A multiple-beam tuning-fork gyroscope with high quality factors

This paper presents the design, theoretical analysis, fabrication, and experimental results of a multiple-beam tuning-fork gyroscope (MB-TFG). Based on a numerical model of thermoelastic damping, a multiple-beam tuning-fork structure is designed with high quality factors (Qs) in its two operation modes. A comprehensive theoretical analysis of the MB-TFG design is conducted to relate the design parameters to its operation parameters and further performance parameters. In conjunction with a mask that defines the device through trenches to alleviate previously identified severe fabrication effect on anchor loss, a simple one-mask fabrication process is employed to implement this MB-TFG design on silicon-on-insulator wafers. Experimental results of the fabricated MB-TFGs are thoroughly compared with the theoretical analysis for accurate interpretation. The highest measured Qs of the fabricated MB-TFGs in vacuum are 255,000 in the drive-mode and 103,000 in the sense-mode, at a frequency of 15.7 kHz. Under a frequency difference of 4 Hz between the two modes (operation frequency is 16.8 kHz) and a drive-mode vibration amplitude of 3.0 μm, the measured rate sensitivity is 80 μVPP/°/s with an equivalent impedance of 2.5 MΩ. The calculated overall rate resolution of this device is 0.37°/h/√Hz, while the measured angle random walk (ARW) and bias instability are 6.67°/√h and 95°/h, respectively.