Hemispherical Shell Resonators Research Articles

Microsacle PolySilicon Hemispherical Shell Resonating Gyroscopes with Integrated Three-dimensional Curved Electrodes

A novel approach for fabrication of polysilicon hemispherical resonator gyroscopes with integrated 3-D curved electrodes is developed and experimentally demonstrated. The 3-D polysilicon electrodes are integrated as a part of the hemispherical shell resonator’s fabrication process, and no extra assembly process are needed, ensuring the symmetry of the shell resonator. The fabrication process and materials used are compatible with the traditional semiconductor process, indicating the gyroscope has a high potential for mass production and commercial development. Without any trimming or tuning of the n=2 wineglass frequencies, a 28 kHz shell resonator demonstrates a 0.009% frequency mismatch between two degenerate wineglass modes, and a 13.6 kHz resonator shows a frequency split of 0.03%. The ring-down time of a fabricated resonator is 0.51 s, corresponding to a Q of 22000, at 0.01 Pa vacuum and room temperature. The prototype of the gyroscope is experimentally analyzed, and the scale factor of the gyro is 1.15 mV/°/s, the bias instability is 80 °/h.

Anchor Loss in Hemispherical Shell Resonators

Micromachined hemispherical shell resonators (HSRs) can be used in high accuracy vibratory gyroscopes. These resonators need to have very low energy loss to achieve very high quality factor. Energy might be lost through the anchor, fluid-structure interaction, thermoelastic dissipation, phonon-phonon and phonon-electron interactions, and the resonator surface. This paper investigates energy loss through the anchor of HSRs using a numerical approach. To numerically determine wave radiation from the anchor to the infinite substrate, a perfectly matched layer is used around a finite substrate. Anchor loss investigations in HSRs are classified into four categories. First, the effects of shell properties-material, geometry, and imperfections-are investigated. Second, the relationships between anchor loss and properties of the stem, such as material, geometry, and stemshell misalignments, are studied. Third, the effects of substrate characteristics-substrate material, attachment material between the stem and substrate, and attachment configuration of the substrate and stem-are investigated. Finally, the effects of external motions, such as shock and rotation, are analyzed. It is found that anchor loss in HSRs strongly depends on the shell, stem, and substrate properties. This study also shows that any imperfection in the shell or any misalignment between the shell and stem increases anchor loss by orders of magnitude.

Miniature hemispherical shell resonator with large-scale effective electrodes based on piezoelectric drive mechanism

Miniature resonators with three-dimensional curved surface are mostly driven by electrostatic capacitive. However, it is quite difficult to fabricate a curved surface electrostatic resonator with large-scale effective electrodes. This paper presents the first miniature hemispherical shell resonator with large-scale effective electrodes based on piezoelectric drive mechanism. The vibrating body and electrodes of the piezoelectric resonator are easily integrated without micro-scale or nano-scale narrow capacitive gap. Vibration experiment and finite element analysis both reveal that there exist seven significant vibration modes between 10 kHz and 100 kHz. Mode shape validation is also carried out by measuring the vibration velocity of upper perimeter and lateral perimeter with laser doppler vibrometer. Special vibration characteristics of each vibration mode are described in detail, based on which the resonator may be used for many specific applications. Compared with common electrostatic resonators, even smaller drive voltage applied to the piezoelectric resonator may produce larger vibration displacement at atmosphere. According to the experiment results, the resonator may provide a new way of realizing high performance three-dimensional miniature devices for communication and inertial navigation applications.

Hemispherical wineglass resonators fabricated from the microcrystalline diamond

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.

Vibration Character Analysis and Calculation for Hemispherical Resonator Gyro

Hemispherical Resonator Gyro is rotation-sensing instrument and has the merits of reliability and longevity etc. The precision of HRG is depended on the vibration character of hemispherical shells. Using the semi-analytic method, this paper discussed vibration character of hemispherical shell resonator and derived an algorithm of semi-analytic spherical elements. The method applies displacement function with toroidal analysis and axial discrete, so original two dimension problem is reduced to one dimension problem. The new method is very much simplified and can efficiently calculate the correlative physical character of hemispherical shell resonator, so it has high practical value for engineering application.