微加速度計論文：支撐梁有誤差力平衡式微加速度計性能的研究

1、微加速度計論文：支撐梁有誤差的力平衡式微加速度計性能 研究【中文摘要】基于靜電驅(qū)動與檢測技術的力平衡式微加速度計具有線性度好、動態(tài)范圍大、靈敏度高和可靠性強等優(yōu)點。由于微加工 工藝的不完善，微加速度計的實際參數(shù)與設計參數(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 梁誤差的存在將導致支撐梁的抗彎剛度不對稱，進而使得檢測質(zhì)量塊 在沿靜電力的方向作橫向運動的同時還作扭轉(zhuǎn)運動。 這樣的兩自由度 復合運動勢必會影響到力平衡式微加速度計的性能。本文提出這個新 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

2、折疊梁式的力平 衡式微加速度計三種常見微機電系統(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算式不 同。等效剛度的計算為分析靜電 MEM的機電耦合特性提供了必備條件。靜電MEM產(chǎn)品的性能與系統(tǒng)中的機電耦合特性具有密切的關 系。為了研究支撐梁誤差對機電耦合特性的影響，本文建立了單邊平板電容系統(tǒng)和雙邊平板電容系統(tǒng)的兩自由度機電耦合宏模型，分析了兩種系統(tǒng)的機電耦合特性。對于單邊平板電容系統(tǒng)，本文分析了靜電剛度效應，推導了靜電剛度矩陣；

3、分析了系統(tǒng)的靜態(tài)電壓響應，運用優(yōu)化理論計算了靜態(tài)吸附電壓，其結(jié)果得到了有限元仿真方法的驗證;除此之外,還分析了系統(tǒng)的動態(tài)電壓響應。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)出不同的運動形式；運用 優(yōu)化理論,計算出了動態(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，并計算出了靜態(tài)吸附電壓。通過這些方面的研究，為力平衡式微加速度計的性能分析奠定了理論和方法基礎。（3）利用本文所建立的平板電容系統(tǒng)作兩自由度復合運動時的機電耦合理論 和分析方法，建立了力平衡式微加速度計作兩自由度復合運動時的機 電耦合分析模型，分析了支撐梁誤差對微加速度計的性能影響，包括 靈敏度、非線

4、性誤差和零偏等。研究結(jié)果表明：支撐梁誤差對微加速 度計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 電壓增益進行弱化；當反饋增益足夠大時，支撐梁誤差的影響可以忽 略不計。而熱殘余應力等干擾外力對存在支撐梁誤差的加速度計的靈 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?Force-bala need micro-accelerometer, based onelectrostatic driv ing and sensing tech no logy, has many adva ntageous attributes, s

5、uch as good lin earity, wide dyn amic ran ge, high sen sitivity, and strong reliability. Due to the faulty of micromachining, there always exist errors between the actual p arameters and that desig ned, for in sta nces, the size error of support beams, the gap error of comb fin gers and the cen ter

6、offset of proo f-mass. The errors in support beams certa inly cause the bending rigidity of the support beams asymmetry and lead to the proo f-mass to tran slate in the directi on of electrostatic force and turn round as well. This two-degree-of-freedom compoundmotion of the proof-mass surely has so

7、me effects on the p erforma nee of a force-bala need micro-accelerometer. This thesis will focus on this new issue.The main work and con clusi ons of this thesis are as followi ngs:(1) Three com mon used structures of MEMS (MicroElectroMecha nical System), i.e. p arallel cap acitor system with two-e

8、 nd fixed beam, micro-accelerometer with two-e nd fixed beam and micro-accelerometer with double folded beams, are toke n as the exa mples to an alyze the deflecti on of supporting beams with errors un der the app lied forces. The formulas corresponding to the resistances to the applied force for th

9、e three structures, n amed equivale nt stiffness, are derived. It is shown that the resistances to the applied force for all the three structures are in a same manner of two-dime nsio nal equivale nt stiffness while the on ly differe nee lies in the formula to calculate the eleme nts of equivale nts

10、tiffness matrix. The equivale nt stiff nessis n ecessary for the an alysis of electromecha ni cal coup li ng characteristics ofelectrostatic MEMS.(2) There is a strong relationshipbetween the p erforma nee of electrostatic MEMS and itseleetromeehanicalcoupling characteristics. For the purpose to inv

11、 estigate the in flue nee of errors in support beams on eleetromeeha ni cal coup li ng characteristics, eleetromeeha ni cal coup li ng macro models with two degrees of freedom for both sin gle p arallel cap acitor system and double p arallel cap acitor system are established resp ectively, and the p

12、erformances of these two systems are analyzed. This thesis an alyzes the effect of electrostatic stiffness, and theelectrostaticstiffnessmatrix is derived. The static response of the system is an alyzed, the static p ull-i n voltage is obta ined by the method of op timizatio n, and it is verified by

13、 fin ite eleme nt simulati on. In additi on to these, the dyn amic response of the system is also an alyzed pro vided 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 op timizati on, the dyn amic p u

14、ll-i n voltage for this system is also obta in ed. Along the same line, static response of the double p arallel cap acitor system is an alyzed, and thestatic pull-involtage is obtained. All the work above lays down the foun dati on for the an alysis of p erforma nces offorce-bala need micro-accelero

15、meter.(3) App lyi ng the methods prop osed in this thesis and the results concerned with the electromecha ni cal coup li ng characteristics as the p arallel cap acitor system un derg oing the two-degree-of-freedomcompoundmotion, an electromechanicalcoupling model with two degrees of freedom for forc

16、e-bala need micro-accelerometer is established. The in flue nces caused by the errors in the support beams on the p erforma nces of the micro-accelerometer, in cludi ng sen sitivity, non li near errors, zero bias, are analyzed. The results show that the errors in the support beams will affect the se

17、n sitivity and nonlin earity errors of the micro-accelerometer, but the affecti on may be reduced by increasing the gain of feedback voltage, even when the gain of the feedback is large eno ugh, the in flue nee can be compi etely n eglected. The exter nal p erturb ing force, such as thermal residual

18、 stress, has no effects on the sen sitivity of theaccelerometer. But it will cause bias and additionalnonlinear errors, and no matter what the gain of feedback is, the zero bias and non li near errors cannot be reduced.【關鍵詞】微加速度計機電耦合支撐梁誤差吸附電壓 【英文關鍵詞】 micro-accelerometerelectromecha ni cal coup li ngerrors in the support beamsp ull-i n voltage【目錄】支撐梁有誤差的力平衡式微加速度計性能研究 摘要6-7 Abstract 7-8 第1章緒論11-191.1微機械電子系統(tǒng)概述11-121.2靜電MEM機電耦合特性研究概況12-141.3力平衡式微加速度計研究概況14-171.4本文研究的主要目標和內(nèi)容17-19 第2章常見MEM結(jié)構(gòu)的等效剛度推導 19-332.1引言19-202.2系統(tǒng)的受力和變形分析20-322.2.1雙端固支梁式平板電容系統(tǒng)20-242.2.2雙端固支梁式微加速度計24-282.2.3