In order to study the dynamic characteristics of the rotor bearing system with gas foil bearings,the classical finite element rotor dynamics models were set up based on the rotor system of the high speed turbo expander.The corresponding critical speed of the rotor system was obtained and the influence of bearing stiffness on the critical speed of the rotor system was analyzed through the numerical calculation model.The rotor swirl frequency with the change of speed was revealed,and the influence of bearing stiffness and damping characteristics on stability of bearing was discussed.In order to describe the motion state of the rotor more accurately,the timedomain analysis of the rotor system was carried out,and the orbit of rotor center and the corresponding frequency analysis was obtained,it was found that the results of time-domain analysis matched well with the experiment results.The results show that the wide operating speed range and better stability are obtained in the high speed turbo expander due to the excellent stiffness and damping characteristics of foil gas bearings,and the motion state of the rotor is described more accurately by applying time-domain analysis,which is verified by the numeral calculations.