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Research Papers

The Power and Efficiency Limits of Piezoelectric Energy Harvesting

[+] Author and Article Information
Michael W. Shafer

Assistant Professor
College of Engineering,
Forestry, and Natural Sciences,
Northern Arizona University,
Flagstaff, AZ 86011
e-mail: michael.shafer@nau.edu

Ephrahim Garcia

Professor
Sibley School of Mechanical and
Aerospace Engineering,
Cornell University,
Ithaca, NY 14853
e-mail: eg84@cornell.edu

Loss factor is defined as the energy lost per radian divided by the peak strain energy. See Ref. [27], Sec. 2.7.

See Ref. [27], Sec. 2.6.

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 21, 2013; final manuscript received October 17, 2013; published online December 24, 2013. Assoc. Editor: Brian P. Mann.

J. Vib. Acoust 136(2), 021007 (Dec 24, 2013) (13 pages) Paper No: VIB-13-1022; doi: 10.1115/1.4025996 History: Received January 21, 2013; Revised October 17, 2013

The fundamental limits of cantilevered piezoelectric energy harvesters have not been well established. As with any other power generation technology, it is critical to establish the limits of power output and efficiency. Mathematical models for piezoelectric energy harvester power output have seen continued refinement, but these models have mainly been used and compared to individual harvester designs. Moreover, existing models all assume power scales with acceleration input, and take no account for the upper limit of the acceleration due to the ultimate strength of the piezoelectric material. Additionally, models for efficiency have been developed, but the limits have not been thoroughly explored. In this paper, we present the upper limits of input acceleration and output power for a piezoelectric harvester device. We then use these expressions, along with a previously developed ideal design method, to explore the upper limits of power production across a range of system masses and excitation frequencies. We also investigate general efficiency limits of these devices. We show the upper limit using an existing model and develop an alternate model that is applicable to excitation sources that are not capable of energy recovery.

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Figures

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Fig. 1

Fully laminated bimorph piezoelectric energy harvester

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Fig. 2

Circuit diagram for the standard piezoelectric harvester signal rectification and dissipation

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Fig. 3

Boundaries and energy flow in the energy harvesting system for the two assumptions surrounding energy transferred to the excitation source. Work of excitation source: We. Work done by harvester on load (harvested energy): Wh. Damped energy in harvester: Qd. Energy dissipated by excitation source due to inability to recapture We-: Qe.

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Fig. 4

Waveform of input power from base excitation

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Fig. 5

Efficiency for ζ = 0.01 for both conservative and nonconservative cases. Resonances at Ω = 1 and Ω=1+ke2 highlighted with dashed line.

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Fig. 6

Efficiency for ζ = 0.03 for both conservative and nonconservative cases. Resonances at Ω = 1 and Ω=1+ke2 highlighted with dashed line.

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Fig. 7

Efficiency for ζ = 0.05 for both conservative and nonconservative cases. Resonances at Ω = 1 and Ω=1+ke2 highlighted with dashed line.

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Fig. 8

Normalized nondimensional power and efficiency as a function of frequency ratio for ke2=0.6 at ζ = 0.03. Efficiency shown for both cases when excitation source is capable and is not capable of energy recovery.

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Fig. 9

(a) Efficiency as a function of ke2/ζ for Ω = 1, both for the conservative and nonconservative cases for all three damping ratios under consideration. (b) Deviations of the efficiencies for Ω=1+ke2 from the Ω = 1 result for the three damping ratios under consideration.

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Fig. 10

General diagram of harvester beam cross section

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Fig. 11

Maximum power for L/w = 1 and cML = 45.6 kg/m3. Low mass and natural frequency shown in (b) shows the results for systems of low mass and natural frequency.

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Fig. 12

Maximum power for L/w = 5 and cML = 45.6 kg/m3. Low mass and natural frequency shown in (b) shows the results for systems of low mass and natural frequency.

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Fig. 13

Maximum power for L/w = 10 and cML = 45.6 kg/m3. Low mass and natural frequency shown in (b) shows the results for systems of low mass and natural frequency.

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Fig. 14

Maximum power for L/w = 5 and cML = 364 kg/m3. Beams that are shorter relative their the mass. (b) Shows the results for systems of low mass and natural frequency.

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Fig. 15

Maximum power for L/w = 5 and cML = 5.69 kg/m3. Beams that are longer relative their the mass. (b) Shows the results for systems of low mass and natural frequency.

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