Dynamic Modeling and Analysis of a 3-DOF Ultra-precision Positioning Stage with Air Bearinga

This paper presents an approach to investigate the dynamic characteristic of a 3-DOF stage. The stage is levitated by high-stiffness air bearing and the positioning accuracy can reach nanometer level. The mover of the stage, whose lowest order nature frequency is much higher than control bandwidth, is regarded as rigid body. The air bearing is equivalent to a series of linear and torsion springs, so that the dynamic performance of air bearing can be simulated and the impact to the positioning accuracy caused by air bearing can be studied. Then, an analytical modeling method of the stage based on analysis of rigid body finite rotation is proposed, and the general equation of dynamics with virtual power form is obtained. By using method, the vibration characteristics of the stage when positioning are obtained. The modal experiment is performed on the stage. The experiment results are in good agreement with analysis results, which has verified the equivalence method of the air bearing and the dynamic modeling method of the stage.