Natural Frequency Analysis of Cluster Dither with Partially Tapered Spokes for Three-Axis Ring Laser Gyroscopes

The ring laser gyroscope (RLG), a representative type of optical gyroscope, exhibits a lock-in region in which very small angular velocity inputs cannot be measured due to backscattering from the mirrors. Generally, this lock-in effect is mitigated by applying a high-amplitude sinusoidal vibration to the gyro body. The mechanical device used to induce this sinusoidal vibration is referred to as a dither. Dithers vary in configuration depending on the size of the gyro; while single-axis dithers are applied to gyros with relatively large optical paths, a cluster dither—which simultaneously applies sinusoidal vibrations to three-axis gyroscopes—is used for those with smaller optical paths. Unlike in the single-axis dither, the gyro body is mounted on the cluster dither at a specific angle. Furthermore, while the dither fixing hole in a single-axis dither is located at the center of the gyro body, it is positioned on the periphery in a cluster dither. Consequently, the center of rotation for a cluster dither is located at the center of the dither itself, rather than coinciding with the center of the gyro body. To increase the natural frequency of the cluster dither with such a configuration, this paper proposes a design employing a partially tapered non-uniform and heterogeneous cantilever beam, rather than the uniform and homogeneous cantilever beam used in conventional single-axis dither spokes, and presents a corresponding natural frequency analysis method. The accuracy of the proposed natural frequency analysis method is validated through modeling and simulation (M&S) and through experimental testing of fabricated prototypes.