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Research Papers

On Improvement of the Frequency Bandwidth of Nonlinear Vibration Energy Harvesters Using a Mechanical Motion Rectifier

[+] Author and Article Information
Wei-Che Tai

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: wchtai@vt.edu

Mingyi Liu, Yue Yuan

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

Lei Zuo

Professor
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 14, 2017; final manuscript received February 21, 2018; published online April 19, 2018. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 140(5), 051008 (Apr 19, 2018) (11 pages) Paper No: VIB-17-1367; doi: 10.1115/1.4039534 History: Received August 14, 2017; Revised February 21, 2018

This paper presents a broadband vibration energy harvester (VEH) which consists of a monostable Duffing oscillator connected to an electromagnetic generator via a mechanical motion rectifier. The mechanical motion rectifier converts the bidirectional vibratory motion of the oscillator induced by ambient environment vibrations into unidirectional rotation of the generator and causes the harvester to periodically switch between a large- and small-inertia system, resulting in nonlinearity in inertia. By means of analytical and numerical methods, this inertia nonlinearity is shown to have two advantages. First, it allows for more stiffness nonlinearity without inducing nonuniqueness of energy branches and enhances bandwidths of energy harvesting. The effect of mitigating nonuniqueness of energy branches occurs to steady-state and transient responses of the harvester and is experimentally verified by a prototype. The experimental results show a nearly 50% increase in the half power bandwidth via mechanical motion rectification (MMR). Second, it enlarges the basin of attraction of the high-energy branch when multiple energy branches are present. A numerical example shows that a more than 50% increase in the basin area can be achieved via MMR.

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Figures

Grahic Jump Location
Fig. 1

Working principle of MMR. Note that the mounting bearings are not shown.

Grahic Jump Location
Fig. 2

The proposed MMR-Duffing VEH, consisting of a monostable Duffing oscillator connected to an electromagnetic generator via the MMR shown in Fig. 1. Left: engagement state; right: disengagement state.

Grahic Jump Location
Fig. 3

Comparison of simulated (Δ: swept-up; *: swept-down) and analytically predicted (solid lines: stable solutions; dashed lines: unstable solutions) steady-state responses. Note that ξ=0.1, ρ=0.5, and ε=0.9. (a) μ = 0.2 and γ = 1. No jump phenomenon occurs. (b) μ = 0.2 and γ = 4. Jump phenomenon occurs.

Grahic Jump Location
Fig. 4

Critical cubic nonlinearity (γρ)cr as a function of mass ratio μ and electrical damping strength ε: (a) (γρ)MMR/non−MMRcr versus μ and ε. (b) (γρ)MMRcr (solid line) and (γρ)non−MMRcr (dashed line) versus μ when ε=0.9. J.P.: jump phenomenon. ζ=0.1 is used.

Grahic Jump Location
Fig. 5

Simulated steady-state responses of the MMR harvester (solid lines: swept-up; dashed lines: swept-down) and non-MMR harvester (dotted lines: swept-up; dotted dash lines: swept-down) under frequency sweep excitation. Note that a and Ω denote dimensionless amplitude and excitation frequency, respectively. γ = 2, ρ=0.05, ξ=0.1,and ε=0.9.

Grahic Jump Location
Fig. 6

Comparison of frequency bandwidths between three MMR-Duffing VEHs, one non-MMR harvester, and one equivalent linear harvester. ζ=0.1, μ=0.4, and ρ=0.05.

Grahic Jump Location
Fig. 7

Simulated transient responses of the (a) non-MMR and (b) MMR harvesters under frequency sweep excitation (sweep rate: 1.46×10−2 Hz/s). Solid lines: swept-up; dash-dotted lines: swept-down. (c) Comparison of simulated bandwidths. ξ=0.1, ε=0.9, γ = 2, and ρ=0.05.

Grahic Jump Location
Fig. 8

Basins of attraction of the MMR (solid line) and non-MMR (dashed line) at the peak voltages when (a) μ=0.1 and (b) μ=0.2. Markers *: low energy branch. Markers x: high energy branch. Note that the steady-state responses of the MMR and non-MMR harvesters are shown in the insets, and V and Ω denote normalized OC voltage and dimensionless excitation frequency, respectively. γ = 2, ρ=0.05, ξ=0.1, and ϵ=0.9.

Grahic Jump Location
Fig. 9

Experiment rig of the MMR-Duffing harvester. Note that the shaker motion y and the mass relative motion z are indicated by arrows.

Grahic Jump Location
Fig. 10

Experimental results of transient responses of (a) the non-MMR harvesters and (b) MMR system under fast frequency sweep (1.46×10−2 Hz/s, same as in Fig. 7). OC: open-circuit. (c) Comparison of the measured and simulated bandwidths using the system parameters in Table 2.

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