1 Introduction to MEMS Gyro Modeling
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
|'Amplitude of Vibration'|
The properties are as follows
- is the frequency of vibration,
- is the time scale over which the amplitude decays due to energy losses, and
- is the quality factor.
There are reasons for designing a MEMS gyro with a high Q
- higher gain
- narrow frequency response
- 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.
- Mohite, S., Patil, N., Pratap, R., "Design, modeling and simulation of vibratory micromachined gyroscopes.", Journal of Physics: Conference Series 34 (2006), pp. 757-763.
- Thermoelastic Damping and Engineering for High Q MEMS Resonators
- Boa, M. 2004 Micro Mechanical Transducers. 2nd. Elsevier. ISBN 044450558X
- Gaura, E., and Newman, R 2006 Smart MEMS and Sensor Systems. 1st. Imperial College Press. ISBN 1860944930
- Thermoelastic Damping and Engineering for High Q MEMS Resonators, slides 5, 6
- Thermoelastic Damping and Engineering for High Q MEMS Resonators, slides 7