Abstract: Speed conversion has posed a significant impact on the stability of the mixed flow pump in the operation of variable speed. Taking the mixed flow pump as the research object, this study aims to collect the displacement signals of shaft vibration and pressure pulsation inside the pump under different speed conversion modes using a synchronous acquisition system. A systematic analysis was made to clarify the influence of speed conversion modes on the stability of mixed-flow pumps. The results show that the position of the shaft center was inconsistent with before the start of speed conversion at the end of speed conversion. There was the smallest offset distance of the quartic power speed conversion, which was 0.075 mm. The vortex motion of shaft vibration was the most stable under the speed conversion to the quartic power, compared with the rest. In the quartic power speed conversion, the ratio of S_(p-p) to ∆D was only greater than 0.33 at the end of the speed conversion. The maximum kurtosis of the two-dimensional joint was 5.67 (quarter power), 5.61 (linear), and 5.4 (quartic power), respectively, for the three-speed conversion modes. Among them, the proportion of positive joint kurtosis for the shaft vibration was 70% (quarter power), 44% (linear), and 4% (quartic power), respectively. The quartic power speed conversion effectively improved the mechanical impact of shaft vibration. The main frequency of shaft vibration was the rotational frequency f_n under different speed conversion modes. The proportion of high amplitude region was 87.5%, 62.5%, and 12.5% in the descending order of the index under the speed conversion mode. The high amplitude and high-order harmonic frequencies of shaft vibration were concentrated mainly in 2f_n among the three-speed conversion modes. Phase resonance caused the amplitude of higher-order harmonics of pressure pulsation inside the impeller to be stronger than f_BPF(passing frequency of impeller blades) during speed conversion. The proportions of high amplitude areas in 12f_n under the three-speed conversion modes were 75%, 50%, and 5% in the descending order of their indices. The main frequency of shaft vibration velocity still remained in the time-frequency of pressure pulsation inside the pump during speed conversion, indicating the high impact of shaft vibration on pressure pulsation. Finally, the improved TOPSIS was used to quantitatively evaluate the operational stability of mixed-flow pumps under speed conversion modes. The results showed that the operational stability of the mixed flow pump gradually deteriorated, as the speed increased. There was the smallest stability index of the quartic power speed conversion. The mixed flow pump has the best stability during the quartic power speed conversion, only considering shaft vibration and pressure pulsation. The findings can provide a strong reference to improve the stability of mixed flow pumps during speed conversion.