Nonlinear Piezolectric Generators

1
Nonlinear Piezolectric Generators
Francesco Cottone

• N.i.P.S Laboratory Workshop
• Perugia, 10-03-2007
• Castello di Monterone (PG)

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Outline

• Introduction mobile powering issues
• Present Vibration Piezoelectric Power Generators
• Non-linear piezo-osclillator models
• numerical result (Matlab)
• finite elements modelling of linear and
  non-linear oscillators (Comsol)
• Conclusions and forthcoming work

3
Mobile powering
Wireless Sensor Network
source
Streaming Data to/from the Physical World
destination
Multihop Networking
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Applications exsamples of WSN

• Environmental Monitoring
• Habitat Monitoring
• Integrated Biology
• Structural Monitoring

• Interactive and Control
• RFID
• Medical biosensors
• Emergency medial response
• Pursuer-Evader
• Intrusion Detection
• Automation
• Interactive museum exhibits
• Military applications

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Goal requirements for mobile sensors powering

• Small (lt1cm3)
• Lightweight (lt100 gr)
• Low Power (lt100 µW)
• Long-lasting (2-10 yr)
• Inexpensive (lt1 )
• Low data rate
• wireless platforms
• Flexibility

Spec 6/2003 Mote on a chip INTEL
Present (cubic centimeter)
Future (cubic sub-millimeter sub-micrometer)
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Comparison onEnergy and Power sources
S. Roundy 2
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Batteries Vs Renewable Energy Sources
S. Roundy 1
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Batteries Vs Renewable Energy Sources

• If outdoor sunlight, or relatively intense indoor
  light it available, solar cells appear to be the
  best alternative.
• Solar cells are a mature technology and a mature
  research area.
• If projected lifetime is longer than 1 year,
  vibrations offer an attractive alternative for
  certain environments. It was therefore decided
  to pursue research into the conversion of
  vibrations to electricity.

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Vibrations Noise as Energy source
Base of Milling Machine
Microwave Oven Casing
Displacement vs. Frequency
Displacement vs. Frequency
Acceleration vs. Frequency
Acceleration vs. Frequency
S. Roundy 1
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Existing methods for vibration energy scavenging
Capacitive Change in capacitance causes either
voltage or charge increase.
Inductive Coil moves through magnetic field
causing current in wire.

• Piezoelectric
• Strain in piezoelectric
• material causes a charge
• separation (voltage across
• capacitor)

Amirtharajah et. al., 1998
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Energy storage density comparison

• Electrostatic transducers are more readily
  implemented in standard micro-machining
  processes.
• Electrostatic transducers require a separate
  voltage source (such as a battery) to begin the
  conversion cycle.
• Electromagnetic transducers typically output AC
  voltages well below 1 volt in magnitude (too low
  power density)

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Piezoelectric Mechanical-electrical conversion
Constitutive Equations
d strain s stress Y Youngs modulus d
piezoelectric coeff. D electrical
displacement e dielectric constant E electric
field
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Piezoelectric Converters
Where k equivalent spring stiffness of beam
m attached proof mass bm damping
coefficient a1 geometric constant a2
geometric constant d31 piezoelectric
coefficient tc thickness of one
piezo-ceramic layer VR voltage across load
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MEMS µPG PIEZO at micron scale
4 N. E. duToit et al. Cambridge MIT-Institute
2005
3 Y. Ammar et al. TIMA Lab Grenoble VIBES
project, october 2005
2
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Simple linear model of mechanical to electrical
energy conversion

• If acceleration magnitude is relatively constant
  with frequency, output power is inversely
  proportional to frequency.
• There is an optimal level of electrically induced
  damping that is designable.
• It is better to have too much electrical damping
  than too little.

z transducer displacement y magnitude of input
damping
Power assuming w wn. A acceleration
amplitude of input vibrations m proof mass
Wiliams and Yates 6
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Power efficiency of piezoelectric generators
S. Roundy et. Al, Pervasive Computing, 2005

• Narrow frequency
• Actively and passive tuning resonance frequency
  of generator
• Wide bandwith designs
• Proof mass m
• Improve the strain from a given mass
• Coupling coefficient k31
• Thin-film piezoelectric-material properties

for
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The Idea Non-linear oscillators!!
Bi-stable systems
barrier
Piezo Inverted pendulum
w
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Non-linear oscillators numerical simulations
Piezo Beam in a non-linear potential
Exponentially correlated gaussian noise
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Non-linear oscillators numerical simulations
Piezo Beam in a non-linear potential
Parametric Duffing-like stochastic differential
equation (no analytical solution)
Alphagt0
Alphalt0
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Non-linear oscillators numerical simulations
Piezo Beam in a non-linear potential
piezo_inv_pend19_23_02_07.png
beta7.3e10 (max Pv/Pi0.13)
Source exp. correlated gaussian noise Tau0.1s
Efficiency increased more than 4 times of
monostable well case (the increase depends
strongly by bandwith of the vibration source)
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Non-linear oscillators numerical simulations
Piezo Beam in a non-linear potential
piezo_inv_pend12_31_1_07b.png Beta7.3e10
Source colored gaussian noise Corr. Time
Tau0.01s
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Non-linear oscillators numerical simulations
Piezo Beam in a non-linear potential
piezo_inv_pend19_21_02_07_beta.png Pv/Pi(alpha,bet
a) noise sigma1 (max Pv/Pi0.13)
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2D Finite Element Model of inverted
piezo-pendulum
f16.58Hz first resonance mode
Frequency response
Harmonic excitation force _at_ first mode frequency
20000 dof
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2D FEM of an inverted piezo-pendulum
Harmonic Excitation at 6.58Hz
broadening of the resonance peak
W0.1
W0.001
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2D FEM of a magnetic piezo pendulum
Gaussian Noise Excitation µ0 s0.5 - 1 Fs100Hz
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2D FEM of an inverted pendulum
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Energy Efficiency

• Noise Excitation
• Increment up to thirty times when the barrier
  height increase relative to no barrier case
• Harmonic Excitation
• not so much improvement relative to the situation
  of a tuned external force at resonance frequency
• almost one order of magnitude relative to out of
  resonance excitation

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2D FEM of a bi-stable membrane
vertical compression
Differential Pressure

• Stainless steel membrane of 1mm thickness and
  20mm length
• contracting clamping of 0.1mm we induce bistable
  response on displacement when we applicate
  external force (for example harmonic)

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2D FEM of a bi-stable membrane

• Possible applications
• Piezoelectric micro generator
• Using PZT material for membrane
• Pressure sensor
• Actual pressure sensors are based on position
  measurement of the membrane so they are affected
  by aging of material therefore a decalibration in
  time

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Preliminary experimental test
Experimental Setup of driven piezo inverted
pendulum
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Preliminary experimental test
digital simulation and preliminary exp. results
System response to simulated floor vibration
with different spectral properties.
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Conclusions

• Piezoelectric converters appear to be the most
  attractive for meso-scale devices with a maximum
  demonstrated power density of approximately 200
  mW/cm3 vs. 100 mW/cm3 for capacitive MEMS
  devices.
• If external excitation is harmonic and its tuned
  to resonance frequency of the device we can
  obtain high mechanical energy transfer but it is
  possible to reach it even with a bi-stability
  dynamics
• For an external excitation with noise or out of
  resonance, FEA shows that a non-linear bistable
  beahviour amplify up to a factor 30 or more the
  vibrational energy extraction
• Most of vibrational energy sources live al
  relative low frequency (for example near hundred
  Hz) so its hard to tune the resonance mode of
  the device to external frequencies

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Forthcoming works

• We must compare FEA data with further
  experimental measurements for macro and
  sub-millimetric piezo generators
• Scalability is an important issue for
  micropowering
• We want to implement a real sub-centimeter and
  sub-millimeter prototype and characterize its
  power conversion capability
• in order to optimize energy harvesting we need to
• investigate new piezo material with high quality
  factor and high piezoelectric couling constant
• characterize response at various vibrational
  sources

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Bibliography

• S. Roundy, P.K. wright, and J. Rabaey, Energy
  Sacvenging for Wireless Sensor Networks with
  Special Focus on Vibrations, Kluwer Academic
  Press, 2003.
• S. Roundy et al., Improving Power Output for
  Vibration-Based Energy Scavengers, Pervasive
  Computing IEEE 2005.
• 3 Y. Ammar et al. TIMA Lab Grenoble EUSAI
  conference
• N. E. duToit et al. Cambridge MIT-Institute 2005
• S. Roundy et al. A study of low level vibration,
  Computer Communication 2003
• Wiliams, Yates, Analysis of a micro-electric
  generator for microsystems, proceeding of the
  Trasducers 95/Eurosensors (1995) 687-695
• www.intel.com
• http//www.ife.ee.ethz.ch/tvonbuer/energyharvesti
  ng_links.html
• http//www.darpa.mil/mto/mpg/index.html