Published on: **Mar 3, 2016**

- 1. Shyamsananth Madhavan G. K. Ananthasuresh Design of Force-amplifying Compliant Mechanisms for Resonant Accelerometers 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 1
- 2. OUTLINE COMPLIANT MECHANISMS (Force Amplification) RESONANT ACCELEROMETERS Application Prior works and Synthesis Methods of FaCMs Re-design of FaCMs with Selection Maps Structure of Resonant Sensor Requirement of an FaCM 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 Enhancement of Sensitivity of Resonant Accelerometer - Using an FaCM. Improvement in amplification of FaCM with retaining the Topology. 2
- 3. Resonant Accelerometer and Principles Measure inertial loads, acting within the specified operating range. Resonator beams actuated electro-statically at resonance . An external acceleration on proof- mass shifts the natural frequency of the resonator beam. Stress – stiffening effect or Axial – stiffening effect in Resonator Beam. Frequency shift measured through feed back circuit by detecting capacitance change. 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 F NEED FOR MECHANICAL AMPLIFICATION - MOTIVATION Electronic Noise dominates compared to Mechanical Noise Mechanical Signal is more sensitive for small changes of acceleration to be detected 3 4 2 2 4 2 2 ( , ) ( , ) ( , ) 0x w x t w x t w x t EI F A x x t Resonating Mode of the sensor Detect Capacitance Change
- 4. Preliminary works on Force Amplification Initial Mechanical Amplifiers: DaCMs Initial Design – Lever of Second Type Roessig(1995) and Su(2001). Multi-stage Lever –Su (2002). Pederson and Seshia (2004). Adapted from Claus. B. W. Pederson & Ashwin. A. Seshia (2004) 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 Adapted from Su and Yang (2001 and 2002 ) 4
- 5. Synthesis Method of FaCM Method to synthesize FaCMs Topology Optimization Solid Modeling in CAD 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 5 The axial force on the Resonant Beam to be Amplified for Applied External Acceleration Our Objective : Maximize Gradient Based Optimization Algorithm is utilized. out in F F
- 6. Objective Formulation for FaCMs Objective Function Sensitivity Analysis min Max Max Max Max (1) : : 0 (2) 0 1 out in out out out out in in T specified out out in in F A F K U K U F F subject to V V KU F KU F 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 0 1 0 1 0 ( ) ( ) ( ) penal penal penal Tout out in penal penal K k k k U U k U Gradient Based Optimization Algorithm: Svanberg’s MMA or Optimality Criteria. 6 In all Compliant Mechanisms, there are inherent stiffness present in Input and Output ends of the continuum.
- 7. Models of FaCMs: 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 DETF Single Beam Lever1: Based on Su (2001) Specifications: Proof mass:1080 µm × 1030 µm Suspension Beams: 100 µm × 12 µm Thickness : 25 µm 7
- 8. 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 FaCM1 FaCM2 Minimum beam width: 2.5 µm
- 9. 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 FaCM3 FaCM4 Parameters FaCM1 FaCM2 FaCM3 FaCM4 Lever nF 1.45 0.83 26 1.74 4.3 ∆f (Hz) 4 1 37 4.2 6.2
- 10. MICRO FABRICATION : Prototype 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 10
- 11. Re-Design of CMs: Selection Map Technique Selection Map Technique GUI tool for design of SISO compliant mechanisms. Considered as a black-box for users to redesign mechanisms based on the specifications. Involves resizing and reshaping the geometry of mechanism, same topology is retained. Alternative for shape and size optimization procedure. Background of Map technique involves determination (Spring-Lever) SL constants. Predominantly used in DaCMs, Inverters, Grippers, etc. Spring –Lever Model The kinetoelastic model of CMs. Relate the Force/Displacement at input to Displacement/Force at output using Intrinsic Stiffness parameter. Accounts the amplifying and force- transmission features. Represent the static behavior of an elastic structure by a single spring SL model : Developed by Girish Krishnan and G.K.Ananthasuresh Selection Map : Developed by Sudarshan Hegde and G.K.Ananthasuresh ii io i i T io oo o o K K Δx F = K K Δx F 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 11
- 12. Identification of Design Space in Resonant Accelerometer •Compliant Mechanism For Redesign: FaCM3 •Input Port: Proof-mass and FaCM interface •Output Port: FaCM and Resonator Interface •Input Stiffness: Proof-mass suspension stiffness •External Stiffness: Resonator Beam Stiffness 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 12
- 13. Add-in for Existing Selection Map Technique User-specifications in terms of force and displacement In resonant sensor, user -specifications Sensitivity of sensor Base-frequency of sensor Proof-mass area External and input stiffness. Add-in: Transformation of frequency inputs to force input. Specification variable: C Cm = C/Amass Specification Transformation Procedure 0 f f C g 2 2 sin sinh 2 cosh cos 0ab T b a ab a b Remaining Specifications: Static Analysis of the Structure fl = f0 (Cg+1) Use Exact Solution method for axially loaded beam to determine the axial load for given frequency. Axial Force = Fout External Stiffness = Axial Stiffness of Resonator •Resonator Beam: 180 μm × 4 μm × 25 μm, • f0 - 1 MHz, - 40 Hz to 60 Hz •Corresponding Fout - 2 μN to 3 μN f 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 13
- 14. Design Case - 1 Specification variables Min Max Fin (N) 4e-7 6e-7 xin (m) 8e-10 10e-9 Fout (N) 2e-6 3e-6 xout (m) 1e-11 1.2e-11 Kin (N/m) 50 50 Kext(N/m) 0 0 Width Increased from 2.5 to 3.4 µm 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 14
- 15. Design Case - 2 Specification variables Min Max Fin (N) 4e-7 6e-7 xin (m) 8e-10 10e-9 Fout (N) 2e-6 3e-6 xout (m) 1e-11 1.2e-11 Kin (N/m) 500 500 Kext(N/m) 0 0 Stretched 1.254 times in x-direction 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 15
- 16. Design Case - 3 Specification variables Min Max Fin (N) 4e-7 6e-7 xin (m) 9e-9 10e-9 Fout (N) 2e-6 3e-6 xout (m) 1e-11 1.2e-11 Kin (N/m) 50 50 Kext(N/m) 86000 86000 Impractical Specifications for feasible mechanism. 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 16
- 17. Comparison of New Mechanisms FaCM Frequency Shift (Hz) Amplification Factor Original 37 26 Case1 48 28.17 Case2 44 27.32 FaCMs – CAD model and simulated. Comparison of FaCMs based on sensitivity of the sensor using Pre-stressed Eigen analysis. 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 17
- 18. Conclusion Need of an FaCM in resonant sensing, defined design method and redesign method are presented. The synthesis of the mechanisms using topology optimization and Performance of FaCMs is above the existing levers with factor of Six. The redesign of the FaCM using the selection-map tool for a given set of user specifications provides further enhancement. 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 18
- 19. References: G. Krishnan and G. K. Ananthasuresh, “A systematic method for the objective evaluation and selection of compliant displacement amplifying mechanisms for sensor applications,” Journal of Mechanical Design, Vol. 130, no. 10, pp. 102304:1-9, 2008. C. Pedersen, and A. A. Seshia, “On the optimization of compliant force amplifier mechanisms for surface micromachined resonant accelerometers,” IOP Journal of Micromechanics and Microengineering, Vol. 14, No. 10, pp. 1281-1293, 2004. X. P. S. Su and H. S Yang, “Single Stage micro- leverage mechanism optimization in resonant accelerometer,” Structural Multidisciplinary Optimization, Vol.21, pp.246-252, 2000. S. Madhavan and G. K. Ananthasuresh, “Force-amplifying compliant mechanisms for micromachined resonant accelerometers,” The Proceedings of IFToMM Asian Conference on Mechanism and Machine Science, pp. 250027: 1- 7, 2010. Hegde, S., and Ananthasuresh, G. K., “Design of Single-Input-Single-Output Compliant Mechanisms for Practical Applications using Selection Maps,” Journal of Mechanical Design, Vol. 132, August, 2010, pp. 081007:1-8, 2010. 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 19
- 20. THANK YOU 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 1
- 21. QUESTIONS??? 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 21
- 22. Selection Map Procedure User-specifications Determine the SL constants Generate the 2D Map Represent the Existing Mechanism in the map Check the feasibility of mechanism Redesign of Mechanism No Required Mechanism Yes User Specifications •Input Force: •Input Displacement: •Output Force: •Output Displacement: •Actuator Stiffness at Input: •External Stiffness at Output: inL in inHF F F inL in inHx x x outL out outHF F F outL out outHx x x aL a aHk k k extL ext extHk k k Determine SL Constants: kci kco n in out a in ext out ci in F nF k x nk x k x out ext out co out in F k x k x nx Kci Kco n1 n2 7/2/2015 NaCoMM Presentation Compliant Mechanisms_139 22