Abstract
A multibody dynamic model is developed for dynamic analysis of a 5-DOF flexure-based nanopositioning stage in the projection optical system of the semiconductor lithography in this paper. The 5-DOF stage is considered as an assembly of rigid bodies interconnected by elastic flexure hinges. Considering the length effects of flexure hinges, multibody dynamic equations are established according to spatial motions of rigid bodies by using Lagrangian method. The shear effects and the torsional compliances of the commonly used circular flexure hinges are considered to enhance the modeling accuracy. The accuracies of various out-of-plane compliance formulas are also discussed. To verify the developed dynamic model, the finite element analyses (FEA) by using ANSYS and modal hammer experimental tests of the primary flexure-based composition structures and the integral 5-DOF stage are performed. The analytical modal frequencies are well in agreement with FEA and experimental test. The results are significant to analyze and optimize the 5-DOF flexure-based nanopositioning stage.
Highlights
To achieve high imaging resolution in the projection optical system of the semiconductor lithography, flexure-based nanopositioning stages are commonly used to adjust the respective lens during actual use [1, 2]
finite element analyses (FEA) results are well in agreement with experimental test, which validate the precision of the Finite Element (FE) model with local fine meshes in flexure hinges
This paper focuses on the accurate multibody dynamic modeling of a 5-degrees of freedom (DOF) flexure-based nanopositioning stage in the projection optical system of the semiconductor lithography
Summary
To achieve high imaging resolution in the projection optical system of the semiconductor lithography, flexure-based nanopositioning stages are commonly used to adjust the respective lens during actual use [1, 2]. Cross-axis couplings impose difficulties on the dynamic performance evaluation of the 5-DOF flexure-based nanopositioning stage [5, 14,15,16]. Improved FEM is proposed for model reduction, such as using spatial nonprismatic beam element to model circular flexure hinge [18] and the Krylov subspace reduction scheme [19], it is still not convenient to provide the intrinsic relation between the dynamic performance and design parameters of the multiple DOF flexure-based stage. This paper attempts to establish an accurate multibody dynamic model for a 5-DOF flexure-based nanopositioning stage in the projection optical system of the semiconductor lithography.
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