Analysis of Vibratory Gyroscopes: Drive and Sense Mode Resonance Shift by Coriolis Force

In this paper, we demonstrate the analysis of coupling between drive and sense systems of vibratory gyroscopes. Vibratory gyroscopes have attracted a lot of interest recently with the development of MEMS gyroscopes. These gyroscopes made their way through portable devices and smart phones. Novel gyroscope architectures have been proposed and analyzed in detail. However, in most of these analyses, coupling between the sense and drive systems was ignored. We analytically show that drive and sense systems are coupled together via Coriolis and centrifugal force. As a result, system resonances shift as the rotation rate increase for linear and torsional gyroscope systems. Starting from a simple gyro system, we calculated the sense and drive resonant frequency shifts in various configurations. Then, for more complex systems where analytical solution is difficult to obtain, we used commercially available FEM tools to determine corresponding frequency shift. In general, we found that the shift is small and can be ignored for linear vibratory gyroscopes where Q of the sense system is less than 2500 for mode matched gyros. But for higher Q systems, the frequency shift may affect the linearity of these gyroscopes. This sets a fundamental limit for the linearity of vibratory gyroscopes. Based on our calculations the non-linearity is above 1% for linear 2-DOF mode-matched vibratory gyroscopes where Q is above 3000 and for torsional 2-DOF vibratory gyroscopes where Q is above 600. Multi-DOF and ring vibratory gyroscopes are also examined. We find that the effect is less pronounced for Multi-DOF gyros, whereas there is a large effect on the linearity of ring gyroscopes.