A nonlinear transient dynamic model for the shaft system of mixed-flow pumps integrating transient head theory: a speed conversion case

To address the strongly nonlinear and nonstationary characteristics of shaft vibration (SV) observed in mixed-flow pump (MFP) during speed conversion, this study investigates the transient dynamic mechanisms governing the rotor system response. A shaft system dynamic model (SSDM) is established using the lumped parameter method, in which the axial hydraulic thrust (AHT) is dynamically corrected by incorporating transient head (TH) theoretical calculation model (THTCM). The differential equations of motion are solved using nonlinear numerical methods, and the model is systematically validated against experimental data. The results indicate that the proposed THTCM can effectively describe the dynamic evolution of TH during speed conversion process, with good agreement between calculated and experimental results. Deviations in both speed rise and speed drop processes are controlled within ± 10 %. The established SSDM successfully reproduces the main characteristics of SV in both the time and frequency domains. Good consistency is achieved between the simulated and experimental testing signals in terms of amplitude levels and the evolution of the dominant frequency. The discrepancies remain within reasonable limits under both steady-state and transient operating conditions. Comparative analyses performed with and without the proposed THTCM-corrected AHT demonstrate that the introduction of AHT into the SSDM reduces the prediction error by 1.17 %-25.62 % under different speed conversion conditions, thereby improving the simulation accuracy of transient SV responses. A representative comparison with a fluid structure interaction model based on the finite element method indicates that the proposed SSDM involves a substantially smaller computational scale and has the potential to support efficient evaluation of transient SV responses. The findings provide reliable theoretical support for SV mechanism analysis and operational optimization of MFPs under transient conditions.