面向器件行为的MEMS宏建模方法研究

【作者】 吕湘连；

【导师】 苑伟政；

【作者基本信息】 西北工业大学 ， 机械制造及其自动化， 2005， 硕士

【摘要】 随着MEMS产品的多样化和功能结构的复杂化,微机电系统已成为多个学科相互融合的系统,其功能的实现是多个能量域相互耦合、综合作用的结果,这样,系统级建模与仿真越来越依赖于器件级宏模型的准确性。针对强耦合、非线性的MEMS器件,如何有效实现在多能量域耦合分析的基础上提取宏模型,完成系统级多信号仿真分析,成为当前MEMS设计领域的重要课题。本文针对典型的MEMS器件,研究了三种不同适应条件下的半解析宏建模方法,即在原MEMS器件(或子系统)数值计算基础上,通过一定的降阶算法得到解析宏模型。论文结合扭转微镜、微梁、电容式压力传感器等典型MEMS器件对三种宏建模方法的适应性和有效性进行了分析。 本文的主要研究内容包括: 1) 基于振动理论中的模态叠加原理,结合Lagrange动力学方程,研究了能量保守系统的宏建模方法。并用静电-结构耦合的扭转微镜为例,建立其宏模型,在ANSYS中对该宏模型进行分析。 2) 对于MEMS中经常遇到的有阻尼问题的能量耗散系统,针对线性问题研究了基于Arnoldi算法的宏建模方法,并在线性系统Arnoldi算法的基础上,总结其空间投影原理,结合Taylor展开技术,研究了弱非线性系统的宏建模方法。以一个双端固定微梁为例,综合考虑结构-静电-流体(空气阻尼)多域耦合关系,用一个二次系统描述其弱非线性特点,并对该二次系统进行了降阶宏建模,对其准确性进行分析。 3) 针对有阻尼、强非线性的能量耗散系统,研究了基于KL分解的宏建模方法,对MEMS器件在设计空间内进行一定数值计算,利用相应的计算结果作为最初的随机向量,通过KL分解生成基函数,将系统动态特性投影到少量的基函数上,结合Galerkin方法生成与时间相关的各基函数叠加系数,从而获得降阶模型。一个电容式压力传感器为例,用该方法进行宏模型的获取和分析。更多还原

【Abstract】 Due to the nonlinear coupled energy domain behavior of MEMS (Micro Electro Mechanical System) devices, the development of MEMS CAD tools becomes a more challenging task. The coupled relevant field quantities (mechanical, thermal, electric, magnetic, optical, chemical, etc.) are consistently described by a set of time-dependent partial differential equations, direct simulation based on fully meshed structures involves thousands of degrees of freedom. In order to perform efficient prediction on system level, it is essential to build accurate macro models for MEMS devices on device level.In the thesis, three methods of semi-analytic macro modeling compatible with different terms are studied and realized to solve the questions of typical MEMS devices such as the torsion micro mirror, fixed-fixed micro beam, capacitive pressure sensor, etc. The main contents in this thesis are described as follows:1) Based on a modal representation of coupled domains, the behavior of a coupled system can be assembled in Lagrange equation. In the mode superposition method, the thousands of original system freedoms are reduced to several generalized coordinates (mode coordinates). With the example of a torsion micro mirror, the efficient and accuracy is verified. Because of the modularization of the energy domain, the method isn’t available to the energy dissipation system.2) Arnoldi algorithm does not need to solve the original large scale ODEs but directly reduce it to a lower order model by computing an orthogonal subspace which spans the same Krylov subspace. With the Taylor series expansion and the Arnoldi process, weakly nonlinear MEMS devices model is efficiently reduced via a second order system. Unfortunately it can not be used to handle strong nonlinear system accurately.3) To solve the question of strongly nonlinear MEMS devices, the KL decomposition method is studied. In the method, the first and most important is the signals (data shots), which are required to represent the behaviors of the original system well. By the KL decomposition on the signals, the global basis functions are gained. With the Galerkin method, the time-dependent coefficients of each basis function are chosen. A capacitive pressure sensor is used to verify the method.更多还原