Frequency tuning of fused silica cylindrical resonators by chemical etching

The cylindrical resonator gyroscope (CRG) has been attracting more and more attention in recent years for its comprehensive advantages; which are its low cost, small size and high performance. These benefits make the CRG a good choice for tactical grade applications. A balanced resonator is a prerequisite for high-performance CRGs. Aiming at mass production, we seek balancing technology that is both simple and inexpensive for cylindrical fused silica resonators. Inspired by the chemical trimming procedure proposed by M. A. Basarab, we have been investigating the frequency tuning of fused silica cylindrical resonators by chemical etching. In this paper, we present the theoretical derivation, simulation and experimental results on the frequency tuning of fused silica cylindrical resonators by chemical etching. The thickness of the cylindrical resonator has been taken into consideration in theoretical derivation, which provides a more accurate description of the chemical trimming process. The relationship between the chemical trimming parameters and the fourth harmonic error of mass distribution of the cylindrical resonator was derived. The trimming efficiency, trimming rate, the frequency split to be reduced and the operability of the experimental system were considered during the determination of chemical trimming parameters. Simulations on the chemical trimming coefficient (CTC)- meaning the frequency reduced per unit mass-of our resonator show a difference of only 5.6% with theoretical calculation. A series of experiments were carried out on a fused silica cylindrical resonator with an initial frequency split of 1.221Hz and a decay time of 61s. Two sets of chemical etching parameters were designed based on theoretical and simulation results. Three rounds of etching were performed using the first set of parameters, and two rounds of etching were performed using the second set. The frequency split was reduced to 0.061Hz and the decay time was increased to 123s. Experimental results were also in agreement with theoretical calculation, with a CTC difference of 16.4%. Our work demonstrated that frequency tuning by chemical etching is controllable and repeatable, and is suitable for medium-accuracy trimming of cylindrical resonators made from fused silica.