摘要
杯形波动陀螺是利用哥氏效应工作的振动惯性器件,因其能耗小、成本低、可靠性高和寿命长等优点而极具发展潜力。杯形波动陀螺的工作原理是基于其谐振子绕中心轴旋转时产生哥氏效应,使谐振子相对原驻波振动出现一附加的驻波振动。杯形波动陀螺的性能与其谐振子的结构、制造精度密切相关。本文针对杯形波动陀螺的金属谐振子,开展了以下研究:
1.建立了杯形波动陀螺的数学模型,通过环形模型分析了在角速度输入下附加驻波与原驻波幅值之间的关系;通过壳体模型对谐振子的振动特性进行了研究与分析计算。
2.研究了杯形谐振子的结构特征,分析了三种支撑结构的差别。通过谐振子模态仿真,研究了谐振频率与结构尺寸的关系。发现过小的支撑杆直径或过厚的谐振环会带来有害振动;材料密度、弹性模量及谐振环对谐振子的影响最为关键,为谐振子的结构设计提供了依据。
3.针对谐振子样机,通过激光测振仪对谐振子的模态振型进行了测试工作,研究了非理想谐振子的频率裂解及振型误差现象。理论上分析了工艺误差中的各次谐波对频率裂解的影响,得出工艺缺陷中的四次谐波对谐振子精度影响最大,并对谐振子制造所要达到的轮廓精度进行了分析与仿真预测。
4.利用三坐标测量机对谐振子的内外圆轮廓进行了检测,通过对壁厚误差的傅立叶变换分析了其各次谐波分量的大小,对误差成因进行了推测,提出了改善谐振子精度的办法。
5.通过试验与仿真,分析了压电电极尺寸及位置精度对频率裂解的影响,以及谐振子的安装非一致性对谐振频率的影响,为提高谐振子的精度、稳定性提供了依据。
6.依据结构与精度分析,制作杯形波动陀螺样机,并对其性能进行了测试。陀螺仪在动态范围为±100?/s的情况下,刻度因子为60.1mV/(?/s),线性度为0.83%,短期零偏稳定性为0.007?/s。
The cupped wave gyroscope (abbreviated as CWG) is a vibrating inertial instrument based on the Coriolis Effect. It has a promising prospect for its advantages of low power consumption, low cost, high reliability and longevity and so on. The working principle of CWG is based on the Coriolis Effect when the resonator rotates about its axis. An additional standing wave will appear due to the Coriolis force. The performance of CWG is closely connected with the structure, manufacturing accuracy of the resonator. The metallic resonator of CWG, were studied.
1. Mathematical model of the resonator was built. The amplitude relationship between additional standing wave and original wave was analyzed by the ring model. The vibration characteristic of the resonator was analyzed by the shell model.
2. The structure characteristic of the resonator was studied, and differences of the three kinds of support structures were analyzed. The relationship of resonance frequency and size of resonator was studied by the model simulation. It was shown that density, elastic modulus of the material and resonant ring had a major influence on resonator. Small diameter or thick resonant ring was harmful to resonator, which provided a reference for the structure design of CWG resonator.
3. Mode shape of a resonator was observed by the laser vibrometer controller, and the vibration error and frequency split was analyzed. The influence of harmonic terms errors was analyzed in theory. It was shown that the fourth order harmonic terms in resonator imperfection had the main influence on the accuracy of resonator. Finally, the roundness accuracy of the resonator was analyzed and predicted.
4. The roundness of the resonator was measured by CMM. Then, harmonic wave errors in shell thickness were analyzed by Fast Fourier Transform. Finally, the causation of errors was discussed, and the ways of improving manufacturing accuracy were analyzed.
5. Influence of the size and position of piezoelectric elements was analyzed by experimentation and simulation, which provided a reference for the reliability and accuracy of CWG resonator.
6. A CWG is fabricated, and the performance was tested on a rotating floor. The result shows: the dynamic range is±100?/s, the scale factor (or sensitivity) is 60.1mV/(?/s), the nonlinearity is 0.83%, the bias stability in an hour is 0.007?/s.
引文
[1] Neil M Barbour,John M Elwell,Roy H Setterlund.Inertial Instruments:Where to Now. Proceedings of AIAA Guidance,Navigation and Control Conference,Hilton Head Island,USA,August,1992:566~574.
[2] Sergei A Jerebets.Gyro Evaluation for the Mission to Jupiter.Proceedings of IEEE Aerospace Conference,Big Sky,USA,March,2007:1~10.
[3] ISAAKM.OKON , BARABASHOV . Sensing Element of Coriolis Force Gyroscope.U.S. Patent:0154542A1,2010-06-24.
[4]吕志清.哥氏振动陀螺脱颖而出.世界产品与技术,2001,1(2):32~33.
[5]吕志清.哥氏振动陀螺.压电与声光,2004,26(2):98~102.
[6] Andrei M.Shkel . Type I and Type II Micromachined Vibratory Gyroscopes.Aerospace and Electronics Systems,1992,7:40~46.
[7]吴俊伟.惯性技术基础.哈尔滨:哈尔滨工程大学出版社,2002.
[8] D.D.Lynch.Coriolis Vibratory Gyros.Symposium Gyro Technology,Stuttgart,Germany,1998:1.0~1.14.
[9] A.Matthews,EJ.Rybak.Comparison of Hemispherical Resonator Gyro and Optical Gyros.Mechanical & Aerospace Engineering,2006,2(6):586~593.
[10]梁阁亭,惠俊军,李玉平.陀螺仪的发展及应用.飞航导弹,2006,21:38~40.
[11] G.H.Bryan.Vibrations of A Revolving Cylinder or Bell.Proc Camp,1890,1(2):101.
[12] D.D.Lynch,A.Matthews,G.T.Varty.Innovative Mechanizations to Optimize Inertial Sensor for High or Low Rate Operations.Symposium Gyro Technology,Stuttgart,Germany,1997:9.0~9.21.
[13] Voros,Art.Gyro and Accelerometer History.Systems-AC Electronics,2008,1:4.
[14]吕志清.美国半球式振子陀螺仪80年代中期发展概况.压电与声光,1990,12(5):33~40.
[15]章燕申.半球谐振陀螺研究在苏联.机载设备及系统,1989,11:1~2.
[16]杨亚非.固体波动陀螺.北京:国防工业出版社,2009.
[17] CRS03 Single Axis Angular Rate Sensor.CRS03 Datasheet.
[18] V.V.Chikovani,I.M.Okon,A.S.Barabashov.Digitally Controlled High Accuracy Metallic Resonator CVG.Symposium Gyro Technology,Stuttgart,Germany,2006:4.0~4.7.
[19] CORILIS FORCE GYROSCOPE WITH HIGH SENSITIVITY.CVG Datasheet.
[20] T.O.Bakalor , P.M.Bondar . Research of A Low-frequency Spectrum Of Resonators Coriolis Vibrating Gyroscope.Movement Control and Aerospace Technic Engineering,Kyiv,Ukraine,2007:110~114.
[21] Sergii Adolf,Sarapuloff.HIGH-Q SINGLE-CRYSTALLINE RESONATOR FABRICATION OF CRG-1 FOR INCLINOMETRY OF OIL&GAS DRILLING .Special Technologies&Machines,2009,1(2):101.
[22] William S.Watson . Vibrating Structure Gyro Performance Improvements.Symposium Gyro Technology,Stuttgart,Germany,2000:238~243.
[23] William S.Watson,Eau Claire.High Q Angular Rate Sensing Gyroscope.U.S. Patent:6845667B1,2005-01-25.
[24] William S.Watson . Vibratory Gyro Skewed Pick-Off And Driver Geometry. Journal of Micro Machines,2010,4(10):171~179.
[25] Yu.A.Yatsenko , JS.F.Petrenko . TECHNOLOGICAL ASPECTS OF MANUFACTURING OF COMPOUND HEMISPHERICAL RESONATORS FOR SMALL-SIZED VIBRATORY GYROSCOPES.Integrated Navigation Systems,RTO SCI international Conference,St.Petersburg,Russia,May,1999:71~75.
[26]吕志清.半球谐振陀螺研究现状及发展趋势.惯性技术发展动态发展方向研讨会文集,桂林,中国,2003:103~105.
[27] Neil M.Barbour.Resonant Ring MEMS Gyros.Inertial Navigation Sensors,Cambridge,USA,2002:2.14~2.15.
[28] Alexey Tirtichny . Calculation of Vibrating Ring Gyroscope Characteristics. Sensors and Materials,2005,17(4):79~84.
[29]吕志清.振动陀螺的发展趋势.中国惯性技术学会第四届学术年会论文集,北海,中国,1999:196~200.
[30]刘广玉,樊尚春等.新型传感器技术及应用.北京:国防工业出版社,1995.
[31]吕志清.半球谐振陀螺信号处理技术.中国惯性技术学报,2000,3:58~61.
[32]于伟.半球谐振陀螺的信号检测技术:学位论文.哈尔滨:哈尔滨工业大学,2004.
[33]胡晓东,罗康俊,余波等.采用离子束技术对半球振子进行质量调平.中国惯性技术学会第五届学术年会论文集,桂林,中国,2003:247~252.
[34]张坤.半球陀螺加工用球头砂轮修整装置研制与修整工艺研究:学位论文.哈尔滨:哈尔滨工业大学,2008.
[35]李子昂.半球陀螺谐振子的力学性能及振动特性分析:学位论文.哈尔滨:哈尔滨工业大学,2007.
[36]樊尚春,刘广玉,王振均.变厚度轴对称壳谐振子振型的进动研究.仪器仪表学报,1991,12(4):421~426.
[37]吕志清.振动陀螺的模型方程.中国惯性技术学会第五届学术年会论文集,桂林,中国,2003:226~233.
[38]梁嵬.半球陀螺仪谐振子振动特性及其结构研究:学位论文.长春:长春理工大学,2008.
[39]高胜利.半球谐振陀螺的分析与设计:学位论文.哈尔滨:哈尔滨工程大学,2008.
[40]雷霆.半球谐振陀螺控制技术研究:学位论文.重庆:重庆大学,2006.
[41]倪受东,吴洪涛等.微型半球陀螺仪的误差源研究.传感器与微系统,2007,26(1):30~32.
[42]刘长利.半球谐振陀螺仪振动的理论及有限元分析:学位论文.沈阳:东北大学,2001.
[43]易康.半球谐振陀螺误差分析和滤波方法研究:学位论文.长沙:国防科学技术大学研究生院,2005.
[44] V.V.Chikovani,Yu.A.Yatsenko,A.S.Barabashov.Improved Accuracy Metallic Resonator CVG.A&E SYSTEMS,2009,5:40~43.
[45] V.V.Chikovani,I.M.Okon,A.S.Barabashov.A Set of High Accuracy Low Cost Metallic Resonator CVG.Location and Navigation Symposium,Monterey,USA,2008:238~243.
[46]郭秀中等.陀螺仪理论及应用.北京:航空工业出版社,1987.
[47]宋道仁,肖鸣山.压电效应及其应用.北京:科学普及出版社,1987.
[48]曹志远.板壳振动理论.北京:中国铁道出版杜,1989.
[49] Loveday P.W,C.A.Rogers.Free vibration of elastically supported thin cylinders including gyroscopic effects.Journal of Sound and Vibration,1998,217(3):547~562.
[50]吴连元.板壳理论.上海:上海交通大学出版社,1989.
[51]贾乃文,云天铨.弹性力学.广东:华南理工大学出版社,1990.
[52] Yuri A.Yatzenko , BARABASHOV . Sensing Element of Coriolis Force Gyroscope.U.S. Patent:0184798A1,2008-08-07.
[53]陆明炯.实用机械工程材料手册.沈阳:辽宁科学技术出版社,2004.
[54]沈博昌,伊国兴,任顺清,王常虹,方针.半球谐振陀螺仪谐振子振动特性的有限元分析.中国惯性技术学报,2004,12(6):56~60.
[55]温熙森.机械系统建模与动态分析.北京:科学技术出版社,2003.
[56]陈柯,张茂.基于ANSYS的参数化设计与分析方法.机械工程师,2007,1:82~83.
[57]李韬,米双山,刘东升,金卫同.基于VC和ANSYS的破片侵彻参数化有限元分析,2008,27(9):73~78.
[58]崔俊伟,蔡川,徐长太,王建辉.基于VC++调用APDL的GIS断路器电场计算,2007,43(4):289~291.
[59] V.V.Chikovani,E.O.Umakhanov,P.I.Marusyk.The Compensated Differential CVG.Symposium Gyro Technology,Karlsruhe,Germany,2008:3.1~3.8.
[60]李云相.半球谐振陀螺的误差模型研究:学位论文.哈尔滨:哈尔滨工业大学,2005.
[61]陈雪,任顺清,赵洪波.半球谐振子薄壁厚度不均匀性对陀螺精度的影响.空间控制技术及应用,2009,35(3):29~33.
[62]朱拉夫拉夫,克里莫夫.固体波动陀螺.前苏联:苏联科学出版社,1985.
[63]张冲,殷东平.一种薄壁零件的制造工艺技术.电子工艺与技术,2008,29(1):40~42.
[64]费业泰,马修水等.三坐标测量机的动态误差研究分析.仪器仪表学报,2004,25(4):773~776.
[65] Albert Boggess,Francis J,Narcowich.A First Course in Wavelet s with Fourier Analysis.Beijing:Publishing House of Electronic Industry,2002.
[66]商兴国,张帆.圆度误差的快速傅立叶变换分析.唐山学院学报,2005,18(3):88~90.
[67]夏新涛,王中宇.谐波与圆度误差分析的范数理论.仪器仪表学报,2002,22(3):542~544.
[68]王占礼,方滔.车削加工圆度误差预测.中国制造业信息化,2009,38(1):72~77.
[69] WU N H,CHAN K C,LEONG S.Static interactions of surface contacts in a fixture-workpiece system . Internal Journal of Computer Applications in Technology,1997,10(3/4):133~151.
[70]高学平.圆度误差产生的原因及解决方法.机械工人,2002,5:61~64.
[71] Philip Wayne Loveday.Analysis and Compensation of Imperfection Effects in Piezoelectric Vibratory Gyroscopes:PhD Dissertation.Virginia:VirginiaPolytechnic Institute and State University,1999.
[72]彭军.传感器与检测技术.西安:西安电子科技大学出版社,2003.
