Modal Correction And Analysis Of A Flexure-based Positioning Mechanism For Projection Lithographic Lens

The projection lithographic lens are the key components of the lithograph machine. Inorder to meet the strict wave aberration demand and hence assure the transfer accuracy of theexposed images, adjustable lens are set and adjusted specially to eliminate the waveaberration brought by the manufacturing and assembling errors. As the main component foradjusting the lens, the flexible positioning mechanism is a Multi-DOF compliantmicro-precision positioning mechanism, which works relying on the elastic deformation ofthe flexible hinge and the piezoelectric–drive technology. Because the flexible hinges havesmall stiffness and strong responses to the environmental vibrations, dynamic characteristicsof the mechanism should be analyzed for the lens to produce stable and qualified images.Therefore, this thesis conducts the following researches in four aspects.(1) This thesis analyzes the principle and structure properties of the flexible positioningmechanism, and then studies its modeling errors based on comparing the FEA(Finite ElementAnalysis) results with the modal test results. Then according to the harmonic responseanalysis method, the object function, the modified variables and the constraint conditions aredecided to assure the modified modeling error within5%and hence meet the accuracydemand.(2) Based on the theory of the fixed joints’stiffness and damping, the stiffness of the boltconnection face is derived. Using the results as the initial values to modify the variables, aconverged solution is obtained. It varies within10%of the theoretical solution, proving thevalidity of the derivation and the effectiveness of the modify method.(3) Based on the modified model, the relationship between the actuation force and thedisplacement is analyzed to tell the mechanism’s working space. The results show that theeffective strokes meet the design demand in the X, Y, Z directions, respectively.(4) The random vibration analysis is conducted and the important aberrations areanalyzed. The results show that the modified model can correctly reflect the mechanism’sresponse to the environmental vibrations and its influences to the aberrations. This canprovide important basis for the future structure optimization, lens’ deformation analysis aswell as the vibration compensation and control.