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- 1. Mechanical Design ofMEMS Gyroscopes Ahmed Magdy Ahmed Hussein
- 2. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
- 3. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
- 4. I. Ramp-Up <=Analogy=>
- 5. I. Ramp-Up
- 6. I. Ramp-Up"These analogies form the basis of analogue computers, aircraft simulators, etc. in which real-world mass-spring-damper type systems can be simulated with the equivalent electrical analogue circuit. In any such system, if you know the values of m, c and k then you can simulate that system electronically." http://mathinsite.bmth.ac.uk/pdf/msdtheory.pdf
- 7. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII.Conclusion
- 8. II. Basic Mechanical Structure• Based on Conservation of Momentum- Coriolis Acceleration Sense Accelerometer Suspension aC = 2 Ωz × Vx- 2 DOF System Mass Drive Oscillator
- 9. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
- 10. III. Linear Vibratory Gyroscopes• Examples of Linear System 1. In-plane - Motion is in the same plane of the proof mass. - Usually have a large thickness to reject out-of- plane modes. Rotation: z Drive: x Sense: y => Bulk Micromachining• Linear Momentum is conserved
- 11. III. Linear Vibratory Gyroscopes• Examples of Linear System 2. Out-of-plane - Sense Motion is normal to the plane of the mass. - Usually have a small thickness to allow out-of- Rotation: y Drive: x plane deflection of the Sense: -z beams. => Surface Micromachining• Linear Momentum is conserved
- 12. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems
- 13. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems Crab-leg Serpentine Hairpin H-Type U-Beam Symmetry between modes Better less less Better less (can make modes closer) Mode decoupling Not Good Not Good Not Good Better Better(Isolation between D and S) Compliance in orthogonal Same Same Same Different DifferentDirections (causes coupling) (Better) (Better)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)
- 14. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems - Frame Structures Drive Frame Implementation
- 15. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems - Frame Structures Sense Frame Implementation
- 16. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems - Frame Structures Anti-phase Systems Analogy <=>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
- 17. III. Linear Vibratory Gyroscopes 2. Linear Flexure Elements Fixed-Guided Folded Double-FoldedLinearity Low High Higher Axial ky ky/2 kyStiffnessNotes- 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
- 18. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
- 19. IV. Torsional Vibratory Gyroscopes1. Torsional Suspension Systems• Main Components - Rotational Drive Oscillator - Sense Mode Angular Accelerometer => 2 DOF• Angular Momentum is conservedGimbals- Pivoted supports that allow the rotation of an axis about a single axis.- Commonly used in Torsional Gyroscopes to decouple D and S modes.
- 20. IV. Torsional Vibratory Gyroscopes2. Torsional Flexure Elements Out-of-plane deflections In-plane deflections combinations of guided beams Achieved by torsional beams Interior Configuration Exterior Configuration Advantages - Compact Dimensions Reduces Curling Stresses in the structuralDisadvantages - Area Consuming layer can cause curling In thick bulk In thin surface Uses Most Common micromachined Devices micromachined devices
- 21. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
- 22. V. Anisoelasticity and Quadrature Error• The amplitude of the sense-mode response is extremely small. => Any small undesired coupling from the drive motion to the sense-mode could completely mask the Coriolis response.• Suspension elements in real implementations have elastic cross-coupling between their principal axes of elasticity.• This phenomenon is called anisoelasticity, and is the primary cause of mechanical quadrature error in gyroscopes
- 23. V. Anisoelasticity and Quadrature ErrorWithout Couplingcan be written as:With Anisoelasticity:And the Sense equation becomes:Note: Ideally, kxy = kyx = 0 (because the suspension is symmetric), but process variations and imperfections causes mismatch.
- 24. V. Anisoelasticity and Quadrature Error Causes of Cross axial Stiffness• Process Variations and Fabrication Imperfections Caused by DRIENotes- Two forces excites the sense mode, FC=2mCΩzVx and FQ=-kyxx => 90o phase difference exists between FC and FQ => Can be separated during demodulation
- 25. V. Anisoelasticity and Quadrature ErrorIts desired to minimize the Quadrature component because:• Dynamic Range of front-end electronics.• Phase accuracy of demodulation should be very high.
- 26. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
- 27. VI. Damping1. Viscous Damping Slide Film Damping Squeeze Film DampingDamping Depends on Area of the plate (A), vertical distance (d), properties of the fluid
- 28. VI. Damping 2. 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 coriolis component !! (Cant be removed during demodulation) => Vacuum packaging is required
- 29. VI. Damping3. Intrinsic Structural Damping• Beams are not pure springs as a result of thermal energy dissipation due to elastic deformations.
- 30. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
- 31. VII. Conclusion• Mass-spring System is very analogous to LC resonator, 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.
- 32. 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.

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