Pump rotor 2 DOF reduced model and unstable onset speed evaluation

Abstract

Because horizontal multi-stage pumps have journal bearings and a balancing piston with narrow gap, it is needed to prevent self-excited vibrations caused by fluid forces in these gaps. For the rotor system, because it is challenging to find the stability limit with a strict model (1 D-FEM), it is better to reduce degree of freedom by fixing nodes of journal bearings and the balancing piston when one is looking to improve the stability limit. This paper suggests a method for finding the stability limit by 2 DOF model, and provides factors affecting the stability limit for horizontal multi-stage pumps. First, the rotor shape and the stiffness and damping of journal bearings and the balancing piston are configured and the rotor system is reduced to 2 DOF by constrained mode synthesis method based on the configurated shape and coefficients. By comparing the solutions calculated with 2 DOF and 1D-FEM, it is confirmed that 2 DOF models are suitable for unstable vibration analysis. Then, the average whirl λ_eqΩ is calculated by applying Bently-Muszynska model to the coefficients of the journal bearings and the balancing piston and it is concluded that the natural frequency ω_n becomes equal to the average whirl λ_eqΩ at the stability limit. Finally, the influence of the natural frequency ω_n and the average whirl λ_eqΩ on the stability limit is analysed for different cases.