【作者】 王洪喜；

【导师】 贾建援；

【作者基本信息】 西安电子科技大学 ， 机械制造及其自动化， 2006， 博士

【摘要】 静电力作为微机电系统(MEMS)中一种重要的驱动力,广泛应用于微镜、微泵、微马达、微陀螺、微钳、微谐振器、射频开关等微器件中。尽管一部分静电驱动MEMS产品已经从实验室走向商业化,但相关设计理论和设计工具尚不能满足设计需求,设计中仍然以反复试验(trial and error)方法为主,导致成品率低,可靠性差,严重制约了产品的研发速度和产业化水平。本文以静电场、弹性力学、结构动力学、流体力学为理论基础,以计算机仿真作为辅助工具,将实现器件级或系统级设计与分析作为目标,深入研究静电驱动典型微结构的静电力、静力学和动力学等方面的问题,设计了具有明显阀值效应的静电微加速度开关,建立并求解开关的系统仿真模型。本课题对促进静电驱动微结构理论的深入研究具有重要的学术价值,对提高静电驱动微器件的工程设计水平具有一定的指导意义。以平行板电容理论为基础,基于虚位移原理,导出了典型微结构静电力(或力矩)的计算模型,讨论了边缘电场对静电力的影响,分析了不同静电力模型的精度,确定了无限大平行板电极静电力公式的适用条件,为结构的静力学和动力学研究提供理论依据。提出了静电力显微镜(EFM)扫描探针针尖与试样之间的电场假设。基于该假设,建立了计算针尖静电力的解析模型,计算结果与等效电荷、有限元等数值方法以及相关的实验结果相吻合。分析了因微结构弹性力与静电力的耦合作用而产生的吸合效应(pull-in or snap-down)。基于小挠度变形理论,提出了一种计算静电致动微梁变形的数值方法和解析公式,求解了微梁的临界挠度(pull-in deflection),分析了用小挠度变形理论计算微结构变形的合理性。基于小挠度变形理论,建立了静电驱动轴对称圆形薄板(包括带有突台的薄板)的微分方程,并采用伽辽金加权残值法进行求解,确定了带有突台圆形薄板的临界挠度为初始间隙的1/3;根据力矩平衡原理建立了微镜的控制方程并进行求解,分析了气膜阻尼对微镜响应速度的影响。基于本文建立的计算针尖静电力解析模型,求解了静电力扫描探针的变形,分析针尖结构参数对变形的影响,确定了扫描探针的临界挠度与初始间距之比为常值1/2。分别建立了静电驱动微梁、微镜、圆形薄板和扫描探针的动力学微分方程,针对具体问题,采用合适的方法求解系统的时间响应,分析了静电驱动微结构的振动特点。对于含有气膜阻尼作用的微梁振动,提出了采用有限差分与增量加载相结合的计算方法。更多还原

【Abstract】 As an important driving force in Micro Electromechanical System (MEMS), the electrostatic force is widely applied to such microdevices as micromirror, micropump, micromotor, microgyro, microforceps, moicroresonator, and RF switch et al. Although some electrostatically driven MEMS products have been commercialized, the related design theoretics cannot satisfy the devising demands yet. So the method of trial and error, which resulted in low eligible products ratio and low reliability, is the primary technology reason which slows down the step of research and industrialization of the products. Based on the theories of electrostatic field, elastic force, structure dynamics and hydrodynamics, the problems of electrostatic force, statics and dynamics in several typical electrostatically driven microstructures are lucubrated with the aid of compute simulation to achieve the systemic analysis and design. An electrostatically-driven micro-acceleration switch with obvious threshold characteristic is devised, a model of which is established and emulated. The work done in this paper not only has an important academic significance in promoting the study of the theory of microstructures driven by electrostatic force, but also has an instructive significance in improving the design level of electrically actuated microdevices .On the basis of the parallel-plate capacitance theory and the virtual displacement principle, the model for calculating electrostatic force of several typical microstructures is educed. The effect of fringe field on the electrostatic force is discussed. The precision of different models of electrostatic force is analyzed. So the appropriate domain of electrostatic force of infinite parallel-plate is obtained to provide a theoretic basis for the statics and dynamics research of structures.A distributing hypothesis of electric field between the EFM tip and the sample surface is put forward. Based on the hypothesis, an analytic model is set up to calculate the electrostatic force of the tip. The results from the model are consistent not only with those from such numerical means as equivalent charge and FEM, but also (consistent) with the experimental results.The phenomenon of pull-in or snap-down is analyzed, which results from the coupling between the elastic force of microstructure and the electrostatic force. Based on the small deflection theory, a numerical procedure and an analytical formula, by which the pull-in deflection is obtained, are presented to calculate the deflection of microbeam driven by electrostatic force. The rationality is analyzed by using small deflection theory to calculate the deflection of microstructures.Based on the small deflection theory, the differential equation of axis-symmetrically circular laminate driven by electrostatic force is established and calculated through the weighted residual method of Galerkin. With the differential equation established, the pull-in deflection is obtained to be 1/3 of the initial gap. Based on the torque equilibrium principle, the dominating equation of micromirror is established and computed to analyze the effect of air-film damp on the response speed of micromirror.Based on the analytical model established to calculate the electrostatic force of tip, the deflection of EFM tip is acquired. The effect of the structural parameters of EFM tip on the deflection of the tip is analyzed. The pull-in deflection of EFM tip is obtained to更多还原