0.32 mHz frequency mismatch of micro-shell resonator gyroscope without tuning electrodes achieved by ultra-precision mechanical trimming

The frequency mismatch caused by material defects and geometric errors during the manufacturing process is a critical factor limiting the performance of micro-shell resonator gyroscope (MSRG). Compared with other MEMS gyroscopes, the frequency mismatch of MSRG can fundamentally be reduced by mechanical trimming. However, it is challenged by the precise characterization. Previous studies about the characterization of frequency mismatch are almost based on frequency spectrum analysis and sweeping, which can only meet the requirement of trimming efficiency of over 100 mHz, limited by the signal noise and temperature drift. In this paper, a novel characterization method of frequency mismatch based on the quadrature-control force under the self-precession mode is proposed to meet the requirement of high-precision mechanical trimming. Furthermore, the phase errors which affect the accuracy of characterization is analyzed, and methods for the correction of phase errors are proposed. Based on this characterization method, 0.32 mHz frequency mismatch of micro-shell resonator is achieved by mechanical trimming, which is the best-reported performance for mechanical trimming of MEMS gyroscopes so far. More importantly, this novel characterization method can be applied for other kinds of resonators which can be mechanical trimmed.