Resolving Multi-Solution Ambiguity in Unbalanced Mass Identification of Hemispherical Resonator under Linear Vibration Excitation

Identifying the first three harmonic components of unbalanced mass is essential for high precision HRG manufacturing. These components affect quality factor uniformity but are difficult to measure accurately. Existing envelope based methods discard phase information, creating sign ambiguity with 16 possible solutions for each measurement. To address this problem, we proposes an unambiguous identification method based on coherent demodulation. By preserving complete sign information through coherent demodulation, the number of solutions is reduced to 4. Furthermore, a verification method based on the first-harmonic trimming of unbalanced mass is designed to confirm the unique true solution. Simulations validate the effectiveness of the method, achieving unambiguous identification of mass defects and providing reliable technical support for high precision manufacturing of hemispherical resonator gyro.