【作者】 刘广军；

【导师】 王安麟；

【作者基本信息】 上海交通大学 ， 机械工程， 2007， 博士

【摘要】 微结构拓扑设计是结构设计中的难点和热点问题,也是结构设计领域的前沿研究方向。微结构拓扑设计是制约MEMS实用化的关键技术之一,设计和制作出高性能、高灵敏度的微器件结构是MEMS实用化的重要保证。从微结构拓扑出发,同时考虑其内部连接和工作环境,建立微器件高精度行为模型和结构拓扑优化设计方法,是MEMS性能设计和系统设计中的关键性难题。即在MEMS的微小尺度效应和复杂动力学机制下,存在微结构弹性变形同其输出性能(电信号)的高精度映射关系(微器件高精度行为模型)的难题,以及在追求高性能MEMS的评价下,其设计过程中结构拓扑的大自由变量度表征和大计算量(微器件结构拓扑优化设计方法)的难题。从解决此类高性能、高灵敏度微结构拓扑设计的关键性难题出发,本论文以一种体微机械加工技术制备的音叉振动式微机械陀螺为研究对象,提出基于元胞自动机的结构拓扑自组织设计方法。将灵活地表征具有大自由度、复杂动力学机制特征的、自下而上的自组织理论引入微机械陀螺结构拓扑设计中,以提高微机械陀螺的灵敏度和带宽等性能参数为出发点,对微机械陀螺的结构拓扑设计方法进行了系统而深入的研究:(1)基于微机械陀螺的简化模型,分析了音叉振动式微机械陀螺的基本工作原理、空气阻尼特性、驱动与检测方法以及弹性梁的设计。总结了微机械陀螺简化模型在其原理性概念设计中的优点和问题,提出了基于弹性理论的高性能、高灵敏度的微器件结构拓扑设计模型的必要性。(2)为提高设计和解析过程中微机械陀螺检测电容的计算精度,解决高精度微机械陀螺结构解析和优化过程中的计算时间问题,利用弹性理论和多自由度动态有限元解析理论,首次提出了微机械陀螺检测电容的子结构化解析模型,建立了微陀螺结构的弹性变形同其输出性能(电信号)的高精度映射关系,确立了微器件的高精度行为模型,在实现微机械陀螺的高精度解析和分析的基础上,完成了面向微机械陀螺最终输出性能/检测电容的动力学特性与检测特性分析;考虑到工作环境对微机械陀螺的影响不可忽视,采用热-力耦合分析的非线性有限元方法,分析了环境温度对微机械陀螺的固有频率、检测电容输出和带宽等性能参数的影响。(3)为提高微机械陀螺的灵敏度(输出性能)和带宽等性能参数,提出适用于表征大自由度微结构设计的自组织拓扑设计流程,将元胞自动机应用于具有大自由度、非线性、复杂性的微结构拓扑的自组织设计模型表达中。从微机械陀螺的实际结构和动态特性出发,构建微机械陀螺拓扑演化的间接规则,用于驱动结构的自组织演化过程;基于最终输出性能,提出微机械陀螺的性能评价方法。基于微机械陀螺的子结构模型,建立高灵敏度的子结构化的微器件结构拓扑设计模型,解决了拓扑优化中的时间和效率问题。以弹性梁的拓扑优化为算例,将微机械陀螺的自组织拓扑演化规则应用于弹性梁的拓扑演化过程中,实现了微机械陀螺的自组织拓扑优化,优化后的数值计算表明微机械陀螺的整体性能有了大幅度提高,同时保持了很高的品质因子。(4)为实际验证优化后微机械陀螺的性能,根据优化后的结果,进行了改进后微机械陀螺器件的制作、封装和测试。测试结果表明,改进后的微机械陀螺在灵敏度和带宽等性能方面均有了大幅提高,证明了本文提出的自组织设计方法的有效性。微机械陀螺的自组织拓扑设计方法提供了一种缩短实际微机械陀螺研制周期、实现微机械陀螺高效设计的有效途径。更多还原

【Abstract】 Topology design of microstructure is a hot research topic as well as the most challenging and difficult problem in structural design. Topology design of microstructure is also one of the key technologies that limit the practical application of micro-electro-mechanical system (MEMS). Design and fabrication of MEMS device with high performance and high sensitivity is an important assurance of the practical application of MEMS. However, it is very difficult to set out from the topology of microstructure and consider microstructure topology, internal connection and working environment synthetically to build the behavioral model of MEMS device. That is, in the mechanism of the scale effects and complex dynamics, it is difficult to build the high-precision mapping relationship (high-precision behavior model of MEMS device) between elastic deformation and the output performance (electrical signal). In seeking of high-performance MEMS, it is necessary to describe the high degree of freedom and solve the problem of large calculation amount in structural topology design.For the solving of the key problem in topology design of high-performance and high-sensitivity microstructure, this paper focuses on a tuning fork vibratory micromachined gyroscope fabricated by the bulk silicon micromachining procedures. The self-organizing structural topology design methodology using Cellular Automata (CA) is presented for the design and optimization of the micromachined gyroscope. The down-top self-organizing theory with the features of complex dynamics mechanism is applied in the design and optimization of the structural topology of the micromachined gyroscope. To increase the sensitivity and bandwidth of the micromachined gyroscope, the structural topology design methodology for the micromachined gyroscope is researched systemically and in depth. The contents of this paper are as follows:(1) Several issues about the basic working principle, the air damping characteristics, the driving and sensing method, the design of elastic beam are discussed based on the rigid body model of micronmachined gyroscope. And then, the merits and some defects of rigid body model in the concept design are profoundly discussed. The necessity of the high-performance and high-sensitivity structural topology model for MEMS device based on elastic theory is presented.(2) To improve the analytical and design precision of the detection capacitance and solve the problem of long computation time in structural analysis and optimization of the micromachined gyroscope, the detection capacitance analysis method based on the substructuring model is first proposed by employing the dynamic finite element theory of multi-degree of freedom. The high-precision mapping relationship (high-precision behavior model of MEMS device) between elastic deformation and the output performance is therefore built. The performance-oriented analysis and calculation of the dynamics and detecting characteristics for the micromachined gyroscope is realized. Since the working environment cannot be ignored, the nonlinear finite element method for mechanical-thermal coupled field is employed to analysis the influence of environmental temperature on the natural frequencies, the output of detection capacitance and bandwidth of the micromachined gyroscope.(3) To increase the sensitivity (output performance) and bandwidth of the micromachined gyroscope, a procedure for design of microstructure with high degree of freedom is presented. The Cellular Automata is applied in the expression of self-organizing design model of the high degree of freedom, nonlinear and complex microstructure topology. Considering the practical structure and dynamic characteristics of the micromachined gyroscope, the indirect local rule for topology evolution is built to drive the self-organizing evolution process. A performance evaluation function is derived based on the output performance. The high-sensitivity substructuring model for the topology design of the micromachined gyroscope is established to conduct analysis and optimization with a reasonable accuracy and a reduced computational cost. The optimization of the spring beams is processed as a numerical example, and the proposed method is applied in the topology optimization of the spring beams. The self-organizing topology optimization of the micromachined gyroscope is achieved. The optimization result shows that the performance of micromachined gyroscope is promoted greatly without change in the high Q-factors.(4) To test the performance of the optimized structure in practice, the improved micromachined gyroscope is fabricated and tested according to the optimization results. The testing results show that the improved micromachined gyroscope has much promotion on sensitivity and bandwidth, which proves the validity of the self-organizing topology design methodology. The self-organizing topology design provides an effective method to shorten the design period for micromachined gyroscope.更多还原