Capacitive silicon micromachined gyro with mechanical coupling for sensitive signal reading 4

Figure 2 Sensitive acceleration generated under the influence of measured Coriolis force and mechanical coupling

Figure 3 Microgyroscope Structural Model Under Mechanical Coupling Influence

An approximate steady-state solution is obtained based on this coupled model

Among them, E2 is the stiffness coupling influence coefficient, which is related to the stiffness coupling coefficient kxy and the stiffness in the y-direction ky;

E3 is the damping coupling influence coefficient, related to the damping coupling coefficient Cxy and the quality factor Qy in the y-direction.

If the influence of in-phase damping in vacuum silicon gyroscopes is neglected, there must exist a moment t0 where the stiffness coupling effect is zero, such that

When φ1 is very small, the peak sensitive displacement should appear near t0. In gyroscopes with significant nonlinearity, the condition Ω=0 can also be used to locate the point with the minimum absolute value y2 as the zero reference point.

Figure 4 Stiffness-coupled electrical model

Figure 4 shows the electrical simulation model of a one-dimensional vibratory silicon micromachined gyroscope. L1, R1, and C1 represent the mass, damping, and stiffness in the driving axis direction, respectively. L2, R2, and C2 represent the mass, damping, and stiffness in the sensitive axis direction, respectively. V2 is equivalent to the driving force.

The voltage between C1 and C2 is equivalent to the displacement in the driving direction and the sensitive direction. V1 represents the rotational angular velocity. A1 differentiates the displacement in the driving direction to obtain velocity, and A11 performs a multiplication operation to yield the Coriolis force. A13 combines the stiffness coupling and the Coriolis force to form the driving force in the sensitive axis direction. This model can simulate the phase relationship between the sensitive output and the driving force V2 under different conditions. It can also study the phase relationship between stiffness coupling and the sensitive output. The approximate simulation in Figure 4 is primarily used for circuit design discussions.