摇摆质量微陀螺关键技术研究
|
摘要
摇摆质量微陀螺采用了轴对称的傅科摆结构和沿中性面对称的棒状振动质量结构，其驱动模态和检测模态为轴对称弹性体的正交降阶模式。该微陀螺具有工作模态固有频率相同（无需模态匹配）、惯性质量大、灵敏度高等突出优点，具有成为可批量生产的高性能微陀螺的潜质。国外摇摆质量微陀螺的研究得到长足发展，但对我国进行产品和技术封锁。因此，开展摇摆质量微陀螺技术研究，对我国高性能微陀螺技术研究具有重要的战略意义。
国外对摇摆质量微陀螺技术的研究主要集中在谐振结构改善、加工工艺优化和测控方法创新等方面，很少涉及到其结构设计理论。本文设计了一款摇摆质量微陀螺，采用全差分的静电激励和电容检测的工作模式。利用MEMS加工技术、传统精密机械加工技术和高精度对准粘接技术完成微陀螺原理样机的制造。摇摆质量微陀螺制造工艺简单，成本低，具有批量生产的潜力。
本文围绕摇摆质量微陀螺的结构设计理论、能量损耗机理、动态特性分析、MEMS加工工艺和原理样机验证开展研究，主要研究内容如下：
1．设计了一种全差分摇摆质量微陀螺的总体结构，分析了微陀螺在工作模态谐振时的力学特性，提出一种计算微陀螺工作模态固有频率的数值方法和解析模型；建立了微陀螺接口电容、驱动力矩和反馈力矩等电学特性的理论模型；根据力学特性和电学特性的分析结果，获得了微陀螺工作模态固有频率的参数化解析模型，为微陀螺的结构设计提供理论依据。
2．系统研究了摇摆质量微陀螺的能量损耗机理。分别推导了微陀螺各种能量损耗机理（Q值）的理论模型，其中包括空气压膜阻尼、支撑损耗、热弹性阻尼、基底能量损耗和表面能量损耗等。研究结果表明：大气条件下，空气压膜阻尼对微陀螺Q值的影响最显著，微陀螺必须进行真空封装；真空封装后，支撑损耗对微陀螺Q值的影响较大。为了提高微陀螺的Q值，必须尽可能地增大支撑结构与谐振结构之间的厚度比。
3．研究了摇摆质量微陀螺的动态特性。推导了微陀螺哥氏力矩的理论模型，建立了微陀螺的动力学微分方程，分别获取了驱动系统和检测系统振动位移的稳态响应。根据Q值理论模型和稳态响应结果，求得了微陀螺结构灵敏度的解析模型。通过分析不同参数对结构灵敏度的影响机理，对微陀螺的谐振结构进行了优化设计，确定了微陀螺的结构参数。
4．研究了摇摆质量微陀螺的加工工艺。根据微陀螺的结构特征，将其加工工艺分解为硅微结构、玻璃基板（含金属电极）、质量棒和支撑装置等四部分。分别研究了硅微结构、玻璃基板的MEMS加工工艺，设计了一种基于预埋掩膜各向异性湿法腐蚀为主的单晶硅加工工艺，并利用紫外激光划片工艺完成玻璃基板通孔的加工。优化了微陀螺的组装工艺，制作出微陀螺样机，并利用金属管壳焊接技术实现了微陀螺的真空封装。
5．摇摆质量微陀螺样机的原理验证。研制了摇摆质量微陀螺专用的模态测试电路和信号测控电路，对微陀螺样机进行了模态测试和哥氏力信号测试。测试结果初步验证了本文所提出的微陀螺结构设计理论、能量损耗机理、动态特性、结构参数优化方法的正确性以及制造工艺的可行性。
The Rocking Mass Micro-Gyroscope (RMG) adopts an axisymmetric Foucaultpendulum vibratory structure and a centrosymmetric rocking mass post, whoseoperational modes are the perpendicular degeneration modes of the axisymmetric elasticbody. RMG has some important advantages, such as equal natural frequency of theoperational modes without modes matching, large inertia mass, high sensitivity, andthus has the potential to be the high performance microgyroscope which can befabricated in batches. The study on RMG has been greatly developed abroad, but therelated products and technologies are forbidden by the western countries. Therefore,researching the RMG technologies to improve our microgyroscope technologies is ofgreat importance.
The study on RMG technology abroad mainly focused on vibratory structureimproving, fabrication process optimizing, and control method innovating, hardlyinvolved its structure design theory. In this dissertation, we explore a novel rockingmass microgyroscope, which operates based on the method of entirely differentialelectrostatic force actuating and capacitance sensing. The prototype of RMG isfabricated by MEMS process, traditional precision mechanical machining and precisionadherence technologies. RMG has the advantages as simple fabrication process, highprecision, low cost, and also has the potential to be fabricated in batches.
In this dissertation, we present the structure design theory, energy loss mechanism,dynamics analysis, MEMS fabrication process, and performance test of the micro-gyroscope. The main content includes:
1. The differential whole structure of RMG is designed, the mechanics of itsvibratory structure are analyzed, and the natural frequency analytical model of itsoperational modes is deduced. The theoretical models of the microgyroscope’s interfacecapacitance, actuating momentum, and feedback momentum are also deduced. Based onthe analyzed mechanics and electrics results of the microgyroscope, the detailed naturalfrequency analytical model of its operational modes are derived to provide thetheoretical basis for its structure design.
2. All the energy loss mechanisms of RMG are studied, and their theoretical modelof vibratory damping (Q-factors) are respectively deduced, including squeeze-film airdamping, support loss, thermoelastic damping, energy loss of the base, and surface loss.The squeeze-film air damping will badly restrain the Q-factors of the microgyroscope inatmospheric air, and the microgyroscope must be packaged in low vacuum. The supportloss will mainly affect the Q-factors of the microgyroscope in vacuum, and the ratio ofthe thickness between the support structure and the vibratory structure must be designedas larger as possible to improve its Q-factors.
3. The dynamic characteristic of RMG is studied. The Coriolis momentumtheoretical model of the microgyroscope are deduced, then the dynamic differentialequations are built, and the steady-state responses of the actuating mode and sensingmode are derived finally. The analytical model of the structural sensitivity of themicrogyroscope is derived, based on its Q-factor theoretical model and steady-stateresponse results. The whole structure of RMG is optimized, and the parameters of thevibratory structure are achieved, by analyzing the influences of different parameters onthe structural sensitivity.
4. The fabrication process of RMG is studied. Based on the strucaturalcharacteristics of RMG, the fabrication process is divided into four parts, such as siliconstructure, Pyrex base (including metal electrodes), rocking mass post, and supportingpart. The MEMS fabrication processes of the silicon structure and Pyrex base arestudied respectively, a kind of single crystal silicon anisotropic wet etching processbased on pre-buried mask method is designed, and the hole in the center of the Pyrexbase is fabricated by using the UV laser dicing technology. The assembly process ofRMG is optimized, and then the prototype is fabricated and encapsulated in low vacuumby using metal tube welding technology. Finally, the operational modes of theprototypes in atmospheric air and in vacuum are characterized respectively.
5. The RMG prototype is theoretically validated. The special mode test circuit andCoriolis siginal test circuit of RMG are designed and fabricated. The mode frequencyresponse curves and Coriolis signal of RMG prototype are tested. The tested resultsindicate that: the structure design theory, energy loss mechanism, dynamics theory,and structural parameter optimization method in this dissertation are valid; the MEMSfabrication processes are feasible.
国外对摇摆质量微陀螺技术的研究主要集中在谐振结构改善、加工工艺优化和测控方法创新等方面，很少涉及到其结构设计理论。本文设计了一款摇摆质量微陀螺，采用全差分的静电激励和电容检测的工作模式。利用MEMS加工技术、传统精密机械加工技术和高精度对准粘接技术完成微陀螺原理样机的制造。摇摆质量微陀螺制造工艺简单，成本低，具有批量生产的潜力。
本文围绕摇摆质量微陀螺的结构设计理论、能量损耗机理、动态特性分析、MEMS加工工艺和原理样机验证开展研究，主要研究内容如下：
1．设计了一种全差分摇摆质量微陀螺的总体结构，分析了微陀螺在工作模态谐振时的力学特性，提出一种计算微陀螺工作模态固有频率的数值方法和解析模型；建立了微陀螺接口电容、驱动力矩和反馈力矩等电学特性的理论模型；根据力学特性和电学特性的分析结果，获得了微陀螺工作模态固有频率的参数化解析模型，为微陀螺的结构设计提供理论依据。
2．系统研究了摇摆质量微陀螺的能量损耗机理。分别推导了微陀螺各种能量损耗机理（Q值）的理论模型，其中包括空气压膜阻尼、支撑损耗、热弹性阻尼、基底能量损耗和表面能量损耗等。研究结果表明：大气条件下，空气压膜阻尼对微陀螺Q值的影响最显著，微陀螺必须进行真空封装；真空封装后，支撑损耗对微陀螺Q值的影响较大。为了提高微陀螺的Q值，必须尽可能地增大支撑结构与谐振结构之间的厚度比。
3．研究了摇摆质量微陀螺的动态特性。推导了微陀螺哥氏力矩的理论模型，建立了微陀螺的动力学微分方程，分别获取了驱动系统和检测系统振动位移的稳态响应。根据Q值理论模型和稳态响应结果，求得了微陀螺结构灵敏度的解析模型。通过分析不同参数对结构灵敏度的影响机理，对微陀螺的谐振结构进行了优化设计，确定了微陀螺的结构参数。
4．研究了摇摆质量微陀螺的加工工艺。根据微陀螺的结构特征，将其加工工艺分解为硅微结构、玻璃基板（含金属电极）、质量棒和支撑装置等四部分。分别研究了硅微结构、玻璃基板的MEMS加工工艺，设计了一种基于预埋掩膜各向异性湿法腐蚀为主的单晶硅加工工艺，并利用紫外激光划片工艺完成玻璃基板通孔的加工。优化了微陀螺的组装工艺，制作出微陀螺样机，并利用金属管壳焊接技术实现了微陀螺的真空封装。
5．摇摆质量微陀螺样机的原理验证。研制了摇摆质量微陀螺专用的模态测试电路和信号测控电路，对微陀螺样机进行了模态测试和哥氏力信号测试。测试结果初步验证了本文所提出的微陀螺结构设计理论、能量损耗机理、动态特性、结构参数优化方法的正确性以及制造工艺的可行性。
The Rocking Mass Micro-Gyroscope (RMG) adopts an axisymmetric Foucaultpendulum vibratory structure and a centrosymmetric rocking mass post, whoseoperational modes are the perpendicular degeneration modes of the axisymmetric elasticbody. RMG has some important advantages, such as equal natural frequency of theoperational modes without modes matching, large inertia mass, high sensitivity, andthus has the potential to be the high performance microgyroscope which can befabricated in batches. The study on RMG has been greatly developed abroad, but therelated products and technologies are forbidden by the western countries. Therefore,researching the RMG technologies to improve our microgyroscope technologies is ofgreat importance.
The study on RMG technology abroad mainly focused on vibratory structureimproving, fabrication process optimizing, and control method innovating, hardlyinvolved its structure design theory. In this dissertation, we explore a novel rockingmass microgyroscope, which operates based on the method of entirely differentialelectrostatic force actuating and capacitance sensing. The prototype of RMG isfabricated by MEMS process, traditional precision mechanical machining and precisionadherence technologies. RMG has the advantages as simple fabrication process, highprecision, low cost, and also has the potential to be fabricated in batches.
In this dissertation, we present the structure design theory, energy loss mechanism,dynamics analysis, MEMS fabrication process, and performance test of the micro-gyroscope. The main content includes:
1. The differential whole structure of RMG is designed, the mechanics of itsvibratory structure are analyzed, and the natural frequency analytical model of itsoperational modes is deduced. The theoretical models of the microgyroscope’s interfacecapacitance, actuating momentum, and feedback momentum are also deduced. Based onthe analyzed mechanics and electrics results of the microgyroscope, the detailed naturalfrequency analytical model of its operational modes are derived to provide thetheoretical basis for its structure design.
2. All the energy loss mechanisms of RMG are studied, and their theoretical modelof vibratory damping (Q-factors) are respectively deduced, including squeeze-film airdamping, support loss, thermoelastic damping, energy loss of the base, and surface loss.The squeeze-film air damping will badly restrain the Q-factors of the microgyroscope inatmospheric air, and the microgyroscope must be packaged in low vacuum. The supportloss will mainly affect the Q-factors of the microgyroscope in vacuum, and the ratio ofthe thickness between the support structure and the vibratory structure must be designedas larger as possible to improve its Q-factors.
3. The dynamic characteristic of RMG is studied. The Coriolis momentumtheoretical model of the microgyroscope are deduced, then the dynamic differentialequations are built, and the steady-state responses of the actuating mode and sensingmode are derived finally. The analytical model of the structural sensitivity of themicrogyroscope is derived, based on its Q-factor theoretical model and steady-stateresponse results. The whole structure of RMG is optimized, and the parameters of thevibratory structure are achieved, by analyzing the influences of different parameters onthe structural sensitivity.
4. The fabrication process of RMG is studied. Based on the strucaturalcharacteristics of RMG, the fabrication process is divided into four parts, such as siliconstructure, Pyrex base (including metal electrodes), rocking mass post, and supportingpart. The MEMS fabrication processes of the silicon structure and Pyrex base arestudied respectively, a kind of single crystal silicon anisotropic wet etching processbased on pre-buried mask method is designed, and the hole in the center of the Pyrexbase is fabricated by using the UV laser dicing technology. The assembly process ofRMG is optimized, and then the prototype is fabricated and encapsulated in low vacuumby using metal tube welding technology. Finally, the operational modes of theprototypes in atmospheric air and in vacuum are characterized respectively.
5. The RMG prototype is theoretically validated. The special mode test circuit andCoriolis siginal test circuit of RMG are designed and fabricated. The mode frequencyresponse curves and Coriolis signal of RMG prototype are tested. The tested resultsindicate that: the structure design theory, energy loss mechanism, dynamics theory,and structural parameter optimization method in this dissertation are valid; the MEMSfabrication processes are feasible.
引文
[1] D D Lynch. Coriolis Vibratory Gyros[C]. IEEE Proceedings, Symposium GyroTechnology, Stuttgart,1998:1-14.
[2]李新刚,袁建平.微机械陀螺的发展现状[J].力学进展,2003,33(3):289-301.
[3] Y Tao, X Xi, D B Xiao, et al. Precision Balance Method for Cupped Wave GyroBased on Cup-bottom Trimming[J]. Chinese Journal of Mechanical Engineering,2012,25(1):63-70.
[4] F Ayazi, K Najafi. Design and Fabrication of a High-Performance PolysiliconVibrating Ring Gyroscope[C]. Proceedings of11th Annual InternationalWorkshop on Micro Electro Mechanical Systems, Germany,1998:621-626.
[5] K V Shcheglov. Disc Resonator Gyroscope Fabrication Process Requiring NoBonding Alighment [P]. United States Patent: US7,818,871B2, Oct.26,2010.
[6] V Bhadbhade, N Jalili, S N Mahmoodi. A Novel Piezoelectrically ActuatedFlexural/Torsional Vibrating Beam Gyroscope[J]. Journal of Sound and Vibration,2008,311:1305-1324.
[7] L L Dong, Q Zheng, Z Q Gao. A Novel Oscillation Controller for VibrationalMEMS Gyroscopes[C]. Proceedings of the2007American Control Conference,New York, USA, July11-132007:3204-3209.
[8] L L Dong, D Avanesian. High Performance MEMS Gyroscope[R]. http://academic.csuohio.edu/dong_l/research%20lab/publications.html.
[9] F Ayazi, K Najafi. A HARPSS Polysilicon Vibrating Ring Gyroscope [J]. Journalof Microelectromechanical Systems,2001,10(2):169-179.
[10] F Ayazi. The HARPSS Process for Fabrication of Precision MEMS InertialSensors[J]. Mechatronics2002,12:1185-1199
[11] G H He, K Najafi. A Single Crystal Silicon Vibrating Ring Gyroscope[C].Proceedings of15th IEEE MEMS,2002:718-721.
[12] 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.
[13] F Ayazi, M F Zaman, A Sharma, et al. Resonator Star Gyroscope[P]. UnitedStates Patent: US7,360,423B2, Apr.22,2008.
[14] 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
[15] A Gripton. The Application and Future Development of A MEMS SiVSG forCommercial and Military Inertial Products[C]. Proceedings of IEEE PositionLocation and Navigation Symposium,2002:28-35.
[16] I Sturland. Development and Commercialisation of Silicon MEMS Gyroscopes[C]. The IEEE Seminar and Exhibition on MEMS Sensor Technologies,2005.
[17] C Fel. Development of a Second Genesation Low Cost MEMS Gyroscope:Design for Manufacture[C]. The Institution of Engineering and TechnologySeminar on MEMS Sensors and Actuators, London,2006:75-82.
[18] Y M Desta. Fabrication of High Aspect Ratio Vibrating Cylinder MicrogyroscopeStructures by Use of the LIGA Process[D]. Louisiana: Louisiana State University,2005:128-133
[19] D Keymeulen, C Peay, D Foor, et al. FPGA Platform for MEMS Disc ResonanceGyroscope (DRG) control[C]. Micro (MEMS) and Nanotechnologies for Space,Defense, and Security II, edited by T George. Proc. of SPIE Vol.6959,2008.
[20] J J Bernstein. Symmetrical Micromechanical Gyroscope[P]. United States Patent:US5,203,208, Apr.20,1993.
[21] T K Tang, R C Gutierrez, K Hayworth, et al. High Performance Microgyros forSpace Applications[C]. AIAA Space Technology Conference&Exhibit,Albuquerque, September28-30,1999:1-5.
[22] Jason Kwong-Ping Hui. Modeling and Identification of the Jet Propulsion LabVibratory Rate Microgyroscope[D]. Los Angeles: University of California,2002.
[23] http://www.boeing.com/defense-space/space/bass/factsheets/gyro/gyro.html.
[24] J Wellman, K Yee, H Avila. Using Infrared Imaging to Evaluate BondUniformity in Si Structures: JPL Meso-Gyro Failure Analysis Study. http://nepp.nasa.gov/srch/searchfriendly pubilist.cfm.
[25] 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.
[26] R L Kubena, F P Stratton, D T Chang. Cloverleaf Microgyroscope withThrough-Wafer Interconnects and Method of Manufacturing a CloverleafMicrogyroscope with Through-Wafer Interconnects[P]. United States Patent: US7,015,060B1, Mar.21,2006.
[27] R L Kubena. Integrated All-Si Capacitive Microgyro with Vertical DifferentialSense and Control and Process for Preparing an Integrated All-Si CapacitiveMicrogyro with Vertical Differentical Sense[P]. United States Patent: US7,232,700B1, Jun.19,2007.
[28] R L Kubena, F P Stratton, D T Chang. Method of Manufacturing a CloverleafMicrogyroscope and Cloverleaf Microgyroscope[P]. United States Patent: US7,202,100B1, Apr.10,2007.
[29] C M Royle, C H J Fox. The Mechanics of an Oscillatory Rate Gyroscope withPiezoelectric and Actuation and Sensing[J]. Proceedings of the Institution ofMechanical Engineers, Part C: Journal of Mechanical Engineering Science,215,2001:1211-1221.
[30] R V Wrighta, A Patela, M Pealatb. Development of Micromechanical and OpticalDevices Incorporating Deposited PZT Films[J]. Integrated Ferroelectrics,33(1),2001:209-220.
[31] C M Royle, C H J Fox. Rate Sensor with Piezoelectric Actuation and Sensing:Dynamic Analysis Problems. http://sem-proceedings.com/20i/sem.org-IMAC-XX-Conf-S22P02-An-Angular-Rate-Transducer-with-Piezo-electric-Actuation-Sensing-.pdf
[32] A J Harris, J S Burdess, J Cruickshank, et al. A Silicon Membrane Gyroscopewith Electrostatic Actuation[C]. Silicon Fabricated Inertial Instruments, London,1996:5/1-7.
[33] Y Chen, D H B Wicaksono, L J Zhang, et al. Preliminary Study on The Design ofA Silicon Bio-inspired MEMS Gyroscope[C]. Proc. Semiconductor Advances forFuture Electronics, Veldhoven, Netherlands, Nov23-24,2006:379-383.
[34] Y Chen, D H B Wicaksono, L Pakula, et al. Modelling, Design and Fabrication ofa Bio-inspired MEMS Vibratory Gyroscope[C]. Proceedings of MME2007,Guimaraes, Portugal,2007:199-202.
[35] D H B Wicaksono, Y Chen, and P J French. Design and Modelling of aBio-inspired MEMS Gyroscope[C]. Proceedings of the International Conferenceon Electrical Engineering and Informatics Institut Teknologi Bandung, Indonesia,June17-19,2007:226-229.
[36] S Kotru, J Zhong, A Highsmith, et al. Design and Fabrication of a Meso-ScaleGyroscope[C]. Microelectronics and Electron Devices,2008. WMED2008. IEEEWorkshop on, April18-18,2008:5-8.
[37] S Kotru, A Highsmith, J Zhong, et al. Feasibility Study of a MicromachinedSingle-axis Vibratory Gyroscope Using Piezoelectric PNZT Thin Films forActuation and Sensing[J]. Smart Materials and Structures,2010,19:1-11.
[38] Y Watanabe, T Mitsui, et al. Five-axis Motion Sensor with Electrostatic Driveand Capacitive Detection Fabricated by Silicon Bulk Micromachining [J]. Journalof Sensors and actuators A: Physical,2002,97-98:109-115.
[39] T Hanazawa, M Ono, T Miyashita, et al. Stress Detection Method for SensorDevice with Multiple Axis Sensor and Sensor Device Employing this Method[P].United States Patent: US7,320,253B2, Jan22,2008.
[40] S E Alper, T Akin. A Single-Crystal Silicon Symmetrical and Decoupled MEMSGyroscope on an Insulating Substrate[J]. Journal of MicroelectromechanicalSystems,2005,14(4):707-717.
[41] S E Alper, K Azgin, T Akin. High-Performance SOI-MEMS Gyroscope withDecoupled Oscillation Modes[C]. Proceedings of IEEE MEMS, Istanbul, Turkey,2006:70-73.
[42] S E Alper, K Azgin. A High-Performance Silicon-on-Insulator MEMS GyroscopeOperating at Atmospheric Pressure[J]. Journal of Sensors and Actuators A:Physical,2007,135:34-42.
[43] S E Alper, I Ocak1, T Akin. Ultra-Thick and High-Aspect-Ratio NickelMicrogyroscope Using EFAB Multi-Layer Additive Electroforming[C].Proceedings of IEEE MEMS, Istanbul, Turkey,2006:670-673.
[44] L A Oropeza-Ramos, C B Burgner, K L Turner. Robust Micro-rate SensorActuated by Parametric Resonance[J]. Journal of Sensors and Actuators A:Physical,2009,152:80-87.
[45] M Ansari, E Esmailzadeh, N Jalili. Coupled Vibration and Parameter SensitivityAnalysis of Rocking Mass Vibrating Gyroscopes[J]. Journal of Sound andVibration,2009,327:564-583.
[46] M Ansari, E Esmailzadeh, N Jalili. On Coupled Flexural and TorsionalOscillations of a Vibrating Beam Gyroscopic System[C]. Proceedings of theASME2009Dynamic Systems and Control Conference DSCC2009, Hollywood,California, USA, October12-14,2009:1-8.
[47] M Ansari. Modeling and Vibration Analysis of a Rocking Mass GyroscopeSystem[D]. Ontario: University of Ontario Institute of Technology,2008:55-70.
[48] Y H Yao, Z Y Gao, R Zhang, et al. A Silicon Wafer Dissolved VibratingGyroscope[C]. Proceedings of IEEE Instrumentation and MeasurementTechnology Conference, St. Paul, Minnesota,1998:1133-1136
[49] G Z Yan, Y Zhu, C W Wang, R Zhang. Intergrated Bulk MicromachinedGyroscope Using Deep Trench Isolation Technology[C]. Proceedings of IEEESensors,2004:605-608
[50] X X Li, X M Chen, Z H Song, et al. A Microgyroscope with Piezoresistance forBoth High-Performance Coriolis-Effect Detection and Seesaw-Like VibrationControl[J]. Journal of Microelectromechanical Systems,2006,15(6):1698-1707.
[51] X M Chen, X X Li, et al. A Micromachined Gyroscope with Piezoresistance forBoth High Performance Coriolis-effect Detection and Torsional VibrationMonitoring[C]. Proceedings of Transducers, Seoul, June5-9,2005:117-120.
[52]裘安萍,施芹,苏岩,朱欣华.双质量振动式硅微陀螺仪[P].中国专利:200710133223.5,2007-10-12.
[53]李卯辰,吕志清.微石英音叉陀螺精度受参数变化影响的研究[J].压电与声光,2008,30(2):137-140.
[54]金小锋,陶晋,邹江波.石英音叉陀螺误差分析[J].传感技术学报,2008,21(2):252-254.
[55]苏岩,王寿荣,周百令.硅微型两自由度振动轮式陀螺仪原理分析[J].东南大学学报,1999,29(6):56-59.
[56]周百令,蔡体菁.两自由度振动轮式硅微陀螺仪的机理研究[J].船舶工程,2000,(6):44-46.
[57]蒋明,何小元.振动轮式微机械陀螺动态特性的光学测试[J].光学精密工程,2008,16(2):295-299.
[58] H L Chang, W J Jiao, Q Y Fu, et al. Design and Simulation of a MEMS ControlMoment Gyroscope for the Sub-Kilogram Spacecraft[J]. Journal of sensors,2010,10:4130-4144.
[59] H L Chang, B Bai, W L Jiao, et al. Design of a Micro Control MomentGyroscope with a Large Torque Output[J]. Chinese Journal of Sensors andActuators,2011,24(8):1126-1130.
[60] Z N Qin, W Y Chen, F Cui, et al. System-level Simulation of a MicromachinedElectrostatically Suspended Gyroscope[C]. Proceedings of the20105th IEEEInternational Conference on Nano/Micro Engineered and Molecular Systems,Xiamen, China, January20-23,2010:658-661.
[61] G Y Ma, W Y Chen, W P Zhang, et al. Compact H∞Robust Rebalance LoopController Design for a Micromachined Electrostatically Suspended Gyroscope[J].ISA Transactions,2010,49:222-228.
[62] Q J Xiao, W Y Chen, S Y Li, et al. Modeling and Simulation of LevitationControl for a Micromachined Electrostatically Suspended Gyroscope[J].Microsystem Technology,2010,16:357-366.
[63] H T Ding, X S Liu, J Cui, et al. A Bulk Micromachined Z-Axis Single CrystalSilicon Gyroscope for Commercial Applications[C]. Proceedings of the3rd IEEEInt. Conf. on Nano/Micro Engineered and Molecular Systems, Sanya, China,January6-9,2008:1039-1042.
[64] D Keymeulen, W Fink, M I Ferguson, et al. Tuning of MEMS Devices UsingEvolutionary Computation and Open-Loop Frequency Response[C]. IEEEAC,paper#1211, Version3, December7,2004:1-8.
[65] M I. Ferguson, D Keymeulen, K Hayworth, et al. A Hardware Platform forTuning of MEMS Devices Using Closed-Loop Frequency Response[C]. IEEEACpaper#1284, Version4, January10,2005:1-7.
[66] H Urey. Torsional MEMS Scanner Design for High-Resolution DisplaySystems[C]. Optical Scanning II, Proc. SPIE4773, Seattle, Washington, July2002:27-37.
[67] H Urey, C Kan and W O Davis. Vibration Mode Frequency Formulae for Micro-mechanical Scanners[J]. Journal of Micromechanics and Microengineering,2005,15:1713-1721.
[68]钱伟长,叶开沅.弹性力学[M].北京:科学出版社，1956:160-165.
[69] M H Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier,2005:60-62.
[70]王洪喜.微结构的静电驱动特性研究[D].西安:西安电子科技大学，2006:18-24.
[71] D Keymeulen, M I Ferguson, L Breuer, et al. Tuning of MEMS Gyroscope UsingEvolutionary Algorithm and “Switched Drive-angle” Method[C]. IEEEACpaper#162, Version3, January2,2006:1-8.
[72] R Abdolvand, H Johari, G K Ho, et al. Quality Factor in Trench-RefilledPolysilicon Beam Resonators[J]. Journal of Microelectromechanical Systems,2006,15(3):471-478.
[73] M H Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier,2005:124-136.
[74] M H Bao, Y C Sun, J Zhou et al. Squeeze-Film Air Damping of a Torsion Mirrorat a Finite Tilting Angle[J]. Journal of Micromechanics and Microengineering,2006,16:2330-2335.
[75] A K Pandey, R Pratap. A Semi-Analytical Model for Squeeze-Film DampingIncluding Rarefaction in a MEMS Torsion Mirror with Complex Geometry[J].Journal of Micromechanics and Microengineering,2008,18(105003):1-12.
[76] M H Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier,2005:169-170.
[77] R Christian. The Theory of Oscillating-Vane Vaccum Gauges[J]. Journal ofVacuum,1966,16:175-178.
[78] M H Bao, H Yang, H Yin, et al. Energy Transfer Model for Squeeze-Film AirDamping in Low Vacuum[J]. Journal of Micromechanics and Microengineering,2002,12:341-346.
[79] J Zook, D Burns, H Guckel, et al. Characteristics of Polysilicon ResonantMicrobeams[J]. Journal of Sensors and Actuators A: Physical,1992,35:51-59.
[80] C Acar, A Shkel. MEMS Vibratory Gyroscopes Structural Approaches toImprove Robustness[M]. New York: Springer Science+Business Media,2009:106-107.
[81] Z L Hao, A Erbil, F Ayazi. An Analytical Model for Support Loss inMicromachined Beam Resonators with in-Plane Flexural Vibrations[J]. Journal ofSensors and Actuators A: Physical,2003,109:156-164.
[82] Z L Hao, F Ayazi. Support Loss in Micromechanical Disk Resonators[C]. InProceedings of the18th IEEE International Conference on Micro ElectroMechanical Systems, Miami Beach, USA,1–3February,2005:137-141.
[83] J A Judge, D M Photiadis, J F 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.
[84] B Chouvion. Vibration Transmission and Support Loss in MEMS Sensors[D].Nottingham: University of Nottingham,2010: Chapter4and Chapter6.
[85] E Eichler. Plate-Edge Admittances[J]. Journal of acoustical society of America,1964,36:344-348.
[86] A D Pierce. An Introduction to Its Physical Principles and Applications[C].Acoustical Society of America and American Institute of Physics, New York,1981:122.
[87] C Kauffmann. Input Mobilities and Power Flows for Edge-Excited, Semi-InfinitePlates[J]. Journal of Acoustical Society of America,1998,103(4):1874-1884.
[88] J X Su, A T Moorhouse. A Closed Form Solution for the Mobility of anEdge-Excited, Semi-Infinite Plate[J]. Journal of Acoustical Society of America,2004,115(5):2075-2082.
[89] C Benjamin. Vibration Transmission and Support Loss in MEMS Sensors[D].Nottingham: University of Nottingham,2010:206.
[90] C Zener. Internal Friction in Solids[J]. Physical Review,1937,52:230–235;1938,53:90–99;1938,53:100-101.
[91] C Zener. Elasticity and Anelasticity of Metals[M]. Chicago: The University ofChicago Press,1948.
[92] M A Biot. Thermoelasticity and Irreversible Thermodynamics[J]. Journal ofApplied Physics,1956,27:240-253.
[93] F Abroad, A Khan. Thermoelastic Plane Waves in a Rotating IsotropicMedium[J]. Journal of Acoustical Society of America,1999,136:243-247.
[94] P Chadwick. Thermoelasticity: The Dynamical Theory[J]. Progress in SolidMechanics, North-Holland, Amsterdam,1960,1:265-328.
[95] M Daimaruya, M Naitoh. Dispersion and Energy Dissipation of ThermoelasticWaves in a Circular Cylinder[J]. Acustica,1982,51:124-129.
[96] E S Suhubi, J Therm. Longitudinal Wave Propagation in a GeneralizedThermoelastic Cylinder[J]. Journal of Thermal Stresses,1986,9:279-295.
[97] R Lifshitz, M L Roukes. Thermoelastic Damping in Micro-and NanomechanicalSystems[J]. Physical Review B,2000,61(8):5600-5608.
[98] Z L Hao, F Ayazi. Thermoelastic Damping in Flexural-Mode Ring Gyroscope[C].Proceedings of IMECE2005: ASME International Mechanical EngineeringCongress and Exposition, Orlando, Florida, USA, Nov.5-11,2005:1-9.
[99] R Abdolvand, H Johari, G K Ho, et al. Quality Factor in Trench-RefilledPolysilicon Beam Resonators[J]. Journal of Microelectromechanical Systems,2006,15(3):471-478.
[100] R Gutierrez, T K Tang, K Shcheglov. Micromachined Double Resonator[P].United States Patent: US6,367,786B1, Apr.9,2002.
[101]王福楹,王福保,蔡森甫等.高等数学[M].北京:高等教育出版社,2002:311-316.
[102] H Ibach. Adsorbate Induced Surface Stress[J]. Journal of Vacuum ScienceTechnology A,1994,12:2240-2245.
[103] D Sander, Z Tian, J Kirschner. The Role of Surface Stress in Reconstruction,Epitaxial Growth and Stabilization of Mesoscopic Structures[R]. Surface ScienceReports,1997,29:193-263.
[104] 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.
[105] Z L Hao, M F Zaman, A Sharma, et al. Energy Loss Mechanisms in a BulkMicromachined Tuning Fork Gyroscope[C]. IEEE Sensors2006, Daegu, Korea,October22-25,2006:1333-1336.
[106] K Y Yasumura, T D Stowe, E M Chow, et al. Quality Factors in Micron andSubmicron Thick Cantilevers[J]. Journal of Microelectromechanical Systems,2000,9(1):117-125.
[107] A S Nowick, B S Berry. Anelastic Relaxation in Crystalline Solids[M]. NewYork: Academic Press,1972.
[108]孙世贤,黄圳圭.理论力学教程[M].长沙:国防科技大学出版社,2005:116-130.
[109] S. D. Senturia著,刘泽文,王晓红,黄庆安等译.微系统设计MicrosystemDesign[M].北京:电子工业出版社,2004:373-374.
[110] M. F. Zaman. Degree-Per-Hour Mode-Matched Micromachined Silicon VibratoryGyroscopes[D]. Georgia: Georgia Institute of Technology,2008:24-28.
[111]高世桥,刘海鹏.微机电系统力学[M].北京:国防工业出版社,2008:230-235.
[112]杨涛,何叶,魏东梅等.微机电器件的稳健设计[J].工程设计学报,2004,11(3):124-127.
[113]王安麟,善盈盈,刘广军,姜涛.基于灵敏度解析的微机械陀螺结构优化方法[J].浙江工业大学学报,2008,36(6):673-677.
[114] B. A.马特维耶夫等(著);杨亚非,赵辉(译).固体波动陀螺[M].北京:国防工业出版社，2009:201-225.
[115] Y. Tao, X. Xi, D.B. Xiao, et al. Precision Balance Method for Cupped WaveGyro Based on Cup-bottom Trimming[J]. Chinese Journal of MechanicalEngineering,2012,25(1):63-70.
[116] S. Y. Bae, K. J. Hayworth, K. Y. Yee, et al. High Performance MEMSMicro-Gyroscope[C]. Design, Integration, and Pakaging of MEMS/MOEMS2002, Proceedings of SPIE,2002,4755:316-324.
[117] X. F. Zhou, L. F. Che, B. Xiong, et al. Single Wafer Fabrication of a SymmetricDouble-Sided Beam–Mass Structure using DRIE and Wet Etching by a NovelVertical Sidewall Protection Technique[J]. Journal of Micromechanics andMicroengineering,2010,20(115009):1-14.
[118]王寿荣.硅微惯性器件理论及应用[M].南京:东南大学出版社,2000:116-120.
[119] M. Shikida, K. Sato, K. Tokoro, et al. Differences in Anisotropic EtchingProperties of KOH and TMAH Solutions[J]. Journal of Sensors and Actuators APhsycal,2000,80:179-188.
[120] O. Tabata, R. Asahi, H. Funabashi, et al. Anisotropic Etching of Silicon in(CH3)4NOH Solutions[C]. IEEE,1991:811-814.
[121] M. H. Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier B.V.,2005:103-105.
[122] H. Schr der, E. Obermeier, A. Horn, et al. Convex Corner Undercutting of {100}Silicon in Anisotropic KOH Etching: The New Step Flow Model of3-DStructuring and First Simulation Results[J]. Journal of microelectromechanicalsystems,2001,10(1):88-97.
[123] P. Pal, K. Sato, M. Shikida, et al. Study of Corner Compensating Structures andFabrication of Various Shapes of MEMS Structures in Pure and Surfactant AddedTMAH[J]. Journal of Sensors and Actuators A Physical,2009,154:192-203.
[124]江平.蝶翼式硅微陀螺结构设计及制造工艺研究[D].长沙:国防科学技术大学,2007:24-26.
[125]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,2009:77-80.
[126]吴学忠,肖定邦,李圣怡.电容式微加速度计的闭环检测技术研究[J].传感技术学报,2006,19(4):1097-1099.
[127]肖定邦,侯占强,满海鸥等.微陀螺闭环驱动方法[J].国防科技大学学报,2009,31(3):116-121.
[128]焦斌.自动控制原理与应用[M].北京:高等教育出版社,2004:149-150.
[129]周泽龙.四叶片微陀螺结构设计与加工工艺研究[D].长沙:国防科学技术大学，2011:58.
[2]李新刚,袁建平.微机械陀螺的发展现状[J].力学进展,2003,33(3):289-301.
[3] Y Tao, X Xi, D B Xiao, et al. Precision Balance Method for Cupped Wave GyroBased on Cup-bottom Trimming[J]. Chinese Journal of Mechanical Engineering,2012,25(1):63-70.
[4] F Ayazi, K Najafi. Design and Fabrication of a High-Performance PolysiliconVibrating Ring Gyroscope[C]. Proceedings of11th Annual InternationalWorkshop on Micro Electro Mechanical Systems, Germany,1998:621-626.
[5] K V Shcheglov. Disc Resonator Gyroscope Fabrication Process Requiring NoBonding Alighment [P]. United States Patent: US7,818,871B2, Oct.26,2010.
[6] V Bhadbhade, N Jalili, S N Mahmoodi. A Novel Piezoelectrically ActuatedFlexural/Torsional Vibrating Beam Gyroscope[J]. Journal of Sound and Vibration,2008,311:1305-1324.
[7] L L Dong, Q Zheng, Z Q Gao. A Novel Oscillation Controller for VibrationalMEMS Gyroscopes[C]. Proceedings of the2007American Control Conference,New York, USA, July11-132007:3204-3209.
[8] L L Dong, D Avanesian. High Performance MEMS Gyroscope[R]. http://academic.csuohio.edu/dong_l/research%20lab/publications.html.
[9] F Ayazi, K Najafi. A HARPSS Polysilicon Vibrating Ring Gyroscope [J]. Journalof Microelectromechanical Systems,2001,10(2):169-179.
[10] F Ayazi. The HARPSS Process for Fabrication of Precision MEMS InertialSensors[J]. Mechatronics2002,12:1185-1199
[11] G H He, K Najafi. A Single Crystal Silicon Vibrating Ring Gyroscope[C].Proceedings of15th IEEE MEMS,2002:718-721.
[12] 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.
[13] F Ayazi, M F Zaman, A Sharma, et al. Resonator Star Gyroscope[P]. UnitedStates Patent: US7,360,423B2, Apr.22,2008.
[14] 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
[15] A Gripton. The Application and Future Development of A MEMS SiVSG forCommercial and Military Inertial Products[C]. Proceedings of IEEE PositionLocation and Navigation Symposium,2002:28-35.
[16] I Sturland. Development and Commercialisation of Silicon MEMS Gyroscopes[C]. The IEEE Seminar and Exhibition on MEMS Sensor Technologies,2005.
[17] C Fel. Development of a Second Genesation Low Cost MEMS Gyroscope:Design for Manufacture[C]. The Institution of Engineering and TechnologySeminar on MEMS Sensors and Actuators, London,2006:75-82.
[18] Y M Desta. Fabrication of High Aspect Ratio Vibrating Cylinder MicrogyroscopeStructures by Use of the LIGA Process[D]. Louisiana: Louisiana State University,2005:128-133
[19] D Keymeulen, C Peay, D Foor, et al. FPGA Platform for MEMS Disc ResonanceGyroscope (DRG) control[C]. Micro (MEMS) and Nanotechnologies for Space,Defense, and Security II, edited by T George. Proc. of SPIE Vol.6959,2008.
[20] J J Bernstein. Symmetrical Micromechanical Gyroscope[P]. United States Patent:US5,203,208, Apr.20,1993.
[21] T K Tang, R C Gutierrez, K Hayworth, et al. High Performance Microgyros forSpace Applications[C]. AIAA Space Technology Conference&Exhibit,Albuquerque, September28-30,1999:1-5.
[22] Jason Kwong-Ping Hui. Modeling and Identification of the Jet Propulsion LabVibratory Rate Microgyroscope[D]. Los Angeles: University of California,2002.
[23] http://www.boeing.com/defense-space/space/bass/factsheets/gyro/gyro.html.
[24] J Wellman, K Yee, H Avila. Using Infrared Imaging to Evaluate BondUniformity in Si Structures: JPL Meso-Gyro Failure Analysis Study. http://nepp.nasa.gov/srch/searchfriendly pubilist.cfm.
[25] 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.
[26] R L Kubena, F P Stratton, D T Chang. Cloverleaf Microgyroscope withThrough-Wafer Interconnects and Method of Manufacturing a CloverleafMicrogyroscope with Through-Wafer Interconnects[P]. United States Patent: US7,015,060B1, Mar.21,2006.
[27] R L Kubena. Integrated All-Si Capacitive Microgyro with Vertical DifferentialSense and Control and Process for Preparing an Integrated All-Si CapacitiveMicrogyro with Vertical Differentical Sense[P]. United States Patent: US7,232,700B1, Jun.19,2007.
[28] R L Kubena, F P Stratton, D T Chang. Method of Manufacturing a CloverleafMicrogyroscope and Cloverleaf Microgyroscope[P]. United States Patent: US7,202,100B1, Apr.10,2007.
[29] C M Royle, C H J Fox. The Mechanics of an Oscillatory Rate Gyroscope withPiezoelectric and Actuation and Sensing[J]. Proceedings of the Institution ofMechanical Engineers, Part C: Journal of Mechanical Engineering Science,215,2001:1211-1221.
[30] R V Wrighta, A Patela, M Pealatb. Development of Micromechanical and OpticalDevices Incorporating Deposited PZT Films[J]. Integrated Ferroelectrics,33(1),2001:209-220.
[31] C M Royle, C H J Fox. Rate Sensor with Piezoelectric Actuation and Sensing:Dynamic Analysis Problems. http://sem-proceedings.com/20i/sem.org-IMAC-XX-Conf-S22P02-An-Angular-Rate-Transducer-with-Piezo-electric-Actuation-Sensing-.pdf
[32] A J Harris, J S Burdess, J Cruickshank, et al. A Silicon Membrane Gyroscopewith Electrostatic Actuation[C]. Silicon Fabricated Inertial Instruments, London,1996:5/1-7.
[33] Y Chen, D H B Wicaksono, L J Zhang, et al. Preliminary Study on The Design ofA Silicon Bio-inspired MEMS Gyroscope[C]. Proc. Semiconductor Advances forFuture Electronics, Veldhoven, Netherlands, Nov23-24,2006:379-383.
[34] Y Chen, D H B Wicaksono, L Pakula, et al. Modelling, Design and Fabrication ofa Bio-inspired MEMS Vibratory Gyroscope[C]. Proceedings of MME2007,Guimaraes, Portugal,2007:199-202.
[35] D H B Wicaksono, Y Chen, and P J French. Design and Modelling of aBio-inspired MEMS Gyroscope[C]. Proceedings of the International Conferenceon Electrical Engineering and Informatics Institut Teknologi Bandung, Indonesia,June17-19,2007:226-229.
[36] S Kotru, J Zhong, A Highsmith, et al. Design and Fabrication of a Meso-ScaleGyroscope[C]. Microelectronics and Electron Devices,2008. WMED2008. IEEEWorkshop on, April18-18,2008:5-8.
[37] S Kotru, A Highsmith, J Zhong, et al. Feasibility Study of a MicromachinedSingle-axis Vibratory Gyroscope Using Piezoelectric PNZT Thin Films forActuation and Sensing[J]. Smart Materials and Structures,2010,19:1-11.
[38] Y Watanabe, T Mitsui, et al. Five-axis Motion Sensor with Electrostatic Driveand Capacitive Detection Fabricated by Silicon Bulk Micromachining [J]. Journalof Sensors and actuators A: Physical,2002,97-98:109-115.
[39] T Hanazawa, M Ono, T Miyashita, et al. Stress Detection Method for SensorDevice with Multiple Axis Sensor and Sensor Device Employing this Method[P].United States Patent: US7,320,253B2, Jan22,2008.
[40] S E Alper, T Akin. A Single-Crystal Silicon Symmetrical and Decoupled MEMSGyroscope on an Insulating Substrate[J]. Journal of MicroelectromechanicalSystems,2005,14(4):707-717.
[41] S E Alper, K Azgin, T Akin. High-Performance SOI-MEMS Gyroscope withDecoupled Oscillation Modes[C]. Proceedings of IEEE MEMS, Istanbul, Turkey,2006:70-73.
[42] S E Alper, K Azgin. A High-Performance Silicon-on-Insulator MEMS GyroscopeOperating at Atmospheric Pressure[J]. Journal of Sensors and Actuators A:Physical,2007,135:34-42.
[43] S E Alper, I Ocak1, T Akin. Ultra-Thick and High-Aspect-Ratio NickelMicrogyroscope Using EFAB Multi-Layer Additive Electroforming[C].Proceedings of IEEE MEMS, Istanbul, Turkey,2006:670-673.
[44] L A Oropeza-Ramos, C B Burgner, K L Turner. Robust Micro-rate SensorActuated by Parametric Resonance[J]. Journal of Sensors and Actuators A:Physical,2009,152:80-87.
[45] M Ansari, E Esmailzadeh, N Jalili. Coupled Vibration and Parameter SensitivityAnalysis of Rocking Mass Vibrating Gyroscopes[J]. Journal of Sound andVibration,2009,327:564-583.
[46] M Ansari, E Esmailzadeh, N Jalili. On Coupled Flexural and TorsionalOscillations of a Vibrating Beam Gyroscopic System[C]. Proceedings of theASME2009Dynamic Systems and Control Conference DSCC2009, Hollywood,California, USA, October12-14,2009:1-8.
[47] M Ansari. Modeling and Vibration Analysis of a Rocking Mass GyroscopeSystem[D]. Ontario: University of Ontario Institute of Technology,2008:55-70.
[48] Y H Yao, Z Y Gao, R Zhang, et al. A Silicon Wafer Dissolved VibratingGyroscope[C]. Proceedings of IEEE Instrumentation and MeasurementTechnology Conference, St. Paul, Minnesota,1998:1133-1136
[49] G Z Yan, Y Zhu, C W Wang, R Zhang. Intergrated Bulk MicromachinedGyroscope Using Deep Trench Isolation Technology[C]. Proceedings of IEEESensors,2004:605-608
[50] X X Li, X M Chen, Z H Song, et al. A Microgyroscope with Piezoresistance forBoth High-Performance Coriolis-Effect Detection and Seesaw-Like VibrationControl[J]. Journal of Microelectromechanical Systems,2006,15(6):1698-1707.
[51] X M Chen, X X Li, et al. A Micromachined Gyroscope with Piezoresistance forBoth High Performance Coriolis-effect Detection and Torsional VibrationMonitoring[C]. Proceedings of Transducers, Seoul, June5-9,2005:117-120.
[52]裘安萍,施芹,苏岩,朱欣华.双质量振动式硅微陀螺仪[P].中国专利:200710133223.5,2007-10-12.
[53]李卯辰,吕志清.微石英音叉陀螺精度受参数变化影响的研究[J].压电与声光,2008,30(2):137-140.
[54]金小锋,陶晋,邹江波.石英音叉陀螺误差分析[J].传感技术学报,2008,21(2):252-254.
[55]苏岩,王寿荣,周百令.硅微型两自由度振动轮式陀螺仪原理分析[J].东南大学学报,1999,29(6):56-59.
[56]周百令,蔡体菁.两自由度振动轮式硅微陀螺仪的机理研究[J].船舶工程,2000,(6):44-46.
[57]蒋明,何小元.振动轮式微机械陀螺动态特性的光学测试[J].光学精密工程,2008,16(2):295-299.
[58] H L Chang, W J Jiao, Q Y Fu, et al. Design and Simulation of a MEMS ControlMoment Gyroscope for the Sub-Kilogram Spacecraft[J]. Journal of sensors,2010,10:4130-4144.
[59] H L Chang, B Bai, W L Jiao, et al. Design of a Micro Control MomentGyroscope with a Large Torque Output[J]. Chinese Journal of Sensors andActuators,2011,24(8):1126-1130.
[60] Z N Qin, W Y Chen, F Cui, et al. System-level Simulation of a MicromachinedElectrostatically Suspended Gyroscope[C]. Proceedings of the20105th IEEEInternational Conference on Nano/Micro Engineered and Molecular Systems,Xiamen, China, January20-23,2010:658-661.
[61] G Y Ma, W Y Chen, W P Zhang, et al. Compact H∞Robust Rebalance LoopController Design for a Micromachined Electrostatically Suspended Gyroscope[J].ISA Transactions,2010,49:222-228.
[62] Q J Xiao, W Y Chen, S Y Li, et al. Modeling and Simulation of LevitationControl for a Micromachined Electrostatically Suspended Gyroscope[J].Microsystem Technology,2010,16:357-366.
[63] H T Ding, X S Liu, J Cui, et al. A Bulk Micromachined Z-Axis Single CrystalSilicon Gyroscope for Commercial Applications[C]. Proceedings of the3rd IEEEInt. Conf. on Nano/Micro Engineered and Molecular Systems, Sanya, China,January6-9,2008:1039-1042.
[64] D Keymeulen, W Fink, M I Ferguson, et al. Tuning of MEMS Devices UsingEvolutionary Computation and Open-Loop Frequency Response[C]. IEEEAC,paper#1211, Version3, December7,2004:1-8.
[65] M I. Ferguson, D Keymeulen, K Hayworth, et al. A Hardware Platform forTuning of MEMS Devices Using Closed-Loop Frequency Response[C]. IEEEACpaper#1284, Version4, January10,2005:1-7.
[66] H Urey. Torsional MEMS Scanner Design for High-Resolution DisplaySystems[C]. Optical Scanning II, Proc. SPIE4773, Seattle, Washington, July2002:27-37.
[67] H Urey, C Kan and W O Davis. Vibration Mode Frequency Formulae for Micro-mechanical Scanners[J]. Journal of Micromechanics and Microengineering,2005,15:1713-1721.
[68]钱伟长,叶开沅.弹性力学[M].北京:科学出版社，1956:160-165.
[69] M H Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier,2005:60-62.
[70]王洪喜.微结构的静电驱动特性研究[D].西安:西安电子科技大学，2006:18-24.
[71] D Keymeulen, M I Ferguson, L Breuer, et al. Tuning of MEMS Gyroscope UsingEvolutionary Algorithm and “Switched Drive-angle” Method[C]. IEEEACpaper#162, Version3, January2,2006:1-8.
[72] R Abdolvand, H Johari, G K Ho, et al. Quality Factor in Trench-RefilledPolysilicon Beam Resonators[J]. Journal of Microelectromechanical Systems,2006,15(3):471-478.
[73] M H Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier,2005:124-136.
[74] M H Bao, Y C Sun, J Zhou et al. Squeeze-Film Air Damping of a Torsion Mirrorat a Finite Tilting Angle[J]. Journal of Micromechanics and Microengineering,2006,16:2330-2335.
[75] A K Pandey, R Pratap. A Semi-Analytical Model for Squeeze-Film DampingIncluding Rarefaction in a MEMS Torsion Mirror with Complex Geometry[J].Journal of Micromechanics and Microengineering,2008,18(105003):1-12.
[76] M H Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier,2005:169-170.
[77] R Christian. The Theory of Oscillating-Vane Vaccum Gauges[J]. Journal ofVacuum,1966,16:175-178.
[78] M H Bao, H Yang, H Yin, et al. Energy Transfer Model for Squeeze-Film AirDamping in Low Vacuum[J]. Journal of Micromechanics and Microengineering,2002,12:341-346.
[79] J Zook, D Burns, H Guckel, et al. Characteristics of Polysilicon ResonantMicrobeams[J]. Journal of Sensors and Actuators A: Physical,1992,35:51-59.
[80] C Acar, A Shkel. MEMS Vibratory Gyroscopes Structural Approaches toImprove Robustness[M]. New York: Springer Science+Business Media,2009:106-107.
[81] Z L Hao, A Erbil, F Ayazi. An Analytical Model for Support Loss inMicromachined Beam Resonators with in-Plane Flexural Vibrations[J]. Journal ofSensors and Actuators A: Physical,2003,109:156-164.
[82] Z L Hao, F Ayazi. Support Loss in Micromechanical Disk Resonators[C]. InProceedings of the18th IEEE International Conference on Micro ElectroMechanical Systems, Miami Beach, USA,1–3February,2005:137-141.
[83] J A Judge, D M Photiadis, J F 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.
[84] B Chouvion. Vibration Transmission and Support Loss in MEMS Sensors[D].Nottingham: University of Nottingham,2010: Chapter4and Chapter6.
[85] E Eichler. Plate-Edge Admittances[J]. Journal of acoustical society of America,1964,36:344-348.
[86] A D Pierce. An Introduction to Its Physical Principles and Applications[C].Acoustical Society of America and American Institute of Physics, New York,1981:122.
[87] C Kauffmann. Input Mobilities and Power Flows for Edge-Excited, Semi-InfinitePlates[J]. Journal of Acoustical Society of America,1998,103(4):1874-1884.
[88] J X Su, A T Moorhouse. A Closed Form Solution for the Mobility of anEdge-Excited, Semi-Infinite Plate[J]. Journal of Acoustical Society of America,2004,115(5):2075-2082.
[89] C Benjamin. Vibration Transmission and Support Loss in MEMS Sensors[D].Nottingham: University of Nottingham,2010:206.
[90] C Zener. Internal Friction in Solids[J]. Physical Review,1937,52:230–235;1938,53:90–99;1938,53:100-101.
[91] C Zener. Elasticity and Anelasticity of Metals[M]. Chicago: The University ofChicago Press,1948.
[92] M A Biot. Thermoelasticity and Irreversible Thermodynamics[J]. Journal ofApplied Physics,1956,27:240-253.
[93] F Abroad, A Khan. Thermoelastic Plane Waves in a Rotating IsotropicMedium[J]. Journal of Acoustical Society of America,1999,136:243-247.
[94] P Chadwick. Thermoelasticity: The Dynamical Theory[J]. Progress in SolidMechanics, North-Holland, Amsterdam,1960,1:265-328.
[95] M Daimaruya, M Naitoh. Dispersion and Energy Dissipation of ThermoelasticWaves in a Circular Cylinder[J]. Acustica,1982,51:124-129.
[96] E S Suhubi, J Therm. Longitudinal Wave Propagation in a GeneralizedThermoelastic Cylinder[J]. Journal of Thermal Stresses,1986,9:279-295.
[97] R Lifshitz, M L Roukes. Thermoelastic Damping in Micro-and NanomechanicalSystems[J]. Physical Review B,2000,61(8):5600-5608.
[98] Z L Hao, F Ayazi. Thermoelastic Damping in Flexural-Mode Ring Gyroscope[C].Proceedings of IMECE2005: ASME International Mechanical EngineeringCongress and Exposition, Orlando, Florida, USA, Nov.5-11,2005:1-9.
[99] R Abdolvand, H Johari, G K Ho, et al. Quality Factor in Trench-RefilledPolysilicon Beam Resonators[J]. Journal of Microelectromechanical Systems,2006,15(3):471-478.
[100] R Gutierrez, T K Tang, K Shcheglov. Micromachined Double Resonator[P].United States Patent: US6,367,786B1, Apr.9,2002.
[101]王福楹,王福保,蔡森甫等.高等数学[M].北京:高等教育出版社,2002:311-316.
[102] H Ibach. Adsorbate Induced Surface Stress[J]. Journal of Vacuum ScienceTechnology A,1994,12:2240-2245.
[103] D Sander, Z Tian, J Kirschner. The Role of Surface Stress in Reconstruction,Epitaxial Growth and Stabilization of Mesoscopic Structures[R]. Surface ScienceReports,1997,29:193-263.
[104] 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.
[105] Z L Hao, M F Zaman, A Sharma, et al. Energy Loss Mechanisms in a BulkMicromachined Tuning Fork Gyroscope[C]. IEEE Sensors2006, Daegu, Korea,October22-25,2006:1333-1336.
[106] K Y Yasumura, T D Stowe, E M Chow, et al. Quality Factors in Micron andSubmicron Thick Cantilevers[J]. Journal of Microelectromechanical Systems,2000,9(1):117-125.
[107] A S Nowick, B S Berry. Anelastic Relaxation in Crystalline Solids[M]. NewYork: Academic Press,1972.
[108]孙世贤,黄圳圭.理论力学教程[M].长沙:国防科技大学出版社,2005:116-130.
[109] S. D. Senturia著,刘泽文,王晓红,黄庆安等译.微系统设计MicrosystemDesign[M].北京:电子工业出版社,2004:373-374.
[110] M. F. Zaman. Degree-Per-Hour Mode-Matched Micromachined Silicon VibratoryGyroscopes[D]. Georgia: Georgia Institute of Technology,2008:24-28.
[111]高世桥,刘海鹏.微机电系统力学[M].北京:国防工业出版社,2008:230-235.
[112]杨涛,何叶,魏东梅等.微机电器件的稳健设计[J].工程设计学报,2004,11(3):124-127.
[113]王安麟,善盈盈,刘广军,姜涛.基于灵敏度解析的微机械陀螺结构优化方法[J].浙江工业大学学报,2008,36(6):673-677.
[114] B. A.马特维耶夫等(著);杨亚非,赵辉(译).固体波动陀螺[M].北京:国防工业出版社，2009:201-225.
[115] Y. Tao, X. Xi, D.B. Xiao, et al. Precision Balance Method for Cupped WaveGyro Based on Cup-bottom Trimming[J]. Chinese Journal of MechanicalEngineering,2012,25(1):63-70.
[116] S. Y. Bae, K. J. Hayworth, K. Y. Yee, et al. High Performance MEMSMicro-Gyroscope[C]. Design, Integration, and Pakaging of MEMS/MOEMS2002, Proceedings of SPIE,2002,4755:316-324.
[117] X. F. Zhou, L. F. Che, B. Xiong, et al. Single Wafer Fabrication of a SymmetricDouble-Sided Beam–Mass Structure using DRIE and Wet Etching by a NovelVertical Sidewall Protection Technique[J]. Journal of Micromechanics andMicroengineering,2010,20(115009):1-14.
[118]王寿荣.硅微惯性器件理论及应用[M].南京:东南大学出版社,2000:116-120.
[119] M. Shikida, K. Sato, K. Tokoro, et al. Differences in Anisotropic EtchingProperties of KOH and TMAH Solutions[J]. Journal of Sensors and Actuators APhsycal,2000,80:179-188.
[120] O. Tabata, R. Asahi, H. Funabashi, et al. Anisotropic Etching of Silicon in(CH3)4NOH Solutions[C]. IEEE,1991:811-814.
[121] M. H. Bao. Analysis and Design Principles of MEMS Devices[M]. Amsterdam:Elsevier B.V.,2005:103-105.
[122] H. Schr der, E. Obermeier, A. Horn, et al. Convex Corner Undercutting of {100}Silicon in Anisotropic KOH Etching: The New Step Flow Model of3-DStructuring and First Simulation Results[J]. Journal of microelectromechanicalsystems,2001,10(1):88-97.
[123] P. Pal, K. Sato, M. Shikida, et al. Study of Corner Compensating Structures andFabrication of Various Shapes of MEMS Structures in Pure and Surfactant AddedTMAH[J]. Journal of Sensors and Actuators A Physical,2009,154:192-203.
[124]江平.蝶翼式硅微陀螺结构设计及制造工艺研究[D].长沙:国防科学技术大学,2007:24-26.
[125]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,2009:77-80.
[126]吴学忠,肖定邦,李圣怡.电容式微加速度计的闭环检测技术研究[J].传感技术学报,2006,19(4):1097-1099.
[127]肖定邦,侯占强,满海鸥等.微陀螺闭环驱动方法[J].国防科技大学学报,2009,31(3):116-121.
[128]焦斌.自动控制原理与应用[M].北京:高等教育出版社,2004:149-150.
[129]周泽龙.四叶片微陀螺结构设计与加工工艺研究[D].长沙:国防科学技术大学，2011:58.