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Schematic of Gyroscope
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This paper describes a procedure for identifying and correcting anisoinertia and anisoelasticity present in a micro-ring gyroscope. The major disadvantages of popular tuning methods such as mass trimming using laser ablation or focussed ion beam is that it can only be employed prior to packaging. Therefore tuning to correct for environmental or str...
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Citations
... The mode shapes and natural frequencies of a perfect axisymmetric ring are well known and are available in the literature [1], [5], [13], [16]–[18]. In the single axis ring gyroscope the modes are sensitive to angular velocities applied about the polar axis of the ring and the in-plane flexural modes of circumferential order are of practical interest [1]–[9]. ...
... The major benefit of employing an electrostatic scheme to minimize anisoinertia and anisoelasticity over the trimming techniques reported in [10]–[13] is that it may be performed and updated and does not produce permanent damage to the structure. The subject of electrostatic tuning of vibrating gyroscopes is available in the literature [2], [14]–[16]. While [2] does provide experimental evidence of electrostatic tuning, its does not however provide any procedural information or analysis. ...
... In addition, the procedure and analytical model are supported with extensive experimental results. Partial electrostatic tuning of a ring gyroscope is reported in [16]. The analysis presented does not illustrate the electrode arrangement required to completely remove the effect of structural imperfections and thus tune the natural frequencies. ...
This paper describes a procedure for identifying mass and stiffness imperfections present in a microring gyroscope. In general mass and stiffness imperfections will be present as a result of fabrication variances and will contribute to mistuning of the gyroscope. Both mass and stiffness imperfections are treated as perturbations of the ideal isotropic mass and stiffness. The mass and stiffness perturbations are combined to form a structural imperfection, which is shown to be determinable from Nyquist plots of the frequency response functions. An analysis of electrostatic "tuning" is presented and demonstrates that the nonlinear negative spring component produced from a particular arrangement of capacitive electrodes is capable of removing such structural imperfections. If uncorrected the structural imperfections would otherwise result in anisoinertia and anisoelasticity. A comparison between the theoretically predicted tuning voltage and the experimentally derived value is made and shown to be in agreement. The major advantage of electrostatic tuning is that it may be implemented on-chip during operation thus providing active tuning. This is in contrast to the trimming techniques employing laser ablation or focussed ion beam, which may only be done prepackaging.
This paper investigates the effects of resonator-electrode assembly errors on the electrostatic tuning ability in micro umbrella shell resonators. Theoretically analyzed the resonator-electrode capacitance effect, which refers to the stiffness adjustment of the shell by applying a voltage between the electrode and the shell. Then the electrostatic tuning models are established in the COMSOL Multiphysics, including spherical, cylindrical and bottom electrodes. Based on the electrostatic tuning models, two resonator-electrode assembly error models are established, including parallel moving error and tilting error, and the capacitance change between the resonator and the electrode caused by assembly errors is studied by finite element method. The simulation results show that the parallel moving error affects the electrostatic tuning ability of the spherical and cylindrical electrodes more than that of the bottom electrodes, while tilting error has less effects on the electrostatic tuning ability of the spherical and cylindrical electrodes compared with that of the bottom electrodes.
