The hemispherical resonator gyro (HRG) is low loss and high stability, spurring recent interest in micro-scale hemispherical resonators. To achieve mode-matching and high-Q performance in a hemispherical resonator, geometric symmetry in combination with low thermoelastic damping structural material are critical. In this work, we describe the development of millimeter scale 3D hemispherical shell resonators fabricated from polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. The relation between the fourth harmonic (4θ) in a Fourier analysis of the resonator's radius r(θ) and frequency mismatch (Δf) of the 2θ elliptical vibration modes of the shell resonator is demonstrated.

Micromachined polycrystalline diamond hemispherical shell resonators

We present the development of millimeter scale 3D hemispherical shell resonators fabricated from the polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. These hemispherical wineglass resonators with 1.1 mm diameter are fabricated through a combination of micro-electro discharge machining (EDM) and silicon micromachining techniques. Using piezoelectric and electrostatic excitation and optical vibration measurement, the elliptical wineglass vibration mode is determined to be at 18.321 kHz, with the two degenerate wineglass modes having a relative frequency mismatch of 0.03%. A study on the effect of the size and misalignment of the anchor and resonator’s radius variation on both the average frequency and frequency mismatch of the 2θ elliptical vibration modes is carried out. It is shown that the absolute frequency of a wineglass resonator will increase with the anchor size. It is also demonstrated that the fourth harmonic of radius variation is linearly related to the frequency mismatch. (Some figures may appear in colour only in the online journal)

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Hemispherical wineglass resonators fabricated from the microcrystalline diamond

We report, for the first time, experimental demonstration of a 3-D spherical shell resonator microelectromechanical systems gyroscope fabricated using wafer-scale glassblowing. The gyroscope utilizes a 1-mm-diameter 10-μm-thick spherical isotropic shell surrounded by eight cofabricated satellite spheres serving as actuation and detection electrodes. To demonstrate functionality of the new device, a four-node wineglass mode at a 945-kHz frequency was utilized as the drive mode of a Coriolis vibratory gyroscope. The input rotation causes the transfer of energy from the drive mode to the sense mode, which is a complementary four-node wineglass mode oriented at a 45 ° angle. Sense-mode vibrations were capacitively detected using cofabricated 3-D metal electrodes. Experimental characterization of the spherical shell gyroscope demonstrated a wide linear range of 1000°/s, currently limited only by the experimental setup.

Three-Dimensional Spherical Shell Resonator Gyroscope Fabricated Using Wafer-Scale Glassblowing

This paper reports a 1.5 mm batch-fabricated polycrystalline diamond Cylindrical Resonator (CR) for gyroscope applications. The device is fabricated in a cylindrical shape using silicon on insulator (SOI) wafers and deep reactive ion etching (DRIE), which allows flexibility of choosing different geometries and materials for the resonator structure. A quality factor (Q) of 313,100 is measured at the 23 kHz 2 theta elliptical wineglass modes, producing a ring-down time of 4.32 seconds. Annealing CRs at 700 °C in a nitrogen atmosphere improved Q from 75,000 to over 300,000. The highly symmetric fabrication results in CRs with an excellent frequency mismatch of 3 Hz (130 ppm) between the 2 theta degenerate wineglass modes without applying any tuning voltage.

http://ieeexplore.ieee.org/iel7/7041251/7050861/07051080.pdf

Batch-fabricated high Q-factor microcrystalline diamond cylindrical resonator

Electronic gain error (EGE) is one of the most important error sources for whole-angle mode Coriolis Vibrating Gyros (CVG). This paper analyzes the influence mechanism of EGE on precession angle (θ) drift and proposes a simple novel method of EGE compensation for whole-angle mode CVG. It is demonstrated that this method can compensate EGE and characterize the damping asymmetry of CVG with high Q factor (million-order) conveniently. Additionally, the drift of the precession angle can be effectively suppressed after compensating EGE. Finally, the approach in this paper is also widely applicable to other inertial sensors equipped with multielectrodes, which may be useful for further researches on inertial sensors with high accuracy.

Electronic Gain Error Compensation For Whole-Angle Mode Coriolis Vibrating Gyroscopes With High Q Factor

The JPL Inertial Reference Unit (IRU) is the single most sophisticated assembly on the Cassini spacecraft. At the core of the IRU is the state-of-the-art, Litton Hemispherical Resonator Gyro (HRG). Launched in October 1997, Cassini's trajectory utilizes gravity assist maneuvers around Venus (two), Earth, and Jupiter over a seven year period, arriving at Saturn in June 2004. Its tour of the Saturnian system will last an additional four years. Although the Stellar Reference Unit (SRU) provides the ultimate reference for the spacecraft Attitude and Articulation Control System (AACS) and can be used to control the spacecraft under benign conditions, the Cassini IRU is essential during maneuvers and fault recovery operations, and for precision attitude stabilization during science data acquisition. Therefore, IRU reliability over the long Cassini mission is a critical concern. Following an extensive evaluation of possible alternatives, the Hemispherical Resonator Gyro (HRG) based IRU developed by Litton Guidance and Control Systems, was chosen for the Cassini mission. The HRG is an attitude rate sensor that has no physical wear-out mechanisms. Based on a principle first described by G. H. Bryan (1890) in his paper, 'On Beats in the Vibrations of a Revolving Cylinder or Bell', the HRG is created by vibrating a quartz resonator. This paper discusses the theory and modifications required to the design of the standard Space Inertial Reference Unit to adapt it to meet the requirements of the Cassini mission and the AACS interface. The Cassini mission is the first use of an IRU for a deep space planetary mission that does not use a spun-mass sensor.

Lennor L. Gresham

Papers

Hemispherical Resonator Gyro: an IRU for Cassini