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结构参数对静电驱动微机械陀螺动态性能的影响

李欣业 王雅雪 张华彪 张利娟 于涛

李欣业,王雅雪,张华彪,张利娟,于涛. 结构参数对静电驱动微机械陀螺动态性能的影响 [J]. 应用数学和力学,2021,42(12):1248-1257 doi: 10.21656/1000-0887.410316
引用本文: 李欣业,王雅雪,张华彪,张利娟,于涛. 结构参数对静电驱动微机械陀螺动态性能的影响 [J]. 应用数学和力学,2021,42(12):1248-1257 doi: 10.21656/1000-0887.410316
LI Xinye, WANG Yaxue, ZHANG Huabiao, ZHANG Lijuan, YU Tao. Effects of Structure Parameters on Dynamic Performances of Electrostatic Drive Micro-Machined Gyroscopes[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1248-1257. doi: 10.21656/1000-0887.410316
Citation: LI Xinye, WANG Yaxue, ZHANG Huabiao, ZHANG Lijuan, YU Tao. Effects of Structure Parameters on Dynamic Performances of Electrostatic Drive Micro-Machined Gyroscopes[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1248-1257. doi: 10.21656/1000-0887.410316

结构参数对静电驱动微机械陀螺动态性能的影响

doi: 10.21656/1000-0887.410316
基金项目: 国家自然科学基金(11972145;11302223)
详细信息
    作者简介:

    李欣业(1966—),男,教授,博士,博士生导师 (通讯作者. E-mail:xylihebut@163.com)

  • 中图分类号: O322

Effects of Structure Parameters on Dynamic Performances of Electrostatic Drive Micro-Machined Gyroscopes

  • 摘要:

    为研究结构参数对静电驱动微机械陀螺动态性能的影响,考虑支承刚度的三次非线性和静电力的分式非线性,基于两自由度动力学模型,利用谐波平衡法结合留数定理求解了系统的周期响应,得到了驱动电极的梳齿厚度、梳齿间隙以及检测电极的极板面积、极板间隙变化时电容变化量随驱动力频率和载体角速度的变化曲线,以及电容灵敏度和非线性度随这些参数的变化曲线。结果表明,检测电容变化量随驱动力频率的变化曲线会呈现明显的非线性特征,即第二个峰向右倾斜,从而引起跳跃现象。驱动电极的梳齿厚度、梳齿间隙和检测电极的极板间隙对检测电容变化量随载体角速度的变化影响较大,而检测电极的极板面积的影响很小。驱动电极梳齿厚度、梳齿间隙以及检测电极的极板面积对电容灵敏度和非线性度的影响基本上是线性的,但检测电极的极板间隙对电容灵敏度和非线性度的影响是非线性的。

  • 图  1  微机械陀螺结构示意

    Figure  1.  The schematic of the micro-machined gyroscope

    图  2  微机械陀螺系统的幅频特性曲线

    Figure  2.  The amplitude-frequency curves of the micro-machined gyroscope

    图  3  不同驱动电极梳齿厚度对应的检测电容变化量随驱动力频率的变化

    Figure  3.  Variation of the detection capacitance with the driving force frequency for different thicknesses of driving electrode comb teeth

    图  4  不同驱动电极梳齿间隙对应的检测电容变化量随驱动力频率的变化

    Figure  4.  Variation of the detection capacitance with the driving force frequency for different gaps of driving electrode comb teeth

    图  5  不同驱动电极梳齿厚度对应的检测电容变化量随载体角速度的变化

    Figure  5.  Variation of the detection capacitance with the carrier angular velocity for different thicknesses of driving electrode comb teeth

    图  6  不同驱动电极梳齿间隙对应的检测电容变化量随载体角速度的变化

    Figure  6.  Variation of the detection capacitance with the carrier angular velocity for different gaps of driving electrode comb teeth

    图  7  电容灵敏度随驱动电极梳齿厚度的变化

    Figure  7.  Variation of the sensitivity with the thickness of driving electrode comb teeth

    图  8  非线性度随驱动电极梳齿厚度的变化

    Figure  8.  Variation of the nonlinearity with the thickness of driving electrode comb teeth

    图  9  电容灵敏度随驱动电极梳齿间隙的变化

    Figure  9.  Variation of the sensitivity with the gap of driving electrode comb teeth

    图  10  非线性度随驱动电极梳齿间隙的变化

    Figure  10.  Variation of the nonlinearity with the gap of driving electrode comb teeth

    图  11  不同检测极板面积对应的检测电容变化量随驱动力频率的变化

    Figure  11.  Variation of the detection capacitance with the driving force frequency for different detecting electrode plate areas

    图  12  不同检测极板间隙对应的检测电容变化量随驱动力频率的变化

    Figure  12.  Variation of the detection capacitance with the driving force frequency for different gaps between detecting electrode plates

    图  13  不同检测极板面积对应的检测电容变化量随载体角速度的变化

    Figure  13.  Variation of the detection capacitance with the carrier angular velocity for different detecting electrode plate areas

    图  14  不同检测极板间隙对应的检测电容变化量随载体角速度的变化

    Figure  14.  Variation of the detection capacitance with the carrier angular velocity for different gaps between detecting electrode plates

    图  15  电容灵敏度随检测极板面积的变化

    Figure  15.  Variation of the sensitivity with the detecting electrode plate area

    图  16  非线性度随检测极板面积的变化

    Figure  16.  Variation of the nonlinearity with the detecting electrode plate area

    图  17  电容灵敏度随检测极板间隙的变化

    Figure  17.  Variation of the sensitivity with the gap between detecting electrode plates

    图  18  非线性度随检测极板间隙的变化

    Figure  18.  Variation of the nonlinearity with the gap between detecting electrode plates

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出版历程
  • 收稿日期:  2020-10-19
  • 录用日期:  2021-03-31
  • 修回日期:  2021-01-27
  • 刊出日期:  2021-12-01

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