半球谐振陀螺测量误差分析
摘要
陀螺仪是一种重要的惯性元件,在航天,航海,航空,兵器以及一些民用领域中有着广泛的和重要的应用。
半球陀螺的测试原理是基于理想的半球谐振子,理想谐振子的振动具有解析解,可以解释半球陀螺的测试原理。但实际的谐振子总是存在各种缺陷,如质量的不均、阻尼的不均以及阻尼的缓慢变化、激励和信号采集系统缺陷等,导致实际制作完成的半球陀螺总是存在误差。实际半球陀螺出现误差后,需分析产生误差的原因以及如何在后端电路测试系统中进行误差补偿。
本文从陀螺基本构造和工作原理入手,着重对其信号检测环节做了分析。简要介绍了半球谐振陀螺(HRG)的闭环检测原理,并用有限元软件ABAQUS对其进行仿真,再建立动力学方程,用均值法求出该方程的理论解,对该原理进行了论证。最后对陀螺由于初始激励引起的测量误差进行分析,从而为实际陀螺系统消除该影响因素提供依据。
The gyroscope ,an important inertial component ,is widely applied in navigation, aerospace, aviation, weapons and other civil fields.
The test principle of hemisphere gyro is based on the ideal hemisphere harmonic oscillator,of which the vibration can explain it.But actually the harmonic oscillator is always exist various kinds of defects.Such as, the inequality of quality and damping,the slow changing of damping, the defects of incentive and signal acquisition system etc.All of those defects lead to the error of the hemisphere gyros completed.however,when the error appears,it necessary for us to analysis the causes and find a way to have a error compensation in the rear circuit testing system.
Beginning from the basic structure and working principle, this article focuses on the analysis of the signal detecting .The closed-loop detecting principle of hemisphere harmonic oscillator (HRG) is introduced and simulated by using finite element software ABAQUS.Then,the dynamic equations are establisheed and the theoretical solution is worked out by using average method to demonstrate the principle.Finally, the measurement error of hemisphere harmonic oscillator (HRG) caused by initial exciting is worked out to provide a basis for actual gyro system to eliminate the influence of this factors.
半球陀螺的测试原理是基于理想的半球谐振子,理想谐振子的振动具有解析解,可以解释半球陀螺的测试原理。但实际的谐振子总是存在各种缺陷,如质量的不均、阻尼的不均以及阻尼的缓慢变化、激励和信号采集系统缺陷等,导致实际制作完成的半球陀螺总是存在误差。实际半球陀螺出现误差后,需分析产生误差的原因以及如何在后端电路测试系统中进行误差补偿。
本文从陀螺基本构造和工作原理入手,着重对其信号检测环节做了分析。简要介绍了半球谐振陀螺(HRG)的闭环检测原理,并用有限元软件ABAQUS对其进行仿真,再建立动力学方程,用均值法求出该方程的理论解,对该原理进行了论证。最后对陀螺由于初始激励引起的测量误差进行分析,从而为实际陀螺系统消除该影响因素提供依据。
The gyroscope ,an important inertial component ,is widely applied in navigation, aerospace, aviation, weapons and other civil fields.
The test principle of hemisphere gyro is based on the ideal hemisphere harmonic oscillator,of which the vibration can explain it.But actually the harmonic oscillator is always exist various kinds of defects.Such as, the inequality of quality and damping,the slow changing of damping, the defects of incentive and signal acquisition system etc.All of those defects lead to the error of the hemisphere gyros completed.however,when the error appears,it necessary for us to analysis the causes and find a way to have a error compensation in the rear circuit testing system.
Beginning from the basic structure and working principle, this article focuses on the analysis of the signal detecting .The closed-loop detecting principle of hemisphere harmonic oscillator (HRG) is introduced and simulated by using finite element software ABAQUS.Then,the dynamic equations are establisheed and the theoretical solution is worked out by using average method to demonstrate the principle.Finally, the measurement error of hemisphere harmonic oscillator (HRG) caused by initial exciting is worked out to provide a basis for actual gyro system to eliminate the influence of this factors.
引文
[1] Matthews, F.J.Rybak. Comparison of Hemispherical Resonator Gyro and Optical Gyros[J]. IEEE Aerospace and Electronics Systems Magazine,1992,7(5):40-46.
[2] G.Londerville, R.Ciolino, D.Hahey虎刚译.利用固态半球谐振陀螺的空间惯性基准单元的飞行实验[R].控制工程, 1997(4):44-56.
[3]朱拉夫拉夫B.固体波动陀螺[M].苏联科学院应用力学所,1985.
[4]许国桢.百年理论变现实—半球谐振陀螺投产[J].航空制造工程, 1999,10:45.
[5] Jack Dickinson, Carl R.Strandt,HRG Strapdown Navigator[J] IEEE PLANS. 1990,20(7):110-117.
[6]何传五.几种新型陀螺简介[J].控制学报, 2001,(2):107-114.
[7] Lynch, D;Matthews, A;Varty, G T.Innovative mechanization to optimize inertial sensors for high or low rate operations[J]. Symposium Gyro Techonology, 1997,16:9.0-9.21.
[8]吴旭峰,吕志清,半球谐振陀螺仪[J].半球谐振陀螺技术文, 1999:1-6.
[9]方针,张巧云,吕志清.惯性技术的新发展[J].惯性技术发展动态发展方向研讨会, 2004:90-96.
[10]吕志清.半球谐振陀螺在宇宙飞船上的应用[J].压电与声光, 1999,21(5):349-353.
[11]章燕申.半球谐振陀螺研究在苏联[J].国际航空, 1989,11:56-56.
[12] Chan-Shin CHOU, Chin-OU CHANG.Modal Precession of A Hemeispherical Shell Gyro xcited By Electrostatic Field.Journal Appl.Phys[J]. 1997 vol.36:7073-7082.
[13] E.A.Izmailov, M.M.Kolensnik, A.M.Osipov, A.V.Akimov.Hemispherical Rresonator GyroTechnology problems and Possible Ways of their Solutions[C]. ROT SCI International conference on”Integrated Navigation Systems”St Petersburg Russia 25~26 May 1990,6-1~6-9.
[14] Stripling, W.W.Baskett Johnr.Hemispherical Resonator Gyro: Principle,Design, and Performance[D]. NASA N93-22784 Delco Electronics,Goleta,CA, 1993:1-6.
[15]任思聪,王博.一种值得重视的新型陀螺仪——半球谐振子陀螺仪HGR.导航,1985.
[16] P.W.Loveday C.A.Rogers. The Influence of Control System Design on The Performance of Vibration Gyroscopers.Journal of Sound and Vibration[J]. 2002 255(3),417-432.
[17]林凡,崔燕,陈峰浴.半球谐振陀螺机理分析[J].中国惯性技术学报, 1996,4(3):42-45.
[18] Tony Matthwes; Roy H.Farmer.Applications of HRG to Strategic Missions[J]. Proceedings of the Annual Meeting-Institute of Navigation, 1999:551-558.
[19]于伟.半球谐振陀螺的信号检测技术[D].哈尔滨工业大学硕士学位论文. 2004.3.
[20]李云相.半球谐振陀螺的误差模型研究[D].哈尔滨工业大学硕士学位论文. 2005.
[21]樊尚春,刘广玉,王振均.半球谐振陀螺的理论与实验室研究[J].测控技术, 1994,13(1):29-33.
[22]刘延东,陈文良,陈立群.振动力学[M].第1版.北京:高等救教育出版社, 1998:282-290.
[23]朱伯芳.有限单元法原理与应用第2版[M].北京:中辊水利水电出版社, 1998.
[24]王勖成,邵敏.有限单元法基本原理和数值方法2版[M].北京:清华大学出版社, 1997.
[25]刘珏林. MSC/PATRAN基础培训教程[M]. USA:The MacNeal-Schwendler Corporation.
[26]石亦平,周玉蓉. ABAQUS有限元分析实例详解[M].机械工业出版社.
[27]庄茁,张帆,岑松等. ABAQUS非线性有限元分析与实例[M].北京:科学出版社, 2004.
[28]吴家龙.弹性力学[M].第2版.上海.同济大学出版社, 1996.
[29]张汝清.固体力学变分原理及其应用[M].第1版.重庆.重庆大学出版社, 1991.
[30]庄表中,王行新.随机振动概论[M].地震出版社, 1982.
[31]刘延柱,陈文良,陈立群.振动力学[M].北京:高等教育出版社, 1998.
[32] Finlayson,B.A. he Method of Weighted Residuals and Variational Principles with Application in Fluid Mechanics[J]. Heat and Mass Transfer Academic Press, 1972.
[33]夏志斌,潘有吕.结构稳定理论[M].北京:高等教育出版社, 1988.
[34] Finlayson.B.A.and L.E.Seroven.The Mehtod of Weighted Residualsa Review[J]. Applied Mechanics Review, 1996:9~19.
[35] Eason,E,D. A Reviwe of Leat-squares Methods for Solving Partial Differential Equations-Intern[J]. Jou.of Num. in Engg. 1996,10.
[36]方同著.工程随机振动[M].北京:国防工业出版社, 1995.
[37] Zheng Ruifen. The Dynamic Response of Hypar shells and its Programming on Microcompater[J]. EPMESC PAPER. 1985,8.
[38]沈博昌,伊国兴.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.
[39] Bryan G H. On the beats in the vibrations of a revolving cylinder or bell. Proc.Roy.Soc.London,1890,(47):101-111.
[40]胡国荣,崔伟宏.组合GPS/GLONASS加权单点定位方法[J].兵工学报,2002,(2).
[41]沈博昌,伊国兴.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.
[42]于伟杨亚非凌明祥结构误差造成的半球谐振陀螺闭环检测误差分析中国惯性技术学报2003,11( 4):4 0-44.
[2] G.Londerville, R.Ciolino, D.Hahey虎刚译.利用固态半球谐振陀螺的空间惯性基准单元的飞行实验[R].控制工程, 1997(4):44-56.
[3]朱拉夫拉夫B.固体波动陀螺[M].苏联科学院应用力学所,1985.
[4]许国桢.百年理论变现实—半球谐振陀螺投产[J].航空制造工程, 1999,10:45.
[5] Jack Dickinson, Carl R.Strandt,HRG Strapdown Navigator[J] IEEE PLANS. 1990,20(7):110-117.
[6]何传五.几种新型陀螺简介[J].控制学报, 2001,(2):107-114.
[7] Lynch, D;Matthews, A;Varty, G T.Innovative mechanization to optimize inertial sensors for high or low rate operations[J]. Symposium Gyro Techonology, 1997,16:9.0-9.21.
[8]吴旭峰,吕志清,半球谐振陀螺仪[J].半球谐振陀螺技术文, 1999:1-6.
[9]方针,张巧云,吕志清.惯性技术的新发展[J].惯性技术发展动态发展方向研讨会, 2004:90-96.
[10]吕志清.半球谐振陀螺在宇宙飞船上的应用[J].压电与声光, 1999,21(5):349-353.
[11]章燕申.半球谐振陀螺研究在苏联[J].国际航空, 1989,11:56-56.
[12] Chan-Shin CHOU, Chin-OU CHANG.Modal Precession of A Hemeispherical Shell Gyro xcited By Electrostatic Field.Journal Appl.Phys[J]. 1997 vol.36:7073-7082.
[13] E.A.Izmailov, M.M.Kolensnik, A.M.Osipov, A.V.Akimov.Hemispherical Rresonator GyroTechnology problems and Possible Ways of their Solutions[C]. ROT SCI International conference on”Integrated Navigation Systems”St Petersburg Russia 25~26 May 1990,6-1~6-9.
[14] Stripling, W.W.Baskett Johnr.Hemispherical Resonator Gyro: Principle,Design, and Performance[D]. NASA N93-22784 Delco Electronics,Goleta,CA, 1993:1-6.
[15]任思聪,王博.一种值得重视的新型陀螺仪——半球谐振子陀螺仪HGR.导航,1985.
[16] P.W.Loveday C.A.Rogers. The Influence of Control System Design on The Performance of Vibration Gyroscopers.Journal of Sound and Vibration[J]. 2002 255(3),417-432.
[17]林凡,崔燕,陈峰浴.半球谐振陀螺机理分析[J].中国惯性技术学报, 1996,4(3):42-45.
[18] Tony Matthwes; Roy H.Farmer.Applications of HRG to Strategic Missions[J]. Proceedings of the Annual Meeting-Institute of Navigation, 1999:551-558.
[19]于伟.半球谐振陀螺的信号检测技术[D].哈尔滨工业大学硕士学位论文. 2004.3.
[20]李云相.半球谐振陀螺的误差模型研究[D].哈尔滨工业大学硕士学位论文. 2005.
[21]樊尚春,刘广玉,王振均.半球谐振陀螺的理论与实验室研究[J].测控技术, 1994,13(1):29-33.
[22]刘延东,陈文良,陈立群.振动力学[M].第1版.北京:高等救教育出版社, 1998:282-290.
[23]朱伯芳.有限单元法原理与应用第2版[M].北京:中辊水利水电出版社, 1998.
[24]王勖成,邵敏.有限单元法基本原理和数值方法2版[M].北京:清华大学出版社, 1997.
[25]刘珏林. MSC/PATRAN基础培训教程[M]. USA:The MacNeal-Schwendler Corporation.
[26]石亦平,周玉蓉. ABAQUS有限元分析实例详解[M].机械工业出版社.
[27]庄茁,张帆,岑松等. ABAQUS非线性有限元分析与实例[M].北京:科学出版社, 2004.
[28]吴家龙.弹性力学[M].第2版.上海.同济大学出版社, 1996.
[29]张汝清.固体力学变分原理及其应用[M].第1版.重庆.重庆大学出版社, 1991.
[30]庄表中,王行新.随机振动概论[M].地震出版社, 1982.
[31]刘延柱,陈文良,陈立群.振动力学[M].北京:高等教育出版社, 1998.
[32] Finlayson,B.A. he Method of Weighted Residuals and Variational Principles with Application in Fluid Mechanics[J]. Heat and Mass Transfer Academic Press, 1972.
[33]夏志斌,潘有吕.结构稳定理论[M].北京:高等教育出版社, 1988.
[34] Finlayson.B.A.and L.E.Seroven.The Mehtod of Weighted Residualsa Review[J]. Applied Mechanics Review, 1996:9~19.
[35] Eason,E,D. A Reviwe of Leat-squares Methods for Solving Partial Differential Equations-Intern[J]. Jou.of Num. in Engg. 1996,10.
[36]方同著.工程随机振动[M].北京:国防工业出版社, 1995.
[37] Zheng Ruifen. The Dynamic Response of Hypar shells and its Programming on Microcompater[J]. EPMESC PAPER. 1985,8.
[38]沈博昌,伊国兴.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.
[39] Bryan G H. On the beats in the vibrations of a revolving cylinder or bell. Proc.Roy.Soc.London,1890,(47):101-111.
[40]胡国荣,崔伟宏.组合GPS/GLONASS加权单点定位方法[J].兵工学报,2002,(2).
[41]沈博昌,伊国兴.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.
[42]于伟杨亚非凌明祥结构误差造成的半球谐振陀螺闭环检测误差分析中国惯性技术学报2003,11( 4):4 0-44.