1、微加速度計(jì)論文：支撐梁有誤差的力平衡式微加速度計(jì)性能研究【中文摘要】基于靜電驅(qū)動與檢測技術(shù)的力平衡式微加速度計(jì)具有線性度好、動態(tài)范圍大、靈敏度高和可靠性強(qiáng)等優(yōu)點(diǎn)。由于微加工工藝的不完善,微加速度計(jì)的實(shí)際參數(shù)與設(shè)計(jì)參數(shù)之間總是存在誤差,比如支撐梁尺寸誤差、梳齒間隙誤差、檢測質(zhì)量塊質(zhì)心偏移等。支撐梁誤差的存在將導(dǎo)致支撐梁的抗彎剛度不對稱,進(jìn)而使得檢測質(zhì)量塊在沿靜電力的方向作橫向運(yùn)動的同時(shí)還作扭轉(zhuǎn)運(yùn)動。這樣的兩自由度復(fù)合運(yùn)動勢必會影響到力平衡式微加速度計(jì)的性能。本文提出這個(gè)新的研究課題,并對此展開研究。論文的主要研究工作和結(jié)論如下：(1)以雙端固支梁式的平板電容系統(tǒng)、雙端固支梁式和雙折疊梁式的力平衡

2、式微加速度計(jì)三種常見微機(jī)電系統(tǒng)(MEMS)結(jié)構(gòu)為例,分析了它們在支撐梁存在誤差的情況下的受力及變形,推出了三種結(jié)構(gòu)抵抗外力作用的等效剛度計(jì)算式。研究表明：三種結(jié)構(gòu)都是以二維等效剛度矩陣抵抗外力作用,只是對于不同的結(jié)構(gòu),等效剛度矩陣的元素計(jì)算式不同。等效剛度的計(jì)算為分析靜電MEMS的機(jī)電耦合特性提供了必備條件。(2)靜電MEMS產(chǎn)品的性能與系統(tǒng)中的機(jī)電耦合特性具有密切的關(guān)系。為了研究支撐梁誤差對機(jī)電耦合特性的影響,本文建立了單邊平板電容系統(tǒng)和雙邊平板電容系統(tǒng)的兩自由度機(jī)電耦合宏模型,分析了兩種系統(tǒng)的機(jī)電耦合特性。對于單邊平板電容系統(tǒng),本文分析了靜電剛度效應(yīng),推導(dǎo)了靜電剛度矩陣；分析了系統(tǒng)的靜態(tài)電

3、壓響應(yīng),運(yùn)用優(yōu)化理論計(jì)算了靜態(tài)吸附電壓,其結(jié)果得到了有限元仿真方法的驗(yàn)證；除此之外,還分析了系統(tǒng)的動態(tài)電壓響應(yīng)。研究表明：如果忽略系統(tǒng)中的阻尼影響,系統(tǒng)隨加載電壓的不同表現(xiàn)出不同的運(yùn)動形式；運(yùn)用優(yōu)化理論,計(jì)算出了動態(tài)吸附電壓。對于雙邊平板電容系統(tǒng),分析了系統(tǒng)的靜態(tài)電壓響應(yīng),并計(jì)算出了靜態(tài)吸附電壓。通過這些方面的研究,為力平衡式微加速度計(jì)的性能分析奠定了理論和方法基礎(chǔ)。(3)利用本文所建立的平板電容系統(tǒng)作兩自由度復(fù)合運(yùn)動時(shí)的機(jī)電耦合理論和分析方法,建立了力平衡式微加速度計(jì)作兩自由度復(fù)合運(yùn)動時(shí)的機(jī)電耦合分析模型,分析了支撐梁誤差對微加速度計(jì)的性能影響,包括靈敏度、非線性誤差和零偏等。研究結(jié)果表明：

4、支撐梁誤差對微加速度計(jì)的靈敏度和非線性誤差會產(chǎn)生一定的影響,但可以通過增大反饋電壓增益進(jìn)行弱化；當(dāng)反饋增益足夠大時(shí),支撐梁誤差的影響可以忽略不計(jì)。而熱殘余應(yīng)力等干擾外力對存在支撐梁誤差的加速度計(jì)的靈敏度沒有影響,但會引起零偏和額外的非線性誤差,并且改變反饋增益不能弱化零偏及非線性誤差?！居⑽恼縁orce-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.【關(guān)鍵詞】微加速度計(jì) 機(jī)電耦合 支撐梁誤差 吸附電壓【英文關(guān)鍵詞】micro-accelerometer electromechanical coupling errors in the support beams pull-in voltage【目錄】支撐梁有誤差的力平衡式微加速度計(jì)性能研究 摘要 6-7 Abstract 7-8 第1章 緒論 11-19 1.1 微機(jī)械電子系統(tǒng)概述 11-12 1.2 靜電MEMS機(jī)電耦合特性研究概況 12-14 1.3 力平衡式微加速度計(jì)研究概況 14-17 1.4 本文研究的主要目標(biāo)和內(nèi)容 17-19 第2章 常見MEMS結(jié)構(gòu)的等效剛度推導(dǎo) 19-33 2.1 引言 19-20 2.2 系統(tǒng)的受力和變形分析 20-32 2.2.1 雙端固支梁式平板電容系統(tǒng) 20-24 2.2.2 雙端固支梁式微加速度計(jì) 24-28