静电梳齿结构的MEMS分析和优化设计
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摘要
微机电系统(MEMS)器件的构成涉及微电子、微机械、微动力、微热力、微流体学、材料、物理、化学、生物等多个领域,形成了多能量域并交叉耦合。为其产品的建模、仿真以及优化设计带来了较大的难度。由于静电驱动的原理简单使其成为MEMS器件中机械动作的主要来源。而梳齿结构在MEMS器件中有广泛的应用:微谐振器、微机械加速度计、微机械陀螺仪、微镜、微镊、微泵等。所以做为MEMS的重要驱动方式和结构形式,静电驱动梳齿结构MEMS器件的耦合场仿真分析以及优化设计对MEMS的开发具有很重要的意义。本课题的研究对静电驱动梳齿结构MEMS器件的设计具有较大的理论研究意义。
本文的研究工作主要包括以下几个方面:
1、采用降阶宏建模技术快速求解静电梳齿驱动器静电—结构耦合问题,降阶建模被用于表示微谐振器的静态动态特性。论文采用降阶建模方法详细分析了静电梳齿驱动器的各参数对所产生静电力以及驱动位移的关系;并对静电梳齿驱动器梳齿电容结构的静电场进行分析和模拟,深入讨论了边缘效应的影响;还对微谐振器动态特性的各个模态进行仿真分析,并计算分析了前六阶模态的频率和谐振幅值。仿真结果表明降阶建模方法能够快速、准确地实现多耦合域的求解。
2、从系统角度出发考虑了各个子系统对叉指式微机械陀螺仪特性的影响,系统详细地分析了与叉指状微机械陀螺仪性能指标—灵敏度密切相关的结构特性、电子电路、加工工艺和空气阻尼,并在此分析的基础上建立了陀螺的统一多学科优化模型并对其进行多学科优化设计。将遗传算法和差分进化算法的全局寻优与陀螺仪系统级优化相结合,证实了遗传算法和差分进化算法在MEMS系统级优化中的可行性,并比较遗传算法和差分进化算法的优化结果,差分进化算法的优化结果较大地改善了器件的性能。
3、从系统角度出发考虑了各个子系统对梳齿式微加速度计特性的影响,在对梳齿式微加速度计各个学科的设计要素进行分析的基础上,对各个子系统分别建立相对独立的优化模型,采用差分进化算法和多目标遗传算法对其进行优化设计。证实了差分进化算法和多目标遗传算法对多个子系统耦合的系统级优化的可行性,并比较了将多目标转换为单目标进行优化和采用多目标进行优化的区别和结果,优化结果使器件的性能得到了改善。
The composition of micro-electromechanical systems (MEMS) relates to many scientific fields such as: micro-electronics, micro-mechanics, micro-dynamics, micro-thermotics, micro-fluidics, material, physics, chemistry and biology. They forms many cross coupled energy domains, which bring difficulty to the modeling, simulation and optimization of MEMS. Electrostatic force is the main method to drive the mechanic action because of its simple principles. Comb-finger structure is widely used in MEMS apparatus such as micro resonators, micromachined silicon accelerometer, micromachined gyroscope, micro mirrors, micro grippers and micro stages. The simulation analysis and optimization design of the coupled electrical fields for comb-finger structure MEMS are quite important.
The three main points of this paper are as following:
1. electrostatic-structure coupled problem in electrostatic comb-finger drives was solved with reduced order macro modeling technique in which reduced order modeling (ROM) was used to present the static and dynamic characteristics of micro resonators. This paper analyzed the relationship between the parameters of the static comb-finger drives and the electrostatic force and the displace. The static electrical field of the electrostatic comb-finger drives was simulated and analyzed and the edge effect was also discussed deeply. Besides, six modes of the dynamic characteristics of the micro resonators were analyzed and their frequency and harmonic amplitude were calculated. The simulation result showed that the ROM could solve coupled fields rapidly and exactly.
2. The influence of each subsystem to the comb-finger micromachined gyroscope was discussed from the system aspect. The configuration characteristic, electronic circuit, processing technique and air-damping of the comb-finger micromachined gyroscope which related to its sensitivity were detailedly analyzed. And the unified multidisciplinary design optimization (MDO) model for micromachined gyroscope was founded. The genetic algorithm (GA) and differential evolution algorithm(DE) were proved feasible in MEMS optimization by combining the global optimimazation of GA and DE with the the system level optimization of the gyroscope. The optimization results of GA and DE were compared. The differential evolution algorithm improved the performance of the system markedly.
3. The influence of each subsystem to the comb-finger micromachined silicon accelerometer was discussed from the system aspect. Optimization model of each subsystem is respectively built based on the analysis of the design factors of the comb-finger micromachined silicon accelerometer. The differential evolution algorithm and multi-objective genetic algorithm (MOGA) were used for optimization and were proved feasible in the optimization of systems coupled with multi-sub systems. The optimization results solved by transforming multi-objective to single objective and the results solved with multi-objective were compared. These results improve the performance of system.
本文的研究工作主要包括以下几个方面:
1、采用降阶宏建模技术快速求解静电梳齿驱动器静电—结构耦合问题,降阶建模被用于表示微谐振器的静态动态特性。论文采用降阶建模方法详细分析了静电梳齿驱动器的各参数对所产生静电力以及驱动位移的关系;并对静电梳齿驱动器梳齿电容结构的静电场进行分析和模拟,深入讨论了边缘效应的影响;还对微谐振器动态特性的各个模态进行仿真分析,并计算分析了前六阶模态的频率和谐振幅值。仿真结果表明降阶建模方法能够快速、准确地实现多耦合域的求解。
2、从系统角度出发考虑了各个子系统对叉指式微机械陀螺仪特性的影响,系统详细地分析了与叉指状微机械陀螺仪性能指标—灵敏度密切相关的结构特性、电子电路、加工工艺和空气阻尼,并在此分析的基础上建立了陀螺的统一多学科优化模型并对其进行多学科优化设计。将遗传算法和差分进化算法的全局寻优与陀螺仪系统级优化相结合,证实了遗传算法和差分进化算法在MEMS系统级优化中的可行性,并比较遗传算法和差分进化算法的优化结果,差分进化算法的优化结果较大地改善了器件的性能。
3、从系统角度出发考虑了各个子系统对梳齿式微加速度计特性的影响,在对梳齿式微加速度计各个学科的设计要素进行分析的基础上,对各个子系统分别建立相对独立的优化模型,采用差分进化算法和多目标遗传算法对其进行优化设计。证实了差分进化算法和多目标遗传算法对多个子系统耦合的系统级优化的可行性,并比较了将多目标转换为单目标进行优化和采用多目标进行优化的区别和结果,优化结果使器件的性能得到了改善。
The composition of micro-electromechanical systems (MEMS) relates to many scientific fields such as: micro-electronics, micro-mechanics, micro-dynamics, micro-thermotics, micro-fluidics, material, physics, chemistry and biology. They forms many cross coupled energy domains, which bring difficulty to the modeling, simulation and optimization of MEMS. Electrostatic force is the main method to drive the mechanic action because of its simple principles. Comb-finger structure is widely used in MEMS apparatus such as micro resonators, micromachined silicon accelerometer, micromachined gyroscope, micro mirrors, micro grippers and micro stages. The simulation analysis and optimization design of the coupled electrical fields for comb-finger structure MEMS are quite important.
The three main points of this paper are as following:
1. electrostatic-structure coupled problem in electrostatic comb-finger drives was solved with reduced order macro modeling technique in which reduced order modeling (ROM) was used to present the static and dynamic characteristics of micro resonators. This paper analyzed the relationship between the parameters of the static comb-finger drives and the electrostatic force and the displace. The static electrical field of the electrostatic comb-finger drives was simulated and analyzed and the edge effect was also discussed deeply. Besides, six modes of the dynamic characteristics of the micro resonators were analyzed and their frequency and harmonic amplitude were calculated. The simulation result showed that the ROM could solve coupled fields rapidly and exactly.
2. The influence of each subsystem to the comb-finger micromachined gyroscope was discussed from the system aspect. The configuration characteristic, electronic circuit, processing technique and air-damping of the comb-finger micromachined gyroscope which related to its sensitivity were detailedly analyzed. And the unified multidisciplinary design optimization (MDO) model for micromachined gyroscope was founded. The genetic algorithm (GA) and differential evolution algorithm(DE) were proved feasible in MEMS optimization by combining the global optimimazation of GA and DE with the the system level optimization of the gyroscope. The optimization results of GA and DE were compared. The differential evolution algorithm improved the performance of the system markedly.
3. The influence of each subsystem to the comb-finger micromachined silicon accelerometer was discussed from the system aspect. Optimization model of each subsystem is respectively built based on the analysis of the design factors of the comb-finger micromachined silicon accelerometer. The differential evolution algorithm and multi-objective genetic algorithm (MOGA) were used for optimization and were proved feasible in the optimization of systems coupled with multi-sub systems. The optimization results solved by transforming multi-objective to single objective and the results solved with multi-objective were compared. These results improve the performance of system.
引文
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