2016 idetc

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)

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)

• Introduction




• 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)

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

(0.183% strain)()

(0.183% strain)() ()

Mode Shape Efficiency


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

• Introduction




• 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


PCM

𝒂𝒎𝒊𝒏 𝒂𝒎𝒂𝒙

Softening effect

Wide bandwidth harvests more energy

Stiffening effect

Cantilever experimentPCM experiment

• 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→ ∞

• Assumed mode:

• Time domain model:

PCM Time Domain Model

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A function of base excitation and voltage

Analytical 1st mode

• Introduction




• Conclusions

Outline

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Displacement DistributionsCantilever theoryCantilever experimentPCM theoryPCM experiment

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PCM

Large curvature near the clamped end

No longer parabolic

Bridge structure => Self-limiting design =>

Improved robustness

Strain DistributionsCantilever experimentPCM experiment

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PCM

Degrades and fails in less time

Uniform strain distribution

Max strain at the tip due to beam tip hinge causing max curvature

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

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

• Introduction




• 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

2016 idetc

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