Achieving Sub-5-mHz Frequency Split Trimming of Micro Hemispherical Resonator Gyroscope With Method of Mass–Stiffness Decoupling

Precise frequency trimming is essential for improving the mode-match gyroscope performance. Femtosecond laser ablation has been proven an efficient process in mechanical trimming of micro hemispherical resonator gyroscope (mHRG). However, achieving frequency trimming below 100 mHz is still a big challenge for mHRG at present. This article reveals that the trimming precision is limited by mass–stiffness coupling as the frequency splits reduce and reports the millihertz-level trimming precision for the first time. First, finite element model simulation is conducted to analyze the impact of mass–stiffness coupling on trimming accuracy. By analyzing variations in frequency split under different diameters and depths of trimming holes, the influence of trimming hole diameter on local structural stiffness and trimming hole depth on local mass is concluded. Further analysis indicates that mass–stiffness can be decoupled when the trimming depth exceeds a threshold. Therefore, a high-precision trimming method that effectively decouples mass–stiffness by controlling the depth-to-width ratio parameter is then proposed. The experiment demonstrates that the frequency split is successfully reduced below 5 mHz. Performance tests of the mHRG are conducted under the force-to-balance mode, the angular random walk (AWR) of 0.0107°/ $\surd $ h, and the bias stability of 0.04°/h. Furthermore, the achievement of millihertz-level frequency split trimming significantly reduces the requirement for electrostatic tuning voltage.