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A Trimming Strategy for Mass Defects in Hemispherical Resonators Based on Multi-Harmonic Analysis.
Yimo Chen1, Fanrui Kong1, Kai Zeng1
1College of Intelligence Science, National University of Defense Technology, Changsha 410073, China.
Micromachines
|April 26, 2025
Summary
This study introduces a novel discrete trimming scheme for hemispherical resonators, significantly reducing frequency split variations during 1st harmonic trimming. This method enhances mass balancing technology by improving trimming efficiency and minimizing damage.
Area of Science:
- Mechanical Engineering
- Applied Physics
- Microelectromechanical Systems (MEMS)
Background:
- Advancing mass balancing technology requires extending identification and trimming from frequency split to multiple harmonics in hemispherical resonators.
- Structural geometric errors in resonators commonly introduce the 1st harmonic of the mass distribution.
- Etching parameters critically influence multiple harmonics of the mass distribution, posing challenges for precise resonator tuning.
Purpose of the Study:
- To investigate the impact of etching trimming parameters on multiple harmonics of mass distribution in hemispherical resonators.
- To propose and validate a novel discrete trimming scheme for the 1st harmonic to address frequency split and mode mismatch.
- To achieve efficient and low-damage trimming of the 1st harmonic.
Main Methods:
- Developed a multi-harmonic identification scheme using spurious mode detection, considering the first three harmonics.
- Employed Finite Element Method (FEM) modeling to analyze the influence of geometric errors and simulated etching grooves.
- Introduced a discrete trimming scheme decomposing the task into primary and auxiliary etching grooves for harmonic compensation.
Main Results:
- FEM analysis confirmed that structural geometric errors significantly introduce the 1st harmonic.
- Spectral analysis showed etching groove depth and width dictate introduced harmonic amplitudes and gradients.
- The discrete trimming scheme effectively compensated for the 4th harmonic, decoupling the 1st harmonic from frequency split.
Conclusions:
- The proposed discrete trimming scheme significantly reduces frequency split variation (to 11% of single-point trimming) for similar 1st harmonic reduction.
- This method offers efficient and low-damage trimming of the 1st harmonic in hemispherical resonators.
- The study advances mass balancing techniques for high-precision resonant devices.
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