Dynamic analysis of a planar multi-stage centrifugal pump rotor system based on a novel coupled model

The coupled rotor-dynamics issue is always one of the most important and difficult research for multi-stage pump system due to the complexity of multiple fluid-induced forces and multi-degree of freedom rotor model. In this paper, the Reynolds equation of journal bearing is solved by the finite difference method and corresponding fluid-induced force is obtained by small parameter method. In addition, the dynamic coefficients of annular seal are calculated according to bulk-flow model and perturbation method. Furthermore, a novel rotor system model fully considering the coupled effects of bearing and seal is proposed by matrix manipulation method. Then the coupled rotor-dynamics for multi-stage pump system is investigated subsequently based on the novel model. Finally, the Lomakin effect of annular seal is studied in detail. The calculated results indicate that the fluid-induced force of seal exerting on the rotor system should not be ignored in the calculation of coupled dynamic characteristics. Smaller length and clearance of annular seal are good for the stability of coupled rotor system. Compared with asymmetric structure, the symmetric sealing structure has a larger stability margin on condition of 'rigid rotor' status. Moreover, the Lomakin effect on stability presents linear superposition property. The proposed method can provide valuable reference for the design and modeling of multi-dimensional matrix system.