Angle parametrized macro modelling method of micro-electro-mechanism system

Abstract

The invention discloses an angle parametrized macro modelling method of micro-electro-mechanism system, belonging to a field of micro-electro-mechanism system design and model order reduction. The method comprises: firstly, randomly selecting one from microstructure with same geometric shape as a reference microstructure, extracting macro model thereof by the numerical value order reduction method; then establishing conversion equations between force and displacement of other orientation microstructures relative to reference microstructure by employing a matrix coordinate transform method, and finally, substituting the conversion equations between force and displacement into a behavior equation of the macro model, and implementing angle parametrized macro modeling of MEMS. The method of the invention implements angle parametrized macro modeling by the matrix coordinate transform method, and by setting relative angle parameters, avoids identity of structure and repeat macro modeling process of MEMS microstructure of different initial orientations, thereby increasing speed of MEMS grade modeling and emulation based on the macro model, and further raising design efficiency of entire MEMS.

Description

technical field [0001] The invention relates to a micro-electro-mechanical system (MEMS) angle parameterized macro modeling method, which belongs to the field of micro-electro-mechanical system design and model reduction. Background technique [0002] With the rapid development of MEMS design technology and process level, the structure of MEMS devices has become more and more complex, and a large number of new devices have been produced one after another. However, structural symmetry is still a major feature of developing MEMS devices, that is, in the design of MEMS, there are a large number of functional components or microstructures with identical geometric shapes but different initial orientations. The process of reducing the degrees of freedom of the finite element models of these microstructures and establishing low-order models that can characterize the input and output behaviors of microstructures is called the macro-modeling process, and the extracted low-order model...

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Problems solved by technology

[0003] In his doctoral dissertation "Modeling and Simulation for Design of Suspended MEMS", Qi Jing from Carnegie Mellon University used the coordinate transformation method to realize the angle parameterization for the MEMS lumped parameter model, but the lumped parameter model used matrix structure analysis and electrostatic Field and other classical theoretical methods are extracted through analytical derivation, which is different from the macro-modeling method in which angle parameterization is applied to numerical order reduction in the present invention

In addition, in recent years, great progress has been made in parametric macro-modeling methods. Professor E.B. Rudnyi from IMTEK in Germany, Dr. Luca Daniel from MIT in the United States, and Professor Bai Zhaojun from UC Davis have conducted extensive and in-depth research on parametric macro-modeling methods. However, it is mainly aimed at the parameterization of geometric dimensions and material properties of MEMS structures, and the research on angle parameterization macro-modeling methods has not yet been involved.

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