【作者】 李伟剑；

【导师】 苑伟政；

【作者基本信息】 西北工业大学 ， 机械工程， 2004， 博士

【摘要】 随着微机电系统(MEMS)技术的逐渐成熟,越来越多的MEMS器件或相关产品投入市场,为降低制作成本、缩短研制周期、提高产品可靠性,迫切需要引入有效的设计方法。另一方面伴随着MEMS加工工艺的标准化,使得MEMS设计在一定程度上可与具体工艺相分离,从而大大地促进了MEMS建模与仿真技术的迅速发展,与以前相比MEMS CAD更具实际应用价值。 微机电系统融合了力、电、流体、光、磁、热等多个物理域,这些物理域之间的复杂耦合效应对MEMS的建模与仿真提出了巨大挑战。为准确预测在这些物理域共同作用下系统的行为特性,需要深入研究物理域之间的耦合机理,探讨快速分析与模拟系统行为的有效方法。此外在MEMS的设计过程中,需要从整体的角度出发综合考虑微传感器、微致动器、电子接口电路、控制电路、工艺等多学科或子系统,并权衡它们对系统特性的影响,因而研究有效的系统设计与优化方法非常必要。本文针对静电致动微梁和微机械振动陀螺的多域耦合问题展开深入研究,并在对多个子系统分析的基础上对微机械陀螺进行多学科设计优化。 本文的主要研究内容包括: 1)应用降阶宏建模技术快速求解MEMS多能域耦合问题。论文详细论述了面向多域耦合分析的MEMS宏建模方法,如基于节点分析法的参数化宏建模方法、基于Churn过程的非线性宏建模方法以及基于Amoldi算法的自动宏建模方法,并讨论了这些方法各自的优缺点及应用场合。 2)采用基于Churn过程和基于Arnoldi算法的宏建模方法求解静电致动微梁的多能域耦合问题。当器件工作于无阻尼、非线性情况时,利用基于Churn过程的宏建模方法对其进行静电—结构耦合分析;当器件工作于有阻尼、线性条件时,采用基于Krylov子空间的Amoldi算法对原始状态空间模型实行降阶,由降阶模型实现微梁的静电—结构—阻尼等多域耦合分析,仿真结果表明宏建模方法能快速、准确地实现多域耦合MEMS器件的瞬态分析。 3)将基于物理级数值模拟的集总参数宏建模技术应用于微机械陀螺的多域耦合分析中。通过适当的方式将结构域、静电域、空气阻尼域进行分离,提取每一物理域的集总参数宏模型,然后在系统级仿真器中利用集总参数模型建立微机械陀螺的多域耦合模型,快速地实现了陀螺的瞬态分析。 4)由静电场的数值模拟准确地捕捉电容的边缘效应,准确地提取静电驱动梳齿和检测平板中电容与位移关系;根据热—流体控制方程类似原理,在数值模拟的更多还原

【Abstract】 With the rapid progress in microelectromechanical systems (MEMS) technology, MEMS-specific modeling and simulation environments are increasingly needed to improve performance of MEMS device before costly and time-consuming prototyping. In addition, more and more MEMS fabrication processes are standardized to meet the requirement of commercialization of MEMS products which accelerate the development of modeling and simulation.Generally speaking, MEMS couple multiple physical domains such as mechanical, electrical, fluidic, optical, magnetic and thermal to implement their functions. The inherent coupled property poses difficult challenges for modeling and simulation of MEMS. It is necessary to require an effective method to predict the behavior of MEMS device through researching on these tightly coupling effects. On the other hand, most of MEMS integrate micro-transducers with readout and control circuit on a common board, design and optimization of MEMS require comprehensive consideration for the coupling effects of fabrication process, structure physical parameters, operational environments, and electronics.In the thesis, electrostatically-actuated microbeam and micromachined gyroscope are taken as examples to demonstrate the procedure of multi-domain coupling analysis and system design optimization of MEMS. The main contents in this thesis are described as follows:1) Model order reduction (MOR) techniques are proposed to quickly solve the coupling problems existing in MEMS. Parameterized macromodeling method based on nodal analysis technique, nonlinear macromodeling method based on Churn process, and automatically macromodeling method based on Arnoldi algorithm are detailedly discussed. Their appropriate applications are identified through comparison among these macromodeling methods.2) In the case of non-damping and nonlinear condition, electrostatic-structural coupling analysis is performed for the flexible electrostatic fixed-fixed microbeam using Churn process. When damping and nonlinear conditions are concerned, discretized ordinary differential equations (ODEs) are firstly derived from the original partial differential equations using finite differential method (FDM), and then Arnoldi process based onKrylov subspace is applied to generate reduced order model (ROM). Electrical-structural-fluidic multi-domain coupling analysis is implemented using the generated ROM. The results prove that macromodeling methods can quickly solve the coupling problem with little compromising accuracy.3) The multiple domains can be decomposed into elastic field, electrostatic field and air-damping field. The lumped parameter macromodeling method for every domain, therefore, is utilized to analyze coupling effects in micromachined gyroscope based on physically numerical simulation. The obtained lumped models can be described using hardware description language (HDL) and then inserted into system level model to do transient analysis of micromachined gyroscope.4) The electrostatic numerical analysis is performed to capture fringing effect in micro structural capacitance so that the relationship of capacitance with displacement can be accurately extracted. The principle of thermal-fluidic analogy is used to extract lumped parameters (damping coefficient and squeeze stiffness) of squeeze film damping in perforation plate structure. Modal analysis technology is used to extract the effective stiffness and mass in driving and sensing modes of gyroscope.5) Multidisciplinary design optimization idea is introduced for the overall preliminary design of micromachined gyroscope. To optimize the whole performance of microgyroscope such as sensitivity a multidisciplinary design model is proposed with consideration of the coupling effects of fabrication process, structure physical parameters, environmental quality factor, and electronics.6) Genetic algorithm is applied to optimize the proposed MDO problem and obtain the global trade-off optimum. The prototype of microgyroscope is fabricated with optimal parameters, and test results for the gyroscope show that MDO methodology is a promising approach to effectively explore system trade-off and design space for complex MEMS.更多还原