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Piezoelectric Compliant MechanismEnergy Harvesters
Excited Under Large Base AccelerationsXiaokun Ma*
Susan Trolier-McKinstry†Christopher D. Rahn*
*Department of Mechanical and Nuclear Engineering†Department of Materials Science and Engineering
The Pennsylvania State University
August 22nd 2016
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• Introduction
• Piezoelectric Compliant Mechanism (PCM) Under Small Base Excitation Review
• PCM Nonlinear Model
• PCM Under Large Base Excitation Results
• Conclusions
Outline
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• Weak base excitation Low frequency (< 10 ) Low amplitude (< 1)
• Shock rather than vibration inputs Broad band (not tonal) frequency distribution Potential for damage due to large shocks
• Small footprint required on the order of
Energy Harvesting from Human MotionHas Unique Challenges
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Acceleration
Wrist acceleration data during running(Lach, 2013, University of Virginia)
Dominant motion frequency of common human activities(Gorlatova, 2013, Columbia University)
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Impulse-excited energy harvester(Pillatsch, 2012, Smart Materials and Structures)
Piezoelectric Energy Harvesting Devices
Bimorph cantilever with a tip proof mass(Erturk, 2009, Smart Materials and Structures)
Buckled slender bridges(Jung, 2010, Applied Physics Letters)
Alternative beam geometries(Roundy, 2005, Pervasive Computing)
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• Proof mass cantilever (Ajitsaria2007, Renaud2007, Erturk2008, Xue2008, Erturk2009, Shen2015)
• Magnetically actuated beams (Kulah2008, Zorlu2011, Pillatsch2012, Pillatsch2013)
• Frequency up-conversion devices (Jung2010, Gu2011, Galchev2012, Liu2012)
• Improving strain uniformity in cantilever (Glynne-Jones2001, White2001, Roundy2005)
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• Introduction
• Piezoelectric Compliant Mechanism (PCM) Under Small Base Excitation Review
• PCM Nonlinear Model
• PCM Under Large Base Excitation Results
• Conclusions
Outline
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Impedance matching
Quadratic boundary condition
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PCM Design
Clamped => Reliable connection
Bridge structure => Self-limiting design =>
Improve robustness
PCM energy harvester(Ma, 2016, Journal of Vibration and Acoustics)
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Experimental Setup
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Proof Mass Cantilever
PCM
Voltage Power
PCM theoryPCM experiment: optimal stiffnessPCM experiment: lower stiffnessPCM experiment: higher stiffness 8/21
Cantilever theoryCantilever experiment
Optimal stiffness produces
max power
Linear Model Validation:Voltage & Power
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(0.183% strain)()
(0.183% strain)() ()
Mode Shape Efficiency
Proof Mass Cantilever
Theory 5.62 6.02 21.0 28.6%
Experiment 4.72 4.24 20.2%
PCMTheory 10.3 20.2 20.2 99.9%
Experiment 9.06 15.6 77.4%
2x larger voltage with the same
max strain
4x larger power with the same
max strain
4x higher mode shape efficiency
1st Mode Shape Strain Distribution
Cantilever theoryCantilever experimentPCM theoryPCM experiment: optimal stiffnessPCM experiment: lower stiffnessPCM experiment: higher stiffness
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PCM with optimal stiffness has most uniform strain
Linear Model Validation:Displacement & Strain
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• Introduction
• Piezoelectric Compliant Mechanism (PCM) Under Small Base Excitation Review
• PCM Nonlinear Model
• PCM Under Large Base Excitation Results
• Conclusions
Outline
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• Maximum power is obtained under large base excitations• Linear model is only valid for small displacements• The compliant mechanism introduces a stretching effect under large excitations, which may enhance the
generated power
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Understanding Nonlinearity: The Key to High Power Harvester Design
Proof Mass Cantilever
PCM
𝒂𝒎𝒊𝒏 𝒂𝒎𝒂𝒙
Softening effect
Wide bandwidth harvests more energy
Stiffening effect
Cantilever experimentPCM experiment
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• Nonlinear axial strain
PCM Nonlinear Governing Equations
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Strain due to stretching
Strain due to bending
• Equation of motion
• Electrical circuit equation
Mechanical coupling
Axial stretchingLarge curvature
for the pinned-pinned beam
𝑘→ ∞
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• Assumed mode:
• Time domain model:
PCM Time Domain Model
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A function of base excitation and voltage
Analytical 1st mode
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• Introduction
• Piezoelectric Compliant Mechanism (PCM) Under Small Base Excitation Review
• PCM Nonlinear Model
• PCM Under Large Base Excitation Results
• Conclusions
Outline
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Displacement DistributionsCantilever theoryCantilever experimentPCM theoryPCM experiment
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𝒂𝒎𝒊𝒏 𝒂𝒎𝒂𝒙
Proof Mass Cantilever
PCM
Large curvature near the clamped end
No longer parabolic
Bridge structure => Self-limiting design =>
Improved robustness
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Strain DistributionsCantilever experimentPCM experiment
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𝒂𝒎𝒊𝒏 𝒂𝒎𝒂𝒙
Proof Mass Cantilever
PCM
Degrades and fails in less time
Uniform strain distribution
Max strain at the tip due to beam tip hinge causing max curvature
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Power & Power-Strain Sensitivity
Cantilever theoryCantilever experimentPCM theoryPCM experiment
Larger axial stretching
strain
Worse mode shape 17/21
3.5x larger power under the same max strain
Around 2x larger power under the same max strain
Power mismatch increases due to changing mode shape at high accelerations
The PCM outperforms cantilever
above
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Model Mismatch at Large Base Excitation𝒂𝒎𝒊𝒏 𝒂𝒎𝒂𝒙
Time Domain
Frequency Domain
Linear, single mode response with minimal harmonics
PCM theoryPCM experiment
Higher harmonics in the experimental frequency response
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Mode shape mismatch
Voltage dips in the experimental time response
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• Introduction
• Piezoelectric Compliant Mechanism (PCM) Under Small Base Excitation Review
• PCM Nonlinear Model
• PCM Under Large Base Excitation Results
• Conclusions
Outline
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Conclusions The PCM energy harvester shows a stiffening effect
The PCM has a much wider bandwidth than the proof mass cantilever
The PCM tip displacement is smaller than the proof mass cantilever midpoint displacement
The PCM is experimentally demonstrated to produce 50% more power than the proof mass cantilever at 0.31g base acceleration
The PCM generates 2x more power than the proof mass cantilever with the same maximum strain
Potential for uniform strain design at large amplitude
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• AcknowledgmentThis work was supported by the National Science Foundation ASSIST Nanosystems ERC under Award Number EEC-1160483
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Thank you!
Hammond Building @ PSU