Precise Frequency Split Characterization of Micro Hemispherical Resonators Based on Omni-Directional Geometric Parameters

Micro hemispherical resonator gyroscopes (mHRGs) are widely recognized for their high precision, compact size, and low cost, and they are ideal for industrial applications in inertial navigation and precision sensing. However, the accuracy of mHRGs is critically influenced by the frequency split of resonators, which is governed primarily by geometric parameters. To address this challenge, a novel method for precisely characterizing the frequency split in micro hemispherical resonators is proposed. A dynamic model based on motion equations is developed to quantitatively analyze the frequency split, leveraging omni-directional geometric parameters for enhanced precision and utilizing Taylor expansion to streamline the computational process. A 3-D reconstruction geometric model is subsequently obtained via the computed tomography (CT) technique to provide rapid and rich data extraction of omni-directional geometric parameters, facilitating integration into a dynamic model. Furthermore, the high-temperature blowing technique enables the fabrication of diverse geometric parameters for model validation. Experiments demonstrate that the proposed method achieves 7% accuracy in characterizing the frequency split, with sensitivity analysis identifying thickness defects as the most critical factor. This method enables precise frequency split characterization during fabrication and provides precise trimming guidance, which contributes to improving resonator manufacturing performance.