A Study on the Trimming Effects on the Quality Factor of Micro-Shell Resonators Vibrating in Wineglass Modes

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 (Q_TED) and anchor loss (Q_anchor) 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 Q_TED and Q_anchor are studied here, respectively. It is found that trimming grooves ablated in the rim of the resonator can cause a ~1-10% reduction of Q_TED, and the length of trimming groove is positively related to the reduction of Q_TED. The reduction of Q_TED 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 Q_anchor. 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.