Vibratory MEMS Gyroscopes
 Vibratory MEMS Gyroscopes Sensors MEMS In order to prevent spam, users must register before they can edit or create articles.

## 1 Introduction to Vibratory MEMS Gyroscopes

Figure 1: Generic 2-axis mass-spring-damper model

All MEMS gyroscopes currently use vibrating proof masses. Those masses typically vibrate at a high frequency. As the sensor housing rotates in inertial space a Coriolis force is induced on the proof mass. The Coriolis force causes a vibration in an orthogonal plane and the amplitude of the orthogonal motion can be measured.

## 2 Operating Principle of MEMS vibratory gyros[1]

A simplified model of vibratory gyros is shown in Figure 1. The system has 2 orthogonal vibration modes; one mode corresponds to the vibration of the mass in the x-direction, the other the y-direction. The vibration frequency of the x-axis is ωx and the equivalent for the y-axis is ωy. Typically ωx is almost equal to ωy.

When powered on, the mass is driven in the x-direction with a driving frequency ωd which is close to ωy. When the entire MEMS gyro is rotated about the z-axis (out of the plane of the screen), an alternating force in the y-direction is caused by the Coriolis force. The amplitude of this vibration in the y-direction is used as a measure of the angular rate.

All MEMS gyroscopes use the Coriolis effect.

 $LaTeX: F=2M\nu \times \Omega$

where:

$LaTeX: F$ is the force of the proof mass,
$LaTeX: M$ is the proof mass,
$LaTeX: \nu$ is the velocity of the mass, and
$LaTeX: \Omega$ is the angular velocity of the reference frame (or sensor housing).

### 2.1 The role of mechanical resonance in vibratory gyros

Figure 1: Draper Tuning Fork Gyroscopes

The Coriolis force is typically weak. As a result mechanical resonance is used to amplify the motion and thus keep the signal to noise ratio high over the desired bandwidth. The driving frequency, ωd, and the 2 resonance frequencies, ωx and ωy, must be designed carefully.

## 3 Types of Resonating MEMS Gyroscopes[2]

All MEMS gyros require a resonating mass. The most common types of resonating MEMS gyros are

• Tuning Fork Gyros (TFG)
• Hemispherical Resonating Gryo (HRG) or Wine Glass Resonator Gyro
• Vibrating-Wheel Gyros
• Foucault Pendulum Gyros

## 4 Resources

### 4.1 Notes

1. Boa, pp. 16-19
2. Sensormag