微陀螺动力学建模与非线性分析

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (4) : 69-73.

论文

微陀螺动力学建模与非线性分析

文永蓬 1 ，尚慧琳 2

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Dynamical Modeling and Nonlinear Analysis of Microgyroscope

WEN Yong-peng 1 SHANG Hui-lin 2

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文章历史 +

摘要

建立了微陀螺的动力学模型，采用多尺度方法对微陀螺的非线性模型进行求解，探讨了驱动微弹性梁和检测微弹性梁的非线性刚度对微陀螺输出的影响规律，研究了微陀螺的带宽在非线性刚度作用下的设计原则，结果表明：微陀螺振动系统的检测灵敏度和带宽呈反比关系；微弹性梁的非线性刚度会使得输入角速度与检测输出呈非线性关系。因此，从微弹性梁的设计角度出发，可根据较大的输出或者较小的非线性要求选取合适的驱动微弹性梁；而检测微弹性梁则需要选取较小的非线性刚度。

Abstract

This paper presents dynamics analysis model of microgyroscope, a multi-scale method is used to solve the nonlinear model of the microgyroscope. The influence of the output of the microgyroscope for the diving and the sensing spring beams is disscussed. The design principle of the bandwidth of micromachined gyroscope is studied considering the nonlinear stiffness. The results show that for the vibration system of microgyroscope, the detection sensitivity correlates negatively with the bandwidth. The input angular velocity has a nonlinear relationship with the detection output due to nonlinear stiffness of the mircromachined sping beams of the microgyroscope. Therefore, In the view of the design for the spring beams, the couple effects for the stiffness of the driving spring beam is relatively low, the appropriate spring beam can be selected according to the larger output or smaller nonlinear requirements. The stiffness of the sensing spring beam can be selected for a smaller nonlinear stiffness.