Effect of geometric imperfections on anchor loss and characterisation of a gyroscope resonator with high quality factor
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ffect of Geometric Imperfections on Anchor Loss and Characterisation of a Gyroscope Resonator with High Quality Factor Gireesh N. Sharmaa, *, T. Sundararajanb, and S. Singh Gautamc aISRO
b
Inertial Systems Unit, Thiruvananthapuram, Kerala, 695013 India Vikram Sarabhai Space Centre, Thiruvananthapuram, Kerala, 695022 India c Indian Institute of Technology, Guwahati, 781039 India *e-mail: [email protected] Received March 13, 2020; revised June 23, 2020; accepted June 23, 2020
Abstract—A critical functional part of a hemispherical resonator gyroscope (HRG) is the mechanical resonator, and a few million quality factor (Q-factor) is needed for the lowest resolution. This paper focuses on anchor loss of a HRG of a few millimeters in size. A detailed parametric study of dimensions and shell imperfections due to fabrication is carried out. A sensitivity study of the effect of shell mean radius, shell thickness, stem radius, stem height on the Qanchor is carried out. The effect of geometric imperfections such as shell offset, shell tilt, shell thickness variation, and unbalance is studied in detail. From the study, it is inferred that the anchor loss becomes very significant and approaches other loss mechanisms even with minor geometric imperfections in the hardware realisation. Based on the sensitivity study, the dimensional and geometric tolerances are arrived for precision fabrication. Precision resonator is fabricated as per the requirement of minimum anchor loss. The significance of other damping mechanisms such as air damping, excitation-induced damping, thermoelastic dynamic damping and surface dissipation is also discussed. Surface characterisation before and after surface treatment has been carried out using nanoindentation technique with regard to surface loss. Functional parameters of operating frequency and Q-factor are evaluated using laser Doppler vibrometry (LDV). Keywords: hemispherical resonator gyroscope, Q-factor, anchor loss, elastic wave energy, nanoindentation DOI: 10.1134/S2075108720030074
INTRODUCTION Hemispherical resonator gyroscope (HRG) is a high-performance inertial navigation sensor with good accuracy, highest resolution and high reliability with lesser number of parts. The solid-state HRG is the appropriate kind of gyroscope for future interplanetary spacecrafts [1]. Operation of this sensor is based on Coriolis acceleration. The resonator is excited in its functional vibrating mode. When the resonator is subjected to an angular rate, precession of the vibrating pattern occurs. The rate of the precession is different from the input angular rate. The difference between these rotations is proportional to the input rotation of the body. The most critical part is the mechanical resonator. High Q-factor of the order of a few million is required for achieving very fine resolution in measurements. Qfactor is the ratio of energy stored to energy lost during vibration. Major damping sources in a resonator are air damping due to operating medium, surface dissipation, excitation-induced damping,
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