Mechanical design of mems gyroscopes

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Mechanical design of mems gyroscopes

  1. 1. Mechanical Design ofMEMS Gyroscopes Ahmed Magdy Ahmed Hussein
  2. 2. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
  3. 3. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
  4. 4. I. Ramp-Up <=Analogy=>
  5. 5. I. Ramp-Up
  6. 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. 7. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII.Conclusion
  8. 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. 9. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
  10. 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. 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. 12. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems
  13. 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. 14. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems - Frame Structures Drive Frame Implementation
  15. 15. III. Linear Vibratory Gyroscopes1. Linear Suspension Systems - Frame Structures Sense Frame Implementation
  16. 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. 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. 18. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
  19. 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. 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. 21. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
  22. 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. 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. 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. 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. 26. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
  27. 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. 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. 29. VI. Damping3. Intrinsic Structural Damping• Beams are not pure springs as a result of thermal energy dissipation due to elastic deformations.
  30. 30. OUTLINEI. Ramp-UpII. Basic Mechanical StructureIII. Linear Vibratory GyroscopesIV. Torsional Vibratory GyroscopesV. Aniso-elasticity and Quadrature ErrorVI. DampingVII. Conclusion
  31. 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. 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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