KEYWORDS: Sensors, Finite element methods, Motion models, Gyroscopes, Modeling and simulation, Signal processing, 3D modeling, Optimization (mathematics), Oscillators, Shape analysis
The focus of this paper is 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 coupled, mechanical oscillators representing the drive
and the sense unit. To minimize energy loss during operation, the device is connected at one single point to the
substrate. This kind of suspension is especially advantageous when choosing an antiphase torsional motion between the
drive and sense unit. Furthermore, temperature effects on the device characteristics are reduced. The drive unit is
typically excited in the frequency range of 10 to 15 kHz using electrostatic forces. To achieve optimized signal levels
the geometry of the sensor is completely parameterized. An analytical model is set up via the so-called deformation
algorithm applying the Ritz method. Next, the eigenfrequencies and mode shapes of the sensor were calculated. After
including the effects of the Coriolis force, the corresponding change in capacity of the sense unit is determined. An
advanced hill climbing algorithm is used varying two geometrical parameters simultaneously. This pair of parameters is
changed in such a way that the difference in drive and sense frequencies is fixed to 200 Hz. Based on this procedure an
optimized design could be found with an increase in signal levels of about 450% concerning an earlier version (e.g.
from 3 to 17 aF°/s). In addition, FEM (Finite Element Method) simulations are performed to check the analytically
calculated eigenfrequencies and mode shapes. Both approaches show comparable results.
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