Optimizing the performance of a Coriolis-based angular rate sensor applying an analytical approach

This paper focuses on the optimization of a novel angular rate sensor element based on the Coriolis force working principle. The device is resonantly excited and consists of two mechanically coupled oscillators representing the drive and the sense unit. In order to minimize energy losses during operation, the device employs a single point suspension to the substrate. This is especially advantageous when choosing an antiphase torsional motion for the sense mode. Furthermore, thermally-induced stress resulting in undesired drift effects of the device is minimized. The excitation frequency of the electrostatic drive unit was chosen to be in the range from 10 to 15 kHz, according to automotive requirements. The optimization process started with a complete parameterization of the sensor geometry, providing the basis for an analytical model. This was set up via the so-called deformation algorithm, applying the Ritz method. Next, the eigenfrequencies and mode shapes of the sensor were calculated analytically and compared with FEM results. The inclusion of the Coriolis force induced response of the sense unit yielded signal values from the differential capacitive pickup. An advanced hill climbing algorithm was used, varying two geometrical parameters simultaneously in such a way that the difference in drive and sense frequencies was kept at a constant value of 200 Hz. Based on this procedure an optimized design was found with an increase in signal level of about 450% as compared to earlier versions (e.g. from 3 to 17 aF/°/s). In a last step, fabrication related perforation holes which are typical for surface micromachined devices were included in the model. For this configuration, a frequency matching step was performed by FEM calculations. Resulting stiffness values were fed into the analytical model yielding a final output signal of the sensor of 16 aF/°/s.