The modeling of the fractional-order shafting system for a water jet mixed-flow pump during the startup process

The modeling of traditional shafting systems mainly pays attention to the running states in the small fluctuations. However, the dynamic behaviors of the shafting system for a water jet mixed-flow pump in the transient states play a key role in maintaining safety and stability. In this paper, a dynamic mathematical model of the shafting system for a water jet mixed-flow pump during the startup process is established considering fractional-order damping forces, rub-impact forces and misalignment faults. Furthermore, we analyzed the characteristics of the above system during the startup process with different impact forces through the above fractional-order mathematical model. Moreover, the effect of the fractional-order on the startup process is also studied by bifurcation diagrams, time waveforms and phase orbits. Fortunately, some laws are found from the numerical simulation results. Finally, compared with the physical experimental data, the fractional-order model of the shafting system for the water jet mixed-flow pump has certain advantage and effectiveness.