微机电陀螺工艺允差分析及优化设计
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摘要
相对于传统陀螺,微机电陀螺以其体积小、功耗低、成本低等特性,在对精度要求不高的惯性导航、姿态测量领域有广泛的应用。采用体硅工艺制造的微机电陀螺其测量精度受工艺误差影响较大,且工艺误差对陀螺性能的影响与陀螺结构有关,因而工艺允差分析及陀螺结构的优化设计显得尤为重要。
本文研究的是Z轴线振动式微机电陀螺。首先建立陀螺动力学模型,再利用拉格朗日原理建立其在驱动方向和检测方向的动力学方程。Z轴陀螺可舍去一部分耦合作用项得到简化动力学方程,通过解方程得到驱动检测方向位移、品质因数、机械灵敏度、工作带宽等陀螺重要特性表达式。对静电梳齿电容驱动检测机理、静电调谐以及支撑梁刚度及其矩阵表达式进行了总体分析。
Z轴陀螺因耦合项引起的原理性误差可以忽略。基于陀螺动力学及静电驱动理论分析了加工工艺引起的质心偏移、电容梳齿结构误差、梁结构误差以及工艺残余应力对陀螺性能的影响,给出相对误差或其作用项表达式。
利用ANSYS对陀螺重要组件及整体进行仿真计算。两种支撑梁模态分析及刚度计算结果表明梁结构满足设计需要；梳齿电容仿真数据表明电容对梳齿宽度变化较敏感,梳齿刚度分析表明其在正常工作电压范围内可抗吸附。陀螺3D模型及2D模型模态分析及刚度计算表明陀螺模态频率符合匹配约束,刚度满足解耦要求,且2D模态分析与3D模态分析结果近似。陀螺3D模型及2D模型的过载分析结果表明陀螺满足过载要求。
由陀螺各结构工艺相对误差及作用项表达式、陀螺仿真数据、结构参数结合陀螺技术指标计算各结构工艺允差范围。
根据微机电陀螺动力学及仿真分析结果,确定其主要性能指标要求。考虑陀螺的指标性约束和设计性约束条件,将梁结构中长宽量作为设计变量,利用ANSYS中优化组件基于不同优化目标函数完成陀螺结构的优化设计
MEMS gyroscope has been applied widely in low precision inertial navigation and attitude determination systems for its smaller volume, lower power consumption, lower cost and some other features compared with traditional gyroscope. Measuring accuracy of MEMS gyroscope is great affected by bulk-silicon manufacture processing error, and the processing error effect on gyroscope performance is related with the gyroscope structure, so the analysis of processing tolerance and the gyroscope structure optimal design are very important.
In this paper, the dynamic model of Z-axis linear vibration MEMS gyroscope was established firstly, and then the dynamic equations of drive and detect direction were attained by Lagrange Principle. Some coupling terms were discarded and the simplified kinetic equations of Z-axis gyroscope were achieved. The expression of driven displacement related with driving force, the quality factor, the mechanical sensitivity related with modal frequency, the bandwidth and other important gyroscope characteristics were obtained by solving the simplified kinetic equation. The drive and detection mechanism of electrostatic comb capacitive, electrostatic tuning, the support beam stiffness and its matrix expressions were analyzed overall.
The theoretical error caused by coupling term can be ignored. Based on gyroscope dynamic and electrostatic drive theory, the effects on the gyroscope caused by center offset of mass, structure deviation of capacitor, structure deviation of beam and residual stress were analyzed. The expression of relative error and interaction term caused by processing error was listed.
The model simulated calculation of important component and the entire gyroscope were done used ANSYS software. The model analysis of two folding support beam structures indicated that the stiffness of folding beam meet the design requirements; the simulation data of comb capacitor indicated that the capacitance is more sensitive for variation of comb width; the comb operated in normal voltage range can be anti-adsorption. The gyroscope mode analysis and stiffness calculations of 3D and 2D model show that gyroscope mode frequency satisfied matching constraints, stiffness meet the decoupling requirements and modal analysis of 2D have approximate result with 3D modal analysis. The overload results of 3D and 2D model show that the gyroscope anti-overload requirement has been satisfied.
From relative processing error expression of different gyroscope structures, the interaction term expressions caused by process error, gyroscope simulation data and structural parameters combined with gyroscope technology targets, the different processing tolerance ranges were calculated.
According to the gyroscope dynamics and simulation results, the major MEMS gyroscope performance requirements were determined. The target constraints and design constraints were both taken into account, the length and width of beam structure were set as design variables, the optimal design of gyroscope structure was completed based on different objective functions used optimal component in ANSYS.
本文研究的是Z轴线振动式微机电陀螺。首先建立陀螺动力学模型,再利用拉格朗日原理建立其在驱动方向和检测方向的动力学方程。Z轴陀螺可舍去一部分耦合作用项得到简化动力学方程,通过解方程得到驱动检测方向位移、品质因数、机械灵敏度、工作带宽等陀螺重要特性表达式。对静电梳齿电容驱动检测机理、静电调谐以及支撑梁刚度及其矩阵表达式进行了总体分析。
Z轴陀螺因耦合项引起的原理性误差可以忽略。基于陀螺动力学及静电驱动理论分析了加工工艺引起的质心偏移、电容梳齿结构误差、梁结构误差以及工艺残余应力对陀螺性能的影响,给出相对误差或其作用项表达式。
利用ANSYS对陀螺重要组件及整体进行仿真计算。两种支撑梁模态分析及刚度计算结果表明梁结构满足设计需要；梳齿电容仿真数据表明电容对梳齿宽度变化较敏感,梳齿刚度分析表明其在正常工作电压范围内可抗吸附。陀螺3D模型及2D模型模态分析及刚度计算表明陀螺模态频率符合匹配约束,刚度满足解耦要求,且2D模态分析与3D模态分析结果近似。陀螺3D模型及2D模型的过载分析结果表明陀螺满足过载要求。
由陀螺各结构工艺相对误差及作用项表达式、陀螺仿真数据、结构参数结合陀螺技术指标计算各结构工艺允差范围。
根据微机电陀螺动力学及仿真分析结果,确定其主要性能指标要求。考虑陀螺的指标性约束和设计性约束条件,将梁结构中长宽量作为设计变量,利用ANSYS中优化组件基于不同优化目标函数完成陀螺结构的优化设计
MEMS gyroscope has been applied widely in low precision inertial navigation and attitude determination systems for its smaller volume, lower power consumption, lower cost and some other features compared with traditional gyroscope. Measuring accuracy of MEMS gyroscope is great affected by bulk-silicon manufacture processing error, and the processing error effect on gyroscope performance is related with the gyroscope structure, so the analysis of processing tolerance and the gyroscope structure optimal design are very important.
In this paper, the dynamic model of Z-axis linear vibration MEMS gyroscope was established firstly, and then the dynamic equations of drive and detect direction were attained by Lagrange Principle. Some coupling terms were discarded and the simplified kinetic equations of Z-axis gyroscope were achieved. The expression of driven displacement related with driving force, the quality factor, the mechanical sensitivity related with modal frequency, the bandwidth and other important gyroscope characteristics were obtained by solving the simplified kinetic equation. The drive and detection mechanism of electrostatic comb capacitive, electrostatic tuning, the support beam stiffness and its matrix expressions were analyzed overall.
The theoretical error caused by coupling term can be ignored. Based on gyroscope dynamic and electrostatic drive theory, the effects on the gyroscope caused by center offset of mass, structure deviation of capacitor, structure deviation of beam and residual stress were analyzed. The expression of relative error and interaction term caused by processing error was listed.
The model simulated calculation of important component and the entire gyroscope were done used ANSYS software. The model analysis of two folding support beam structures indicated that the stiffness of folding beam meet the design requirements; the simulation data of comb capacitor indicated that the capacitance is more sensitive for variation of comb width; the comb operated in normal voltage range can be anti-adsorption. The gyroscope mode analysis and stiffness calculations of 3D and 2D model show that gyroscope mode frequency satisfied matching constraints, stiffness meet the decoupling requirements and modal analysis of 2D have approximate result with 3D modal analysis. The overload results of 3D and 2D model show that the gyroscope anti-overload requirement has been satisfied.
From relative processing error expression of different gyroscope structures, the interaction term expressions caused by process error, gyroscope simulation data and structural parameters combined with gyroscope technology targets, the different processing tolerance ranges were calculated.
According to the gyroscope dynamics and simulation results, the major MEMS gyroscope performance requirements were determined. The target constraints and design constraints were both taken into account, the length and width of beam structure were set as design variables, the optimal design of gyroscope structure was completed based on different objective functions used optimal component in ANSYS.
引文
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[2]杨培根,龚智炳.光电惯性技术[M].北京：兵器工业出版社,1999.
[3]Eddy.D.S, Sparks.D.R. Application of MEMS Technology in Automotive Sensors and Actuators [DB/OL]. Proc. IEEE,1998,86(8):1747-1755.
[4]蒋庆华.音叉电容式微机械陀螺接口电路设计研究[D].西安：西北工业大学,2004,3：1-7.
[5]熊斌.栅结构微机械振动式陀螺[D].上海：中国科学院上海微系统与信息技术研究所,2001.
[6]谢建兵.Z轴微机械陀螺的集成设计技术[D].西安：西北工业大学,2006.
[7]Bernstein.J, Cho.S, King.A.T, Kourepenis.A, et al. A Micromachined Comb-drive Tuningfork Rate Gyroscope [C]. Proc. IEEE Micro Electro Mechanical Systems Workshop (MEMS'93), Fort Lauderdale, FL, Feb.1993:143-148.
[8]Weinberg. M, Bernstein. J, Cho. S, King. A. T, et al. A Micromachined Comb-drive Tuning Fork Gyroscope for Commercial Applications[M].Proc.Sensor Expo, Cleveland, OH, 1994:187-193.
[9]施芹.提高硅微陀螺仪性能若干关键技术研究[D].南京：东南大学,2005：1-12.
[10]罗跃生.硅微型陀螺仪的力学分析和数学模型[D].哈尔滨：哈尔滨工程大学,2003：1-8.
[11]Boxenhom.B, Greiff.P.A Vibratory Micromachined Guroscope[C]. AIAA Guidance and control conference, Minnespolis, Mn, August 15-17,1988:1033-1039.
[12]Greiff.P, Boxenhorn.B, T.king, et al. Silicon Monolithic Micromachined Gyroscope[C]. Tech. Dig.6th Int Conf. Solid-state Sensors and Actuators (Transducers'91), San Francisco, CA, June,1991:1033-1039.
[13]Kuisma.H, Ryhanen.T, Lahdenpera. J, et al. A Bulk Micromachined Silicon Angular Rate Sensor[C]. Tech. Dig.v 9th Int. Conf. Solid-state Sensors and Actuators (Transducers'97), Chicago, IL, June 1997:875-878.
[14]Tanaka.K, Mochida.Y, Sugimoto.M, et al. A Micromachined Vibrating Gyroscope[C]. Proc. IEEE Micro Electro Mechanical Systems Workshop (MEMS'95), Amsterdam, Jan. 29-Feb.2,1995:278-281.
[15]Tanaka.K, Mochida.Y, Sugimoto.M, et al. A Micromachined Vibrating Gyroscope [J]. Sensors and Actuators,1995, A(50):111-115.
[16]Weinberg.M, Bemstein.J, Cho.S, et al. A Micro-machined Comb-drive Tuning Fork Gyroscope for Commercial Application [M]. Froc. Sensoe Expo, Cleveland, OH, 1994:187-193.
[17]Oh.Y.S, Lee.B.L, Baek.S.S, et al. A Surface Micromachined Tunable Vibratory Gyroscope[C]. Froc. IEEE Micro Electro Mechanical Systems Workshop (MEMS'97), Japan,1997:272-277.
[18]Voss.R, Bauer.K, Ficker.W, et al. Silicon Angular Rate Sensor for Automotive Applications with Piezoelectric Drive and Piezoresistive Read-out[C]. Tech. Dig.9th Int. Conf. Solid-state Sensors and Actuators, Chicago, IL, June 1997:879-882.
[19]Jan Soderkvist. Micromachined Gyroscope [J]. Sensors and Actuators,1994, A(43):65-71.
[20]Bochobza-Degani Ofir, Seter.Dan J, Socher.E, et al. A Novel Micromachined Vibrating Rate-gyroscope with Optical Sensing and Electrostatic Actuation[J]. Sensors and Actuators A (83) 2000:54-60.
[21]苏岩,杨拥军,王寿荣,等.微机械电子隧穿陀螺仪初步研究[J].传感技术学,1999,12(4)：223-228.
[22]韩天.解耦结构微机械陀螺特性研究[D].哈尔滨：哈尔滨工业大学：2-3.
[23]Bernstein.J, Cho.S, king.A.T, et al. A Micromachined Comb-drive Tuning Fork Rate Gyroscope[C]. Frco. IEEE Micro Elentro Mechanical Systems Workshop (MEMS'93), Fort Lauderdale, FL, Feb.1993:143-148.
[24]Maenaka.K, Fujita.T. Analysis of A Highly Sensitive Silicon Gyroscope with Cantilever Beam as Vibrating Mass [J]. Sensors and Actuators,1996, A(54):568-573.
[25]Wood.D, Cooper.G, Burdess.J, et al. A Silicon Membrane Gyroscope with Electrostatic Actuation and Sensing[C]. Proc. SPIE 1995 Symp.
[26]Ayazi.F, Najafi.K. A HARPSS Polysilicon Vibrating Ring Gyroscope[J]. Micro-electromech. Syst.,2001, Vol.10(2):169-179.
[27]Cimoo Song, Byeoungju Ha, Sukhan Lee. Micromachined Inertial Sensors[C]. Proceedings of the 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems,1999.
[28]NAVID YAZDI, Farrokh Ayazi, Khalil Najafi. Micromachined Inertial Sensors [J]. Proceedings of the IEEE, August 1998,86 (8):1640-1659.
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