Key Takeaways & Executive Findings
- •• Scratches above 55° latitude induce frequency splitting solely via stiffness changes, while lower-latitude scratches affect mass and damping. • Frequency splitting from scratches at the rim is about 50% of that near the transition fillet for the same scratch size, highlighting location-dependent sensitivity. • Frequency splitting increases linearly with the volume of material removed by scratches, enabling predictive modeling for trimming. • Scratches have negligible effect on thermoelastic damping, but the first three harmonics of unbalanced mass at the rim dominate anchor loss, guiding defect mitigation strategies.
Abstract
The fused quartz hemispherical resonator is the core component of the hemispherical resonator gyroscope. It features a complex shape and is made from a material that is difficult to process. Scratches are easily introduced during grinding, potentially degrading the mass-stiffness-damping symmetry; however, the underlying mechanisms of this influence have not been fully understood. This paper aims to investigate the effects of scratch defects on the frequency splitting and quality factor of the hemispherical resonator. First, finite element models of the hemispherical resonator with scratches are established. Then, the effects of the mass-stiffness factor, as well as the latitude and length of the scratches, on frequency splitting are analyzed. Furthermore, the impacts of latitude, length, and the first four harmonics of the unbalanced mass caused by scratches on thermoelastic damping and anchor loss are examined. Simulation results indicate that scratches above 55° latitude cause frequency splitting solely due to stiffness changes. Frequency splitting caused by scratches of the same size on the inherent rigidity shaft at the rim is approximately 50% of that near the transition fillet. Frequency splitting varies linearly with the volume of material removed by scratches. Scratches have little effect on thermoelastic damping. The first three harmonics of the unbalanced mass due to scratches at the rim are the primary contributors to anchor loss. Finally, focused ion beam trimming experiments are conducted at different locations on the hemispherical resonator. The trends observed in the experimental results are consistent with the simulation results. This work provides guidance for evaluating the impact of scratches on the performance of hemispherical resonators and for developing appropriate trimming processes.
1. Introduction
The hemispherical resonator gyroscope (HRG) is considered a disruptive technology in the field of high-precision navigation. It offers advantages such as high precision, long lifespan, high reliability, and strong resistance to impact and electromagnetic interference [1–3]. The fused quartz hemispherical resonator is the core component of the HRG. It is a hard, brittle, thin-walled hemispherical structure. A high-performance hemispherical resonator should exhibit minimal frequency splitting and a high quality factor (Q-factor) [4–6].
The machining process of the hemispherical resonator includes blank forming, ultra-precision grinding, magnetorheological polishing, chemical etching, and focused ion beam trimming [7–12]. Scratch defects are easily introduced during the grinding stage. Although magnetorheological polishing can effectively eliminate these scratches, it suffers from low processing efficiency. To balance the requirements for high performance and high processing efficiency, the magnetorheological polishing step can be omitted, and chemical etching can be performed directly after ultra-precision grinding. While chemical etching effectively removes subsurface damage, it can also enlarge and passivate existing scratches [13]. Scratches of varying sizes and positions may degrade the local mass-stiffness-damping symmetry of the hemispherical resonator, leading to frequency splitting and a reduction in the Q-factor.
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Jingyang Guo, Henan Liu, Mingjun Chen, Jian Cheng (2025). Simulation Analysis of How Scratches Influence Frequency Splitting and Energy Dissipation of Hemispherical Resonator. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01350-3
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Frequently Asked Questions
What is the main focus of this study?
The study investigates how scratch defects on a hemispherical resonator affect frequency splitting and energy dissipation (thermoelastic damping and anchor loss), using finite element simulations and focused ion beam trimming experiments.
How do scratches influence frequency splitting?
Scratches cause frequency splitting by altering the mass-stiffness-damping symmetry. The effect depends on the scratch's latitude, length, and volume of material removed. Scratches above 55° latitude cause splitting solely due to stiffness changes, and splitting increases linearly with removed volume.
What is the impact of scratches on energy dissipation?
Scratches have little effect on thermoelastic damping, but they significantly affect anchor loss. The first three harmonics of the unbalanced mass caused by scratches at the rim are the primary contributors to anchor loss.
What are the practical implications of this research?
The findings provide guidance for evaluating the impact of scratches on hemispherical resonator performance and for developing appropriate trimming processes to minimize frequency splitting and energy dissipation, thereby improving gyroscope accuracy and reliability.
How were the simulation results validated?
Focused ion beam trimming experiments were conducted at different locations on the hemispherical resonator, and the trends observed in the experimental results were consistent with the simulation results, validating the models.
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