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As an important part of the Roots hydrogen circulation pump, the rotor system has a significant impact on the dynamic characteristics of the Roots hydrogen circulation pump. In this paper, the finite element model of the rotor system of the Roots hydrogen circulation pump in the fuel cell hydrogen supply system was built, and the dynamic characteristics of the coupled dual-rotor system were studied. Through the modal analysis of the rotor system, the first six-order natural modes and natural frequencies of the uncoupled single-rotor system and the coupled dual-rotor system were obtained. The harmonic response characteristics of the rotor system were analyzed on the basis of the modal analysis, and the harmonic response characteristic curves of the gear and the edge of the impeller were obtained.