蝶翼式微陀螺零偏稳定性提升关键技术研究
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摘要
陀螺仪是测量运载体角运动的传感器，是惯性导航系统的基础核心器件之一，在军事和民用领域都具有非常重要的应用价值。与传统的机械转子陀螺、静电陀螺、激光陀螺和光纤陀螺相比，微机电陀螺具有体积小、成本低、功耗低、易于批量化生产等显著特点，在制导弹药、无人作战系统等武器装备中具有广泛的应用前景。国外对高性能微机电陀螺实行产品和技术的严格控制，而目前我国研制的微机电陀螺整体水平与应用需求还存在较大差距。作为陀螺仪的核心技术指标之一，零偏稳定性的提升是高性能微机电陀螺研制的关键技术。
微机电陀螺虽然体积小，结构相对简单，却是一个非常复杂的机电耦合系统。其结构精度容易受设计水平、制造误差等条件限制，同时在工程应用中又会面临温变、振动冲击等复杂环境，零偏稳定性的形成机理非常复杂。本实验室针对国内武器装备对微机电陀螺的迫切需求，研制了一种蝶翼式硅微陀螺。掌握了该微陀螺的结构设计、加工工艺和信号检测等基本理论和关键技术，成功研制了原理样机。本论文以蝶翼式微陀螺为对象，围绕微机电陀螺零偏稳定性的提升方法开展研究，重点解决蝶翼式微陀螺的模态耦合误差、结构应力、制造误差等关键问题，为我国发展高性能微机电陀螺提供新的设计理论和方法。主要研究内容如下：
1.介绍了蝶翼式微陀螺的总体结构和工作原理，并对其动态特性和测控技术进行了系统研究。重点推导了各向异性条件下平行四边形截面支撑梁的弯曲刚度和扭转刚度，理论分析了蝶翼式微陀螺的系统阻尼、驱动力矩和哥氏力矩。建立了微陀螺工作模态频率的理论模型和动力学方程，得到了机械灵敏度、带宽等动力学特性的解析表达式。采用了基于双正弦载波的微弱电容检测方法和基于PID振动幅值控制的闭环驱动方法，成功地实现了驱动信号和检测信号的分离。最终得出了理想情况下蝶翼式微陀螺角速度输出信号的理论模型。
2.研究了蝶翼式微陀螺零偏稳定性产生机理及其主要误差来源。建立了蝶翼式微陀螺的模态耦合误差模型，主要包括：静电力耦合误差、哥氏力耦合误差、驱动-检测振动耦合误差、检测-驱动振动耦合误差。分别研究了结构误差、电路误差和环境误差等确定性误差对蝶翼式微陀螺零偏稳定性的影响规律。
3.研究了蝶翼式微陀螺加工过程中形成的结构应力及其对微陀螺零偏稳定性的影响规律，并对微陀螺结构进行了优化设计。理论分析了静电吸合效应、轴向热应力、贴片封装应力对蝶翼式微陀螺结构变形和动态特性的影响规律。通过悬臂梁和双端固支梁结构的对比，建立了蝶翼式微陀螺自由状态下和轴向热应力作用下模态频率的理论模型。分别设计了蝶翼式微陀螺的应力释放槽结构、弹性支撑框架结构以及基于材料补偿方法的应力平衡结构。改进后，微陀螺接口电容、模态频率、品质因子和零偏输出的温度特性得到了明显提升。
4.研究了蝶翼式微陀螺的结构制造误差及其对零偏稳定性的影响规律，并采用激光微加工的方法对结构误差进行了精密修形实验。重点分析了材料几何形状误差和制造过程中的对准误差及湿法腐蚀加工误差对微陀螺结构加工精度和零偏稳定性的影响规律。研究了蝶翼式微陀螺结构制造误差精密修形的工作原理，并采用紫外激光微加工系统对蝶翼式微陀螺的敏感结构进行了精密修形实验。激光修形后，微陀螺的模态耦合误差显著减小。
5.对改进前后蝶翼式微陀螺的主要性能指标进行了对比测试，主要包括标度因数、标度因数非线性度、标度因数温度系数、零偏稳定性、零偏温度灵敏度等。测试结果表明，微陀螺的标度因数非线性、标度因数温度系数、短时启动下的零偏稳定性以及零偏温度灵敏度都得到了大幅提升。
Gyroscope is the sensor that measures the rate of rotation of a carrier. It is one ofthe basical core devices in inertial navigation system and has very important militaryand civil applications. Because of its small size, low cost, low power consumption andbatch fabrication compared to traditional mechanical spinning gyroscope, electrostaticgyroscope, laser gyroscope and fiber optical gyroscope, micromachined gyroscope hasan extensive application prospect in the weapons such as guided munitions andunmanned combat vehicles. The related products and technologies of high performancegyroscopes are embargoed against China by foreign countries while most domesticmicromachined gyroscopes can not meet the demands. Therefore, improvement in biasstability which is one of the core performance specifications is the key technology fordeveloping high performance micromachined gyroscope.
Although it has a small volume and simple structure, the micromachined gyroscopeis a complex electromechanical coupling system. Its structural precision is easilyrestricted by design level, fabrication imperfections, etc. Meanwhile, it is faced withtemperature variations, vibrations and shocks in engineering applications. So theformation mechanism of bias is complicated. Aiming at the urgent demands of weaponequipment, we developed a micromachined butterfly gyroscope. The basical theoriesand key technologies of structure designing, micromachining and signal processingwere studied. This dissertation focuses on the methods of improving the bias stability ofmicromachined gyroscopes, which takes the micromachined butterfly gyroscope as theobject. Breakthroughs were made on the key technologies such as modal coupling error,structural stress and fabrication imperfection. The research results will provide a noveldesign theory and method for developing high performance micromachined gyroscopes.The main research contents of this dissertation are as follows:
1. The structure and operation principle of the micromachined butterfly gyroscopewere presented, and its dynamic characteristics and readout technologies weresystematically studied. Emphatically, the bending and torsional stiffnesses of thesuspension beam, which has a parallelogram cross section, were derived considering theanisotropic properties of monocrystalline silicon. The damp, driving and Coriolismoments of the gyroscope were derived. The operation modal frequencies and thedynamic equation of the gyroscope were theoretically modeled. Then, expressions ofthe mechanical sensitivity and bandwidth of the gyroscope were obtained. According toits capacitive output characteristics, capacitance detection using double sinusoidalcarriers and closed loop excitation using PID controller were adopted in the readoutcircuit. The driving singal and sensing signal were successfully extracted from eachother. Finally, the theoretical model of the output signal of the gyroscope due to angular rate inputs was obtained.
2. The formation mechanism and major sources of bias stability of the gyroscopewere studied. The model of the modal coupling errors which contain electrostatic forcecoupling error, Coriolis force coupling error, vibration coupling between drivingoscillator and sensing oscillator was established. Finally, the systematic errors such asstructural error, circuit error and environmental error and their influence on the biasstability were studied.
3. Structural stresses induced during the fabrication process and their effectmechanisms were studied, and the mechanical structure of the gyroscope was optimized.Structure deformation and dynamic characterictics affected by the pull-in effect, axialthermal stress and internal stresses induced by the die attachment and package weretheoretically analyzed. In order to theoretically model the modal frequency of thegyroscope under action of the axial thermal stress, two types of structures whichadopted a clamped-free suspension beam and a clamped-clamped suspension beam weredesigned and characterized. Structures adopting stress release groove, flexural supportframe and stress balancing were designed and characterized. The temperatureperformance of the capacitance output, modal frequency, quality factor and bias outputwere evidently improved.
4. Fabrication imperfections of the micromachined gyroscope and their influenceson the bias stability were studied. The structural trimming method was experimentallycharacterized by UV laser micromachining. Emphatically, geometric errors of thematerials and fabrication imperfections due to misalignments and etching defect andtheir influences on the structure precision and bias stability were analyzed. Theoperation principle of structure trimming was studied and experimentally characterizedby UV laser micromachining. The experimental results showed that the modal couplingerror of the gyroscope was decreased significantly after laser trimming.
5. Test and comparison of the major performance specifications including scalefactor, nonlinearity, bias stability, temperature sensitivities of scale factor and biasstability were carried out for the micromachined butterfly gyroscopes before and afterimproving. The results showed that the nonlinearity, temperature sensitivities and biasstability under short in-run time were improved significantly.
微机电陀螺虽然体积小，结构相对简单，却是一个非常复杂的机电耦合系统。其结构精度容易受设计水平、制造误差等条件限制，同时在工程应用中又会面临温变、振动冲击等复杂环境，零偏稳定性的形成机理非常复杂。本实验室针对国内武器装备对微机电陀螺的迫切需求，研制了一种蝶翼式硅微陀螺。掌握了该微陀螺的结构设计、加工工艺和信号检测等基本理论和关键技术，成功研制了原理样机。本论文以蝶翼式微陀螺为对象，围绕微机电陀螺零偏稳定性的提升方法开展研究，重点解决蝶翼式微陀螺的模态耦合误差、结构应力、制造误差等关键问题，为我国发展高性能微机电陀螺提供新的设计理论和方法。主要研究内容如下：
1.介绍了蝶翼式微陀螺的总体结构和工作原理，并对其动态特性和测控技术进行了系统研究。重点推导了各向异性条件下平行四边形截面支撑梁的弯曲刚度和扭转刚度，理论分析了蝶翼式微陀螺的系统阻尼、驱动力矩和哥氏力矩。建立了微陀螺工作模态频率的理论模型和动力学方程，得到了机械灵敏度、带宽等动力学特性的解析表达式。采用了基于双正弦载波的微弱电容检测方法和基于PID振动幅值控制的闭环驱动方法，成功地实现了驱动信号和检测信号的分离。最终得出了理想情况下蝶翼式微陀螺角速度输出信号的理论模型。
2.研究了蝶翼式微陀螺零偏稳定性产生机理及其主要误差来源。建立了蝶翼式微陀螺的模态耦合误差模型，主要包括：静电力耦合误差、哥氏力耦合误差、驱动-检测振动耦合误差、检测-驱动振动耦合误差。分别研究了结构误差、电路误差和环境误差等确定性误差对蝶翼式微陀螺零偏稳定性的影响规律。
3.研究了蝶翼式微陀螺加工过程中形成的结构应力及其对微陀螺零偏稳定性的影响规律，并对微陀螺结构进行了优化设计。理论分析了静电吸合效应、轴向热应力、贴片封装应力对蝶翼式微陀螺结构变形和动态特性的影响规律。通过悬臂梁和双端固支梁结构的对比，建立了蝶翼式微陀螺自由状态下和轴向热应力作用下模态频率的理论模型。分别设计了蝶翼式微陀螺的应力释放槽结构、弹性支撑框架结构以及基于材料补偿方法的应力平衡结构。改进后，微陀螺接口电容、模态频率、品质因子和零偏输出的温度特性得到了明显提升。
4.研究了蝶翼式微陀螺的结构制造误差及其对零偏稳定性的影响规律，并采用激光微加工的方法对结构误差进行了精密修形实验。重点分析了材料几何形状误差和制造过程中的对准误差及湿法腐蚀加工误差对微陀螺结构加工精度和零偏稳定性的影响规律。研究了蝶翼式微陀螺结构制造误差精密修形的工作原理，并采用紫外激光微加工系统对蝶翼式微陀螺的敏感结构进行了精密修形实验。激光修形后，微陀螺的模态耦合误差显著减小。
5.对改进前后蝶翼式微陀螺的主要性能指标进行了对比测试，主要包括标度因数、标度因数非线性度、标度因数温度系数、零偏稳定性、零偏温度灵敏度等。测试结果表明，微陀螺的标度因数非线性、标度因数温度系数、短时启动下的零偏稳定性以及零偏温度灵敏度都得到了大幅提升。
Gyroscope is the sensor that measures the rate of rotation of a carrier. It is one ofthe basical core devices in inertial navigation system and has very important militaryand civil applications. Because of its small size, low cost, low power consumption andbatch fabrication compared to traditional mechanical spinning gyroscope, electrostaticgyroscope, laser gyroscope and fiber optical gyroscope, micromachined gyroscope hasan extensive application prospect in the weapons such as guided munitions andunmanned combat vehicles. The related products and technologies of high performancegyroscopes are embargoed against China by foreign countries while most domesticmicromachined gyroscopes can not meet the demands. Therefore, improvement in biasstability which is one of the core performance specifications is the key technology fordeveloping high performance micromachined gyroscope.
Although it has a small volume and simple structure, the micromachined gyroscopeis a complex electromechanical coupling system. Its structural precision is easilyrestricted by design level, fabrication imperfections, etc. Meanwhile, it is faced withtemperature variations, vibrations and shocks in engineering applications. So theformation mechanism of bias is complicated. Aiming at the urgent demands of weaponequipment, we developed a micromachined butterfly gyroscope. The basical theoriesand key technologies of structure designing, micromachining and signal processingwere studied. This dissertation focuses on the methods of improving the bias stability ofmicromachined gyroscopes, which takes the micromachined butterfly gyroscope as theobject. Breakthroughs were made on the key technologies such as modal coupling error,structural stress and fabrication imperfection. The research results will provide a noveldesign theory and method for developing high performance micromachined gyroscopes.The main research contents of this dissertation are as follows:
1. The structure and operation principle of the micromachined butterfly gyroscopewere presented, and its dynamic characteristics and readout technologies weresystematically studied. Emphatically, the bending and torsional stiffnesses of thesuspension beam, which has a parallelogram cross section, were derived considering theanisotropic properties of monocrystalline silicon. The damp, driving and Coriolismoments of the gyroscope were derived. The operation modal frequencies and thedynamic equation of the gyroscope were theoretically modeled. Then, expressions ofthe mechanical sensitivity and bandwidth of the gyroscope were obtained. According toits capacitive output characteristics, capacitance detection using double sinusoidalcarriers and closed loop excitation using PID controller were adopted in the readoutcircuit. The driving singal and sensing signal were successfully extracted from eachother. Finally, the theoretical model of the output signal of the gyroscope due to angular rate inputs was obtained.
2. The formation mechanism and major sources of bias stability of the gyroscopewere studied. The model of the modal coupling errors which contain electrostatic forcecoupling error, Coriolis force coupling error, vibration coupling between drivingoscillator and sensing oscillator was established. Finally, the systematic errors such asstructural error, circuit error and environmental error and their influence on the biasstability were studied.
3. Structural stresses induced during the fabrication process and their effectmechanisms were studied, and the mechanical structure of the gyroscope was optimized.Structure deformation and dynamic characterictics affected by the pull-in effect, axialthermal stress and internal stresses induced by the die attachment and package weretheoretically analyzed. In order to theoretically model the modal frequency of thegyroscope under action of the axial thermal stress, two types of structures whichadopted a clamped-free suspension beam and a clamped-clamped suspension beam weredesigned and characterized. Structures adopting stress release groove, flexural supportframe and stress balancing were designed and characterized. The temperatureperformance of the capacitance output, modal frequency, quality factor and bias outputwere evidently improved.
4. Fabrication imperfections of the micromachined gyroscope and their influenceson the bias stability were studied. The structural trimming method was experimentallycharacterized by UV laser micromachining. Emphatically, geometric errors of thematerials and fabrication imperfections due to misalignments and etching defect andtheir influences on the structure precision and bias stability were analyzed. Theoperation principle of structure trimming was studied and experimentally characterizedby UV laser micromachining. The experimental results showed that the modal couplingerror of the gyroscope was decreased significantly after laser trimming.
5. Test and comparison of the major performance specifications including scalefactor, nonlinearity, bias stability, temperature sensitivities of scale factor and biasstability were carried out for the micromachined butterfly gyroscopes before and afterimproving. The results showed that the nonlinearity, temperature sensitivities and biasstability under short in-run time were improved significantly.
引文
[1] IEEE STD528-1994. IEEE Standard for Inertial Sensor Terminology.
[2]刘俊,石云波,李杰.微惯性技术[M].北京:电子工业出版社,2005.
[3] N. Yazdi, F. Ayazi, and K. Najafi. Micromachined Inertial Sensors[J].Proceedings of the IEEE.1998,86(8):1640-1659.
[4] R. H. Dixon, J. Bouchaud. Markets and applications for MEMS inertialsensors[C]. Proc. SPIE2006,6113,1-13.
[5] T. Brown, B. Davis, D. Hepner, J. Faust, C. Myers, P. Muller, T. Harkins, M.Hollis, C. Miller and B. Placzankis. Strap-down microelectromechanical (MEMS)sensors for high-g munition applications[C]. IEEE Transactions on magnetic,37(1):336-342, January2001.
[6] K. Najafi, J. Chae, H. Kulah and Guohong He. Micromachined SiliconAccelerometers and Gyroscopes[C]. Proceedings of the2003IEEE/RSJ,International Conference on Intelligent Robots and Systems, Las Vegas, Nevada,2003:2353-2358.
[7] A. Sharma, M. Zaman, M. Zucher, F. Ayazi. A0.1°/h Bias Drift ElectronicallyMatched Tuning Fork Microgyroscope. Proceedings of IEEE MEMS, Tucson,AZ,2008:6-9
[8] P. Greiff, B. Boxenhorn, T. King, et al. Silicon Monolithic MicromechanicalGyroscope[C]. Proceedings of International Conference on Solid-State Sensorsand Actuators,1991:966-968.
[9] ADXR646Datasheet. www.analog.com,2011.
[10] IBG21Datasheet. www.imego.com,2012.
[11] SAR10Gyro Sensor Series Datasheet. www.sensonor.com,2012.
[12] CRS09Datasheet. www.siliconsensing.com,2012.
[13] J. Bernstein. A Micromachined Comb-drive Tuning Fork Rate Gyroscope[C].Proceedings of IEEE MEMS,1993:143-148.
[14] R. Neul, U. M. Gómez, K. Kehr. Micromachined Angular Rate Sensors forAutomotive Applications[J]. IEEE Sensors Journal,2007,7(2):302-309.
[15] M. Lutz, W. Golderer, J. Gerstenmeier, J. Marek. A Precision Yaw Rate Sensorin Silicon Micromachining[C]. Proceedings of International Conference onSolid-State Sensors and Actuators, Chicago, IL,1997:847-850.
[16] A. Thomae, R. Schellin, M. Lang, W. Bauer. A Low Cost Angular Rate Sensor inSi-surface Micromachining Technology for Automotive Application[C].Proceedings of SAE, Detroit,1999:0931-0936.
[17] W. Geiger, W. Butt, A. GaiBer, J. Frech. Decoupled Microgyros and the DesignPrinciple DAVED[J]. Sensors and Actuators A,2002,95:239-249.
[18] Geiger, B. Folkmer, U. Sobe, H. Sandrnaier. New Designs of MicromachinedVibrating Rate Gyroscopes with Delcoupled Oscillation Modes[C]. Proceedingsof International Conference on Solid-State Sensors and Actuators, Chicago,1997:1129-1132.
[19] W. Geiger, J. Bartholomeyczik, U. Breng, et al. MEMS IMU for AHRSApplications[C]. Proceedings of the IEEE.2008:225-231.
[20] C. Acar. Robust Micromachined Vibratory Gyroscopes[D]. PhD thesis, UCIrvine,2004.
[21] C. Acar and A. Shkel. Inherently Robust Micromachined Gyroscopes with2-DOF Sense-Mode Oscillator[J]. Journal of Microelectromechanical Systems,2006,15(2):380-387.
[22] A. R. Schofield, A. A. Trusov and A. M. Shkel. Effects of Operational FrequencyScaling in Multi-Degree of Freedom MEMS Gyroscopes[J]. Journal ofMicroelectromechanical Systems,2008,8(10):1672-1680.
[23] C. Acar, A. R. Schofield, A. A. Trusov and A. M. Shkel. Environmentally RobustMEMS Vibratory Gyroscopes for Automotive Applications[J]. IEEE SensorsJournal,2009,9(12):1895-1906.
[24] A. A. Trusov, A. R. Schofield and A. M. Shkel. Performance Characterization ofA New Temperature-robust Gain-bandwidth Improved MEMS GyroscopeOperated in Air[J]. Sensors and Actuators A,2009,155:16-22.
[25] A. A. Trusov, A. R. Schofield and A. M. Shkel. Micromachined Rate GyroscopeArchitecture with Ultra-high Quality Factor and Improved Mode Ordering[J].Sensors and Actuators A,2011,165:26-34.
[26] A. R. Schofield, A. A. Trusov and A. M. Shkel. Micromachined GyroscopeConcept Allowing Interchangeable Operation in Both Robust and PrecisionModes[J]. Sensors and Actuators A,2011,165:35-42.
[27] C. Acar, A. Shkel. An Approach for Increasing Drive-Mode Bandwidth ofMEMS Vibratory Gyroscopes[J]. Journal of Microelectromechanical Systems,2005,14(3):520-528.
[28] A. A. Trusov, I. P. Prikhodko, S. A. Zotov and A. M. Shkel. Low-DissipationSilicon Tuning Fork Gyroscopes for Rate and Whole Angle Measurements[J].IEEE Sensors Journal,2011,11(11):2763-2770.
[29] S. A. Zotov, I. P. Prikhodko, A. A. Trusov and A. M. Shkel. FrequencyModulation Based Angular Rate Sensor[C]. Proceedings of IEEE MEMS,Mexico,2011:577-580.
[30] I. P. Prikhodko, S. A. Zotov, A. A. Trusov and A. M. Shkel. Sub-degree-per-hourSilicon MEMS Rate Sensor with1Million Q-factor[C]. Transducers’11, Beijing,2011:2809-2812.
[31] S.A. Zotov, A.A. Trusov and A.M. Shkel. High-Range Angular Rate SensorBased on Mechanical Frequency Modulation[J]. Journal of Microelectro-mechanical Systems,2012,21(2):398-405.
[32] I.P. Prikhodko, S.A. Zotov, A.A. Trusov and A.M. Shkel. Thermal Calibration ofSilicon MEMS Gyroscopes[C]. IMAPS8th International Conference andExhibition on Device Packaging, Scottsdale, AZ,2012.
[33] I. P. Prikhodko, A. A. Trusov and A. M. Shkel. North-finding with0.004RadianPrecision Using A Silicon MEMS Quadruple Mass Gyroscope with Q-factor of1Million[C]. Proceedings of IEEE MEMS, Paris,2012:164-167.
[34] I. P. Prikhodko, S. A. Zotov, A. A. Trusov and A. M. Shkel. Foucault Pendulumon A Chip: Rate integrating silicon MEMS gyroscope [J]. Sensors and ActuatorsA,2012,177:67-78.
[35] Z. Hao, M. F. Zaman, A. Sharma and F. Ayazi. Energy Loss Mechanisms in aBulk-Micromachined Tuning Fork Gyroscope[J]. Proceedings of IEEE Sensors,Korea,2006:1333-1336.
[36] Z. Hao and F. Ayazi. Support Loss in The Radial Bulk-mode Vibrations ofCenter-supported Micromechanical Disk Resonators[J]. Sensors and Actuators A,2007,134:582-593.
[37] Z. Hao, Y. Xu and S. K. Durgam. A Thermal-energy Method for CalculatingThermoelastic Damping in Micromechanical Resonators[J]. Journal of Sound andVibration,2009,322:870–882.
[38] Z. Hao, A. Erbil and F. Ayazi. An Analytical Model for Support Loss inMicromachined Beam Resonators with In-plane Flexural Vibrations[J]. Sensorsand Actuators A,2003,109:156–164.
[39] Z. Hao and Y. Xu. Vibration Displacement on Substrate Due to Time-harmonicStress Sources from A Micromechanical Resonator[J]. Journal of Sound andVibration,2009,322:196–215.
[40] M. F. Zaman, A. Sharma, Z. Hao and F. Ayazi. A Mode-Matched Silicon-YawTuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation BiasInstability[J]. Journal of Microelectromechanical Systems,2008,17(6):1526-1536.
[41] M. F. Zaman, A. Sharma, M. Zucher and F. Ayazi. A0.1°/hr Bias DriftElectronically Matched Tuning Fork Microgyroscope[C]. Proceedings of IEEEMEMS, Tucson, AZ, USA,2008:6-9.
[42] A. Sharma, M. F. Zaman and F. Ayazi. A Sub-0.2°/hr Bias DriftMicromechanical Silicon Gyroscope With Automatic CMOS Mode-Matching[J].IEEE Journal of Solid-state Circuits,2009,44(5):1593-1608.
[43] Y. Xu, R. Wang, S. K. Durgam, Z. Hao, L. Vahala. Numerical models andexperimental investigation of energy loss mechanisms in SOI-based tuning-forkgyroscopes[J]. Sensors and Actuators A,2009,152:63-74.
[44] R. Wang, P. Cheng, F. Xie, D. Young, Z. Hao. A Multiple-beam Tuning-forkGyroscope with High Quality Factors[J]. Sensors and Actuators A,2011,166:22-33.
[45] M. F. Zaman, A. Sharma, N. Jalili, F. Ayazi. The Resonating Star Gyroscope: ANovel Multiple-Shell Sicilion Gyroscope with Sub-5deg/hr Allan Deviation BiasInstability[J]. IEEE Sensors Journal,2009(9):616-624.
[46] F. Ayazi. Multi-DOF Inertial MEMS: From Gaming to Dead Reconing[C].Transducers’11, Beijing,2011:2804-2808.
[47] W.K. Sung, M. Dalal and F. Ayazi. A Mode-matched0.9MHz SingleProof-mass Dual-axis Gyroscope[C]. Transducers’11, Beijing,2011:2821-2824.
[48] G. Casinovi, W.K. Sung, M. Dalal, A. N. Shirazi and F. Ayazi. EletrostaticSelf-calibration of Vibratory Gyroscopes[C]. Proceedings of IEEE MEMS, Paris,2012:559-562.
[49] F. Ayazi and K Najafi. Design and Fabrication of a High-PerformancePolysilicon Vibrating Ring Gyroscope[C]. Proceedings of11th AnnualInternational Workshop on Micro Electro Mechanical Systems, Germany,1998:621-626.
[50] F. Ayazi, H. H. Chen, F. Kocer, G. He and K. Najafi. A High Aspect-RatioPolysilicon Vibrating Ring Gyroscope[C]. Proceedings of InternationalConference on Solid-State Sensors and Actuators,2000:289-292.
[51] F Ayazi and K Najafi. A HARPSS Polysilicon Vibrating Ring Gyroscope[J].Journal of Microelectromechanical Systems,2001,10(2):169-179.
[52] G. He and K. Najafi. A Single Crystal Silicon Vibrating Ring Gyroscope[C].Proceedings of15th IEEE MEMS,2002:718-721.
[53] J. Cho, J.A. Gregory, and K. Najafi. Single-crystal-silicon Vibratory Cylindericalrate Integrating Gyroscope(CING)[C]. Transducers’11, Beijing,2011:2813-2816.
[54] S. Zarabadi, T. Vas, D. Sparks, et al. A Resonating Comb/Ring Angular RateSensor Vacuum Packaged Via Wafer Bonding[C]. In International Congress andExposition, Detroit, USA, March01-04,1999:1043.
[55] T. K. Tang, R. C. Gutierrez, K. Hayworth, et al. High Performance Microgyrosfor Space Applications[C]. AIAA Space Technology Conference&Exhibit,Albuquerque,1999:1-5.
[56] Jason Kwong-Ping Hui. Modeling and Identification of the Jet Propulsion LabVibratory Rate Microgyroscope[D]. Los Angeles: University of California,2002.
[57] R M Closkey, A D Challoner. Modeling, Identification and Control of MicroSensor Prototypes[C]. Proceeding of the2004American Control Conference,Boston, Massachusetts, June30-July2,2004:9-24.
[58] G. Andersson, N. Hedenstierna and P. Svensson. A Novel Silicon BulkGyroscope[C]. Proceedings of International Conference on Transducers, Sendai,1999:902-905.
[59] G. Andersson, N. Hedenstierna and P. Svensson. An Arrangement for MeasuringAngular Velocity[P]. WO:99/38016,1998.
[60] N. Hedenstierna, S. Habibi and S. Nilsen. Bulk Micromachined Angular RateSensor Based on the 'Butterfly' Gyro Structure[C]. Proceedings of the14th IEEEInternational Conference on MEMS, Interlaken,2001:178-183.
[61] A. Kulygin, U. Schmid and H. Seidel. Investigation on the Pressure-DependentPerformance of a Surface Micromachined Gyroscope[C]. Proceedings of theIEEE,2007:1183-1186.
[62] A. Kulygin, U. Schmid and H. Seidel. Characterization of A NovelMicromachined Gyroscope Under Varying Ambient Pressure Conditions[J].Sensors and Actuators A,2008,145-146:52-58.
[63] A. Kulygin, C. Kirsch, P. Schwarz, U. Schmid and H. Seidel. Decoupled SurfaceMicromachined Gyroscope With Single-Point Suspension[J]. Journal ofMicroelectromechanical Systems,2012,21(1):206-216.
[64] T. Juneau, A. Pisano and J. Smith. Dual Axis Operation of a Micromachined RateGyroscope[C]. Proceedings of International Conference on Solid-State Sensorsand Actuators, Chicago,1997:883-886.
[65] X. Jiang, J. Seeger and M. Kraft. A Monolithic Surface Micromachined Z-AxisGyroscope with Digital Output[C]. Symposium on VLSl Circuits,2000:16-19.
[66] M. Palaniapan, R. Howe and J. Yasaitis. Performance Comparison of IntegratedZ-axis Frame Microgyroscopes[C]. Proceedings of the IEEE MEMS, Kyoto,2003:482-485.
[67] A. Seshia, R. Howe and S. Montague. An Integrated MicroelectromechanicalResonant Output Gyroscope. Proceedings of the IEEE MEMS,2002:722-726.
[68] H. Xie and G. K. Fedder. Fabrication, Characterization, and Analysis of a DRIECMOS-MEMS Gyroscope[J]. IEEE Sensors Journal,2003,3(5):622-631.
[69] S. R. Poreddy. Design and Dynamic analysis of MEMS Gyroscopes[D].Columbia: University of Missouri,2004.
[70] Y. LEE. A Study of Parametric Excitation Applied to A MEMS Tuning ForkGyroscope[D]. Columbia: University of Missouri,2007.
[71] S. Alper and T. Akin. A Single-Crystal Silicon Symmetrical and DecoupledMEMS Gyroscope on an Insulating Substrate[J]. Journal ofMicroelectromechanical Systems,2005,14(4):707-717.
[72] S. Alper, K. Azgin and T. Akin. High-Performance SOI-MEMS Gyroscope withDecoupled Oscillation Modes[C]. Proceedings of IEEE MEMS, Istanbul, Turkey,2006:70-73.
[73] S. Alper and K. Azgin. A High-Performance Silicon-on-Insulator MEMSGyroscope Operating at Atmospheric Pressure[J]. Sensors and Actuators A,2007,135:34-42.
[74]姜岩峰译.硅微机械加工技术[M].北京:化学工业出版社,2007:339-344.
[75]王寿荣.硅微惯性器件理论及应用[M].南京:东南大学出版社,2000:102-130.
[76]石庚辰,郝一龙.微机电系统技术基础[M].北京:中国电力出版社,2006:61-86.
[77] S. Lee, S. Park, J. Kim, S. Lee and D. Cho. Surface/Bulk Micromachined SingleCrystalline Silicon Micro Gyroscope[J]. Journal of MicroelectromechanicalSystems,2000,9(4):557-567.
[78] A. Trusov, C. Acar and A. M. Shkel. Comparative analysis of distributed massmicromachined gyroscopes fabricated in SCS-SOI and EFAB[J]. Proc. of SPIE,2001,6174:1-12.
[79] Y. B. Gianchandani, H. Kim, M. Shinn, B. Ha, B. Lee, K. Najafi and C. Song. AFabrication Process for Integrating Polysilicon Microstructures withPost-processed CMOS Circuits[J]. J. Micromech. Microeng,2000,10:380-386.
[80] M. Weinberg, A. Kourepenis, W. Sawyer. Tuning Fork Gyroscope[P]. US Patent:6862934B2,2005.
[81] D. R. Sparks, S. M. Ansari and N. Najafi. Chip-Level Vacuum Packaging ofMicromachines Using NanoGetters[J]. IEEE Transactions on AdvancedPackaging,2003,26(3):277-282.
[82] T. J. Harpster, S. A. Nikles, M. R. Dokmeci and K. Najafi. Long-TermHermeticity and Biological Performance of Anodically Bonded Glass-SiliconImplantable Packages[J]. IEEE Transactions on Devices and Materials Reliability,2005,5(3):458-466.
[83] B. H. Stark and K. Najafi. A Mold and Transfer Technique for Lead-FreeFluxless Soldering and Application to MEMS Packaging[J]. Journal ofMicroelectromechanical Systems,2006,15(4):849-858.
[84] N. Ito, K. Yamada, H. okada, et al. A Rapid and Selective Anodic BondingMethod[C]. Solid-State Sensors and Actuators, Stockholm, Sweden,1995:277-280.
[85] R. Inzinga, T. Lin, M. Yadav, et al. Control and Quantification of ResidualStresses in Anodically Bonded MEMS Structures[C]. Proceedings of the SEMAnnual Conference,2010:269-273.
[86] C. Fell. Development of a Second Generation Low Cost MEMS Gyroscope:Design for Manufacture. The Institution of Engineering and Technology Seminaron MEMS Sensors and Actuators, London,2006:75-82.
[87] R. N. Jazar. Nonlinear Approaches in Engineering Applications[C]. SpringerScience Business Media. LLC,2012:41-104.
[88] Y. G. Martynenko, I. V. Merkuryev, V.V. Podalkov. Nonlinear Dynamics ofMEMS Turning Fork Gyroscope[J]. Science China Technological Sciences,2011,54(5):1078-1083.
[89] S. Gunthner, M. Egretzberger, A. Kugi, K. Kapser, B. Hartmann, U. Schmid andH. Seidel. Compensation of Parasitic Effects for a Silicon Tuning ForkGyroscope[J]. IEEE Sensors Journal,2006,6:596-604.
[90] C. Acar and A. Shkel. MEMS Vibratory Gyroscopes: Structural Approaches toImprove Robustness[M]. Springer Science Business Media. LLC,2009:128-132.
[91] J. A. Geen, S. J. Sherman, J. F. Chang, et al. Single-Chip Surface MicromachinedIntegrated Gyroscope with50o/h Allan Deviation[J]. IEEE Journal of Solid-StateCircuits,2002,37(12):1860-1866.
[92] M. I. Ferguson, D. Keymeulen, C. Peay and K. Yee. Effect of temperature onMEMS vibratory rate gyroscope[C]. Proceeding of IEEE,2005:1-6.
[93] M. A. Hopcroft, M. Agarval, et al. Temperature Compensation of a MEMSResonator using Quality Factor as a Thermometer[C]. MEMS2006, Istanbul,Turkey,2006:222-226.
[94] B. Kim, M. A. Hopcroft, R. N. Candler, C. M. Jha, M. Agarwal, R. Melamud, S.A. Chandorkar, G. Yama and T. W. Kenny. Temperature dependence of qualityfactor in MEMS resonators[J]. Journal of Microelectromechanical Systems,2008,17:755-766.
[95] R. Melamud, B. Kim, et al. Composite Flexural-mode Resonator withControllable Turnover Temperature[C], Proceedings of IEEE MEMS, Kobe,Japan,2007:199-202.
[96] R. G. Azevedo, W. Huang, O. M. O’Reilly, A. P. Pisano. Dual-modeTemperature Compensation for a Comb-driven MEMS Resonant Strain Gauge[J].Sensors and Actuators A,2008,144:374-380.
[97] R. Arnaudov and Y. Angelov. Improvement in the Method for Bias DriftCompensation in Micromechanical Gyroscopes[J]. Radioengineering,2005,14:7-12.
[98] S. W. Yoon, N. Yazdi，N. C. Perkins, K. Najafi. Micromachined Integrated ShockProtection for MEMS[J]. Sensors and Actuators A,2006,130-131:166-175.
[99] S. W. Yoon, S. Lee, N. C. Perkins and K. Najafi. Vibration Sensitivity of MEMSTuning Fork Gyroscopes[J]. Proceedings of IEEE Sensors,2007:115-119.
[100] S. W. Yoon, S. Lee, N. C. Perkins and K. Najafi. Analysis and Wafer-levelDesign of a High-order Silicon Vibration Isolator for Resonating MEMSDevices[J]. Journal of Micromechanics and Microengineering.2011,21:015017.
[101] S. W. Yoon, S. Lee, N. C. Perkins and K. Najafi. Shock-Protection ImprovementUsing Integrated Novel Shock-Protection Technologies[J]. Journal ofMicroelectromechanical Systems,2011,20(4):1016-1031.
[102] S. W. Yoon, S. Lee and K. Najafi. Vibration Sensitivity Analysis of MEMSVibratory Ring Gyroscopes[J]. Sensors and Actuators A,2011,171:163-177.
[103] S. W. Yoon, S. Lee and K. Najafi. Vibration-induced Errors in MEMS TuningFork Gyroscopes[J]. Sensors and Actuators A,2012.
[104]董煜茜,高钟毓,陈志勇,张嵘.微机械振动轮式陀螺样机的实验研究[J].宇航学报,2000,21(1):65-70.
[105]杨军,高钟毓,张嵘,陈志勇,周斌.线振动硅微机械陀螺结构误差参数分离和辨识[J].2007,15(3):327-333.
[106] W. Zhou, B. Zhou, Z. Chen and R. Zhang. Effects of Combs on Coupling Error inthe Vibratory MEMS Gyroscope with Various Air Dampings[J]. The NinthInternational Conference on Electronic Measurement&Instruments,2009:298-301.
[107]刘忠卿,张嵘.微机械陀螺管芯测试方法[J].传感器与微系统,2008,27(4):111-116.
[108] Z. Guo, L. Lin, Q. Zhao, Z. Yang, H. Xie and G. Yan. A Lateral-AxisMicroelectromechanical Tuning-Fork Gyroscope With Decoupled Comb DriveOperating at Atmospheric Pressure[J]. Journal of MicroelectromechanicalSystems,2010,19(3):458-468.
[109] Z. Guo, Z. Yang, L. Lin, Q. Zhao, J. Cui, X. Chi and G. Yan. Decoupled CombCapacitors for Microelectromechanical Tuning-Fork Gyroscopes[J]. IEEEElectron Device Letters,2010,31(1):26-28.
[110] J. Cui, Z. Guo, Z.Yang, Y. Hao, G. Yan. Electrical Coupling Suppressing for aMicrogyroscope Using Ascending Frequency Drive with2-DOF PIDController[J]. Transducers’11, Beijing,2010:2002-2005.
[111] Z. Guo, L. Lin, Q. Zhao, Z. Yang, H. Xie and G. Yan. A lateral-axismicromachined tuning fork gyroscope with torsional Z-sensing and electrostaticforce-balanced driving[J]. J. Micromech. Microeng.2010,20:025007.
[112] B. Lv, X. Liu, Z. Yang and G. Yan. Simulation of a Novel Lateral AxisMicromachined Gyroscope in the Presence of Fabrication Imperfections[J].Microsystem Technologies,2008,14:711-718.
[113] J. Cui, X. Liu, Z. Guo, Q. Zhao, L. Lin and G. Yang, Y. Hao and G. Yan. AnExperimental Investigation on Decoupling Performance for a Lateral AxisMicromachined Gyroscope with Varying Environmental Parameters[J]. ScienceChina Technological Sciences,2011,54(12):3415-3423.
[114] Q. Zhao, X. Liu, L. Lin, Z. Guo, J. Cui, X. Chi, Z. Yang and G. Yan. A DoublyDecoupled Micromachined Vibrating Wheel Gyroscope[J]. Transducers2009,Denver, USA,2009:296-299.
[115] X Liu, Z. Yang, X. Chi, J. Cui, H. Ding, Z. Guo, B. Lv, L. Lin, Q. Zhao and G.Yan. A Doubly Decoupled Lateral Axis Micromachined Gyroscope[J]. Sensorsand Actuators A,2009,154:218-223.
[116] H. Ding, X. Liu, L. Lin, X. Chi, J. Cui, M. Kraft, Z. Yang and G. Yan. AHigh-Resolution Silicon-on-Glass Z Axis Gyroscope Operating at AtmosphericPressure[J]. IEEE Sensors Journal,2010,10(6):1064-1074.
[117] D. Liu, N. Lu, J. Cui, L. Lin, H. Ding, Z. Yang, Y. Hao and G. Yan. DigitalClosed-Loop Control Based on Adaptive Filter for Drive Mode of a MEMSGyroscope [C]. Proceedings of IEEE Sensors,2010:1722-1726.
[118] J Cui, X. Chi, H. Ding, L. Lin, Z. Yang and G. Yan. Transient Response andStability of the AGC-PI Closed-loop Controlled MEMS Vibratory Gyroscopes[J].J. Micromech. Microeng,2009,19:125015.
[119] J. Cui, Z. Guo, Q. Zhao, Z. Yang, Y. Hao and G. Yan. Force RebalanceController Synthesis for a Micromachined Vibratory Gyroscope Based onSensitivity Margin Specifications[J]. Journal of Microelectromechanical Systems,2011,20(6):1382-1394.
[120]叶甫.硅微机械陀螺仪结构设计与比较研究[D].南京:东南大学,2008.
[121]殷勇,王寿荣,王存超,盛平.结构解耦的双质量微陀螺仪结构方案设计与仿真[J].东南大学学报(自然科学版),2008,38(5):918-922.
[122] B. Yang, Y. Yong, L. Huang, S. Wang and H. Li. Research on a New DecoupledDual-mass Micro-Gyroscope[C]. The Tenth International Conference onElectronic Measurement&Instruments,2011:205-208.
[123]杨波,王寿荣,李宏生,黄丽斌,李坤宇,殷勇.解耦硅微陀螺仪的结构误差分析和系统性能测试[J].纳米技术与精密工程,2010,8(6):545-552.
[124]谢明媚. z轴硅微陀螺仪残余应力分析及结构优化研究[D].南京:东南大学,2004.
[125]施芹.提高硅微陀螺仪性能若干关键技术研究—正交误差与杂散电容分析研究[D].南京:东南大学,2005.
[126]裘安萍,蔡体菁,周百令,王寿荣.音叉式硅微机械振动陀螺仪的粘滞阻尼研究[J].东南大学学报(自然科学版),2000,30(1):131-135.
[127]盛平,王寿荣,吉训生,许宜申.硅微机械谐振陀螺仪的非线性分析[J].中国惯性技术学报,2006,14(6):60-62.
[128]王宏. Z轴硅微振动陀螺仪温度特性的研究[D].南京:东南大学,2006.
[129]程龙. Z轴硅微机械陀螺仪温度补偿的技术研究[D].南京:东南大学,2008.
[130]吉训生,王寿荣.硅微陀螺阵列信号处理技术研究[J].宇航学报,2009,30(1):235-239.
[131]王元山,熊敏敏,王寿荣.单片集成三轴微机械陀螺技术初步研究[J].测控技术,2005,25(4):73-75.
[132] L. Xu, B. Yang, S. Wang, H. Li and L. Huang. Research on ThermalCharacteristics and On-Chip Temperature-Controlling for SiliconMicro-Gyroscope[C]. Proceeding of the IEEE International Conference onInformation and Automation,2011:807-812.
[133]宗登刚.微机械材料力学性能测量[D].上海:中国科学院上海微系统与信息技术研究所,2003.
[134]许晓昕,高翔,徐静,吴亚明. Pyrex玻璃的湿法深刻蚀及表面布线工艺[J].功能材料与器件学报,2007,13(6):566-571.
[135]冷悦,焦继伟,张颖,顾佳烨,颜培力,宓斌玮.微机械陀螺DRIE刻蚀过程中的局域掩膜效应[J].传感技术学报,2010,23(8):1070-1074.
[136]邢向龙,焦继伟, D. Mark,王跃林, C. Hyung.用于MEMS结构的光刻胶牺牲层接触平坦化技术[J].功能材料与器件学报,2006,12(2):135-138.
[137]熊斌,车录锋,王跃林.一种栅型结构微机械陀螺的研究[J].中国机械工程,2003,14(3):184-186.
[138]车录锋,熊斌,王跃林.振子框架式微机械陀螺的优化设计及电学模拟[J].航空学报,2002,23(3):211-214.
[139]陈永.振子框架式微机械陀螺的优化设计及电学模拟[D].上海:中国科学院上海微系统与信息技术研究所博士学位论文,2004.
[140]施芹,裘安萍,苏岩.硅微陀螺仪的机械耦合误差分析[J].光学精密工程,2008,16(5):894-898.
[141]彭首军.微陀螺工艺允差分析及优化设计[D].西安工业大学硕士学位论文,2011.
[142]江平.蝶翼式硅微机械陀螺结构设计及制造工艺研究[D].长沙:国防科学技术大学,2007.
[143]肖定邦.新型蝶翼式微机械陀螺关键技术研究[D].长沙:国防科学技术大学,2009.
[144]李昕，蒋瑞兴，陈洪荪，龚俊杰著，弹性与非弹性的测量和应用[M].北京：冶金工业出版社，1999.
[145] J. Wortman and R. Evans. Young’s Modulus, Shear Modulus, and Poisson’sRatio in Silicon and Germanium[J]. Journal of Applied Physics.1964,32:153-156.
[146]程昌钧，朱媛媛.弹性力学[M].上海:上海大学出版社,2005.
[147] R. Abdolvand, H. Johari, G. Ho, et al. Quality Factor in Trench-RefilledPolysilicon Beam Resonators[J]. Journal of Microelectromechanical Systems,2006,15(3):471-478.
[148] M Bao. Analysis and Design Principles of MEMS Devices[M]. Elsevier,2005.
[149] C Zener. Internal Friction in Solids [J]. Proceedings of the Physical Society.1940,52(1):152~166.
[150] C Zener. Elasticity and Anelasticity of Metals[M]. Chicago: The University ofChicago Press,1948.
[151] Z Hao, F Ayazi. Thermoelastic Damping in Flexural-Mode Ring Gyroscope[C].Proceedings of IMECE2005: ASME International Mechanical EngineeringCongress and Exposition, Orlando, Florida, USA,2005:1-9.
[152] J Judge, D Photiadis, J Vignola. Attachment Loss of Micromechanical andNano-Mechanical Resonators in the Limits of Thick and Thin SupportStructures[J]. Journal of Applied Physics,2007,101(013521):1-11.
[153] A Trusov, A Schofield and A Shkel. A Substrate Energy Dissipation Mechanismin In-phase and Anti-phase Micromachined Z-axis Vibratory Gyroscopes[J]Journal of Micromechanics and Microengineering,2008,18:095016.
[154] A Grossman, W Erley, J B Hannon, et al. Giant Surface Stress in HeteroepitaxialFilms: Invalidation of a Classical Rule in Epitaxy[J]. Physical Review Letters,1996,77:127-130.
[155] J Yang, T Ono, M Esashi. Energy Dissipation in Submicrometer ThickSingle-crystal Silicon Cantilevers[J]. Journal of Microelectromechanical Systems,2002,11(6):775-783.
[156] M Bao. Micro Mechanical Transducers: Pressure Sensors, Accelerometers andGyroscopes[M]. Elsevier,2000
[157]牛正一.单片集成三轴微加速度计关键技术研究[D].长沙:国防科学技术大学,2010.
[158]侯占强，董培涛，肖定邦，吴学忠.一种避免静电黏附失效的低应力阳极键合技术[J].纳米技术与精密工程,2011,9(5):446-450.
[159] Y Cheng, W Hsu, K Najafi, C Nguyen and L Lin. Vacuum PackagingTechnology Using Localized Aluminum/silicon-to-glass Bonding[J]. Journal ofMicroelectromechanical Systems,2002,11(5):556-565.
[160] J Wu, G Fedder, L Carley. A Low-Noise Low-Offset Capacitive SensingAmplifier for a50μg/Hz1/2Monolithic CMOS MEMS Accelerometerp[J]. IEEEJournal of Solid-state Circuits,2004,39(5):722-730.
[161] R Leland. Mechanical Thermal Noise in Vibrational Gyroscopes[J]. IEEESensors Journal,2005,5(3):493-500.
[162]田野.振动式微机械陀螺系统噪声分析及低噪声电路设计[D].哈尔滨:哈尔滨工业大学,2009.
[163]张宪起,董冀,俞瑛.微机械陀螺仪性能指标测试及计算方法[J].集成电路通讯,2009,27(4):31-35.
[164] IEEE Std1431TM-2004. IEEE Standard Specification Format Guide and TestProcedure for Coriolis Vibratory Gyros.
[165]李新刚.微机电陀螺误差建模及其在飞行器组合导航中的应用[D].西安:西北工业大学,2003.
[166] S Gunthner, M Egretzberger, A Kugi, K Kapser, B Hartmann, U Schmid and HSeidel, Compensation of Parasitic Effects for a Silicon Tuning Fork Gyroscope[J].IEEE Sensors Journal,2006,6(3):596-604.
[167] Z Hou, D Xiao, X Wu, P Dong, Z Niu, Z Zhou and X Zhang. Effect of ParasiticResistance on MEMS Vibratory Gyroscopes due to Temperature Fluctuations[C].The6th IEEE International Conference on Nano/Micro Engineered andMolecular Systems,2011, pp.293-296.
[168]谭一云,于虹,黄庆安等.温度对硅纳米薄膜杨氏模量的影响[J].电子器件,2007,30(6):755-758.
[169] X Li, T Ono, Y Wang, et al. Study on Ultra-thin NEMS Cantilevers-High YieldFabrication and Size-effect on Young's Modulus of Silicon[J]. IEEE,2002:427-430.
[170] W Li, B Huang, Z Bi. Analysis and Applications of Thermal Stress[M]. Beijing:China Electric Power Press,2004:60-61.
[171]谢官模.振动力学[M].北京:国防工业出版社,2007:212-214.
[172]张厥宗.硅片加工技术[M].北京:化学工业出版社,2009:29-43.
[173]贾陈,屈梁生.单晶硅晶圆晶向的精确标定方法[J].西安交通大学学报,2002,36(5):528-531.
[174]卢涛.激光微加工系统研制[D].郑州:郑州大学,2002.
[2]刘俊,石云波,李杰.微惯性技术[M].北京:电子工业出版社,2005.
[3] N. Yazdi, F. Ayazi, and K. Najafi. Micromachined Inertial Sensors[J].Proceedings of the IEEE.1998,86(8):1640-1659.
[4] R. H. Dixon, J. Bouchaud. Markets and applications for MEMS inertialsensors[C]. Proc. SPIE2006,6113,1-13.
[5] T. Brown, B. Davis, D. Hepner, J. Faust, C. Myers, P. Muller, T. Harkins, M.Hollis, C. Miller and B. Placzankis. Strap-down microelectromechanical (MEMS)sensors for high-g munition applications[C]. IEEE Transactions on magnetic,37(1):336-342, January2001.
[6] K. Najafi, J. Chae, H. Kulah and Guohong He. Micromachined SiliconAccelerometers and Gyroscopes[C]. Proceedings of the2003IEEE/RSJ,International Conference on Intelligent Robots and Systems, Las Vegas, Nevada,2003:2353-2358.
[7] A. Sharma, M. Zaman, M. Zucher, F. Ayazi. A0.1°/h Bias Drift ElectronicallyMatched Tuning Fork Microgyroscope. Proceedings of IEEE MEMS, Tucson,AZ,2008:6-9
[8] P. Greiff, B. Boxenhorn, T. King, et al. Silicon Monolithic MicromechanicalGyroscope[C]. Proceedings of International Conference on Solid-State Sensorsand Actuators,1991:966-968.
[9] ADXR646Datasheet. www.analog.com,2011.
[10] IBG21Datasheet. www.imego.com,2012.
[11] SAR10Gyro Sensor Series Datasheet. www.sensonor.com,2012.
[12] CRS09Datasheet. www.siliconsensing.com,2012.
[13] J. Bernstein. A Micromachined Comb-drive Tuning Fork Rate Gyroscope[C].Proceedings of IEEE MEMS,1993:143-148.
[14] R. Neul, U. M. Gómez, K. Kehr. Micromachined Angular Rate Sensors forAutomotive Applications[J]. IEEE Sensors Journal,2007,7(2):302-309.
[15] M. Lutz, W. Golderer, J. Gerstenmeier, J. Marek. A Precision Yaw Rate Sensorin Silicon Micromachining[C]. Proceedings of International Conference onSolid-State Sensors and Actuators, Chicago, IL,1997:847-850.
[16] A. Thomae, R. Schellin, M. Lang, W. Bauer. A Low Cost Angular Rate Sensor inSi-surface Micromachining Technology for Automotive Application[C].Proceedings of SAE, Detroit,1999:0931-0936.
[17] W. Geiger, W. Butt, A. GaiBer, J. Frech. Decoupled Microgyros and the DesignPrinciple DAVED[J]. Sensors and Actuators A,2002,95:239-249.
[18] Geiger, B. Folkmer, U. Sobe, H. Sandrnaier. New Designs of MicromachinedVibrating Rate Gyroscopes with Delcoupled Oscillation Modes[C]. Proceedingsof International Conference on Solid-State Sensors and Actuators, Chicago,1997:1129-1132.
[19] W. Geiger, J. Bartholomeyczik, U. Breng, et al. MEMS IMU for AHRSApplications[C]. Proceedings of the IEEE.2008:225-231.
[20] C. Acar. Robust Micromachined Vibratory Gyroscopes[D]. PhD thesis, UCIrvine,2004.
[21] C. Acar and A. Shkel. Inherently Robust Micromachined Gyroscopes with2-DOF Sense-Mode Oscillator[J]. Journal of Microelectromechanical Systems,2006,15(2):380-387.
[22] A. R. Schofield, A. A. Trusov and A. M. Shkel. Effects of Operational FrequencyScaling in Multi-Degree of Freedom MEMS Gyroscopes[J]. Journal ofMicroelectromechanical Systems,2008,8(10):1672-1680.
[23] C. Acar, A. R. Schofield, A. A. Trusov and A. M. Shkel. Environmentally RobustMEMS Vibratory Gyroscopes for Automotive Applications[J]. IEEE SensorsJournal,2009,9(12):1895-1906.
[24] A. A. Trusov, A. R. Schofield and A. M. Shkel. Performance Characterization ofA New Temperature-robust Gain-bandwidth Improved MEMS GyroscopeOperated in Air[J]. Sensors and Actuators A,2009,155:16-22.
[25] A. A. Trusov, A. R. Schofield and A. M. Shkel. Micromachined Rate GyroscopeArchitecture with Ultra-high Quality Factor and Improved Mode Ordering[J].Sensors and Actuators A,2011,165:26-34.
[26] A. R. Schofield, A. A. Trusov and A. M. Shkel. Micromachined GyroscopeConcept Allowing Interchangeable Operation in Both Robust and PrecisionModes[J]. Sensors and Actuators A,2011,165:35-42.
[27] C. Acar, A. Shkel. An Approach for Increasing Drive-Mode Bandwidth ofMEMS Vibratory Gyroscopes[J]. Journal of Microelectromechanical Systems,2005,14(3):520-528.
[28] A. A. Trusov, I. P. Prikhodko, S. A. Zotov and A. M. Shkel. Low-DissipationSilicon Tuning Fork Gyroscopes for Rate and Whole Angle Measurements[J].IEEE Sensors Journal,2011,11(11):2763-2770.
[29] S. A. Zotov, I. P. Prikhodko, A. A. Trusov and A. M. Shkel. FrequencyModulation Based Angular Rate Sensor[C]. Proceedings of IEEE MEMS,Mexico,2011:577-580.
[30] I. P. Prikhodko, S. A. Zotov, A. A. Trusov and A. M. Shkel. Sub-degree-per-hourSilicon MEMS Rate Sensor with1Million Q-factor[C]. Transducers’11, Beijing,2011:2809-2812.
[31] S.A. Zotov, A.A. Trusov and A.M. Shkel. High-Range Angular Rate SensorBased on Mechanical Frequency Modulation[J]. Journal of Microelectro-mechanical Systems,2012,21(2):398-405.
[32] I.P. Prikhodko, S.A. Zotov, A.A. Trusov and A.M. Shkel. Thermal Calibration ofSilicon MEMS Gyroscopes[C]. IMAPS8th International Conference andExhibition on Device Packaging, Scottsdale, AZ,2012.
[33] I. P. Prikhodko, A. A. Trusov and A. M. Shkel. North-finding with0.004RadianPrecision Using A Silicon MEMS Quadruple Mass Gyroscope with Q-factor of1Million[C]. Proceedings of IEEE MEMS, Paris,2012:164-167.
[34] I. P. Prikhodko, S. A. Zotov, A. A. Trusov and A. M. Shkel. Foucault Pendulumon A Chip: Rate integrating silicon MEMS gyroscope [J]. Sensors and ActuatorsA,2012,177:67-78.
[35] Z. Hao, M. F. Zaman, A. Sharma and F. Ayazi. Energy Loss Mechanisms in aBulk-Micromachined Tuning Fork Gyroscope[J]. Proceedings of IEEE Sensors,Korea,2006:1333-1336.
[36] Z. Hao and F. Ayazi. Support Loss in The Radial Bulk-mode Vibrations ofCenter-supported Micromechanical Disk Resonators[J]. Sensors and Actuators A,2007,134:582-593.
[37] Z. Hao, Y. Xu and S. K. Durgam. A Thermal-energy Method for CalculatingThermoelastic Damping in Micromechanical Resonators[J]. Journal of Sound andVibration,2009,322:870–882.
[38] Z. Hao, A. Erbil and F. Ayazi. An Analytical Model for Support Loss inMicromachined Beam Resonators with In-plane Flexural Vibrations[J]. Sensorsand Actuators A,2003,109:156–164.
[39] Z. Hao and Y. Xu. Vibration Displacement on Substrate Due to Time-harmonicStress Sources from A Micromechanical Resonator[J]. Journal of Sound andVibration,2009,322:196–215.
[40] M. F. Zaman, A. Sharma, Z. Hao and F. Ayazi. A Mode-Matched Silicon-YawTuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation BiasInstability[J]. Journal of Microelectromechanical Systems,2008,17(6):1526-1536.
[41] M. F. Zaman, A. Sharma, M. Zucher and F. Ayazi. A0.1°/hr Bias DriftElectronically Matched Tuning Fork Microgyroscope[C]. Proceedings of IEEEMEMS, Tucson, AZ, USA,2008:6-9.
[42] A. Sharma, M. F. Zaman and F. Ayazi. A Sub-0.2°/hr Bias DriftMicromechanical Silicon Gyroscope With Automatic CMOS Mode-Matching[J].IEEE Journal of Solid-state Circuits,2009,44(5):1593-1608.
[43] Y. Xu, R. Wang, S. K. Durgam, Z. Hao, L. Vahala. Numerical models andexperimental investigation of energy loss mechanisms in SOI-based tuning-forkgyroscopes[J]. Sensors and Actuators A,2009,152:63-74.
[44] R. Wang, P. Cheng, F. Xie, D. Young, Z. Hao. A Multiple-beam Tuning-forkGyroscope with High Quality Factors[J]. Sensors and Actuators A,2011,166:22-33.
[45] M. F. Zaman, A. Sharma, N. Jalili, F. Ayazi. The Resonating Star Gyroscope: ANovel Multiple-Shell Sicilion Gyroscope with Sub-5deg/hr Allan Deviation BiasInstability[J]. IEEE Sensors Journal,2009(9):616-624.
[46] F. Ayazi. Multi-DOF Inertial MEMS: From Gaming to Dead Reconing[C].Transducers’11, Beijing,2011:2804-2808.
[47] W.K. Sung, M. Dalal and F. Ayazi. A Mode-matched0.9MHz SingleProof-mass Dual-axis Gyroscope[C]. Transducers’11, Beijing,2011:2821-2824.
[48] G. Casinovi, W.K. Sung, M. Dalal, A. N. Shirazi and F. Ayazi. EletrostaticSelf-calibration of Vibratory Gyroscopes[C]. Proceedings of IEEE MEMS, Paris,2012:559-562.
[49] F. Ayazi and K Najafi. Design and Fabrication of a High-PerformancePolysilicon Vibrating Ring Gyroscope[C]. Proceedings of11th AnnualInternational Workshop on Micro Electro Mechanical Systems, Germany,1998:621-626.
[50] F. Ayazi, H. H. Chen, F. Kocer, G. He and K. Najafi. A High Aspect-RatioPolysilicon Vibrating Ring Gyroscope[C]. Proceedings of InternationalConference on Solid-State Sensors and Actuators,2000:289-292.
[51] F Ayazi and K Najafi. A HARPSS Polysilicon Vibrating Ring Gyroscope[J].Journal of Microelectromechanical Systems,2001,10(2):169-179.
[52] G. He and K. Najafi. A Single Crystal Silicon Vibrating Ring Gyroscope[C].Proceedings of15th IEEE MEMS,2002:718-721.
[53] J. Cho, J.A. Gregory, and K. Najafi. Single-crystal-silicon Vibratory Cylindericalrate Integrating Gyroscope(CING)[C]. Transducers’11, Beijing,2011:2813-2816.
[54] S. Zarabadi, T. Vas, D. Sparks, et al. A Resonating Comb/Ring Angular RateSensor Vacuum Packaged Via Wafer Bonding[C]. In International Congress andExposition, Detroit, USA, March01-04,1999:1043.
[55] T. K. Tang, R. C. Gutierrez, K. Hayworth, et al. High Performance Microgyrosfor Space Applications[C]. AIAA Space Technology Conference&Exhibit,Albuquerque,1999:1-5.
[56] Jason Kwong-Ping Hui. Modeling and Identification of the Jet Propulsion LabVibratory Rate Microgyroscope[D]. Los Angeles: University of California,2002.
[57] R M Closkey, A D Challoner. Modeling, Identification and Control of MicroSensor Prototypes[C]. Proceeding of the2004American Control Conference,Boston, Massachusetts, June30-July2,2004:9-24.
[58] G. Andersson, N. Hedenstierna and P. Svensson. A Novel Silicon BulkGyroscope[C]. Proceedings of International Conference on Transducers, Sendai,1999:902-905.
[59] G. Andersson, N. Hedenstierna and P. Svensson. An Arrangement for MeasuringAngular Velocity[P]. WO:99/38016,1998.
[60] N. Hedenstierna, S. Habibi and S. Nilsen. Bulk Micromachined Angular RateSensor Based on the 'Butterfly' Gyro Structure[C]. Proceedings of the14th IEEEInternational Conference on MEMS, Interlaken,2001:178-183.
[61] A. Kulygin, U. Schmid and H. Seidel. Investigation on the Pressure-DependentPerformance of a Surface Micromachined Gyroscope[C]. Proceedings of theIEEE,2007:1183-1186.
[62] A. Kulygin, U. Schmid and H. Seidel. Characterization of A NovelMicromachined Gyroscope Under Varying Ambient Pressure Conditions[J].Sensors and Actuators A,2008,145-146:52-58.
[63] A. Kulygin, C. Kirsch, P. Schwarz, U. Schmid and H. Seidel. Decoupled SurfaceMicromachined Gyroscope With Single-Point Suspension[J]. Journal ofMicroelectromechanical Systems,2012,21(1):206-216.
[64] T. Juneau, A. Pisano and J. Smith. Dual Axis Operation of a Micromachined RateGyroscope[C]. Proceedings of International Conference on Solid-State Sensorsand Actuators, Chicago,1997:883-886.
[65] X. Jiang, J. Seeger and M. Kraft. A Monolithic Surface Micromachined Z-AxisGyroscope with Digital Output[C]. Symposium on VLSl Circuits,2000:16-19.
[66] M. Palaniapan, R. Howe and J. Yasaitis. Performance Comparison of IntegratedZ-axis Frame Microgyroscopes[C]. Proceedings of the IEEE MEMS, Kyoto,2003:482-485.
[67] A. Seshia, R. Howe and S. Montague. An Integrated MicroelectromechanicalResonant Output Gyroscope. Proceedings of the IEEE MEMS,2002:722-726.
[68] H. Xie and G. K. Fedder. Fabrication, Characterization, and Analysis of a DRIECMOS-MEMS Gyroscope[J]. IEEE Sensors Journal,2003,3(5):622-631.
[69] S. R. Poreddy. Design and Dynamic analysis of MEMS Gyroscopes[D].Columbia: University of Missouri,2004.
[70] Y. LEE. A Study of Parametric Excitation Applied to A MEMS Tuning ForkGyroscope[D]. Columbia: University of Missouri,2007.
[71] S. Alper and T. Akin. A Single-Crystal Silicon Symmetrical and DecoupledMEMS Gyroscope on an Insulating Substrate[J]. Journal ofMicroelectromechanical Systems,2005,14(4):707-717.
[72] S. Alper, K. Azgin and T. Akin. High-Performance SOI-MEMS Gyroscope withDecoupled Oscillation Modes[C]. Proceedings of IEEE MEMS, Istanbul, Turkey,2006:70-73.
[73] S. Alper and K. Azgin. A High-Performance Silicon-on-Insulator MEMSGyroscope Operating at Atmospheric Pressure[J]. Sensors and Actuators A,2007,135:34-42.
[74]姜岩峰译.硅微机械加工技术[M].北京:化学工业出版社,2007:339-344.
[75]王寿荣.硅微惯性器件理论及应用[M].南京:东南大学出版社,2000:102-130.
[76]石庚辰,郝一龙.微机电系统技术基础[M].北京:中国电力出版社,2006:61-86.
[77] S. Lee, S. Park, J. Kim, S. Lee and D. Cho. Surface/Bulk Micromachined SingleCrystalline Silicon Micro Gyroscope[J]. Journal of MicroelectromechanicalSystems,2000,9(4):557-567.
[78] A. Trusov, C. Acar and A. M. Shkel. Comparative analysis of distributed massmicromachined gyroscopes fabricated in SCS-SOI and EFAB[J]. Proc. of SPIE,2001,6174:1-12.
[79] Y. B. Gianchandani, H. Kim, M. Shinn, B. Ha, B. Lee, K. Najafi and C. Song. AFabrication Process for Integrating Polysilicon Microstructures withPost-processed CMOS Circuits[J]. J. Micromech. Microeng,2000,10:380-386.
[80] M. Weinberg, A. Kourepenis, W. Sawyer. Tuning Fork Gyroscope[P]. US Patent:6862934B2,2005.
[81] D. R. Sparks, S. M. Ansari and N. Najafi. Chip-Level Vacuum Packaging ofMicromachines Using NanoGetters[J]. IEEE Transactions on AdvancedPackaging,2003,26(3):277-282.
[82] T. J. Harpster, S. A. Nikles, M. R. Dokmeci and K. Najafi. Long-TermHermeticity and Biological Performance of Anodically Bonded Glass-SiliconImplantable Packages[J]. IEEE Transactions on Devices and Materials Reliability,2005,5(3):458-466.
[83] B. H. Stark and K. Najafi. A Mold and Transfer Technique for Lead-FreeFluxless Soldering and Application to MEMS Packaging[J]. Journal ofMicroelectromechanical Systems,2006,15(4):849-858.
[84] N. Ito, K. Yamada, H. okada, et al. A Rapid and Selective Anodic BondingMethod[C]. Solid-State Sensors and Actuators, Stockholm, Sweden,1995:277-280.
[85] R. Inzinga, T. Lin, M. Yadav, et al. Control and Quantification of ResidualStresses in Anodically Bonded MEMS Structures[C]. Proceedings of the SEMAnnual Conference,2010:269-273.
[86] C. Fell. Development of a Second Generation Low Cost MEMS Gyroscope:Design for Manufacture. The Institution of Engineering and Technology Seminaron MEMS Sensors and Actuators, London,2006:75-82.
[87] R. N. Jazar. Nonlinear Approaches in Engineering Applications[C]. SpringerScience Business Media. LLC,2012:41-104.
[88] Y. G. Martynenko, I. V. Merkuryev, V.V. Podalkov. Nonlinear Dynamics ofMEMS Turning Fork Gyroscope[J]. Science China Technological Sciences,2011,54(5):1078-1083.
[89] S. Gunthner, M. Egretzberger, A. Kugi, K. Kapser, B. Hartmann, U. Schmid andH. Seidel. Compensation of Parasitic Effects for a Silicon Tuning ForkGyroscope[J]. IEEE Sensors Journal,2006,6:596-604.
[90] C. Acar and A. Shkel. MEMS Vibratory Gyroscopes: Structural Approaches toImprove Robustness[M]. Springer Science Business Media. LLC,2009:128-132.
[91] J. A. Geen, S. J. Sherman, J. F. Chang, et al. Single-Chip Surface MicromachinedIntegrated Gyroscope with50o/h Allan Deviation[J]. IEEE Journal of Solid-StateCircuits,2002,37(12):1860-1866.
[92] M. I. Ferguson, D. Keymeulen, C. Peay and K. Yee. Effect of temperature onMEMS vibratory rate gyroscope[C]. Proceeding of IEEE,2005:1-6.
[93] M. A. Hopcroft, M. Agarval, et al. Temperature Compensation of a MEMSResonator using Quality Factor as a Thermometer[C]. MEMS2006, Istanbul,Turkey,2006:222-226.
[94] B. Kim, M. A. Hopcroft, R. N. Candler, C. M. Jha, M. Agarwal, R. Melamud, S.A. Chandorkar, G. Yama and T. W. Kenny. Temperature dependence of qualityfactor in MEMS resonators[J]. Journal of Microelectromechanical Systems,2008,17:755-766.
[95] R. Melamud, B. Kim, et al. Composite Flexural-mode Resonator withControllable Turnover Temperature[C], Proceedings of IEEE MEMS, Kobe,Japan,2007:199-202.
[96] R. G. Azevedo, W. Huang, O. M. O’Reilly, A. P. Pisano. Dual-modeTemperature Compensation for a Comb-driven MEMS Resonant Strain Gauge[J].Sensors and Actuators A,2008,144:374-380.
[97] R. Arnaudov and Y. Angelov. Improvement in the Method for Bias DriftCompensation in Micromechanical Gyroscopes[J]. Radioengineering,2005,14:7-12.
[98] S. W. Yoon, N. Yazdi，N. C. Perkins, K. Najafi. Micromachined Integrated ShockProtection for MEMS[J]. Sensors and Actuators A,2006,130-131:166-175.
[99] S. W. Yoon, S. Lee, N. C. Perkins and K. Najafi. Vibration Sensitivity of MEMSTuning Fork Gyroscopes[J]. Proceedings of IEEE Sensors,2007:115-119.
[100] S. W. Yoon, S. Lee, N. C. Perkins and K. Najafi. Analysis and Wafer-levelDesign of a High-order Silicon Vibration Isolator for Resonating MEMSDevices[J]. Journal of Micromechanics and Microengineering.2011,21:015017.
[101] S. W. Yoon, S. Lee, N. C. Perkins and K. Najafi. Shock-Protection ImprovementUsing Integrated Novel Shock-Protection Technologies[J]. Journal ofMicroelectromechanical Systems,2011,20(4):1016-1031.
[102] S. W. Yoon, S. Lee and K. Najafi. Vibration Sensitivity Analysis of MEMSVibratory Ring Gyroscopes[J]. Sensors and Actuators A,2011,171:163-177.
[103] S. W. Yoon, S. Lee and K. Najafi. Vibration-induced Errors in MEMS TuningFork Gyroscopes[J]. Sensors and Actuators A,2012.
[104]董煜茜,高钟毓,陈志勇,张嵘.微机械振动轮式陀螺样机的实验研究[J].宇航学报,2000,21(1):65-70.
[105]杨军,高钟毓,张嵘,陈志勇,周斌.线振动硅微机械陀螺结构误差参数分离和辨识[J].2007,15(3):327-333.
[106] W. Zhou, B. Zhou, Z. Chen and R. Zhang. Effects of Combs on Coupling Error inthe Vibratory MEMS Gyroscope with Various Air Dampings[J]. The NinthInternational Conference on Electronic Measurement&Instruments,2009:298-301.
[107]刘忠卿,张嵘.微机械陀螺管芯测试方法[J].传感器与微系统,2008,27(4):111-116.
[108] Z. Guo, L. Lin, Q. Zhao, Z. Yang, H. Xie and G. Yan. A Lateral-AxisMicroelectromechanical Tuning-Fork Gyroscope With Decoupled Comb DriveOperating at Atmospheric Pressure[J]. Journal of MicroelectromechanicalSystems,2010,19(3):458-468.
[109] Z. Guo, Z. Yang, L. Lin, Q. Zhao, J. Cui, X. Chi and G. Yan. Decoupled CombCapacitors for Microelectromechanical Tuning-Fork Gyroscopes[J]. IEEEElectron Device Letters,2010,31(1):26-28.
[110] J. Cui, Z. Guo, Z.Yang, Y. Hao, G. Yan. Electrical Coupling Suppressing for aMicrogyroscope Using Ascending Frequency Drive with2-DOF PIDController[J]. Transducers’11, Beijing,2010:2002-2005.
[111] Z. Guo, L. Lin, Q. Zhao, Z. Yang, H. Xie and G. Yan. A lateral-axismicromachined tuning fork gyroscope with torsional Z-sensing and electrostaticforce-balanced driving[J]. J. Micromech. Microeng.2010,20:025007.
[112] B. Lv, X. Liu, Z. Yang and G. Yan. Simulation of a Novel Lateral AxisMicromachined Gyroscope in the Presence of Fabrication Imperfections[J].Microsystem Technologies,2008,14:711-718.
[113] J. Cui, X. Liu, Z. Guo, Q. Zhao, L. Lin and G. Yang, Y. Hao and G. Yan. AnExperimental Investigation on Decoupling Performance for a Lateral AxisMicromachined Gyroscope with Varying Environmental Parameters[J]. ScienceChina Technological Sciences,2011,54(12):3415-3423.
[114] Q. Zhao, X. Liu, L. Lin, Z. Guo, J. Cui, X. Chi, Z. Yang and G. Yan. A DoublyDecoupled Micromachined Vibrating Wheel Gyroscope[J]. Transducers2009,Denver, USA,2009:296-299.
[115] X Liu, Z. Yang, X. Chi, J. Cui, H. Ding, Z. Guo, B. Lv, L. Lin, Q. Zhao and G.Yan. A Doubly Decoupled Lateral Axis Micromachined Gyroscope[J]. Sensorsand Actuators A,2009,154:218-223.
[116] H. Ding, X. Liu, L. Lin, X. Chi, J. Cui, M. Kraft, Z. Yang and G. Yan. AHigh-Resolution Silicon-on-Glass Z Axis Gyroscope Operating at AtmosphericPressure[J]. IEEE Sensors Journal,2010,10(6):1064-1074.
[117] D. Liu, N. Lu, J. Cui, L. Lin, H. Ding, Z. Yang, Y. Hao and G. Yan. DigitalClosed-Loop Control Based on Adaptive Filter for Drive Mode of a MEMSGyroscope [C]. Proceedings of IEEE Sensors,2010:1722-1726.
[118] J Cui, X. Chi, H. Ding, L. Lin, Z. Yang and G. Yan. Transient Response andStability of the AGC-PI Closed-loop Controlled MEMS Vibratory Gyroscopes[J].J. Micromech. Microeng,2009,19:125015.
[119] J. Cui, Z. Guo, Q. Zhao, Z. Yang, Y. Hao and G. Yan. Force RebalanceController Synthesis for a Micromachined Vibratory Gyroscope Based onSensitivity Margin Specifications[J]. Journal of Microelectromechanical Systems,2011,20(6):1382-1394.
[120]叶甫.硅微机械陀螺仪结构设计与比较研究[D].南京:东南大学,2008.
[121]殷勇,王寿荣,王存超,盛平.结构解耦的双质量微陀螺仪结构方案设计与仿真[J].东南大学学报(自然科学版),2008,38(5):918-922.
[122] B. Yang, Y. Yong, L. Huang, S. Wang and H. Li. Research on a New DecoupledDual-mass Micro-Gyroscope[C]. The Tenth International Conference onElectronic Measurement&Instruments,2011:205-208.
[123]杨波,王寿荣,李宏生,黄丽斌,李坤宇,殷勇.解耦硅微陀螺仪的结构误差分析和系统性能测试[J].纳米技术与精密工程,2010,8(6):545-552.
[124]谢明媚. z轴硅微陀螺仪残余应力分析及结构优化研究[D].南京:东南大学,2004.
[125]施芹.提高硅微陀螺仪性能若干关键技术研究—正交误差与杂散电容分析研究[D].南京:东南大学,2005.
[126]裘安萍,蔡体菁,周百令,王寿荣.音叉式硅微机械振动陀螺仪的粘滞阻尼研究[J].东南大学学报(自然科学版),2000,30(1):131-135.
[127]盛平,王寿荣,吉训生,许宜申.硅微机械谐振陀螺仪的非线性分析[J].中国惯性技术学报,2006,14(6):60-62.
[128]王宏. Z轴硅微振动陀螺仪温度特性的研究[D].南京:东南大学,2006.
[129]程龙. Z轴硅微机械陀螺仪温度补偿的技术研究[D].南京:东南大学,2008.
[130]吉训生,王寿荣.硅微陀螺阵列信号处理技术研究[J].宇航学报,2009,30(1):235-239.
[131]王元山,熊敏敏,王寿荣.单片集成三轴微机械陀螺技术初步研究[J].测控技术,2005,25(4):73-75.
[132] L. Xu, B. Yang, S. Wang, H. Li and L. Huang. Research on ThermalCharacteristics and On-Chip Temperature-Controlling for SiliconMicro-Gyroscope[C]. Proceeding of the IEEE International Conference onInformation and Automation,2011:807-812.
[133]宗登刚.微机械材料力学性能测量[D].上海:中国科学院上海微系统与信息技术研究所,2003.
[134]许晓昕,高翔,徐静,吴亚明. Pyrex玻璃的湿法深刻蚀及表面布线工艺[J].功能材料与器件学报,2007,13(6):566-571.
[135]冷悦,焦继伟,张颖,顾佳烨,颜培力,宓斌玮.微机械陀螺DRIE刻蚀过程中的局域掩膜效应[J].传感技术学报,2010,23(8):1070-1074.
[136]邢向龙,焦继伟, D. Mark,王跃林, C. Hyung.用于MEMS结构的光刻胶牺牲层接触平坦化技术[J].功能材料与器件学报,2006,12(2):135-138.
[137]熊斌,车录锋,王跃林.一种栅型结构微机械陀螺的研究[J].中国机械工程,2003,14(3):184-186.
[138]车录锋,熊斌,王跃林.振子框架式微机械陀螺的优化设计及电学模拟[J].航空学报,2002,23(3):211-214.
[139]陈永.振子框架式微机械陀螺的优化设计及电学模拟[D].上海:中国科学院上海微系统与信息技术研究所博士学位论文,2004.
[140]施芹,裘安萍,苏岩.硅微陀螺仪的机械耦合误差分析[J].光学精密工程,2008,16(5):894-898.
[141]彭首军.微陀螺工艺允差分析及优化设计[D].西安工业大学硕士学位论文,2011.
[142]江平.蝶翼式硅微机械陀螺结构设计及制造工艺研究[D].长沙:国防科学技术大学,2007.
[143]肖定邦.新型蝶翼式微机械陀螺关键技术研究[D].长沙:国防科学技术大学,2009.
[144]李昕，蒋瑞兴，陈洪荪，龚俊杰著，弹性与非弹性的测量和应用[M].北京：冶金工业出版社，1999.
[145] J. Wortman and R. Evans. Young’s Modulus, Shear Modulus, and Poisson’sRatio in Silicon and Germanium[J]. Journal of Applied Physics.1964,32:153-156.
[146]程昌钧，朱媛媛.弹性力学[M].上海:上海大学出版社,2005.
[147] R. Abdolvand, H. Johari, G. Ho, et al. Quality Factor in Trench-RefilledPolysilicon Beam Resonators[J]. Journal of Microelectromechanical Systems,2006,15(3):471-478.
[148] M Bao. Analysis and Design Principles of MEMS Devices[M]. Elsevier,2005.
[149] C Zener. Internal Friction in Solids [J]. Proceedings of the Physical Society.1940,52(1):152~166.
[150] C Zener. Elasticity and Anelasticity of Metals[M]. Chicago: The University ofChicago Press,1948.
[151] Z Hao, F Ayazi. Thermoelastic Damping in Flexural-Mode Ring Gyroscope[C].Proceedings of IMECE2005: ASME International Mechanical EngineeringCongress and Exposition, Orlando, Florida, USA,2005:1-9.
[152] J Judge, D Photiadis, J Vignola. Attachment Loss of Micromechanical andNano-Mechanical Resonators in the Limits of Thick and Thin SupportStructures[J]. Journal of Applied Physics,2007,101(013521):1-11.
[153] A Trusov, A Schofield and A Shkel. A Substrate Energy Dissipation Mechanismin In-phase and Anti-phase Micromachined Z-axis Vibratory Gyroscopes[J]Journal of Micromechanics and Microengineering,2008,18:095016.
[154] A Grossman, W Erley, J B Hannon, et al. Giant Surface Stress in HeteroepitaxialFilms: Invalidation of a Classical Rule in Epitaxy[J]. Physical Review Letters,1996,77:127-130.
[155] J Yang, T Ono, M Esashi. Energy Dissipation in Submicrometer ThickSingle-crystal Silicon Cantilevers[J]. Journal of Microelectromechanical Systems,2002,11(6):775-783.
[156] M Bao. Micro Mechanical Transducers: Pressure Sensors, Accelerometers andGyroscopes[M]. Elsevier,2000
[157]牛正一.单片集成三轴微加速度计关键技术研究[D].长沙:国防科学技术大学,2010.
[158]侯占强，董培涛，肖定邦，吴学忠.一种避免静电黏附失效的低应力阳极键合技术[J].纳米技术与精密工程,2011,9(5):446-450.
[159] Y Cheng, W Hsu, K Najafi, C Nguyen and L Lin. Vacuum PackagingTechnology Using Localized Aluminum/silicon-to-glass Bonding[J]. Journal ofMicroelectromechanical Systems,2002,11(5):556-565.
[160] J Wu, G Fedder, L Carley. A Low-Noise Low-Offset Capacitive SensingAmplifier for a50μg/Hz1/2Monolithic CMOS MEMS Accelerometerp[J]. IEEEJournal of Solid-state Circuits,2004,39(5):722-730.
[161] R Leland. Mechanical Thermal Noise in Vibrational Gyroscopes[J]. IEEESensors Journal,2005,5(3):493-500.
[162]田野.振动式微机械陀螺系统噪声分析及低噪声电路设计[D].哈尔滨:哈尔滨工业大学,2009.
[163]张宪起,董冀,俞瑛.微机械陀螺仪性能指标测试及计算方法[J].集成电路通讯,2009,27(4):31-35.
[164] IEEE Std1431TM-2004. IEEE Standard Specification Format Guide and TestProcedure for Coriolis Vibratory Gyros.
[165]李新刚.微机电陀螺误差建模及其在飞行器组合导航中的应用[D].西安:西北工业大学,2003.
[166] S Gunthner, M Egretzberger, A Kugi, K Kapser, B Hartmann, U Schmid and HSeidel, Compensation of Parasitic Effects for a Silicon Tuning Fork Gyroscope[J].IEEE Sensors Journal,2006,6(3):596-604.
[167] Z Hou, D Xiao, X Wu, P Dong, Z Niu, Z Zhou and X Zhang. Effect of ParasiticResistance on MEMS Vibratory Gyroscopes due to Temperature Fluctuations[C].The6th IEEE International Conference on Nano/Micro Engineered andMolecular Systems,2011, pp.293-296.
[168]谭一云,于虹,黄庆安等.温度对硅纳米薄膜杨氏模量的影响[J].电子器件,2007,30(6):755-758.
[169] X Li, T Ono, Y Wang, et al. Study on Ultra-thin NEMS Cantilevers-High YieldFabrication and Size-effect on Young's Modulus of Silicon[J]. IEEE,2002:427-430.
[170] W Li, B Huang, Z Bi. Analysis and Applications of Thermal Stress[M]. Beijing:China Electric Power Press,2004:60-61.
[171]谢官模.振动力学[M].北京:国防工业出版社,2007:212-214.
[172]张厥宗.硅片加工技术[M].北京:化学工业出版社,2009:29-43.
[173]贾陈,屈梁生.单晶硅晶圆晶向的精确标定方法[J].西安交通大学学报,2002,36(5):528-531.
[174]卢涛.激光微加工系统研制[D].郑州:郑州大学,2002.