Chen Yimo, Kong Fanrui, Zeng Kai, Xi Xiang, Shi Yan, Xiao Dingbang, Wu Xuezhong
College of Intelligence Science, National University of Defense Technology, Changsha 410073, China.
Micromachines (Basel). 2025 Apr 18;16(4):480. doi: 10.3390/mi16040480.
This study investigates the impact of etching trimming parameters on the multiple harmonics of the mass distribution in hemispherical resonators and proposes a novel 1st harmonic trimming scheme. As mass balancing technology advances, the extension of identification and trimming from frequency split to multiple harmonics remains a challenge. Initially, a multi-harmonic identification scheme based on spurious mode detection was established, considering the influence of the first three harmonics of the mass distribution on the dynamic characteristics of hemispherical resonators. Finite element method modeling and analysis revealed that common structural geometric errors significantly introduce the 1st harmonic. By integrating a rectangular pulse function into the mass distribution function to simulate etching grooves, spectral analysis revealed that groove depth and width determine the amplitude and gradient of introduced harmonics. This research introduces an innovative discrete trimming scheme aimed at addressing the frequency split and mode mismatch issues associated with traditional single-point trimming of the 1st harmonic. By decomposing the trimming task into primary and auxiliary etching grooves, the 4th harmonic introduced by the primary etching is compensated by the secondary 4th harmonic introduced by the auxiliary etching, achieving decoupling of the 1st harmonic from frequency split during the trimming process. The scheme was verified through finite element simulations and experimental testing. Results demonstrate that, for a similar reduction in the 1st harmonic, the variation in frequency split during the discrete trimming process is only 11% of that observed in single-point trimming, facilitating efficient and low-damage trimming of the 1st harmonic.
本研究调查了蚀刻修整参数对半球形谐振器质量分布多谐波的影响，并提出了一种新颖的基波修整方案。随着质量平衡技术的发展，从频率分裂的识别和修整扩展到多谐波的识别和修整仍然是一个挑战。首先，考虑到质量分布的前三个谐波对半球形谐振器动态特性的影响，建立了一种基于杂散模式检测的多谐波识别方案。有限元方法建模与分析表明，常见的结构几何误差会显著引入基波。通过将矩形脉冲函数集成到质量分布函数中来模拟蚀刻槽，频谱分析表明槽深和槽宽决定了引入谐波的幅度和梯度。本研究引入了一种创新的离散修整方案，旨在解决与传统基波单点修整相关的频率分裂和模式失配问题。通过将修整任务分解为主蚀刻槽和辅助蚀刻槽，主蚀刻引入的四阶谐波由辅助蚀刻引入的二阶四阶谐波进行补偿，在修整过程中实现了基波与频率分裂的解耦。该方案通过有限元模拟和实验测试得到了验证。结果表明，对于类似的基波降低量，离散修整过程中频率分裂的变化仅为单点修整中观察到的变化的11%，便于高效且低损伤地修整基波。
