MEMS Gyro Modeling

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 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

See Also

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

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

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.