This paper presents the single objective optimization and the multi-objective optimization for a flexible rotor system with magnetic bearings. The weight of rotor shaft and the transmitted forces at the magnetic bearings are minimized either individually or simultaneously under the constraints on the critical speeds and the control currents of magnetic bearings. The design variables are the cross-sectional area of the shaft, the bias currents of magnetic bearings, and the positions of the disk and the magnetic bearings. The dynamic characteristics are analyzed using the generalized polynomial expansion method and the sensitivity analysis is also studied. For single objective optimization, the method of feasible directions (MFD) is applied. For multi-objective optimization, the methods including the weighting method (WM), goal programming method (GPM), and the fuzzy method (FM) are employed. It is found that the system design can be significantly affected by the choices of the bias currents of magnetic bearings, the position of the disk with unbalance and the magnetic bearings. The results also show that a better compromized design can always be obtained for multi-objective optimization.

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