Model Order Reduction for Coupled Dynamic Characterization of Torsional Micromirrors

Numerical solutions could not perform rapid system-level simulation of the behavior of micro-electro-mechanical systems（MEMS） and analytic solutions for the describing partial differential equations are only available for simple geometries.Model order reduction（MOR） can extract approximate low-order model from the original large scale system.Conventional model order reduction algorithm is based on first-order system model,however,most structure mechanical MEMS systems are naturally second-order in time.For the purpose of solving the above problem,a direct second-order system model order reduction approach based on Krylov subspace projection for the coupled dynamic study of electrostatic torsional micromirrors is presented.The block Arnoldi process is applied to create the orthonormal vectors to construct the projection matrix,which enables the extraction of the low order model from the discretized system assembled through finite element analysis.The transfer functions of the reduced order model and the original model are expanded to demonstrate the moment-matching property of the second-order model reduction algorithm.The torsion and bending effect are included in the finite element model,and the squeeze film damping effect is considered as well.An empirical method considering relative error convergence is adopted to obtain the optimal choice of the order for the reduced model.A comparison research between the full model and the reduced model is carried out.The modeling accuracy and computation efficiency of the presented second-order model reduction method are confirmed by the comparison research results.The research provides references for MOR of MEMS.

Design and Simulation of Silicon-based NiCrAu MEMS Torsion Micromirror with Tilted Back-electrode

Torsion micromirror is a key structure of optical devices in micro-electro-mechanical system(MEMS), such as MEMS optical switches, MEMS variable optical attenuator, MEMS scanning micromirror array and so on. A silicon-based NiCrAu MEMS torsion micromirror is theoretically analyzed. It is shown that in order to have 15° rotation, the driven voltage should be about 20V and the thickness of the supporting beam must be controlled in the range of submicron orders of magnitude. This very thin beam makes the structure more unstable and unreliable, and also makes the fabrication more complicated. Based on parallel back-electrode analysis and testing, a tilted back-electrode has been designed to replace the parallel back-electrode in order to decrease the driven voltage and difficulty of fabricating processing. By theoretical analysis and simulation, a conclusion can be drown that the thickness can be improved from submicron to micron by using tilted back-electrode when using the same driven voltage. Tilted back-electrode is very effective to improve the stability and reliability of the micromirror structure.

Stability analysis of quasicrystal torsion micromirror actuator based.on the strain gradient theory

Electrostatic torsional micromirrors are widely applied in the fields·of micro-optical switches,optical attenuators,optical scanners,and optical displays.In previous lectures,most of the micromirrors were twisted along the urtiaxial or biaxial direction,which limited the range of light reflection.In this·paper,a quasicrystal torsional micromirror that can be deflected in any direction is designed and the dynamic model of the electrostatically driven micromirror is established.The static and dynamic phenomena and pull-in characteristics are analyzed through the numerical solution of the strain gradient theory.The results of three kinds of mirror deflection directions are compared and analyzed.The results show the significant differences in the torsion models with different deflection axis directions.When the deflection angle along the oblique axis reaches 45°,the instability voltage is the smallest.The pull-in instability voltage increases with the increment ofphonon-phason coupling elastic modulus and phason elastic modulus.The perrriittivity of quasicrystal,the strain gradient parameter,and the air damping influence the torsion of the micromirror dynaniic system.A larger pull-in instability voltage generates with the decrease of surface distributed forces.