The Research Of Static And Dynamic Performance Of Microcantilever Based On Model Reduction

Micro Electro-Mechanical system(MEMS)is one of the most important scientific technologies in this century,and widely used in various fields of social development.As the basic structure component of micro-computer electrical appliances in MEMS,the optimization design of MEMS micro-cantilever is very important.MEMS micro-cantilever has many characteristics of coupling and non-linearity,previous design and solution methods for its multi parameter simulation are expensive,slow and lack of accuracy.The experimental method and the simulation method are usually used in the design of MEMS micro-cantilever.With the rapid development of microelectronics technology,the demand for the optimization design space of microcomputer electrical components is getting higher and higher.The current simulation solution method is difficult to achieve the design space and optimization of device parameters.The model order reduction method is one of the effective measures to solve this problem.The optimal solution for the optimum design of the microprocessor-based electrical components can be obtained by the construction of its original equation.Therefore,a mathematical model of micro cantilever is built.The static and dynamic characteristics of micro cantilever are studied by using the mainstream algorithm,Arnoldi reduction algorithm and Galerkin mapping algorithm.The main contents of this paper are as follows:(1)Through the electrostatic mechanical coupling of electrostatic fluid field of micro cantilever beam theory and energy principle and fluid squeeze film damping effect,and the use of Euler beam equation and Reynolds equation,the dynamic equation of cantilever beam static mathematical model is established.Based on this mathematical model,a reduced order algorithm for Arnoldi reduction which based on the improved Krylov space method is proposed.In the case of ensuring the accuracy,the speed of the solution is greatly improved.(2)By constructing the MEMS multi-layer cantilever model and solving the equivalent parameters,transformed the reduced order solution to the single layer beam,which provides a new reduction method for solving the multi-layer MEMS cantilever beam.The error caused by neglecting the thickness of the depositionlayer has been analyzed in the process of solving the problem.Analysis of the influence of the main parameters on the accuracy of the solution which provide a theoretical basis for ensuring the effectiveness of the parameter optimization results.Through the use of Conventorware simulation software verified the accuracy of the model order reduction solution.(3)Based on the Galerkin linear modal function,the dynamic reduction model of the micro cantilever beam is established,and the single mode freedom degree model of the device is established in Simulink.The study of the dynamic characteristics of the micro cantilever beam and emphatically analyzed on the dynamic characteristics of Pull-in verified the validity of the model reduction.Based on the research in this paper,an effective model reduction algorithm is provided for subsequent MEMS micro-cantilever multi parameter simulation design and seeking for design space,which provides a theoretical basis for computer aided design(MEMSCAD)to solve similar problems quickly.It provides a solution for the study of the multi-layer cantilever beam optimization and the study of the reduced order model of the dynamic characteristics of the micro cantilever.