Abstract: The three-dimensional solid model of a turbo expander rotor system, supported by active magnetic bearing (AMB), is established by using ANSYS software. And the correct finite element model built with some appropriate methods is used for modal analysis. The modeling method of the AMB and their effect on the rotor system are explored. A set of measured controller parameters combined with the calculation method for the actual structure and stiffness-damping of the AMB are used to calculate the stiffness and damping coefficients of the AMB. By using these as input parameters, the first eight critical speeds and mode shapes of the rotor system are obtained through ANSYS modal analysis. Each of the first six critical speeds is far lower than the operating speed of the system, corresponding to the vibration modes of torsion, axial translation and rigid swing respectively. The other two critical speeds are close to the operating speed of the system, corresponding to the 1st bending vibration. The calculation results show that the rotor cannot run stably at the scheduled operating speed under the existing structure and parameter conditions, and the design needs improving. It is known from the analysis of the calculation result that the axial active magnetic bearing has certain effect on the dynamic characteristics of the rotor and it should not be ignored in some cases. The theoretical calculation results are basically in accordance with the experimental results. This research provides a theoretical basis for the rotor system design. The ideas and methods can be used as a reference for the study of dynamic characteristics of similar systems.

Key words: Active magnetic bearing, Critical speed, Modal analysis, Mode shape, Rotor