Maximizing the rate sensitivity of resonating gyroscopes using nonlinear shape optimization

Abstract

In this work we demonstrate how one can improve the angular rate sensitivity of ring/disk resonating gyroscopes by tailoring their nonlinear behavior by systematic shaping of the gyroscope body and electrodes, and by the tuning of bias voltages on segmented electrodes. Of specific interest are the drive and sense mode Duffing nonlinearities, which limit their dynamic ranges, and the intermodal dispersive coupling between these modes that provides parametric amplification of the sense mode output signal. These two effects have the same physical origins and are in competition in terms of system performance, which naturally calls for optimization considerations. The present analysis is based on a systematic modeling of the nonlinear response of these devices by which we explore ways in which one can optimize the angular rate sensitivity by manipulating the mechanical and electrostatic contributions to the nonlinearities. In particular, non-uniform modifications of the gyroscope body thickness are employed to affect the mechanical contributions to these parameters, while the electrostatic components are manipulated via shaping of the resonator-electrode gap and by applying non-uniform bias voltages among segmented electrodes around the gyroscope body. These models predict that such relatively simple alterations can achieve improvements in gain by about an order of magnitude when compared to devices with uniform layouts.