Efficient and Sensitive Energy Harvesting Using Piezoelectric Compliant Mechanisms

Xiaokun Ma*Hong Goo Yeo†

Christopher D. Rahn*Susan Trolier-McKinstry†

*Department of Mechanical and Nuclear Engineering†Department of Materials Science and Engineering

The Pennsylvania State University

August 4th 2015

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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 on the order of

• Fragile thin films and structures Shock inputs can damage structure Self limiting design for robust performance (bump stops or bridges)

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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• Piezoelectric Compliant Mechanism (PCM) Design and Model

• PCM Quadratic Boundary Condition and Maximum Power Analysis

• Analysis Results (PZT)

• Experimental Results (PVDF)

• Conclusions and Future Work

Outline

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Impedance matching

Quadratic boundary condition

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PCM Design

No friction

Clamped => Reliable connection Bridge structure => Self-limiting design =>

Improve robustness

• Equation of motion

Boundary conditions:

Moment balance at : Shear balance at :

• Electrical circuit equation

Governing Equations

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Bending stiffness Mass

Strain rate damping

Air damping

Electrical coupling

Mechanical coupling

• Frequency domain model Transcendental transfer functions:

• Time domain model Eigenfunction:

Modal analysis:

PCM Model

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• Piezoelectric Compliant Mechanism (PCM) Design and Model

• PCM Quadratic Boundary Condition and Maximum Power Analysis

• Analysis Results (PZT)

• Experimental Results (PVDF)

• Conclusions and Future Work

Outline

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where , , and

PCM Quadratic Boundary ConditionUniform strain

throughout the PZTQuadratic

mode shapeShear force at is zeroMoment at is nonzero

must satisfy:

Boundary conditions at :

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Maximum Power Analysis• Mode shape efficiency

: obtained when the maximum strain in the PZT reaches its limit : obtained when the entire volume of the PZT is sinusoidally strained to its limit at a given

frequency

• Key assumptions Base excitation sinusoidally excites the structure at one frequency The entire PZT volume is uniformly strained to when excited by base acceleration at PZT is strained in 1 direction with field generated in the 3 direction ( mode) Load impedance is a resistor

Electrical circuit equation:𝐺 (𝑠)=

𝑉 (𝑠 )𝑆1(𝑠)

=𝐴h𝑝𝐸𝑝𝑑31𝑅𝑙 𝑠𝐴𝜀33

𝑆 𝑅𝑙 𝑠+h𝑝

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𝑆1 (𝑡 )=𝑆𝑙𝑖𝑚sin (𝜔𝑡 )𝑑𝑃𝑑𝑅 𝑙

=0

• Piezoelectric Compliant Mechanism (PCM) Design and Model

• PCM Quadratic Boundary Condition and Maximum Power Analysis

• Analysis Results (PZT)

• Experimental Results (PVDF)

• Conclusions and Future Work

Outline

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Frequency Domain Comparison

() ()Power

Sensitivity()

Max Strain Sensitivity

()(0.1% strain)

() ()Mode Shape

Efficiency

Proof Mass Cantilever 4.95 138 22.8 3.24% 21.7 106 20.5%

PCM 5.01 136 215 5.05% 84.3 107 78.6%

Voltage PowerRelative Tip Displacement

Proof Mass Cantilever

PCM

9x larger power

sensitivity

4x larger power with the same

maximum strain

4x higher mode shape

efficiency

Transcendental transfer functionState space model

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Time Domain ComparisonVoltage PowerTip Displacement

Proof Mass Cantilever

PCM

Wrist Acceleration During Running 1.75

10.7

Average Power() Running Jogging Walking

Proof Mass Cantilever 1.75 0.716 0.0247

PCM 10.7 3.60 0.0667

6x larger average power 13

• Piezoelectric Compliant Mechanism (PCM) Design and Model

• PCM Quadratic Boundary Condition and Maximum Power Analysis

• Analysis Results (PZT)

• Experimental Results (PVDF)

• Conclusions and Future Work

Outline

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Experimental Setup

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Tip Displacement Frequency Response

()Tip Displacement Sensitivity

()

Proof Mass Cantilever

Theory 5.22 0.179

Experiment 5.28 0.175

PCMTheory 5.02 0.0864

Experiment 5.13 0.0829

Proof Mass Cantilever PCM

Cantilever theoryCantilever experimentPCM theoryPCM experiment: optimal stiffness

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Voltage & Power Frequency Responses

Proof Mass Cantilever

PCM

Voltage Power

Cantilever theoryCantilever experimentPCM theoryPCM experiment: optimal stiffnessPCM experiment: lower stiffnessPCM experiment: higher stiffness 17

Mode Shape and Strain Distribution1st Mode Shape

Voltage Sensitivity

()

Power Sensitivity

()

Max Strain Sensitivity

()(1% Strain)

()(1% Strain)

() ()Mode Shape

Efficiency

Proof Mass Cantilever

Theory 154 4.50 3.29% 46.8 0.416 1.75 23.8%

Experiment 136 3.53 3.52% 38.6 0.285 16.3%

PCMTheory 90.5 1.56 1.05% 86.2 1.41 1.68 84.2%

Experiment 80.8 1.24 1.01% 80.0 1.22 72.4%

2x larger voltage with the same

maximum strain

4x larger power with the same

maximum strain

4x higher mode shape efficiency

Strain Distribution

Cantilever theoryCantilever experimentPCM theoryPCM experiment: optimal stiffnessPCM experiment: lower stiffnessPCM experiment: higher stiffness

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• Piezoelectric Compliant Mechanism (PCM) Design and Model

• PCM Quadratic Boundary Condition and Maximum Power Analysis

• Analysis Results (PZT)

• Experimental Results (PVDF)

• Conclusions and Future Work

Outline

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Conclusions and Future Work

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• Conclusions The PCM energy harvester can harvest energy within the bandwidth of human movement

without a large proof mass Careful stiffness tuning enforces a PCM quadratic boundary condition, making the PCM first

mode shape closer to a parabola and more efficient The PCM has 9 times higher power sensitivity at resonance and 6 times higher average power

in response to realistic base excitation input than the proof mass cantilever at the same damping ratio

The PCM generates twice more voltage and 4 times more power than the proof mass cantilever with the same maximum strain

The PCM improves mode shape efficiency by 4 times, from 20% to 80%

• Future Work Study the nonlinear effect of the PCM energy harvester under large base excitation Investigate the PCM energy harvester with an initially-curved or pre-buckled piezoelectric

beam

Thank you!21

• Acknowledgment The authors thank Shanshan Chen and Dr. John Lach in the University of Virginia for providing

the wrist acceleration data The authors thank Andrew Wilson for the help in the PCM energy harvester fabrication This work was supported by the National Science Foundation ASSIST Nanosystems ERC

under Award Number EEC-1160483