A study on Q factor of the trimmed resonator for vibratory cupped gyroscopes

• In this paper, the Q factor of the trimmed resonator for the vibratory cupped gyroscopes is studied.
• We found that the Q factor is sensitive to the depth variation of the trimming groove.
• When the eigenmode vibrates along the trimming positions, the Q factor of the cupped resonator can be significantly changed.

Trimming of resonators is an important process to achieve mass balance of vibratory cupped gyroscopes. Material removing via trimming grooves can eliminate frequency splits of the resonators. However, these trimming grooves simultaneously change local mass and stiffness distribution of the cupped resonators. Hence elastic energy and energy losses near the trimming grooves can be altered. In this paper, we found that structural damping of a trimmed cupped resonator is not circumferentially homogeneous. Thus Quality factor (Q factor) of a balanced resonator is influenced. A detailed model analyzing the trimming problem and Q factor of the trimmed cupped resonator is provided. The numerical solutions show that when the 4-node standing wave eigenmode of the resonator vibrates along different radial axes, the Q factor of the trimmed resonator will be different. Experiments were also set up to observe the Q factors of the trimmed cupped resonators by using frequency analysis equipments.