Design and development of auto-parametrically resonating angular rate sensors

The main objective of this research is to develop single axis angular rate sensors that would be robust to variations in its operating voltage and frequencies. The sensors are developed to overcome the shortcomings, including narrow frequency bandwidths and unstable scale factors, of conventional mode-matched micromachined vibratory gyroscopes (MVGs) in open loop operations. The developed sensors utilize inherent forcing and inertial nonlinearities, arising from electrostatic forces and fabrication imperfections respectively, to auto-parametrically excite the sense mode via 2:1 (two-to-one) autoparametric resonance (AR) which yields a wider bandwidth frequency response for the sense mode of the sensor. In this dissertation, three such angular rate sensors based on 2:1 AR are designed, fabricated and tested. Three sensors are referred as auto-parametrically resonating angular rate sensors or shortly ARARS I, II, and III. The sensors are designed and analyzed, via Finite Element Analysis (FEA), using CoventorMP, MEMS+, and MATLAB tools. Nonlinear dynamics phenomena, including energy transfer between the modes due to 2:1 AR and saturation phenomenon, are first confirmed via FEA. The sensor designs are then fabricated using wafer-level vacuum encapsulated MIDIS process from Teledyne Dalsa. The nonlinear dynamics of the sensors are mathematically modeled, and their derived equations of motion are solved both numerically and using an approximate analytical technique or a perturbation method, namely the method of multiple time scales. The angular rate testing results of all three fabricated sensors are compared with state-of-the-art commercial single axis MVGs and with a previously developed angular rate sensor at Simon Fraser University. The sense mode's -3dB frequency bandwidth of 320.7 Hz, 301.6 Hz, and 507.8 Hz are experimentally achieved via 2:1 AR for ARARS I, II, and III respectively. The scale factors of 36.77 μV/°/s, 64.01 μV/°/s, and 52.86 μV/°/s with dynamic range of ±270 °/s, ±300 °/s, and ±330 °/s are experimentally obtained for ARARS I, II, and III respectively. The bias instability of ARARS I, II, and III are experimentally found to be 71.3 °/hr, 69.7 °/hr, and 6.4 °/hr respectively. ARARS I, II, and III demonstrate stable scale factors for a frequency mismatch, between the excitation and sense mode resonant frequencies, of 0.94%, 1.3%, and 2.5% respectively.