies of any other shafts, and the proportions of the three frequencies are different at different input speed. The test signals from the test rig validated the theoretical model, which shows the modeling method in this paper can describe the dynamics of the geared rotor system well. The dynamic analysis and design strategy based on the separated single-shaft rotor systems may lose some important dynamic properties and might cause failures in the machine operation. And the geared rotor system of the integrally centrifugal compressor is more complex not only for its multi-shafts coupled by the helical gears, but also for all the output shafts always suffering changed loads in processing. So the interaction and restriction among all the paralleled shafts must be considered.