Fused silica (FS) micro hemispherical resonators have attracted considerable interest for application in high-performance sensors. Manufacturing of resonators with extremely high quality factor and acceptable cost is currently the main challenge. Here, we demonstrate the application of ultrafast laser in manufacturing of three-dimensional (3D) FS micro hemispherical resonators with unrestricted edge shapes. The 3D FS structures fabricated from micro glassblowing are detached from substrates by direct laser ablation with amplification tines, which is useful for improving the performance of the resonators. Resonators fabricated from direct laser ablation are experimentally characterized, exhibiting quality factors over millions via electrostatically characterization. This is the first time that ultrafast lasers are exploited in the manufacturing of mechanical resonators, while obtaining satisfactory performance. Effective integration of the laser ablation into current devices will greatly improve the fabrication ability, generating important implications for future micro electronic devices.

In recent years, the application prospects of high-precision MEMS gyroscopes have been shown to be very broad, but the large temperature drift of MEMS gyroscopes limits their application in complex temperature environments. In response to this, we propose a method that combines mode reversal and real-time multiple regression compensation to compensate for the temperature drift of gyroscope bias. This method has strong adaptability to the environment, low computational cost, the algorithm is online in real time, and the compensation effect is good. The experimental results show that under the temperature cycle of −20~20 °C and the temperature change rate of 4 °C/min, the method proposed in this paper can reduce the zero-bias stability from about 27.8°/h to 0.4527°/h, and the zero-bias variation is reduced from 65.88°/h to 1.43°/h. This method improves the zero-bias stability of the gyroscope 61-fold and the zero-bias variation 46-fold. Further, the method can effectively suppress the zero-bias drift caused by the heating of the gyroscope during the start-up phase of the gyroscope. The zero-bias stability of the gyroscope can reach 0.0697°/h within 45 min of starting up, and the zero-bias repeatability from 0 to 5 min after startup is reduced from 0.629°/h to 0.095°/h.

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 100mHz is still a big challenge for mHRG at present. This paper reveals that the trimming precision is limited by mass-stiffness coupling as the frequency splits reduce and reports the mHz-level trimming precision for the first time. Firstly, 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. Experimental demonstrates that the frequency split is successfully reduced below 5mHz. Performance tests of the mHRG are conducted under force-to-balance mode, the angular random walk (AWR) of 0.0107°/√h, and the bias stability of 0.04°/h. Furthermore, the achievement of mHz-level frequency split trimming significantly reduces the requirement for electrostatic tuning voltage.

This study presents a scheme for the identification and trimming of the first three harmonics of mass defects in micro hemispherical resonators (MHRs), aiming to refine their mass balancing techniques. Given the manufacturing and structural uniqueness of MHRs, a multimodal elastic electrode substrate is designed to respond to the first three harmonics. Configured as cantilever beams with a load platform, this substrate forms an identification assembly with the MHR. The radial eccentric forces generated by the 1st and 3rd harmonics in the MHR can excite the swing modes of the assembly, while the axial force generated by the 2nd harmonic can induce axial mode vibrations along the Z-axis. A method is proposed to decompose the vibration information of the elastic electrode substrate into double-cycle, single-cycle, and offset components under the N = 2 modes, enabling the extraction of swing mode and Z-axis translational mode response signals and the retro-calculation of the first three harmonics. Finite element simulation, based on a model of the identification assembly, validates the proposed scheme by simulating the identification and trimming process. Subsequently, an identification assembly sample is fabricated and subjected to identification and trimming of the first three harmonics using a laser vibrometer and femtosecond laser ablation process. After multiple iterations, the first three harmonics are reduced by 92.8%, 89.3%, and 75.5%, respectively, effectively suppressing the swing modes and axial translation modes induced by unbalanced mass.

This study investigates the impact of etching trimming parameters on the multiple harmonics of the mass distribution in hemispherical resonators and proposes a novel 1st harmonic trimming scheme. As mass balancing technology advances, the extension of identification and trimming from frequency split to multiple harmonics remains a challenge. Initially, a multi-harmonic identification scheme based on spurious mode detection was established, considering the influence of the first three harmonics of the mass distribution on the dynamic characteristics of hemispherical resonators. Finite element method modeling and analysis revealed that common structural geometric errors significantly introduce the 1st harmonic. By integrating a rectangular pulse function into the mass distribution function to simulate etching grooves, spectral analysis revealed that groove depth and width determine the amplitude and gradient of introduced harmonics. This research introduces an innovative discrete trimming scheme aimed at addressing the frequency split and mode mismatch issues associated with traditional single-point trimming of the 1st harmonic. By decomposing the trimming task into primary and auxiliary etching grooves, the 4th harmonic introduced by the primary etching is compensated by the secondary 4th harmonic introduced by the auxiliary etching, achieving decoupling of the 1st harmonic from frequency split during the trimming process. The scheme was verified through finite element simulations and experimental testing. Results demonstrate that, for a similar reduction in the 1st harmonic, the variation in frequency split during the discrete trimming process is only 11% of that observed in single-point trimming, facilitating efficient and low-damage trimming of the 1st harmonic.