考虑边缘效应的MEMS梳齿谐振器的静动力学特性分析
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摘要
MEMS梳齿谐振器是一种高精度微机械电子元件,广泛应用在航天航空、精密测量、国防军事、通讯等领域,其静动力学问题受到研究人员的广泛关注。静电激励力是研究MEMS动力学的基础,但由于梳齿高纵深比的结构特性,其静电力存在很强的边缘效应现象。采用最小二乘法拟合了在边缘效应基础上梳齿结构静电力的模型,分析了边缘效应对MEMS梳齿谐振器动力学行为的影响。探讨了梳齿微谐振器的横向稳定性、谐振频率、软硬特性的区分标准以及线性过渡现象的参数表达式。结果表明:边缘效应模型导致系统稳定区间减小,经典模型高估了微梳齿谐振器的振动稳定性;边缘效应会导致系统固有频率的减小,软化行为增强,线性过渡电压减小;随着梳齿初始间距的增大,系统的线性过渡下的最优设计电压逐渐变大,对应谐振频率逐渐减小。
Micro-electro-mechanical systems( MEMS) comb resonator is a micro mechanical & electronic component with high precision and widely applied in aerospace,precision measurement,national defense and military,communications and other fields.Its static and dynamic characteristics receive more and more attentions.Due to the particularity of comb structure,the fringe effect of its electrostatic force is very strong.Here,a MEMS comb resonator's electrostatic force model considering the fringe effect was fitted with the least-squares method.The influence of fringe effect on the dynamic characteristics of a MEMS comb resonator was analyzed.The system's lateral stability and resonance frequency were explored.The criterion to distinguish the hard character from the soft one was defined.Moreover,two explicit formulas to describe the optimal DC voltage and the equivalent natural frequency when a linear-like state appeared were deduced,respectively.The results showed that the model with the fringe effect causes a smaller stable region of the system compared to the traditional model,the latter over-estimates the stability of a MEMS comb resonator;the fringe effect also causes decrease in the system natural frequency and the transient voltage from hard character to soft one,and enhancement of softening behavior; with increase in the initial spacing of the comb,the designed optimal system voltage increases gradually,while the corresponding resonance frequency decreases.
Micro-electro-mechanical systems( MEMS) comb resonator is a micro mechanical & electronic component with high precision and widely applied in aerospace,precision measurement,national defense and military,communications and other fields.Its static and dynamic characteristics receive more and more attentions.Due to the particularity of comb structure,the fringe effect of its electrostatic force is very strong.Here,a MEMS comb resonator's electrostatic force model considering the fringe effect was fitted with the least-squares method.The influence of fringe effect on the dynamic characteristics of a MEMS comb resonator was analyzed.The system's lateral stability and resonance frequency were explored.The criterion to distinguish the hard character from the soft one was defined.Moreover,two explicit formulas to describe the optimal DC voltage and the equivalent natural frequency when a linear-like state appeared were deduced,respectively.The results showed that the model with the fringe effect causes a smaller stable region of the system compared to the traditional model,the latter over-estimates the stability of a MEMS comb resonator;the fringe effect also causes decrease in the system natural frequency and the transient voltage from hard character to soft one,and enhancement of softening behavior; with increase in the initial spacing of the comb,the designed optimal system voltage increases gradually,while the corresponding resonance frequency decreases.
引文
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[3]张琪昌,任环,韩建鑫.时滞控制下的微梳状驱动器动力学研究[J].振动与冲击,2016,35(18):40-45.ZHANG Qichang,REN Huan,HAN Jianxin.Nonlinear dynamics of folded-MEMS comb drive resonators with timedelayed control[J].Journal of Vibration and Shock,2016,35(18):40-45.
[4]NGUYEN T C,HOWE R T.An integrated CMOS micromechanical resonator high-Q oscillator[J].IEEE Journal of Solid-State Circuits,1999,34(4):440-455.
[5]ELSHURAFA A M,KHIRALLAH K,TAWFIK H H,et al.Nonlinear dynamics of spring softening and hardening in folded-MEMS comb drive resonators[J].Journal of Microelectromechanical Systems,2011,20(4):943-958.
[6]HAN J,ZHANG Q,WANG W.Static bifurcation and primary resonance analysis of a MEMS resonator actuated by two symmetrical electrodes[J].Nonlinear Dynamics,2015,80(3):1585-1599.
[7]ZHONG Z Y,ZHONG W M,MENG G,et al.Inclination effects on the frequency tuning of comb-driven resonators[J].Journal of Microelectromechanical Systems,2013,22(4):865-875.
[8]张峰,苑伟政,常洪龙,等.静电梳齿驱动结构的稳定性分析[J].传感技术学报,2011,27(8):1122-1125.ZHANG Feng,YUAN Weizheng,CHANG Honglong,et al.Analysis of lateral stability of electrostatic comb-drive structure[J].Chinese Journal of Sensors and Actuators,2011,24(8):1122-1125.
[9]袁丽芸,向宇,陆静.考虑边缘效应的扭转微镜的动力响应分析[J].振动与冲击,2007,26(12):122-126.YUAN Liyun,XIANG Yu,LU Jing.Analysis on dynamic characteristics of torsional micromirror model with consideration of edge effects[J].Journal of Vibration and Shock,2007,26(12):122-126.
[10]DONG L,HUO W,YAN H,et al.Analysis of fringe effect of MEMS comb capacitor with slot structures[J].Integrated Ferroelectrics,2011,129(1):122-132.
[11]高世桥,刘海鹏.微机电系统力学[M].北京:国防工业出版社,2008.
[12]姚峰林,高世桥.微陀螺梳齿静电驱动力的计算方法[J].传感技术学报,2011,24(9):1265-1269.YAO Fenglin,GAO Shiqiao.The calculation method of the electrostatic drive force of micro machined groscope comb[J].Chinese Journal of Sensors and Actuators,2011,24(9):1265-1269.
[13]赵剑,王洪喜,贾建援.计及边缘效应的静电驱动微结构静电力计算[J].微纳电子技术,2006,43(2):95-97.ZHAO Jian,WANG Hongxi,JIA Jianyuan.Computation of electrostatic force with edge effects for micro-structures[J].Micronanoelectronic Technology,2006,43(2):95-97.
[14]XIAO Z,PENG W,WOLFFENBUTTEL R F,et al.Micromachined variable capacitors with wide tuning range[J].Sensors&Actuators A Physical,2003,104(3):299-305.
[15]DA SILVA M R M C,GLYNN C C.Nonlinear flexuralflexural-torsional dynamics of inextensional beams.II.Forced motions[J].Mechanics Based Design of Structures and Machines,1978,6(4):449-461.
[16]王洪礼,张琪昌.非线性动力学理论及其应用[M].天津:天津科学技术出版社,2000.
[17]KHIRALLAH K.Parametric excitation,amplification,and tuning of MEMS folded-beam comb drive oscillator[J].Journal of Microelectromechanical Systems,2013,22(2):318-330.