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In this paper, a multi-field coupling simulation model, including the motor, shaft, and pump, is established to analyze the motor's influence and the shaft on the pump's operating status. First of all, different forms of simulation calculation models are established according to each device's characteristics. Then, the Predictor-Corrector Newmark-β method (PC Newmark-β method) is used to calculate the operating status of the motor, shaft, and pump under mutual influence. Finally, the validity of the simulation model is verified by comparing the experimental data. The results show that the centrifugal pump, shaft, and motor should be viewed as a complete system to analyze. The torque and speed of different equipment are interrelated and influenced. In addition, the dynamic characteristics of the shaft will also cause the fluctuation of the pump's operating speed. The fluctuation of the centrifugal pump impeller's rotational speed further affects the characteristics of the pressure pulsation on the wall of the centrifugal pump, which is finally reflected in the vibration characteristics of the pump casing.