载体加速度对静电驱动微机械陀螺响应的影响分析

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (5) : 55-62.

论文

张利娟1, 2，张华彪3，李欣业1，王雅雪1，于涛1

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Effect of carrier acceleration on response of electrostatically driven MEMS gyroscope

ZHANG Lijuan1,2, ZHANG Huabiao3, LI Xinye1, WANG Yaxue1, YU Tao1

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摘要

载体的运动会导致微机械陀螺的响应发生变化，因而引起测量误差，甚至导致系统故障。本文针对载体运动对微机械陀螺响应的影响开展研究。考虑载体运动以及微陀螺的非线性支承刚度和非线性静电力，基于拉格朗日方程建立了系统的动力学方程。利用谐波平衡法结合留数定理求解了含分式非线性项的系统的周期响应，研究了载体加速度对系统响应特性的影响，发现驱动方向的载体加速度主要导致系统的灵敏度降低。检测方向的载体加速度除使得系统灵敏度降低，还会导致零偏，且零偏和加速度的大小成正比，但比例系数与驱动电压无关。驱动电压较小时，载体在检测方向较小的加速度对灵敏度和非线性度影响很小；而在驱动电压或者检测方向加速度较大时，系统的灵敏度急剧下降，且非线性度也发生了剧烈变化。

Abstract

Carrier movement may cause measurement errors, and even make MEMS gyroscopes inoperable. The effect of carrier movement on the response of electrostatically actuated MEMS gyroscope is studied in this paper considering the nonlinear support stiffness and the detecting electrostatic force. From the governing differential equation, it is found that only the carrier acceleration may affect the response of the system. The periodic response of the system is obtained by the harmonic balance method and residue theorem. It is shown that the carrier acceleration in the driving direction can reduce the sensitivity of the system, while the acceleration in the detecting direction affects both sensitivity and zero bias. Zero bias is proportional to the magnitude of the acceleration in the detecting direction, and this proportional relationship is independent of the magnitude of the drive voltage. As the driving voltage is small, the acceleration of carrier in the detecting direction has little effect on the sensitivity and nonlinearity. However, when the driving voltage or the acceleration in the detecting direction is large, the sensitivity of the system decreases sharply, and the nonlinearity changes dramatically.

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张利娟1, 2，张华彪3，李欣业1，王雅雪1，于涛1. 载体加速度对静电驱动微机械陀螺响应的影响分析[J]. 振动与冲击, 2021, 40(5): 55-62

ZHANG Lijuan1,2, ZHANG Huabiao3, LI Xinye1, WANG Yaxue1, YU Tao1. Effect of carrier acceleration on response of electrostatically driven MEMS gyroscope[J]. Journal of Vibration and Shock, 2021, 40(5): 55-62

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