Download - Mechanical design of mems gyroscopes
Mechanical Design ofMEMS Gyroscopes
Ahmed MagdyAhmed Hussein
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII. Conclusion
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII. Conclusion
I. Ramp-Up
<=Analogy=>
I. Ramp-Up
I. Ramp-Up
"These analogies form the basis of analoguecomputers, aircraft simulators, etc. in whichreal-world mass-spring-damper type systemscan be simulated with the equivalentelectrical analogue circuit. In any suchsystem, if you know the values of m, c and kthen you can simulate that systemelectronically."
http://mathinsite.bmth.ac.uk/pdf/msdtheory.pdf
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII.Conclusion
II. Basic Mechanical Structure
• Based on Conservation of Momentum
- Coriolis Acceleration
aC = 2 Ωz × Vx
- 2 DOF System
SenseAccelerometer
Drive Oscillator
Mass
Suspension
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII. Conclusion
III. Linear Vibratory Gyroscopes• Examples of Linear System
• Linear Momentum is conserved
1. In-plane
- Motion is in the sameplane of the proof mass.
- Usually have a largethickness to reject out-of-plane modes.
=> Bulk Micromachining
Rotation: zDrive: xSense: y
III. Linear Vibratory Gyroscopes• Examples of Linear System
• Linear Momentum is conserved
2. Out-of-plane
- Sense Motion is normalto the plane of the mass.
- Usually have a smallthickness to allow out-of-plane deflection of thebeams.
=> Surface Micromachining
Rotation: yDrive: xSense: -z
III. Linear Vibratory Gyroscopes1. Linear Suspension Systems
III. Linear Vibratory Gyroscopes
1. Linear Suspension Systems
Notes- Symmetry between modes allows easily locating D and S modes
- It is needed to decouple the D and S modes
because Drive amplitude is much larger than
Sense Amplitude (around 2000 times larger)
Crab-leg Serpentine Hairpin H-Type U-Beam
Symmetry between modes(can make modes closer)
Better less less Better less
Mode decoupling(Isolation between D and S)
Not Good Not Good Not Good Better Better
Compliance in orthogonalDirections (causes coupling)
Same Same Same Different(Better)
Different(Better)
III. Linear Vibratory Gyroscopes
1. Linear Suspension Systems - Frame Structures
Drive Frame Implementation
III. Linear Vibratory Gyroscopes
1. Linear Suspension Systems - Frame Structures
Sense Frame Implementation
III. Linear Vibratory Gyroscopes
1. Linear Suspension Systems - Frame Structures
Anti-phase Systems
Note- For Differential mode detection, response to Coriolis forces are added, but
their common-mode response in the same direction are canceled out.
=> More resistance to Ambient Vibrations
Analogy<=>
III. Linear Vibratory Gyroscopes2. Linear Flexure Elements
Notes- Suspension systems are designed to be compliant along the desired motion
direction, and stiff in other directions.
- Large thickness can reject out-of-plane deflections
Fixed-Guided Folded Double-Folded
Linearity Low High Higher
AxialStiffness
ky ky/2 ky
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII. Conclusion
IV. Torsional Vibratory Gyroscopes
1. Torsional Suspension Systems• Main Components
- Rotational DriveOscillator
- Sense Mode Angular
Accelerometer
=> 2 DOF
• Angular Momentum is conserved
Gimbals
- Pivoted supports that allow the rotation of an axis about a single axis.
- Commonly used in Torsional Gyroscopes to decouple D and S modes.
IV. Torsional Vibratory Gyroscopes2. Torsional Flexure Elements
Out-of-plane deflections In-plane deflections
Achieved by torsional beamscombinations of guided beams
Interior Configuration Exterior Configuration
Advantages - Compact Dimensions Reduces Curling
Disadvantages -Stresses in the structurallayer can cause curling
Area Consuming
Uses Most CommonIn thick bulk
micromachined DevicesIn thin surface
micromachined devices
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII. Conclusion
V. Anisoelasticity and Quadrature Error
• The amplitude of the sense-mode response is extremelysmall.
=> Any small undesired coupling from the drive motionto the sense-mode could completely mask theCoriolis response.
• Suspension elements in real implementations haveelastic cross-coupling between their principal axes ofelasticity.
• This phenomenon is called anisoelasticity, and is theprimary cause of mechanical quadrature error ingyroscopes
And the Sense equation becomes:
Note: Ideally, kxy = kyx = 0 (because the suspension is symmetric), but
process variations and imperfections causes mismatch.
V. Anisoelasticity and Quadrature ErrorWithout Coupling
can be written as:
With Anisoelasticity:
V. Anisoelasticity and Quadrature ErrorCauses of Cross axial Stiffness
• Process Variations and Fabrication Imperfections
Caused by DRIE
Notes
- Two forces excites the sense mode, FC=2mCΩzVx and FQ=-kyxx
=> 90o phase difference exists between FC and FQ
=> Can be separated during demodulation
V. Anisoelasticity and Quadrature Error
It's desired to minimize the Quadrature component because:
• Dynamic Range of front-end electronics.
• Phase accuracy of demodulation should be very high.
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII. Conclusion
VI. Damping1. Viscous Damping
Slide Film Damping Squeeze Film Damping
Damping Depends on Area of the plate (A), vertical distance (d), properties of the fluid
VI. Damping2. Viscous Anisodamping
• Hydrodynamic lift:
when a plate slides over a viscous medium a force
orthogonal to the motion direction is generated.
=> Sense Equation:
• Anisodamping component is in phase with the corioliscomponent !! (Can't be removed during demodulation)
=> Vacuum packaging is required
VI. Damping3. Intrinsic Structural Damping
• Beams are not pure springs as a result of thermal energydissipation due to elastic deformations.
OUTLINE
I. Ramp-Up
II. Basic Mechanical Structure
III. Linear Vibratory Gyroscopes
IV. Torsional Vibratory Gyroscopes
V. Aniso-elasticity and Quadrature Error
VI. Damping
VII. Conclusion
VII. Conclusion
• Mass-spring System is very analogous to LCresonator, and this might help in simulation.
• Vibratory Gyro. is usually a 2 DOF mass-spring System.
• Coupling between D and S modes can occur by:
o Suspension (kxy).
o Anisodamping (cxy).
• Vacuum packaging is required to reduce damping.
References
[1] K. Craig, "Electrical mechanical analogy",http://multimechatronics.com/images/uploads/mech_n/Electrical_Mechanical_Analogy.pdf
[2] C. Acar, A.Shkel, "4 Mechanical design of MEMS gyroscopes," MEMS
Vibratory Gyroscopes, 1st ed., S. Senturia, R. Howe, A. Ricco, Ed :
New York, p.77-109, 2009.