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Modal analysis of a high-precision magnetic suspension stage

Traditional one layer magnetic suspension stage has limited planar traveling ranges. In order to have long traveling ranges and high-precision in x-y directions, a dual magnetic suspension stage with planar motions is proposed in this paper, which the two layers of stages are stacked one on another with the similar configuration. The stage is strongly coupled not only within each layer but also between the two layers. The dynamic equations of the coupled system are derived by Lagrange equation and the modal analysis is finished. The modal parameters of the 10 degrees of freedom (DOF) of the dual stage are all derived from the dynamic model. The computation results show that different mode shapes have different effect on each DOF. However, the natural frequencies and the shapes have little relation to the position and orientation of the upper magnetic suspension stage. The dynamic models and the results of the modal analysis of the dual stage are helpful for designing the optimal mechanical structure, which can improve the positioning precision. And it also can serve for the design of the controller and the selection and optimization of the controller variables.