Frequency Split Modulation in Micro Hemispherical Resonator Based on Rim Width

Abstract

The micro hemispherical resonator is center-symmetric, and the mass and stiffness of the resonator are completely coupled. In instances where manufacturing errors are present, both mass perturbations and stiffness perturbations are introduced concurrently, leading to frequency split. Given that the formation errors of micro hemispherical resonator, specifically mass and stiffness disturbances, are predominantly concentrated in the shell, this paper proposes a micro hemispherical resonator with adjustable rim width, whose rim area is distributed circumferentially around the shell periphery. An equivalent geometric model of the resonator was established, and finite element simulation was used to study the influence of rim width on the frequency split of the resonator under different harmonic errors. It was determined that within a specified error range, adjusting the rim width results in a minimum value for the frequency split. To validate the effectiveness of the simulation results, the rim width was altered using femtosecond laser direct etching, and the resonant frequencies were measured at different rim widths. The experimental findings demonstrated that the frequency split of the resonator attained a minimum at a rim width of 0.7 mm, with a frequency split of only 1.09 Hz (86.44 ppm), which was 8.4 times lower than that at a rim width of 0 mm. Consequently, the method delineated in this paper can effectively mitigate the frequency split of resonator in circumstances where manufacturing errors are unavoidable, thereby significantly reducing the threshold for electrostatic trimming and offering the potential to achieve approximate frequency matching from a structural design perspective.[2025-0088]