DETECTION OF UNSYMMETRICAL FAULTS IN TRANSMISSION LINES USING PHASOR MEASUREM...
NaCoMM Final
1. Shyamsananth Madhavan
G. K. Ananthasuresh
Design of Force-amplifying Compliant Mechanisms
for Resonant Accelerometers
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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
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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.
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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)
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Adapted from Su and Yang (2001 and 2002 )
4
5. Synthesis Method of FaCM
Method to synthesize FaCMs
Topology Optimization
Solid Modeling in CAD
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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
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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:
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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
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
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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
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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
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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
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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
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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.
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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.
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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.
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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.
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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
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