Dynamics of ring-based CVGs including non-linear geometrical effects

Micro-Electro-Mechanical System (MEMS) ring-based Coriolis Vibrating Gyroscopes (CVGs) are devices that use vibration of micro-engineered thin rings to sense the angular rate of moving objects. High performance ring-based CVGs used in inertial navigation applications need to ensure the achievement of high sensitivity and improved signal-to-noise ratio. To achieve improved signal-to-noise ratio, ring-based resonators are designed to ensure low damping and mode-matching between drive and sense modes of vibration, and sensor sensitivity is improved by exciting the drive mode into large amplitude vibration. Large amplitude drive responses can cause the resonator to operate in a regime where geometrical non-linearity effects (i.e. non-linear strain-displacement relations) arise which have potential to alter sensor performance compared to a linear resonator operating at small amplitudes of vibration. This thesis investigates the effects of geometrical non-linearity on the performance of ringbased resonators supported by a generic number of identical supports uniformly spaced around the ring circumference. A mathematical model for the supported ring resonator is developed including ring non-linear flexural vibration and non-linear support stiffness. The equations of motion governing the dynamics of the drive and sense nθ modes of the resonator are developed and used to investigate the non-linear drive and sense responses at large drive amplitudes of vibration under practical operating conditions. The rotational symmetry of supported ring resonators operating at large amplitudes of vibration is investigated. The numbers of supports that maintain the rotational symmetry of a pair of nθ modes of vibration used to sense rotation are considered. This work illustrates that 8 supports maintain the rotational symmetry of practical ring-based resonators operating in the 2θ modes when the resonator operates in the linear regime, but break the symmetry when the ring is excited into large amplitudes. In contrast, 16 supports are shown to maintain the rotational symmetry regardless of the amplitude of vibration. The performance of ring-based CVGs having 8 and 16 supports are compared to investigate the impact on sensor performance. The sense mode response is determined when the ring is driven into large amplitudes of vibration, and the occurrence of quadrature errors and non-linear zero-rate-output response are investigated. Comparisons are made with an equivalent linear resonator in which ring and support geometrical non-linearity is neglected, to investigate non-linear amplification effects. Results illustrate that if the rotational symmetry of the resonator is broken, quadrature errors and non-linear zero-rate-output arise, which can adversely affect sensor performance by degrading the quality of rate measurement and by reducing sensor sensitivity. This work demonstrates that use of 16 supports for ring resonators operating in the 2θ modes mitigates non-linear effects and improves rate measurement. Support geometries that linearise the overall dynamic behaviour of the resonator are investigated and key results are validated against a non-linear Finite Element analysis