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

## 1 Introduction to MEMS Gyro Modeling

Figure 1: Draper Tuning Fork Gyroscopes

MEMS gyroscopes rely on two principles. The first principle is the resonating vibration of the proof mass. The second principle is the Coriolis effect.

## 2 Mechanical Resonator[1]

The amplitude of a mechanical resonator can be described with the following equation

 $LaTeX: x=x_{0}e^{\lambda t}$ 'Amplitude of Vibration'

The properties are as follows

• $LaTeX: \mbox{Im} \left \{ \lambda \right \}$ is the frequency of vibration,
• $LaTeX: \mbox{Re} \left \{ \lambda \right \}$ is the time scale over which the amplitude decays due to energy losses, and
• $LaTeX: Q=\frac{W}{\Delta W}=\frac{\mbox{Im} \left \{ \lambda \right \}}{2 \mbox{Re} \left \{ \lambda \right \}}$ is the quality factor.

There are reasons for designing a MEMS gyro with a high Q

1. higher gain
2. narrow frequency response
3. lower energy loss per cycle

Therefore high Q leads to higher performance MEMS devices.

Modeling of the MEMS gyro principles is key to designing

• the geometry
• the chosen materials
• the resonant frequency

The Q is a result of these properties.

## 3 Thermo-Elastic Damping[2]

Anyone who has dealt with MEMS gyros has come across the fact that they are temperature sensitive. One engineer suggested that what you really bought was a thermometer that happened to put out a rate too.

Mechanical engineers are familiar with the idea that a material stiffness changes with temperature. The hotter a metal gets the softer it gets. On a MEMS scale where the mechanism is extremely small. Coupling of stress, strain, and temperature become a means for energy loss. This is referred to as Thermo-elastic Damping (TED).

The reference material provides a detailed set of equations and examples.

## 4 Resources

### 4.1 Notes

1. Thermoelastic Damping and Engineering for High Q MEMS Resonators, slides 5, 6
2. Thermoelastic Damping and Engineering for High Q MEMS Resonators, slides 7