微加速度计论文支撑梁有误差的力平衡式微加速度计性能研究

1、微加速度计论文：支撑梁有误差的力平衡式微加速度计性能研究【中文摘要】基于静电驱动与检测技术的力平衡式微加速度计具有线性度好、动态范围大、灵敏度高和可靠性强等优点。由于微加工工艺的不完善,微加速度计的实际参数与设计参数之间总是存在误差,比如支撑梁尺寸误差、梳齿间隙误差、检测质量块质心偏移等。支撑梁误差的存在将导致支撑梁的抗弯刚度不对称,进而使得检测质量块在沿静电力的方向作横向运动的同时还作扭转运动。这样的两自由度复合运动势必会影响到力平衡式微加速度计的性能。本文提出这个新的研究课题,并对此展开研究。论文的主要研究工作和结论如下：(1)以双端固支梁式的平板电容系统、双端固支梁式和双折叠梁式的力平衡

2、式微加速度计三种常见微机电系统(MEMS)结构为例,分析了它们在支撑梁存在误差的情况下的受力及变形,推出了三种结构抵抗外力作用的等效刚度计算式。研究表明：三种结构都是以二维等效刚度矩阵抵抗外力作用,只是对于不同的结构,等效刚度矩阵的元素计算式不同。等效刚度的计算为分析静电MEMS的机电耦合特性提供了必备条件。(2)静电MEMS产品的性能与系统中的机电耦合特性具有密切的关系。为了研究支撑梁误差对机电耦合特性的影响,本文建立了单边平板电容系统和双边平板电容系统的两自由度机电耦合宏模型,分析了两种系统的机电耦合特性。对于单边平板电容系统,本文分析了静电刚度效应,推导了静电刚度矩阵；分析了系统的静态电

3、压响应,运用优化理论计算了静态吸附电压,其结果得到了有限元仿真方法的验证；除此之外,还分析了系统的动态电压响应。研究表明：如果忽略系统中的阻尼影响,系统随加载电压的不同表现出不同的运动形式；运用优化理论,计算出了动态吸附电压。对于双边平板电容系统,分析了系统的静态电压响应,并计算出了静态吸附电压。通过这些方面的研究,为力平衡式微加速度计的性能分析奠定了理论和方法基础。(3)利用本文所建立的平板电容系统作两自由度复合运动时的机电耦合理论和分析方法,建立了力平衡式微加速度计作两自由度复合运动时的机电耦合分析模型,分析了支撑梁误差对微加速度计的性能影响,包括灵敏度、非线性误差和零偏等。研究结果表明：

4、支撑梁误差对微加速度计的灵敏度和非线性误差会产生一定的影响,但可以通过增大反馈电压增益进行弱化；当反馈增益足够大时,支撑梁误差的影响可以忽略不计。而热残余应力等干扰外力对存在支撑梁误差的加速度计的灵敏度没有影响,但会引起零偏和额外的非线性误差,并且改变反馈增益不能弱化零偏及非线性误差。【英文摘要】Force-balanced micro-accelerometer, based on electrostatic driving and sensing technology, has many advantageous attributes, such as good linearity, wi

5、de dynamic range, high sensitivity, and strong reliability. Due to the faulty of micromachining, there always exist errors between the actual parameters and that designed, for instances, the size error of support beams, the gap error of comb fingers and the center offset of proof-mass. The errors in

6、 support beams certainly cause the bending rigidity of the support beams asymmetry and lead to the proof-mass to translate in the direction of electrostatic force and turn round as well. This two-degree-of-freedom compound motion of the proof-mass surely has some effects on the performance of a forc

7、e-balanced micro-accelerometer. This thesis will focus on this new issue.The main work and conclusions of this thesis are as followings:(1) Three common used structures of MEMS (MicroElectroMechanical System), i.e. parallel capacitor system with two-end fixed beam, micro-accelerometer with two-end f

8、ixed beam and micro-accelerometer with double folded beams, are token as the examples to analyze the deflection of supporting beams with errors under the applied forces. The formulas corresponding to the resistances to the applied force for the three structures, named equivalent stiffness, are deriv

9、ed. It is shown that the resistances to the applied force for all the three structures are in a same manner of two-dimensional equivalent stiffness while the only difference lies in the formula to calculate the elements of equivalent stiffness matrix. The equivalent stiffness is necessary for the an

10、alysis of electromechanical coupling characteristics of electrostatic MEMS.(2) There is a strong relationship between the performance of electrostatic MEMS and its electromechanical coupling characteristics. For the purpose to investigate the influence of errors in support beams on electromechanical

11、 coupling characteristics, electromechanical coupling macro models with two degrees of freedom for both single parallel capacitor system and double parallel capacitor system are established respectively, and the performances of these two systems are analyzed. This thesis analyzes the effect of elect

12、rostatic stiffness, and the electrostatic stiffness matrix is derived. The static response of the system is analyzed, the static pull-in voltage is obtained by the method of optimization, and it is verified by finite element simulation. In addition to these, the dynamic response of the system is als

13、o analyzed provided the damping in the system is ignored. It is shown that the motion of system will vary with the changing of the input voltage. Employing the method of optimization, the dynamic pull-in voltage for this system is also obtained. Along the same line, static response of the double par

14、allel capacitor system is analyzed, and the static pull-in voltage is obtained. All the work above lays down the foundation for the analysis of performances of force-balanced micro-accelerometer.(3) Applying the methods proposed in this thesis and the results concerned with the electromechanical cou

15、pling characteristics as the parallel capacitor system undergoing the two-degree-of-freedom compound motion, an electromechanical coupling model with two degrees of freedom for force-balanced micro-accelerometer is established. The influences caused by the errors in the support beams on the performa

16、nces of the micro-accelerometer, including sensitivity, nonlinear errors, zero bias, are analyzed. The results show that the errors in the support beams will affect the sensitivity and nonlinearity errors of the micro-accelerometer, but the affection may be reduced by increasing the gain of feedback

17、 voltage, even when the gain of the feedback is large enough, the influence can be completely neglected. The external perturbing force, such as thermal residual stress, has no effects on the sensitivity of the accelerometer. But it will cause bias and additional nonlinear errors, and no matter what

18、the gain of feedback is, the zero bias and nonlinear errors cannot be reduced.【关键词】微加速度计 机电耦合 支撑梁误差 吸附电压【英文关键词】micro-accelerometer electromechanical coupling errors in the support beams pull-in voltage【目录】支撑梁有误差的力平衡式微加速度计性能研究 摘要 6-7 Abstract 7-8 第1章 绪论 11-19 1.1 微机械电子系统概述 11-12 1.2 静电MEMS机电耦合特性研究概况 12-14 1.3 力平衡式微加速度计研究概况 14-17 1.4 本文研究的主要目标和内容 17-19 第2章 常见MEMS结构的等效刚度推导 19-33 2.1 引言 19-20 2.2 系统的受力和变形分析 20-32 2.2.1 双端固支梁式平板电容系统 20-24 2.2.2 双端固支梁式微加速度计 24-28