留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

半球型动压气浮轴承陀螺仪的静态误差模型

李岩 段富海

李岩, 段富海. 半球型动压气浮轴承陀螺仪的静态误差模型[J]. 北京航空航天大学学报, 2018, 44(8): 1705-1711. doi: 10.13700/j.bh.1001-5965.2017.0570
引用本文: 李岩, 段富海. 半球型动压气浮轴承陀螺仪的静态误差模型[J]. 北京航空航天大学学报, 2018, 44(8): 1705-1711. doi: 10.13700/j.bh.1001-5965.2017.0570
LI Yan, DUAN Fuhai. Static error model of a gyroscope with gas-dynamic hemispherical bearings[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(8): 1705-1711. doi: 10.13700/j.bh.1001-5965.2017.0570(in Chinese)
Citation: LI Yan, DUAN Fuhai. Static error model of a gyroscope with gas-dynamic hemispherical bearings[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(8): 1705-1711. doi: 10.13700/j.bh.1001-5965.2017.0570(in Chinese)

半球型动压气浮轴承陀螺仪的静态误差模型

doi: 10.13700/j.bh.1001-5965.2017.0570
基金项目: 

航空科学基金 20150863003

详细信息
    作者简介:

    李岩  男, 博士研究生。主要研究方向:润滑数值计算

    段富海  男, 博士, 教授, 博士生导师。主要研究方向:导航、制导与控制

    通讯作者:

    段富海, E-mail: duanfh@dlut.edu.cn

  • 中图分类号: V241.5+52

Static error model of a gyroscope with gas-dynamic hemispherical bearings

Funds: 

Aeronautical Science Foundation of China 20150863003

More Information
  • 摘要:

    为研究三自由度比力作用下半球型动压气浮轴承气膜变形对平台惯导中三浮陀螺仪输出的影响,提出了一种通过求解Reynolds方程来计算陀螺仪静态误差的数学模型。首先,在考虑气体稀薄效应条件下,针对三浮陀螺仪中的半球型动压气浮轴承给出对应的Reynolds润滑方程;然后,用有限差分法求解气膜压力场,并利用得到的载荷与转子位移计算陀螺仪静态误差;最终,通过回归分析,得到半球型动压气浮轴承陀螺仪的静态误差模型。为简化回归分析的过程,引入干扰力矩与比力的周向夹角和径向干扰力矩作为中间参数,将三元回归分析问题转化为二元回归分析问题。计算结果表明:径向干扰力矩随着轴向比力的增大而增大,随着径向比力的增大呈现先增大后减小的趋势;干扰力矩在周向上超前比力1.35~1.55 rad。本文静态误差模型可预测300 m/s2以内任意方向比力作用下由转子位移所引起的陀螺仪静态误差。

     

  • 图 1  半球型动压气浮轴承的结构

    Figure 1.  Structure of gas-dynamic hemispherical bearing

    图 2  计算域的局部坐标系与网格划分

    Figure 2.  Local coordinate system and meshing of calculation domain

    图 3  三浮陀螺仪的结构简图

    1—传感器; 2—壳体;3—浮筒;4—转子;5—力矩器;6—气浮轴承。

    Figure 3.  Sketch of three-floated gyroscope structure

    图 4  主要变量的计算关系

    Figure 4.  Calculation relationship among main variables

    图 5  气膜压力分布

    Figure 5.  Pressure distribution of gas film

    图 6  径向干扰力矩与2个比力分量的关系

    Figure 6.  Radial interference torque versus specific force in two directions

    图 7  比力与干扰力矩的周向夹角与2个比力分量的关系

    Figure 7.  Circumferential angle between specific force and interference torque versus specific force in two directions

    表  1  计算参数

    Table  1.   Parameters in calculation

    参数 数值
    轴承半径R/mm 6
    轴承宽度b/mm 5
    轴承间隙c/mm 2
    两轴承间距d/mm 8
    沟槽深度hg/μm 1
    沟槽数量Ng 6
    沟槽方向角βg/(°) 45
    转子质量m/g 60
    转子角动量Hr/(kg·m2·s-1) 0.016 7
    气体黏度μ/(Pa·s) 1.79×10-5
    转速n/(r·min-1) 30 000
    环境压力Pa/Pa 1.013×105
    下载: 导出CSV

    表  2  式(10)各系数拟合结果

    Table  2.   Fitted results of each coefficient in Eq.(10)

    系数 数值
    b00/(N·m) 2.48×10-6
    b10/(N·s2) -4.88×10-7
    b01/(N·s2) 1.60×10-6
    b20/(N·s4·m-1) -4.41×10-7
    b11/(N·s4·m-1) -8.13×10-8
    b30/(N·s6·m-2) 4.56×10-7
    b21/(N·s6·m-2) -4.54×10-7
    b40/(N·s8·m-3) -1.11×10-7
    b31/(N·s8·m-3) 1.59×10-7
    下载: 导出CSV

    表  3  式(11)各系数拟合结果

    Table  3.   Fitted values of coefficients in Eq.(11)

    系数 a00/rad a10/(rad·s2·m-1) a01/(rad·s2·m-1)
    数值 1.482 -3.746×10-2 3.608×10-3
    下载: 导出CSV
  • [1] 严恭敏, 李四海, 秦永元.惯性仪器测试与数据分析[M].北京:国防工业出版社, 2015:10-55.

    YAN G M, LI S H, QIN Y Y.Test and data analysis of inertial meter[M].Beijing:National Defense Industry Press, 2015:10-55(in Chinese).
    [2] DELLACORTE C, RADIL K C, BRUCKNER R J, et al.Design, fabrication, and performance of open source generation Ⅰ and Ⅱ compliant hydrodynamic gas foil bearings[J].Tribology Transactions, 2008, 51(3):254-264. doi: 10.1080/10402000701772579
    [3] 秦冬黎. 一种球形气浮气动陀螺仪的设计方法及误差分析研究[D]. 哈尔滨: 哈尔滨工业大学, 2009: 11-27. http://cdmd.cnki.com.cn/Article/CDMD-10213-2010031070.htm

    QIN D L. Research on design method and error analysis of a spherical gas-floated and driven gyroscope[D]. Harbin: Harbin Institute of Technology, 2009: 11-27(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10213-2010031070.htm
    [4] 陈广强, 杨云军, 雷娟棉, 等.锥台型气体润滑动压轴承动力学数值模拟研究[J].机械工程学报, 2016, 52(4):185-191. http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201604027

    CHEN G Q, YANG Y J, LEI J M, et al.Numerical simulation research on cone self-acting gas lubrication bearing dynamics[J].Chinese Journal of Mechanical Engineering, 2016, 52(4):185-191(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201604027
    [5] ARMENISE M N, CIMINELLI C, DELL'OLIO F, et al.Advances in gyroscope technologies[M].New York:Springer Science & Business Media, 2010:52-133.
    [6] 武丽花, 凌林本.三浮陀螺仪漂移模型的建立及MATLAB实现[J].中国惯性技术学报, 2004, 12(6):77-80. http://d.old.wanfangdata.com.cn/Periodical/zggxjsxb200406018

    WU L H, LING L B.Model of gyro drift and realizing in MATLAB[J].Journal of Chinese Inertial Technology, 2004, 12(6):77-80(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/zggxjsxb200406018
    [7] GOLIKOV A N, IGNATOVSKAYA A A.The statement of design and application questions for the gyroscope with a gas-dynamic suspension of ball rotor in the navigation support drilling system[J].Journal of Physics, 2016, 671:012020. http://adsabs.harvard.edu/abs/2016JPhCS.671a2020G
    [8] 刘晶石. 气浮陀螺仪干扰力矩影响因素研究[D]. 哈尔滨: 哈尔滨工业大学, 2011: 18-31. http://cdmd.cnki.com.cn/Article/CDMD-10213-1012000318.htm

    LIU J S. Research on influencing factors of interference torque of gas-floated gyroscope[D]. Harbin: Harbin Institute of Technology, 2011: 18-31(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10213-1012000318.htm
    [9] YANG Q, ZHANG H, LIU Y.Improved modified Reynolds equation for thin-film gas lubrication from an extended slip velocity boundary condition[J].Microsystem Technologies, 2016, 22(12):2869-2875. doi: 10.1007/s00542-015-2667-4
    [10] ZHANG W, MENG G, WEI X, et al.Slip flow and heat transfer in microbearings with fractal surface topographies[J].International Journal of Heat and Mass Transfer, 2012, 55(23-24):7223-7233. doi: 10.1016/j.ijheatmasstransfer.2012.07.045
    [11] CHENG F, JI W.A new model of water-gas turbulent lubrication for analysis of the static and dynamic characteristics in a journal bearing[J].Proceedings of the Institution of Mechanical Engineers, Part J:Journal of Engineering Tribology, 2016, 230(12):1439-1451. doi: 10.1177/1350650116635927
    [12] GERTZOS K P, NIKOLAKOPOULOS P G, PAPADOPOULOS C A.CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant[J].Tribology International, 2008, 41(12):1190-1204. doi: 10.1016/j.triboint.2008.03.002
    [13] BHORE S P, DARPE A K.Investigations on characteristics of micro/meso scale gas foil journal bearings for 100-200 W class micro power systems using first order slip velocity boundary conditions and the effective viscosity model[J].Microsystem Technologies, 2013, 19(4):509-523. doi: 10.1007/s00542-012-1639-1
    [14] LIU R, WANG X L, ZHANG X Q.Effects of gas rarefaction on dynamic characteristics of micro spiral-grooved thrust bearing[J].Journal of Tribology, 2012, 134(2):222011-222017. http://europepmc.org/abstract/med/23904692
    [15] GAD A M, KANEKO S.A new structural stiffness model for bump-type foil bearings:Application to generation Ⅱ gas lubricated foil thrust bearing[J].Journal of Tribology, 2014, 136:0417014. http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1870280
    [16] FENG K, LI W, XIE Y, et al.Theoretical analysis of the slip flow effect on gas-lubricated micro spherical spiral groove bearings for machinery gyroscope[J].Microsystem Technologies, 2016, 22(2):387-399. doi: 10.1007/s00542-015-2487-6
    [17] DEHERI G M, PATEL S J.Combined effect of slip velocity and surface roughness on a magnetic squeeze film for a sphere in a spherical seat[J].Indian Journal of Materials Science, 2015, 1155(10):1-9. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=Doaj000003919282
    [18] CUI D P, YAO Y X, QIN D L.Study on the dynamic characteristics of a new type externally pressurized spherical gas bearing with slot-orifice double restrictors[J].Tribology International, 2010, 43(4):822-830. doi: 10.1016/j.triboint.2009.11.009
    [19] FUKUI S, KANEKO R.A database for interpolation of Poiseuille flow-rates for high Knudsen number lubrication problems[J].Journal of Tribology-Transactions of the ASME, 1990, 112(1):78-83. doi: 10.1115/1.2920234
    [20] 黄平.润滑数值计算方法[M].北京:高等教育出版社, 2012:93-103.

    HUANG P.Lubrication numerical calculation methods[M].Beijing:Higher Education Press, 2012:93-103(in Chinese).
    [21] SAHU M, SARANGI M, MAJUMDAR B C.Thermo-hydrodynamic analysis of herringbone grooved journal bearings[J].Tribology International, 2006, 39(11):1395-1404. doi: 10.1016/j.triboint.2005.11.022
  • 加载中
图(7) / 表(3)
计量
  • 文章访问数:  686
  • HTML全文浏览量:  191
  • PDF下载量:  501
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-09-11
  • 录用日期:  2017-11-03
  • 网络出版日期:  2018-08-20

目录

    /

    返回文章
    返回
    常见问答