Abstract
In this paper, we use the nonlinear hardening stiffness of drive mode deal with the contradiction between gain and bandwidth of the linear micro-gyroscope, to improve the bandwidth and gain in sense direction. Firstly, in order to adjust the distance between two resonant peaks, we changed an incomplete two-degree-of-freedom(2-DoF) sense mode system of the micro-gyroscope into a complete 2-DoF system. Afterward, according to the given nonlinear coefficient of stiffness of drive mode, the structure size of driving micro-beams was designed to obtain a nonlinear micro-gyroscope with controllable stiffness. Finally, we investigated the effects of peaks spacing, damping, and driving nonlinearity on gain and bandwidth, and the nonlinear micro-gyroscope was optimized by orthogonal experiment method and response surface method. The results reveal that the peaks spacing has a great influence on the gain and bandwidth of both linear and nonlinear micro-gyroscopes. The larger the peaks spacing, the lower the gain, but higher gain can be achieved when the resonant frequency of the drive mode is close to the lower-order resonant frequency of the sense mode. Driving nonlinearity leads to the response peak of the Coriolis force to have a hardening characteristic, thus forming a wide platform in the sense direction. Hardening of the response peak of the Coriolis force allows the micro-gyroscope to obtain a higher gain while the bandwidth of the sense mode is also greatly improved. In addition, parameter optimization can make the gain and bandwidth of the micro-gyroscope optimal. When the peaks spacing is small and the nonlinear stiffness coefficient is about 1012.2, under the premise that the gain is basically constant, the bandwidth of the sense mode increases about 1.76 times compared with the linear gyroscope. Damping can suppress the influence of nonlinearity in a micro-gyroscope system. Within a certain range, the frequency response of the nonlinear micro-gyroscope tends to be a linear system with the increase in damping, resulting in narrower bandwidth and lower gain.
Highlights
The micro-gyroscope is the key component of inertial measurement unit and inertial navigation system
In resonant micro-gyroscopes, the device operates at resonance and the resonant frequencies of drive and sense mode are generally matched, which leads to high mechanical gain
Xu et al [2] studied the characteristics of resonant micro-gyroscopes with different frequency mismatches. Their results showed that the frequency mismatch could lead to a significant decrease in the gain of the sense mode and the frequencies can be matched by adjusting the DC voltage of the sense mode to control the resonant frequency
Summary
The micro-gyroscope is the key component of inertial measurement unit and inertial navigation system. In order to realize the arbitrary adjustment of the resonant peaks spacing, Esmaeili et al [4] explored a single-DoF drive mode and two-DoF sense mode (SD-TD) gyroscope They changed the incomplete 2-DoF system into a complete 2-DoF system and arranged two operational regions of the micro-gyroscope, i.e., wide-bandwidth low-gain region and high-gain narrowbandwidth region. Verma et al [5] investigated a SD-TD gyroscope by considering the effect of the Coriolis force, and the frequency response of the sense mode was divided into two bandwidths. Yoon et al [8] investigated a ring resonator micro-gyroscope by considering the damping and electrostatic force nonlinearity Their results showed that the nonlinearity generates high-order coupling terms and cannot be neglected. The effect of nonlinear stiffness on gain and bandwidth are investigated
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