The accurate and complete dynamic model for the hemispherical shell resonator is the basis of error analysis of the Hemispherical Resonator Gyro (HRG). A dynamic modeling method for the hemispherical shell resonator is proposed based on the thin shell theory of elasticity. First, the deformation geometry equation for the hemispherical shell resonator is derived based on the elasticity geometry equation for the thin shell. Second, based on the improvement of calculation accuracy of force analysis, the physical equation for the hemispherical shell resonator is developed. After an analysis of the force equilibrium relationship for the middle surface of the resonator, the equilibrium differential equation for the resonator is obtained. Finally, based on the above dynamic analysis of the whole resonator, the dynamic equation for the resonator is established. After an analysis of the external load forms of the resonator, the second-order resonant dynamic model for the resonator is obtained by using the Bubnov-Galerkin method, and the expressions for the proportion coefficients and second-order resonant frequency of the resonator are also obtained. Comparison shows that the calculation results are consistent with the measured data, proving the accuracy of the dynamic model proposed.
XU Zeyuan
,
YI Guoxing
,
WEI Zhennan
,
ZHAO Wanliang
. A dynamic modeling method for resonator of hemispherical resonator gyro[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018
, 39(3)
: 221624
-221624
.
DOI: 10.7527/S1000-6893.2017.21624
[1] ROZELLE D M. The hemispherical resonator gyro:From wineglass to the planets[C]//Proceeding 19th AAS/AIAA Space Flight Mechanics Meeting. Reston, VA:AIAA, 2009:1157-1178.
[2] XU Z Y, YI G X, QI Z Y, et al. Structural optimization research on hemispherical resonator gyro based on finite element analysis[C]//The 35th Chinese Control Conference. Beijing:Technical Committee on Control Theory, Chinese Association of Automation, 2016:5737-5742.
[3] MATTHEWS A, RYBAK F J. Comparison of hemispherical resonator gyro and optical gyros[J]. IEEE Aerospace and Electronic Systems Magazine, 1992, 7(5):40-46.
[4] MEYER A D, ROZELLE D M. Milli-HRG inertial navigation system[C]//The IEEE/ION Position, Location and Navigation Symposium (PLANS'12). Piscataway, NJ:IEEE Press, 2012:24-29.
[5] ZHBANOV Y K. Vibration of a hemispherical shell gyro excited by an electrostatic field[J]. Mechanics of Solids, 2008, 43(3):328-332.
[6] ZHBANOV Y K. Self-tuning control loop for suppression of quadrature in a hemispherical resonator gyro[J]. Gyroscopy and Navigation, 2007(2):37-42.
[7] 王锦瑜, 冯培德. 激光陀螺速率偏颇系统的分析研究[J]. 航空学报, 2001, 22(1):46-50. WANG J Y, FENG P D. Research on rate-bias system of laser gyro[J]. Acta Aeronautica et Astronautica Sinica, 2001, 22(1):46-50(in Chinese).
[8] 李金涛, 房建成. 高精度光纤IMU的磁屏蔽方法及实验研究[J]. 航空学报, 2011, 32(11):2106-2116. LI J T, FANG J C. Magnetic shielding method and experiment study of inertial measurement unit based on high precision fiber-optic gyroscope[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(11):2106-2116(in Chinese).
[9] 魏玉淼, 董永贵, 李昊. 微机械陀螺非线性特性的自由衰减振荡测量方法[J]. 仪器仪表学报, 2016, 37(11):2465-2472. WEI Y M, DONG Y G, LI H. Free damped oscillation measurement method for the nonlinear features of micromechanical gyroscopes[J]. Chinese Journal of Scientific Instrument, 2016, 37(11):2465-2472(in Chinese).
[10] 李巍, 任顺清, 王常虹. 半球谐振陀螺谐振子品质因数不均匀引起的误差分析[J]. 航空学报, 2013, 34(1):121-129. LI W, REN S Q, WANG C H. Analysis for impact of resonator's Q-factor nonuniformity on the error of hemispherical resonator gyro[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(1):121-129(in Chinese).
[11] SHATALOV M Y, JOUBERT S V, COETZEE C E. The influence of mass imperfections on the evolution of standing waves in slowly rotating spherical bodies[J]. Journal of Sound and Vibration, 2009, 330(1):127-135.
[12] ZHBANOV Y K. Amplitude control contour in a hemispherical resonator gyro with automatic compensation for difference in Q-factors[J]. Mechanics of Solids, 2008, 43(3):328-332.
[13] SHATALOV M Y, COETZEE C E. Dynamics of rotating and vibrating thin hemispherical shell with mass and damping imperfections and parametrically driven by discrete electrodes[J]. Gyroscopy and Navigation, 2011, 2(1):27-33.
[14] 伊国兴, 谢阳光, 王常虹, 等. 加速度对半球谐振陀螺振动检测系统影响分析[J]. 中国惯性技术学报, 2013, 21(5):676-681. YI G X, XIE Y G, WANG C H, et al. Analysis of acceleration influence on HRG vibration detection system[J]. Journal of Chinese Inertial Technology, 2013, 21(5):676-681(in Chinese).
[15] FREITAG S, BEER M, GRAF W, et al. Lifetime prediction using accelerated test data and neural networks[J]. Computers & Structures, 2009, 87(19-20):1187-1194.
[16] WANG X, WU W Q, FANG Z, et al. Temperature drift compensation for hemispherical resonator gyro based on natural frequency[J]. Sensors, 2012, 12(5):6434-6446.
[17] SONG J W, SONG H M, LEE Y J, et al. Design of oscillation control loop with coarse-precision mode transition for solid-state resonant gyroscope[J]. IEEE Sensors Journal, 2016, 16(6):1730-1742.
[18] WANG X, WU W Q, LUO B, et al. Force to rebalance control of HRG and suppression of its errors on the basis of FPGA[J]. Sensors, 2011, 11(12):11761-11773.
[19] ZHURAVLEV V P. Hemispherical resonator gyro with m data electrodes and n control electrodes[J]. Mechanics, 2015, 50(4):375-378.
[20] 徐芝纶. 弹性力学下册[M]. 5版. 北京:高等教育出版社, 2016:100-200. XU Z L. Elasticity[M]. 5th ed. Beijing:Higher Education Press, 2016:100-200(in Chinese).
[21] 赵洪波, 任顺清, 李巍. 半球谐振子动力学方程的建立及固有频率的计算[J]. 哈尔滨工业大学学报, 2010, 42(11):1702-1706. ZHAO H B, REN S Q, LI W. Establishment of dynamics equation of HRG resonator and calculation of natural frequency[J]. Journal of Harbin Institute of Technology, 2010, 42(11):1702-1706(in Chinese).
[22] 谢阳光. 基于半球谐振陀螺的姿态测量系统研究[D]. 哈尔滨:哈尔滨工业大学, 2013:13-36. XIE Y G. Research on attitude measurement systems based on hemispherical resonator gyro[D]. Harbin:Harbin Institute of Technology, 2013:13-36(in Chinese).
[23] BA马特维耶夫, H И利帕特尼科夫, AB阿廖欣, 等. 固体波动陀螺[M]. 北京:国防工业出版社, 2009:1-43. MATVEEV V A, BASARAB M A, ALEKIN A V, et al. Solid state wave gyro[M]. Beijing:National Defense Industry Press, 2009:1-43(in Chinese).
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