Analysis of temperature variation influence on Q-factor and mode-matching of 2-DOF vibratory rotational velocity sensor

J. Nazdrowicz, A. Napieralski
Lodz University of Technology,

Keywords: MEMS Vibratory Gyroscope, Q-factor, mode-matching, eigenfrequency


Temperature is the most important factor influences on MEMS vibratory gyroscope operational performance. It impacts either on geometry deformation or physical properties of the materials whole device composed of. For that reason device disigners should take into consideration target application of the device and enironmental limitation. In the paper authors pointed out the following considerations very important under temperature impact on whole device: - Spring coefficients of resonator and accelerometer variation, - Total damping coefficient change (consisted of slide and squeeze damping), - because of temperature expansion phenomena and Young’s modulus temperature dependency), - thermal expansion coefficient variation as temperature varies, - Young’s Modulus temperature dependency, - Geometry deformation, - Constant mass. Authors in this paper show method of simulation in multi-tools environment gyroscope with temperature dependency. Facts depicted above were entry point to create models in COMSOL (2-DOF) with two masses: inertial central mass and inertial frame. Based on natural frequencies calculation model representing operation of the gyroscope was created in Simulink environment. To automate calculation for different temperature, Simulink model was supported with Matlab script. Results obtained from FEM simulation were compared with these obtained from 2nd order equation results. Moreover FEM simulation results were used to calculate total spring coefficient which is very complex to calculate analytically with use well-known formulas. Because Q factor is crucial quantity in device performance assessment, it was calculated in dependency for both resonator and accelerometer (fig.2). The natural frequency and Q factor is used to simulate dynamics of gyroscope and compare magnitude and phase for different geometry configuration to find optimal geometry for good mode-matching.