Identification and trimming of the unbalanced mass in micro hemispherical resonators based on an elastic electrode substrate

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.