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Research Papers

Energy Harvesting From the Vibrations of Rotating Systems

[+] Author and Article Information
Christopher G. Cooley

Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: chris.cooley@siu.edu

Tan Chai

Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: tchai@siu.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 11, 2016; final manuscript received September 11, 2017; published online October 20, 2017. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 140(2), 021010 (Oct 20, 2017) (11 pages) Paper No: VIB-16-1588; doi: 10.1115/1.4038106 History: Received December 11, 2016; Revised September 11, 2017

This study investigates the vibration of and power harvested by typical electromagnetic and piezoelectric vibration energy harvesters when applied to vibrating host systems that rotate at constant speed. The governing equations for these electromechanically coupled devices are derived using Newtonian mechanics and Kirchhoff's voltage law. The natural frequency for these devices is speed-dependent due to the centripetal acceleration from their constant rotation. Resonance diagrams are used to identify excitation frequencies and speeds where these energy harvesters have large amplitude vibration and power harvested. Closed-form solutions are derived for the steady-state response and power harvested. These devices have multifrequency dynamic response due to the combined vibration and rotation of the host system. Multiple resonances are possible. The average power harvested over one oscillation cycle is calculated for a wide range of operating conditions. Electromagnetic devices have a local maximum in average harvested power that occurs near a specific excitation frequency and rotation speed. Piezoelectric devices, depending on their mechanical damping, can have two local maxima of average power harvested. Although these maxima are sensitive to small changes in the excitation frequency, they are much less sensitive to small changes in rotation speed.

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Figures

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Fig. 1

Schematic of a (a) rotating host system with prescribed translation y(t), (b) electromagnetic vibration energy harvester, and (c) piezoelectric vibration energy harvester

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Fig. 2

(a) Resonance diagram for rotating electromagnetic vibration energy harvesters at (a) ω = 0.5 and varying nondimensional rotation speed and (b) Ω = 0.3 and varying nondimensional excitation frequency. The solid lines are the device's natural frequency. The dashed (red) lines are excitation frequencies at |Ω±ω|. The device has ζ = β = 0.01 and ρ = 10.

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Fig. 3

Nondimensional dynamic response amplitude and phase for the electromagnetic vibration energy harvester at ω = 0.50 for varying nondimensional rotation speed. The dotted (red) and dashed (blue) lines are the response amplitudes A2,1 and phase angles χ2,1 at frequencies Ω ± ω, respectively. The solid (black) line is the rms of the response calculated from Arms=A12+A22. The device has ζ = β = 0.01 and ρ = 10.

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Fig. 4

Nondimensional dynamic response amplitude and phase for the electromagnetic vibration energy harvester at Ω = 0.30 for varying nondimensional excitation frequency. The dotted (red) and dashed (blue) lines are response amplitudes A2,1 and phase angles χ2,1 at frequencies Ω ± ω, respectively. The solid (black) line is the rms calculated from Arms=A12+A22. The device has ζ = β = 0.01 and ρ = 10.

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Fig. 5

Nondimensional average power harvested by the electromagnetic vibration energy harvester at ω = 0.50 for varying nondimensional rotation speed. The device has ζ = β = 0.01 and ρ = 10.

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Fig. 6

Nondimensional average power harvested for the electromagnetic vibration energy harvester at Ω = 0.30 for varying nondimensional excitation frequency. The device has ζ = β = 0.01 and ρ = 10.

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Fig. 7

(a) Contour plot of the nondimensional average power harvested by the electromagnetic vibration energy harvester for varying nondimensional rotation speed and excitation frequency. (b) Region shown by the dashed (red) line in (a). The device has ζ = β = 0.01 and ρ = 10.

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Fig. 8

Maximum nondimensional average power harvested by an electromagnetic device for varying nondimensional viscous damping coefficient. The solid line is the maxima for the rotating device. The circle markers are maxima for the stationary device.

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Fig. 9

Nondimensional (a) electrical damping coefficient, (b) excitation frequency, and (c) rotation speed at the maximum average power harvested by an electromagnetic device for varying nondimensional viscous damping coefficient. The circle markers in (a) are results for an identical stationary device. The dotted (red) lines are (a) β = ζ, (b) ω=2, and (c) Ω=2/2.

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Fig. 10

Nondimensional natural frequencies of rotating piezoelectric vibration energy harvesters with α = 0.1, 1, 10 for varying nondimensional rotation speed. The dashed (red) lines are excitation frequencies |Ω±ω|. The device has ζ = 0.01, γ = 0.2, and ρ = 10.

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Fig. 11

Contour plots of the rms of the nondimensional (a) proof mass deflection Urms=U12+U22 and (b) electric circuit voltage Vrms=V12+V22 for the spinning piezoelectric vibration energy harvester for varying nondimensional rotation speed Ω and excitation frequency ω. The device has ζ = 0.01, γ = 0.2, α = 0.1, and ρ = 10.

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Fig. 12

(a) Contour plot of the nondimensional average power harvested by the rotating piezoelectric vibration energy harvester for varying nondimensional rotation speed Ω and excitation frequency ω. (b) Region shown in the dashed (red) box in (a). The device has ζ = 0.01, γ = 0.2, α = 0.1, and ρ = 10.

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Fig. 13

Maximum nondimensional average power harvested by a rotating piezoelectric vibration energy harvester with γ = 0.2, 0.4, 0.6, and 0.8 for varying nondimensional viscous damping coefficient ζ. The markers denote the maximum average power harvested by a corresponding stationary device.

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Fig. 14

Nondimensional (a) resistance α, (b) excitation frequency ω, and (c) rotation speed Ω for varying nondimensional viscous damping coefficient ζ at the maxima of rotating piezoelectric vibration energy harvesters with γ = 0.2, 0.4, 0.6, and 0.8

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