摘要
本文在建立全对称双级解耦微机械振动式陀螺理论模型的基础上,系统研究了器件的动力学特性。提出一种新颖的全对称双级解耦微机械振动式陀螺仪结构,利用体硅微机械加工技术实现了敏感结构芯片的制备,并进行了相应实验研究和特性测试工作。
首先,工作带宽是微机械陀螺应用的一个重要指标,现有理论认为带宽和灵敏度是一对矛盾,将带宽简单定义为驱动频率与检测模态谐振频率之差。本文基于全对称双级解耦微机械振动式陀螺的理论模型,系统研究了器件的动力学特性,得出了工作带宽与频率匹配度以及检测模态品质因子有关的结论。当角速度的频率等于驱动模态与检测模态谐振频率之差时,灵敏度最大;保持驱动模态品质因子一定,改变检测模态品质因子Qy时,Qy存在一个临界值使检测方向峰值位移也满足3dB带宽的要求,大大扩展了陀螺的工作带宽。其次,提出了一种全对称双级解耦微机械振动式陀螺结构并利用体硅微机械加工技术制备了敏感结构芯片,该陀螺能实现模态频率匹配的同时降低模态之间的耦合。采用全对称结构,驱动模态和检测模态谐振频率容易匹配;双级解耦结构有效降低了驱动模态和检测模态之间的耦合;驱动梳齿和检测梳齿均采用滑膜阻尼结构,在常压下也能获得较高品质因子。考虑耦合弹性系数,建立器件的无阻尼自由振动模型以获得结构模态频率和振型。求解结果表明模态之间的耦合仅为1.56%,驱动和检测模态谐振频率均为2966.9Hz。应用ANSYS对微机械陀螺的模态频率进行了有限元求解,理论求解与有限元求解结果吻合较好。
最后,基于对微机械陀螺动态特性的分析,设计了微陀螺开环检测接口电路。电路主要由C-V转换电路、高/低通滤波器、移相器以及相敏解调电路构成。采用所设计的开环检测微机械陀螺接口电路,对微机械陀螺模态特性、温度特性以及灵敏度等项目进行了测试。构建了显微镜测试平台对微机械陀螺非线性振动进行了测试。测试结果表明,驱动模态产生非线性振动时,谐振频率随振幅增大而增大。模态测试结果表明器件的频率匹配良好,谐振频率分布在2300Hz~2500Hz,与按照实际器件弹性梁宽度计算的谐振频率2774.7Hz较好吻合。温度特性测试表明随温度升高谐振频率和品质因子有所降低,但在不同的温度条件下模态频率仍匹配良好。在常压下测试微陀螺灵敏度为5.61mV/°/s,证实了该陀螺能在常压下工作。
研究结果对全对称双级解耦微机械振动式陀螺的设计具有指导意义,为解决模态频率匹配、模态解耦以及避免真空封装等问题提供了一种解决方案。
Based on the theoretical model of the fully-symmetrical and doubly-decoupled micromachined gyroscope, the dynamic characteristics of the device was researched systematically. A novel fully-symmetrical and doubly-decoupled micromachined gyroscope was presented and fabricated by bulk silicon micromachining technology. Further, corresponding experiments were performed to validate the research.
Firstly, the working bandwidth is an important parameter for the application of MEMS gyroscopes. It was simply defined as the difference between the esonant frequencies of the drive mode and that of the sense mode, or the bandwidth and sensitivity of MEMS gyroscopes were regarded as a conflict qualitatively. Based on the systematical research of the dynamic characteristics of the presented gyroscope model, several conclusions were obtained. When the frequency of the input angular rate is equal to the difference of resonant frequencies between the drive mode and sense mode, the sensitivity reaches maximum. In the condition that the quality factor of the drive mode keeps constant, there is a critical value with the decrease of the quality factor of the sense mode, at which the peak sensitivity satisfies the 3dB bandwidth theory. Thus, the bandwidth is widened significantly.
Secondly, a novel fully-symmetrical and doubly-decoupled micromachined gyroscope, fabricated by bulk micromaching technology, was presented. The fully-symmetrical structure enables the precisely matched frequency for the drive mode and sense mode. The doubly-decoupled structure reduces the cross coupling between the drive mode and sense mode. The free vibrating model without damping of the device was established and solved considering the couple elastic coefficient. The solution indicates that the model couple of the presented gyroscope is 1.56%, and the resonant frequencies of the drive and sense modes are 2966.9Hz. Also, the theoretical model was validated by the finite element model with the software package of ANSYS.
At last, based upon the analysis of dynamic characteristic of micro gyroscope, an open-loop detecting circuit of micro-gyroscope was designed. This circuit was composed of C-V converting circuit, high/low pass filter, phase shifter and phase-sensitive demodulation circuit. The mode characteristic, temperature characteristic and sensitivity of micro gyroscope were tested with this testing board. The nonlinear vibration was tested by the established microscope experimental platform. The test results indicate that the resonant frequency increases with the vibration amplitude. The mode parameters tests prove that the two modes’resonant frequencies are well matched. The resonant frequencies distribute from 2300Hz to 2500Hz, which are in good accordance with the theoretical solution of the fabricated chip. The temperature characteristics tests indicate that resonant frequency and the quality factor decrease with the increasing of temperature, while the frequencies of the two modes match well. The measured sensitivity at atmospheric pressure is 5.61mV/°/s.
The research presents a solution scheme for the frequency match, doubly-decouple, and capable of working at atmospheric pressure of MEMS gyroscopes. The work has some significance to the design of the fully-symmetrical and doubly-decoupled micromachined gyroscope.
引文
1谷庆红.微机械陀螺仪的研制现状.中国惯性技术学报. 2003,11(5):67-72
2 K. Ohwada, Y. Mochida, H. Kawai. Micromachined Silicon Gyroscope. Sensors Update. 1999,6(1):95-116
3 D. Stephane, D. Dick, M. Tony et al. MEMS Gyro for Space Applications Overview of European Activities. AIAA Guidance, Navigation, and Control Conference, San Francisco, United States, 2005:6232-6243
4 K. Najafi l, C. Junseok, K. Haluk et al. Micromachined Silicon accelerometers and Gyroscopes. IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, United States, 2003:2353-2358
5朱健. MEMS技术的发展与应用. 2003,28(1):29-32
6 J. W. Judy. Microelectromechanical Systems (MEMS): Fabrication, Design and Applications. Smart Materials and Structures. 2001, 10(6): 1115-1134
7闫冬,管欣,高振海.基于MEMS技术的微惯性传感器及在汽车上的应用.汽车技术. 2006,2:1-6
8 S. Middelhoek. Celebration of the Tenth Transducers Conference: The Past, Present and Future of Transducer Research and Development. Sensors and Actuators A Phys. 2000,82(1):2-23
9 Yole Developement. MEMS Gyro Markets: New Players & Business Models Give Momentum to Defence, Automotive and Consumer Applications. http://www.yole.fr/pagesAn/products/pdf/MEMSGyroMarket.pdf, 2006
10陈建元.有机械耦合的电容式硅微陀螺敏感信号读取研究.电子测量技术. 2008,31(7):151-154
11 S.H. Choa. Reliability of Vacuum Packaged MEMS Gyroscopes. Microelectronics Reliability. 2005,45(2):361-369
12 K. Jong-Seok, L. Sang-Woo, J. Kyu-Dong et al. Quality Factor Measurement of Micro Gyroscope Structure According to Vacuum Level and Desired Q-Factor Range Package Method. Microelectronics Reliability. 2008,48(6):948-952
13李新刚,袁建平.微机械陀螺的发展现状.力学进展. 2003, 33(3): 289-301
14 N. Yazdi, F. Ayazi, and K. Najafi. Micromachined Inertial SensorsProceedings of the IEEE. 1998,86(8):1640-1658
15 A. M. Shkel. Micromachined Gyroscopes: Challenges, Design Solutions, and Opportunities. Proceedings of SPIE. 2001,4334:74-85
16刘春浩,顾家铭,周赤忠等.陀螺仪电动机转子轴承研究现状与展望.机械工程学报. 2006,42(11):17-23
17宋桂云.陀螺仪的应用及发展.有色金属. 2002,54(4):108-110
18 S. D. Orlosky, H. D. Morris. Quartz Rotation Rate Sensor. Sensors Peterborough, NH, 1995,12(2):27-31
19 P. Greiff, B. Boxenhorn, T. King et al. Silicon Monolithic Micromechanical Gyroscope. Transducers '91,1991:966-968
20 B. Boxenhorn, P. Greiff. A Vibratory Micromechanical Gyroscope. AA Guidance and Control Conference, 1988:1033-1039
21 J. Bernstein, S. Cho, A. T. King, et al. A Micromachined Comb-Drive Tuning Fork Rate Gyroscope. Proc. IEEE Micro Electro Mechanical Systems Workshop (MEMS'93). 1993:143-148
22 M. Weinberg, J. Bernstein, S. Cho, et al. A Micromachined Comb-Drive Tuning Fork Gyroscope for Commercial Applications. Proc. Sensor Expo, 1994:187-193
23 K. Tanaka, Y. Mochida, M. Sugimoto et al. A Micromachined Vibrating Gyroscope. Sensors and Actuators, A: Physical. 1995,50(1-2):111-115
24 Y. S. Oh, B. L. Lee, S. S Baek et al. A Tunable Vibratory Microgyroscope. Sensors and Actuators, A: Physical. 1998,64(1):51-56
25 Y. Mochida, M. Tamura, K. Ohwada. A Micromachined Vibrating Rate Gyroscope with Independent Beams for the Drive and Detection Modes. Sensors and Actuators, A: Physical. 2000,80(2):170-178
26 W. A. Clark, R. T. Howe, R. Horowitz. Surface Micromachined Z-axis Vibratory Rate Gyroscope. Tech. Dig. Solid-state Sensors and Actuators Workshop.1996:283-287
27 K. Park, C. Lee, Y. Oh, Y. Cho. Laterally Oscillated and Force-Balanced Micro Vibratory Rate Gyroscope Supported by Fish-Hook-Shaped Springs. Sensors and Actuators, A: Physical. 1998,64(1):69-76
28 C. Acar, A. M. Shkel. Structurally Decoupled Micromachined Gyroscopes with Post-Release Capacitance Enhancement. Journal of Micromechanicsand Microengineering.2 005,15(5):1092-1101
29 W. Golderer, J. Gerstenmeier, J. Marek et al. Precision Yaw Rate Sensor in Silicon Micromachining. SAE Special Publications. 1998,1312:37-41
30张正福.音叉振动式微机械陀螺结构动态性能解析与健壮性设计.上海交通大学博士学位论文. 2007:10-11
31 S. S. Baek, Y. S. Oh, B.J. Ha et al. A Symmetrical Z-Axis Gyroscope with a High Aspect Ratio Using Simple and New Process. Proceedings of the IEEE Micro Electro Mechanical Systems (MEMS), Orlando, 1999:612-617
32 S. E. Alper, T. Akin. A Symmetric Surface Micromachined Gyroscope with Decoupled Oscillation Modes. Sensors and Actuators, A: Physical. 2002,97-98:347-358
33 S. E. Alper, T. Akin. A Symmetrical and Decoupled Nickel Microgyroscope an Insulating Substrate. Sensors and Actuators, A: Physical. 2005,115(2-3):336-350
34 S. E. Alper, T. Akin. A Single-Crystal Silicon Symmetrical and Decoupled MEMS Gyroscope on an Insulating Substrate. Journal of Microelectromechanical Systems. 2005,14(4):707-717
35 S. E. Alper, K. Azgin, T. Akin. High-Performance SOI-MEMS Gyroscope with Decoupled Oscillation Modes. Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems (MEMS), Istanbul, Turkey, 2005:70–73.
36 S.E. Alper, K. Azgin, T. Akin. A High-Performance Silicon-On-Insulator MEMS Gyroscope Operating at Atmospheric Pressure. Sensors and Actuators, A: Physical. 2007,135(1):34-42
37 S.E. Alper, K. Azgin, T. Akin. A Low-Cost Rate-Grade Nickel Microgyroscope. Sensors and Actuators, A: Physical.2006, 132(1):171-181
38 W. Geiger, W. U. Butt, A. Gaisser, et al. Decoupled microgyros and the design principle DAVED. Sensors and Actuators A: Physical, 95(2-3):239–249, 2002
39 H. Xie, G. K. Fedder. Fabrication, Characterization, and Analysis of a DRIE CMOS-MEMS Gyroscope. IEEE Sensors Journal. 2003,3(5):622-631
40 A. Witvrouw, A. Meth, A. Verbist, et al. Processing of MEMS Gyroscopes on Top of CMOS ICs. IEEE International Solid-State Circuits Conference, SanFrancisco, 2005,48:60-61
41 J. A. Geen, S. J. Sherman, J. F. Chang, and S. R. Lewis. Single-Chip Surface Micromachined Integrated Gyroscope with 50°/Hour Allan Deviation. Journal of Solid-State Circuits, 2002 37(12):1860–1866
42 S. Chang, M. Chia, P. Castillo-Borelley et al. An Electroformed CMOS Integrated Angular Rate Sensor. Sensors and Actuators, A: Physical. 1998,66(1-3):138-143
43 G. Huo, K. Najafi. A Single-Crystal Silicon Vibrating Ring Gyroscope. Proceedings of the IEEE Micro Electro Mechanical Systems (MEMS), Las Vegas, 2002:718-721
44 F. Ayazi, K. Najafi. Design and Fabrication of a High-Performance Polysilicon Vibration Ring Gyroscope. Proceedings of the IEEE Micro Electro Mechanical Systems (MEMS), Heidelberg, Germany, 1998:621-626
45 F.Ayazi, K. Najafi. High Aspect-Ratio Polysilicon Micromachining Technology. Sensors and Actuators, A: Physical. 2000,87(1-2):46-51
46 S. Zarabadi, T. Vas, D. Sparks et al. A Resonating Comb/Ring Angular Rate Sensor Vacuum Packaged Via Wafer Bonding. International Congress and Exposition, Detroit Michigan,1999
47 K. Funk, H. Emmerich, A. Schilp et al. A Surface Micromachined Silicon Gyroscope Using a Thick Polysilicon Layer. Proceedings of the IEEE Micro Electro Mechanical Systems (MEMS), Orlando, 1999:57-60
48 T. Fujita, K. Maenaka, T. Mizuno et al. Disk-Shaped Bulk Micromachined Gyroscope with Vacuum Sealing. Sensors and Actuators, A: Physical. 2000,82(1):198-204
49 S. Rajendran, K. M. Liew. Design and Simulation of an Angular-Rate Vibrating Microgyroscope. Sensors and Actuators, A: Physical. 2004116(2):241-256
50 W. Geiger , B. Folkmer, J. Merz et al. A New Silicon Rate Gyroscope. Sensors and Actuators, A: Physical. 1999,73(1-2):45-51
51 D. Tsai, W. Fang. Design and Simulation of a Dual-Axis Sensing Decoupled Vibratory Wheel Gyroscope. Sensors and Actuators, A: Physical. 2006,126(1):33-40
52 N. Tsai, C. Sue, C. Lin. Micro Angular Rate Sensor Design and NonlinearDynamics. Journal of Micro/ Nanolithography, MEMS, and MOEMS. 2007,6(3):033008
53 N. Tsai, C. Sue, C. Lin. Design and Dynamics of an Innovative Micro Gyroscope Against Coupling Effects. Microsystem Technologies. 2008,14(3):295-306
54 K. Tang, R. C. Gutierrez, C. B. Stell et al. A Packaged Silicon Mems Vibratory Gyroscope for Microspacecraft. IEEE Micro Electro Mechanical Systems Workshop (MEMS'97), 1997:500-505
55 T. George. MEMS/NEMS Development for Space Applications at NASA/JPL. Proceedings of SPIE. 2002,4755:556–567
56 B. Xiong, C. Lufeng, W. Yuelin. A Novel Bulk Micromachined Gyroscope with Slots Structure Working at Atmosphere. Sensors and Actuators, A: Physical. 2003,107(2):137-145
57熊斌,车录锋,王跃林.一种栅型结构微机械陀螺的研究.中国机械工程. 2003(3):184-186
58 Y. Chen, J. Jiao, B. Xiong et al. A Novel Tuning Fork Gyroscope with High Q-factors Working at Atmospheric Pressure. Microsystem Technologies. 2005,11(2-3):111-116
59 J. Jiwei, H. Ming, W. Xiangli, et al. A Digital Demodulation Solution to Achieve Stable Driving for a Micro-Machined Gyroscope with an AGC Mechanism. Proceedings of IEEE Sensors. 2004: 429-432
60陈垚.微机械陀螺的材料及器件设计研究.中国科学院上海微系统与信息技术研究所博士论文. 2000
61 L. Xinxin, B. Minhang, Y. Heng et al. Micromachined Piezoresistive Angular Rate Sensor with a Composite Beam Structure. Sensors and Actuators, A: Physical. 1999,72(3):217-223
62 L. Xinxin, C. Xuemeng. S. Zhaohui et al. A Microgyroscope with Piezoresistance for Both High-Performance Coriolis-Effect Detection and Seesaw-Like Vibration Control. Journal of Microelectromechanical Systems. 2006,(6):1698-1707
63 Y. Heng, B. Minhang, Y. Hao et al. A Novel Bulk Micromachined Gyroscope Based on a Rectangular Beam-Mass Structure. Sensors and Actuators, A: Physical. 2002,96(2-3):145-151
64 Y. Heng, B. Minhang, Y. Hao et al. Two-Dimensional Excitation Operation Mode and Phase Detection Scheme for Vibratory Gyroscopes. Journal of Micromechanics and Microengineering. 2002,12(3):193-197
65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.东南大学博士学位论文. 2005:6-7
66 Y. Weizheng, C. Honglong, L. Weijian et al. Application of an Optimization Methodology for Multidisciplinary System Design of Microgyroscopes. Microsystem Technologies.2006,12(4):315-323
67 Z. Rong, G. Zhongyu, C. Zhiyong. A Bulk Micromachined Vibrating Wheel Rate Gyroscope. Proceedings of SPIE. 2001,4601:54-58
68 D. Haitao, L. Xuesong, C. Jian et al. A Bulk Micromachined Z-Axis Single Crystal Silicon Gyroscope for Commercial Applications. IEEE International Conference on Nano/Micro Engineered and Molecular Systems, NEMS, Sanya, China, 2008:1039-1042
69韩竞科,王东红,陈伟平等.梁式硅微机械陀螺结构的研究.遥测遥控. 2001(11):43-47
70马薇,李世玮,虞吉林.一种新颖的四梁式压电薄膜微型陀螺.中国科学技术大学学报. 2000(30): 401-405
71 D. Joachim, L. Lin. Characterization of Selective Polysilicon Deposition for MEMS Resonator Tuning. Journal of Microelectromechanical Systems. 2003,12(2):193-200
72 S. Enderling, J. Hedley, R. Cheung et al. Characterization of Frequency Tuning Using Focused Ion Beam Platinum Deposition. Journal of Micromechanics and Microengineering. 2007,17(2):213-219
73 N. H. Rizvi, P. Apte. Developments in Laser Micro-Machining Techniques. Journal of Materials Processing Technology. 2002,127(2):206-210
74 R. A. Syms. Electrothermal Frequency Tuning of Folded and Coupled Vibrating Micromechanical Resonators. Journal of Microelectromechanical Systems. 1998,7(2):164-171
75 T. Remtema, L. Lin. Active Frequency Tuning for Micro Resonators by Localized Thermal Stressing Effects. Sensors and Actuators, A: Physical. 2001,90(3):326-332
76 R. P. Leland. Adaptive Mode Tuning for Vibrational Gyroscopes. IEEETransactions on Control Systems Technology. 2003,11(2):242-247
77 H. Kawai, K. I. Atsuchi, M. Tamura et al. High-Resolution Microgyroscope Using Vibratory Motion Adjustment Technology. Sensors and Actuators, A: Physical. 2001,90(1-2):153-159
78 E. Kanso, A. J. Szeri, A. P. Pisano. Cross-Coupling Errors of Micromachined Gyroscopes. Journal of Microelectromechanical Systems. 2004,13(2):323-331
79 A. S. Phani, A. A. Seshia, M. Palaniapa et al. Modal Coupling in Micromechanical Vibratory Rate Gyroscopes. IEEE Sensors Journal. 2006,6(5):1144-1152
80 M. Saukoski, L. Aaltonen, A. I. Kari. Zero-Rate Output and Quadrature Compensation in Vibratory MEMS Gyroscopes. IEEE Sensors Journal. 2007,7(12):1639-1651
81 W. Geiger, W. U. Butt, A. Gaisser, et al. Decoupled microgyros and the design principle DAVED. Sensors and Actuators A-Physical, 95(2-3):239–249, 2002
82 A. M. Madni, R. D. Geddes. Micromachined Quartz Angular Rate Sensor For Automotive And Advanced Inertial Applications. Sensors (Peterborough, NH). 1999,16(8):26-34
83 A.Gripton. The Application and Future Development of a MEMS SIVSG for Commercial and Military Inertial Products. IEEE PLANS, Position Location and Navigation Symposium, 2002:28-35
84 T. George. Overview of MEMS/NEMS Technology Development for Space Applications at NASA/JPL. Proceedings of SPIE. 2003,5116:136-148
85 A. Matthews, F. J. Rybak. Comparison of Hemispherical Resonator Gyro and Optical Gyros. IEEE Aerospace and Electronic Systems Magazine. 1992,7(5):40-46
86 C.Acar, A. M. Shkel. An Approach for Increasing Drive-Mode Bandwidth of MEMS Vibratory Gyroscopes. Journal of Microelectromechanical Systems. 2005,14(3):520-528
87 C.Acar, A. M. Shkel. Nonresonant Micromachined Gyroscopes with Structural Mode-Decoupling. IEEE Sensors Journal. 2003,3(4):497–506
88 C.Acar. Structural Design and Experimental Characterization of TorsionalMicromachined Gyroscopes with Non-Resonant Drive Mode. Journal of Micromechanics and Microengineering. 2004,14(1):15-25
89 B. J. Gallacher, J. Hedley, J. S. Burdess et al. Electrostatic Correction of Structural Imperfections Present in a Microring Gyroscope. Journal of Microelectromechanical Systems. 2005,14(2):221-234
90 R.Oboe, R.Antonello, E.Lasalandra et al. Control of a Z-Axis MEMS Vibrational Gyroscope. IEEE/ASME transactions on mechatronics. 2005,10(4):364-370
91 S. Park. Adaptive control strategies for MEMS gyroscopes. University of California, Berekely. Ph.D. dissertation, 2000
92 H. Xie, G. K. Fedder. Integrated Microelectromechanical Gyroscopes. Journal of Aerospace Engineering. 2003,16(2):65-75
93王寿荣.硅微型惯性器件理论及应用.东南大学出版社. 2000:12-14
94陈世民.理论力学简明教程.高等教育出版社. 2001:172-176
95贾伯年,俞朴.传感器技术.东南大学出版社. 1992:10-12
96陈后金,胡健,薛健.信号与系统.清华大学出版社. 2003:115-136
97 Z. C. Feng, G. Kapil. Dynamic Characteristics of Vibratory Gyroscopes. IEEE Sensors Journal. 2004,4(1): 80-84
98 Y. Hong, J. H. Lee, C. Lee et al. Bandwidth Analysis of a Microgyroscope Vibrating in Two Orthogonal Axes on the Substrate Plane. Proceedings of SPIE. 1999,3680:939-947
99 Y. Hong, S. Kim, and J. H. Lee. Modeling of angular-rate bandwidth for a vibrating microgyroscope. Microsystem Technologies. 2003, 9(6-7):441-448
100黄小振.电容式振动微机械陀螺接口电路的设计、模拟与测试.中国科学院上海冶金研究所硕士论文. 2001:19-20
101熊斌.栅结构微机械振动式陀螺.中国科学院上海微系统与信息技术研究所博士论文. 2001:42-49
102陆学斌,刘晓为,陈伟平等.振动式微机械陀螺的带宽特性分析.传感技术学报. 2008,21(2):337-340
103刘晓为,陈宏,陈伟平等.常压下工作的微机械陀螺的频率和阻尼特性.传感技术学报. 2006,19(5):2268-2271
104 R. P. Leland. Mechanical-Thermal Noise in MEMS Gyroscopes. IEEE Sensors Journal. 2005,5(3):493-500
105黄小振.电容式振动微机械陀螺接口电路的设计、模拟与测试.中国科学院上海冶金研究所硕士论文. 2001:19-20
106 W. A. Clark, R. T. Howe. Surface Micromachined Z-Axis Vibratory Rate Gyroscope. Solid-state Sensors and Actuators Workshop, Hilton Head Island, USA, 1996:283-287
107聂婉琴,孟广伟.材料力学.机械工业出版社, 2004:268-270
108吴徽,刘理天,杨景铭.表面微机械静电梳状驱动结构的研究.清华大学学报(自然科学版). 1999,39(s1):69-73
109徐泰然. MEMS和微系统—设计与制造.王晓浩等译.机械工业出版社, 2004:50-55
110 T. Veijola. M. Turowski. Compact Damping Models for Laterally Moving Microstructures with Gas-Rarefaction E ffects. Journal of Micro Electro Mechanical Systems. 2001,10(2):263-266
111 Y. T. Hsia, G. A. Domoto. An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-low Clearance. J. Lubrication Tech., 1983,105(1):12-130.
112 P. Y. Kwok, M. S. Weinberg, K. S. Breuer. Fluid Effects in Vibrating Micromachined Structures. Journal of Micro Electro Mechanical Systems. 2005, 14(4): 772-775
113 W. A. Clark, R. T. Howc, R. Horowitz. Surface Micromachined Z-axis Vibratory Rate Gyroscope. Tech. Dig. Solid-state Sensors and Actuators Workshop, Hilton Head Island, SC, USA, 1996: 183-287
114 K. Y. Park, C. W. Lee, Y. S. Oh, et al. Laterally Oscillated and Force-balanced Micro Vibratory Rate Gyroscope Supported by Fish Hook Shape Springs. Proc IEEE Micro Electro Mechanical Systems Workshop(MEMS’97), Japan, 1997: 494-499
115 Y. J. Yang, P. C. Yen. An Efficient Micromodeling Methodology for Lateral Air Damping Effects. Journal of Micro Electro Mechanical Systems. 2005, 14(4): 820~823
116 Y. H. Cho, B. M. Kwak, A. P. Pisano et al. Slid Film Damping in Laterally Driven Microstructures. Sensors and Actuators A. 1994, 40: 31-39
117 W. Ye, X. Wang, W. Hemmert et al. Air Damping in Laterally Oscillating Micro-resonators: A Numerical and Experimental Study. Journal of MicroElectro Mechanical Systems. 2003, 12(5): 559-561
118 R. R. Chrig.结构动力学.常岭,李振邦译.人民交通出版社. 1996: 177-250
119 K. Shcheglov, C. Evans, R. Gutierrez et al. Temperature Dependent Characteristics of the JPL Silicon MEMS Gyroscope. Proc. of the IEEE, 2000,1:403-411
120 P. Robert. Mechanical-Thermal Noise in MEMS Gyroscope. IEEE sensors journal,2005,5(3):493-500
121 E. Netzer, I. Porat. A Novel Vibratory Device for Angular Rate Measurement. Dynamic Systems, Measurement and Control. 1995,117:585–91
122 C. C. Painter, A. M Shkel. Structural and Thermal Modeling of a Z-Axis Rate Integrating Gyroscope. J. Micromech. Microeng. 2003,13:229-237
123 K. Hong. Compensation of Nonlinear Thermal Bias Drift of Rsonant Rate Sensor Using Fuzzy Logic. Sensors and Actuators. 1999,78:143-148
124陈怀,张嵘,周斌等.微机械陀螺仪温度特性及补偿算法研究.传感器技术. 2004,23(10):24-26
125凌林本,李滋刚,周百令等.硅微机械陀螺传感器信号的检测方法.中国惯性技术学报. 1999,7(4):61-64
126李锦明.高信噪比电容式微机械陀螺的研究.中北大学博士学位论文. 2005:100-102
127 F. Braghin, F. Resta, E. Leo et al. Nonlinear Dynamics of Vibrating MEMS. Sensors and Actuators. 2006, A95: 1-11
128 http://www.analog.com/static/imported-files/data_sheets/ADXRS300.pdf