Global form-to-performance trimming of hemispherical resonators

The dynamic performance of hemispherical resonator gyroscopes is governed by the mass and stiffness uniformity of the hemispherical resonator. Conventional performance-based trimming cannot simultaneously decouple the 1st to 4th harmonic errors, and trimming low-order harmonics inevitably introduces higher-order ones. To overcome the limitation, this paper proposes a global form-to-performance trimming method that converts measured 3D form errors into a removal distribution, suppressing the 1st to 4th harmonic errors synchronously without performance feedback. Firstly, an analytical model is established, revealing the quantitative relationships of frequency split and anchor loss to the inner and outer surface form errors. Secondly, an objective function for unilateral compensation trimming of the outer surface is formulated, with inner-surface errors as constraints and outer-surface errors as decision variables. Then, the harmonic errors on both surfaces are extracted and 3D-reconstructed using Zernike polynomials and normal cylindrical projection. Finite element simulations confirm that the objective function predictions agree well with simulation results. Finally, a three-axis ion beam global trimming technique is developed that maps the annular error onto a two-dimensional rectangle, performs distortion correction, and solves for the dwell time. Single-pass trimming simultaneously reduced the 1st–4th harmonic errors by over 67.3%, frequency split by 71.2%, and damping asymmetry by 70.7%, while yielding a record-high quality factor of 5.04 × 10⁷. Iterative trimming further validated the proposed relationship models between the objective functions and the dynamic errors. This work provides a deterministic, geometry-driven paradigm that reducing the dependence on repeated performance feedback, enabling efficient manufacturing of navigation-grade resonators.