On ordering of fundamental wineglass modes in toroidal ring gyroscope

In this paper, we discuss the primary sources of frequency splits in degenerate mode Toroidal Ring Gyroscope (TRG) with isotropic concentric rings suspension. We show that operation in the n=3 “wineglass mode” might be preferable for prioritized device symmetry. We demonstrate that by means of structural design it is possible to achieve a desired order of wineglass modes, critical for vibration immunity, and potentially for improved performance of miniature devices. Mode-ordering is accomplished by a proper choice of a number of rings in the suspension and an angle between the spokes connecting the rings. The method of mode-ordering is confirmed through experimental characterization of 2.8 mm diameter TRG prototypes fabricated in <100> and <111> single crystal silicon.