Abstract
Frequency trimming based on mass and stiffness modification is an important post-fabrication process for micro-shell resonators (MSRs). However, the trimming effects on the quality factor are seldom studied, although they may have great influence on the performance of the resonator. This paper presents a study on the quality factor (Q-factor) variation of trimmed micro-shell resonators (MSR). Thermoelastic damping (QTED) and anchor loss (Qanchor) are found to be the dominant energy loss mechanisms resulting in the reduction of the overall Q-factor, according to finite element method (FEM). The effects of different trimming methods on QTED and Qanchor are studied here, respectively. It is found that trimming grooves ablated in the rim of the resonator can cause a ~1–10% reduction of QTED, and the length of trimming groove is positively related to the reduction of QTED. The reduction of QTED caused by the mass adding process is mainly related to the thermal expansion coefficient and density of the additive and contact area between the resonator and additive masses. Besides, the first and second harmonic errors caused by asymmetrical trimming can cause a 10–90% reduction of Qanchor. Finally, trimming experiments were conducted on different resonators and the results were compared with FEM simulation. The work presented in this paper could help to optimize the trimming process of MSRs.
Highlights
Micro shell vibrating gyroscopes (MSVGs) have shown promising performance for navigation-grade gyroscopic application, due to advantages such as a high Q-factor, structural symmetry, and immunity to external vibrations, especially with the development of micro fabrication process technologies [1,2]
The change of QTED and Qanchor has been calculated by finite element method (FEM) simulation in trimmed micro-shell resonators (MSRs)
The simulation results indicate that groove trimming in the rim of the resonator causes a significant reduction of QTED, and the length of the trimming grooves is positively related to the reduction of QTED
Summary
Micro shell vibrating gyroscopes (MSVGs) have shown promising performance for navigation-grade gyroscopic application, due to advantages such as a high Q-factor, structural symmetry, and immunity to external vibrations, especially with the development of micro fabrication process technologies [1,2]. The electrostatic method achieves precise frequency tuning by applying a direct current (DC) voltage on corresponding electrodes to modify the effective stiffness [22,23]. The latest testing results showed as-fabricated MSRs can reach a frequency split less than 10 Hz in the wineglass modes without any post-process [24]. A systematic trimming process was successfully applied to reduce the frequency split of MSRs [25,26], the impact on the Q-factor has not been researched.
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