A model-based approach to multi-modal mass tuning of a micro-scale resonator

The signal-to-noise ratio of axisymmetric vibratory gyroscopes is maximized when a pair of coriolis-coupled modes resonate at the same frequency. The manufacturing process of micro-scale resonators creates random minute mass and stiffness asymmetries that cause the natural frequencies of these modes to deviate from one another, thereby degrading sensor performance. One method of “tuning” these modal frequencies to equality involves using electrostatic forces to selectively soften the stiffness at points in the resonant structure. This generally requires large volume electronics that are incompatible with application requirements common to these sensors. Alternatively, modal frequency tuning by mass perturbation of the resonator is a promising approach because it is permanent and requires no ancillary electronics. In this paper, a novel micro-scale resonator is presented which lends itself to mass perturbation experiments. A resonator model, based on empirical frequency response data, is used to guide the mass perturbation process and demonstrates how multiple pairs of modes can be tuned.