MEMS Gyro Modeling


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MEMS Gyro Modeling
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1 Introduction to MEMS Gyro Modeling

Figure 1: Draper Tuning Fork Gyroscopes
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[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