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.