(19) United States
`(12) Patent Application Publication (10) Pub. No.: US 2011/0048133 A1
`(43) Pub. Date:
`Mar. 3, 2011
`Lin et al.
`
`US 2011 0048133A1
`
`(54)
`
`(75)
`
`(73)
`
`(21)
`(22)
`
`(60)
`
`Assignee:
`
`VIBRATION ELEMENT COUPLED WITH
`NON-LINEAR FORCE TO IMPROVE
`NON-RESONANT FREQUENCY RESPONSE
`Inventors:
`Ji-Tzuoh Lin, Louisville, KY (US);
`Bruce Alphenaar, Louisville, KY
`(US)
`UNIVERSITY OF LOUISVILLE
`RESEARCH FOUNDATION,
`INC., Louisville, KY (US)
`12/871,524
`Aug. 30, 2010
`Related U.S. Application Data
`Provisional application No. 61/238,422, filed on Aug.
`31, 2009.
`
`Appl. No.:
`Filed:
`
`Publication Classification
`
`(51) Int. Cl.
`GOIP 15/09
`
`(2006.01)
`
`(52) U.S. Cl. ..................................................... 73AS14.34
`
`ABSTRACT
`(57)
`Embodiments of the invention couple a non-linear force to a
`vibration element such as a piezoelectric cantilever to intro
`duce chaotic, i.e., non-resonant vibration in the vibration
`element and thereby improve the non-resonant response of
`the vibration element. By doing so, the vibration element is
`responsive to a wider frequency range of vibrations and thus
`may be more efficient in Scavenging energy in environments
`where the vibration frequency is not constant, e.g., in envi
`ronment Subject to multi-mode or random vibration sources.
`
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`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 1 of 18
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`US 2011/0048133 A1
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`
`
`FIG. 1(a)
`
`FIG. 1 (b)
`
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`Cantilever
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`Cantilever
`
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`
`FIG.1(c)
`
`Shaker table
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 2 of 18
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`US 2011/0048133 A1
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`FIG. 2(a)
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`Patent Application Publication
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`US 2011/0048133 A1
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`
`
`##### *******
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`
`
`4(b)
`FIG.
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`(„sigui) ºg / d
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`Frequency (Hz)
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 4 of 18
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`US 2011/0048133 A1
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`Vin
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`FIG. 6(b)
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 5 of 18
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`US 2011/0048133 A1
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`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 6 of 18
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`US 2011/0048133 A1
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 7 of 18
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`US 2011/0048133 A1
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`'Magnetic force'
`... a 'Spring force'
`'ReSUait forces'
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`Distance (mm)
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`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 8 of 18
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`US 2011/0048133 A1
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`Frequency (Hz)
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 9 of 18
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`US 2011/0048133 A1
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`line (sec
`
`FIG. 13(a)
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`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 10 of 18
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`US 2011/0048133 A1
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`..
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`FIG. 14(d)
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 11 of 18
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`US 2011/0048133 A1
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`
`
`
`
`ine (sec
`
`FIG. 15(a)
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`FIG. 15(d)
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 12 of 18
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`US 2011/0048133 A1
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`
`
`
`
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`C.5
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`Woltage
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`FIG.16(c)
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 13 of 18
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`US 2011/0048133 A1
`
`S
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`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 14 of 18
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`US 2011/0048133 A1
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`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 15 of 18
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`US 2011/0048133 A1
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`•
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 16 of 18
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`US 2011/0048133 A1
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`- spring force
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`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 17 of 18
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`US 2011/0048133 A1
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`Magnet Diameter (mm)
`
`FIG. 23
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`FIG. 24(a)
`
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`Patent Application Publication
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`Mar. 3, 2011 Sheet 18 of 18
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`US 2011/0048133 A1
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`
`
`S-3raft separation: 2nt
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`
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`US 2011/0048133 A1
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`Mar. 3, 2011
`
`VIBRATION ELEMENT COUPLED WITH
`NON-LINEAR FORCE TO IMPROVE
`NON-RESONANT FREQUENCY RESPONSE
`
`CROSS-REFERENCE TO RELATED
`APPLICATIONS
`0001. This application claims priority to U.S. Patent Pro
`visional Application Ser. No. 61/238,422 to Ji-TZuoh Lin et
`a1 entitled LINEAR VIBRATION ELEMENT COUPLED
`WITH NON-LINEAR FORCETOIMPROVENON-RESO
`NANT FREQUENCY RESPONSE' and filed on Aug. 31,
`2009, which application is incorporated by reference herein.
`
`GOVERNMENT RIGHTS
`0002 The invention was supported in whole or in part by
`Contract/Grant No. DE-FC26-06NT42795 from the Depart
`ment of Energy and Contract/Grant No. DAAB07-03-D-
`B010/TO-0198 from the United States Navy. The Govern
`ment has certain rights in the invention.
`
`FIELD OF THE INVENTION
`0003. The present invention relates to energy harvesting
`and vibration sensing, and in particular, to harvesting energy
`or otherwise generating an electrical signal responsive to a
`source of vibration.
`
`BACKGROUND OF THE INVENTION
`0004 Scavenging energy from background mechanical
`vibrations in the environment has been proposed as a possible
`method to provide power in situations where battery usage is
`impractical or inconvenient. Proposed energy scavenging
`techniques for generating power including generating energy
`from the vibrations of a linear vibration element such as a
`piezoelectric cantilever, as well as electromagnetic inductive
`coupling and charge pumping across vibrating capacitive
`plates.
`0005 With respect to piezoelectric cantilever-based
`designs, for example, it has been shown that a piezoelectric
`cantilever attached to a vibrating structure can be used to
`power wireless transmission nodes for sensing applications.
`However, in order to generate sufficient power, the frequency
`of the vibration source typically must match the resonant
`frequency of the piezoelectric cantilever. If the source
`vibrates at a fixed, known frequency, the dimensions of the
`cantilever, and the proof mass can be adjusted to ensure
`frequency matching.
`0006. However, many naturally occurring vibration
`sources do not have a fixed frequency of vibration, and vibrate
`over a broad spectrum of frequencies. Lack of coupling of the
`piezoelectric cantilever to the off-resonance vibrations means
`that only a small amount of the available power can be scav
`enged. For example, in many natural environments in which
`energy scavenging could be utilized, e.g., roadways or
`bridges subject to vehicle traffic, oceans or other bodies of
`water Subject to waves and currents, vibrations are random
`and/or are spread over a broad spectrum of frequencies.
`0007. It has been proposed to modify the response char
`acteristics of a piezoelectric cantilever by applying a con
`trolled external force to the cantilever to tune the resonant
`frequency of the cantilever to the frequency of a vibration
`Source. By doing so, at least in principle, a piezoelectric
`cantilever could be actively tuned to match the maximum
`vibrational output of the environment at any particular time,
`
`and thereby maximize the amount of power scavenged. It is
`expected, however, that the power consumed by active tuning
`would completely offset any improvement obtained in the
`Scavenging efficiency.
`0008. It has also been proposed to utilize a passive tuning
`scheme in which a fixed force modifies the frequency
`response of the cantilever beam, without requiring additional
`power input. For example, an attractive magnetic force acting
`above the cantilever beam reduces the spring constant of the
`cantilever and lowers the resonance frequency, while an
`attractive force acting along the axis of the cantilever applies
`axial tension, and increases the resonance frequency. Both of
`the cases above happen only within the linear dynamic range.
`However, while such an approach could effectively tune a
`cantilever to a specific resonant frequency, the magnetic force
`would dampen the cantilever motion and reduce the resulting
`power output. Furthermore, as the force is fixed, the resonant
`frequency of the cantilever would likewise be fixed, and thus
`the Scavenging efficiency would be limited in instances where
`the vibration source was not fixed at a specific frequency.
`0009. Therefore, a need exists in the art for a manner of
`improving the energy scavenging efficiency of a piezoelectric
`cantilever or other type of vibration element over a larger
`range of frequencies.
`
`SUMMARY OF THE INVENTION
`0010 Embodiments of the invention address these and
`other problems associated with the prior art by coupling a
`non-linear force to a vibration element such as a piezoelectric
`cantilever to introduce non-linear dynamics such as chaotic
`(i.e., non-resonant), Sub-harmonic, and amplifying vibration
`in the vibration element and thereby improve the overall
`non-resonant response of the vibration element. By doing so,
`the vibration element is responsive to a wider frequency range
`of vibrations and is thus more efficient in Scavenging energy
`in environments where the vibration frequency is not con
`stant, e.g., in environment Subject to multi-mode or random
`vibration sources.
`0011. In one embodiment consistent with the invention, a
`vibration element Such as a piezoelectric cantilever is subject
`to a non-linear force Such as a static magnetic field. For
`example, a permanent neodymium magnet may be fixed to
`the end of a piezoelectric cantilever, causing it to experience
`a non-linear force as it moves with respect to a stationary
`magnet positioned proximate to the cantilever. By virtue of
`the static magnetic field, the magnetically coupled cantilever
`responds to vibration over a much broader frequency range
`than a conventional cantilever, and exhibits non-periodic or
`chaotic motion. The off-resonance response of the cantilever
`is improved, and often without any appreciable reduction in
`the response at the resonant frequency.
`0012. Therefore, consistent with one aspect of the inven
`tion, an apparatus includes a vibration element having a reso
`nant frequency, wherein the vibration element is coupled to a
`non-linear force that improves a response of the vibration
`element to non-resonant vibrations; and a circuit coupled to
`the vibration element and configured to output an electrical
`signal in response to vibration of the vibration element.
`0013 These and other advantages will be apparent in light
`of the following figures and detailed description.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`0014. The accompanying drawings, which are incorpo
`rated in and constitute a part of this specification, illustrate
`
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`Mar. 3, 2011
`
`embodiments of the invention and, together with a general
`description of the invention given above and the detailed
`description of the embodiments given below, serve to explain
`the principles of the invention.
`0015 FIG. 1(a) is a block diagram of an experimental set
`up for a single piezoelectric cantilever energy scavenging
`device consistent with the invention.
`0016 FIG. 1(b) is a circuit diagram of a circuit used in the
`device of FIG. 1(a) to transfer an AC piezoelectric cantilever
`Voltage (V) into a measured DC output Voltage (V).
`0017 FIG. 1 (c) is a block diagram of an experimental set
`up for a double piezoelectric cantilever energy scavenging
`device consistent with the invention.
`0018 FIG. 2(a) is a graph of an exemplary output of the
`piezoelectric cantilever in the single cantilever device of FIG.
`1(a) as a function of shaker table frequency, with and without
`magnetic coupling being present.
`0019 FIG. 2(b) is a graph of an exemplary output of the
`piezoelectric cantilever in the double cantilever device of
`FIG. 1 (c) as a function of shaker table frequency, with and
`without magnetic coupling being present.
`0020 FIG.2(c) is a graph illustrating the integration of the
`output of the single cantilever device of FIG. 1(a) as a func
`tion of frequency.
`0021
`FIG.2(d) is a graph illustrating the integration of the
`output of the double cantilever device of FIG. 1 (c) as a func
`tion of frequency.
`0022 FIG. 3(a) is a block diagram of a modified one
`dimensional spring force model of the device of FIG. 1(a).
`showing the parameters used to simulate cantilever motion.
`0023 FIG.3(b) is a block diagram of an experimental set
`up for obtaining an empirical measure of the magnetic force
`in the z-direction for the device of FIG. 1(a).
`0024 FIG.4(a) is a graph of magnetic force for the device
`of FIG. 1(a) as a function of cantilever deflection measured
`using the apparatus shown in FIG. 3(b) for three different
`magnet separation distances (4 mm, 5 mm and 10 mm), as
`well as the spring force of the cantilever.
`0025 FIG. 4(b) is a graph of spring potential (dashed line)
`and the potential due to the combination of the restoring force
`and the magnetic force for the 3 magnet separation distances
`in FIG. 4(a).
`0026 FIG. 5 is a graph of a simulated output of the canti
`lever of the device of FIG. 1(a) for the case of no magnetic
`coupling (dashed line) and magnetic coupling (Solid line),
`with a magnet separation distance of about 5 mm and an
`acceleration of about 7 m/s.
`0027 FIG. 6(a) is a circuit diagram of a circuit for per
`forming an open circuit measurement on V, directly from the
`piezoelectric cantilever in the device of FIG. 1(a).
`0028 FIG. 6(b) is a graph of the voltage Vpp over time
`with and without magnetic coupling measured with the cir
`cuit of FIG. 6(a) in "pink' background noise, with a higher
`Swing Voltage reflecting the Voltage generated by coupling
`setup with larger cantilever motions.
`0029 FIG. 7(a) is a circuit diagram of a rectified circuit
`with a resistor coupled across the output for measuring a DC
`voltage output of the device of FIG. 1(a).
`0030 FIG.7(b) is a graph of the output voltage V with and
`without magnetic coupling measured with the circuit of FIG.
`7(a) in "pink' background noise, with the fluctuations of the
`Voltage indicating the increased power generated by a mag
`netic coupled cantilever.
`
`FIG. 8(a) is a circuit diagram of a storage circuit for
`0031
`measuring a DC voltage output of the device of FIG. 1(a).
`0032 FIG. 8(b) is a graph of the output voltage V with and
`without magnetic coupling measured with the circuit of FIG.
`8(a) in "pink background noise, indicating that more charge
`is stored with a magnetic coupling setup.
`0033 FIG. 9 is a graph of the magnitude of magnetic
`forces, spring forces and resultant forces exerted on the can
`tilever of the device of FIG. 1(a).
`0034 FIG. 10 is a graph of the integration of the measured
`forces from FIG. 9, representing the magnetic potential,
`spring potential and the resultant spring potential therefor.
`0035 FIG. 11 is a graph of an exemplary peak to peak
`Voltage output of an exemplary test set up as a function of
`shaker table frequency, using the circuit shown in FIG. 6(a)
`with and without magnetic coupling being present.
`0036 FIG. 12 is a graph of a theoretical calculation of the
`predicted power output of the exemplary test set up used in
`FIG 11.
`0037 FIG. 13(a) is a graph of an exemplary peak to peak
`voltage output of the exemplary test set up used in FIG. 11, in
`response to a 6.5 Hz source of vibration.
`0038 FIG. 13(b) is a graph of a theoretical calculation of
`the predicted peak to peak Voltage output of the exemplary
`test set up used in FIG. 11, in response to a 6.5 Hz source of
`vibration.
`0039 FIG. 13(c) is a Poincaré plot graph showing the
`evolution of velocity and voltage output for the exemplary
`test set up used in FIG. 11, in response to a 6.5 Hz source of
`vibration.
`0040 FIG. 13(d) is a spectrum analysis graph of the exem
`plary test setup used in FIG. 11, in response to a 6.5 Hz source
`of vibration with the magnetic coupling being present.
`0041
`FIGS. 14(a)-14(d) are graphs corresponding to the
`graphs in FIGS. 13(a)-13(d) for the exemplary test setup used
`in FIG. 11, but in response to a 9.5 Hz source of vibration.
`0042 FIGS. 15(a)-15(d) are graphs corresponding to the
`graphs in FIGS. 13(a)-13(d) for the exemplary test setup used
`in FIG. 11, but in response to a 13 Hz source of vibration.
`0043 FIGS. 16(a)-16(d) are graphs corresponding to the
`graphs in FIGS. 13(a)-13(d) for the exemplary test setup used
`in FIG. 11, but in response to a 16 Hz, source of vibration.
`0044 FIGS. 17(a)-17(d) are graphs corresponding to the
`graphs in FIGS. 13(a)-13(d) for the exemplary test setup used
`in FIG. 11, but in response to a 20 Hz, source of vibration.
`0045 FIGS. 18(a) and 18(b) are graphs of exemplary out
`puts from the test set up used in FIGS. 1(a) and 1(b), using a
`source of vibration that provides an acceleration that is above
`(FIG. 18(a)) and below (FIG. 18(b)) a coupling threshold for
`the exemplary test set up.
`0046 FIG. 19 is a graph of voltage output vs. acceleration
`for the exemplary test set up used in FIGS. 1(a) and 1(b), and
`using a 4.8 mm magnet.
`0047 FIGS. 200a) and 200b) are graphs of voltage output
`vs. acceleration for the exemplary test set up used in FIGS.
`1(a) and 1(b), and using 1.6 mm (FIG. 200a)) and 1.0 mm
`(FIG.20(b) magnets.
`0048 FIG. 21 is a graph of the resultant forces of the
`uncoupled and coupled cantilever in the exemplary test set up
`of FIG. 11 with different sizes of magnets.
`0049 FIG.22 is a graph of the potentials of the uncoupled
`and coupled cantilever in the exemplary test set up used in
`FIG. 11 with different sizes of magnets.
`
`IPR2022-00060
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`US 2011/0048133 A1
`
`Mar. 3, 2011
`
`0050 FIG. 23 is a graph illustrating the correspondence of
`experimental and theoretical results of acceleration thresh
`olds vs. magnet size for the exemplary test set up used in FIG.
`11.
`FIGS. 24(a), 24(b) and 24(c) are graphs of an exem
`0051
`plary output of the piezoelectric cantilever in the device of
`FIGS. 1(a) and 1(b) as a function of shaker table frequency,
`respectively with 4.8 mm, 1.6 mm and 1.0 mm, but with the
`same acceleration, and illustrating a higher output but nar
`rower frequency range for larger magnets around the resonant
`frequency of the cantilever responsive to the same accelera
`tion.
`0052. It should be understood that the appended drawings
`are not necessarily to scale, presenting a somewhat simplified
`representation of various features illustrative of the basic
`principles of embodiments of the invention. The specific
`design features of embodiments of the invention as disclosed
`herein, including, for example, specific dimensions, orienta
`tions, locations, and shapes of various illustrated compo
`nents, as well as specific sequences of operations (e.g.,
`including concurrent and/or sequential operations), will be
`determined in part by the particular intended application and
`use environment. Certain features of the illustrated embodi
`ments may have been enlarged or distorted relative to others
`to facilitate visualization and clear understanding.
`
`DETAILED DESCRIPTION
`0053 Embodiments consistent with the invention couple
`or expose a linear vibration element to a non-linear force to
`cause chaotic, or non-resonant vibration in the linear vibra
`tion element, and thereby improve the frequency response of
`the linear vibration element to non-resonant frequencies. In
`addition, it is desirable in many embodiments to provide a
`non-linear force that is symmetrically and bi-directionally
`applied to the linear vibration element such that the non
`linear force is balanced between the positive and negative
`displacement of the linear vibration element, providing Sub
`stantially no bias toward either direction of displacement that
`could otherwise dampen the response of the linear vibration
`element at its resonant frequency. The non-linear force also
`introduces amplifying ultra-harmonic and enhanced Sub-har
`monic components of the resonant frequency
`0054) A vibration element within the context of the inven
`tion may include various types of devices that generate energy
`in response to a vibrational input, including various devices
`with linear responses that generate electrical current via
`piezoelectric, capacitive, electromagnetic and electrostatic
`effects. In addition, a vibration element may include various
`mechanical configurations through which movement is gen
`erated in response to a vibration, e.g., cantilevers, pendulums,
`opposing plates, etc. While in the illustrated embodiments
`below the vibration element is a linear vibration element, in
`other embodiments, non-linear vibration elements may be
`used. For example, a non-linear vibration element may
`include various mechanical configurations that exhibit non
`linear response characteristics, e.g., based upon the use of
`compound springs, springs made of piezoelectric material or
`springs made of magnetic material. In the embodiments dis
`cussed below, a linear vibration element, implemented as a
`piezoelectric cantilever, is used; however, it will be appreci
`ated that the invention is not limited to such devices.
`0055. A non-linear force within the context of the inven
`tion may include various forces that may be applied to a
`vibration element by virtue of a coupling of the vibration
`
`element, or a component mechanically secured to the vibra
`tion element, and another element disposed in proximity to
`the vibration element. In the illustrated embodiments, for
`example, a magnetic force, e.g., as generated by the magnetic
`coupling of a first magnet coupled to the piezoelectric canti
`lever and a second magnet disposed in proximity thereto, is
`utilized to apply a non-linear force to the piezoelectric canti
`lever. However, it will be appreciated that other sources of
`non-linear forces, e.g., other magnetic fields, electromagnetic
`fields, and electrostatic fields, may be used in the alternative.
`0056. It will also be appreciated that the principles of the
`invention may be applied in connection with energy harvest
`ing from a wide variety of vibration sources, including, for
`example, pink noise vibration sources, bridges, roadways,
`buoys, waves, water currents, fences, streetlights, enclosures,
`etc., as well as vibration sources exhibiting random vibra
`tions, fixed frequency vibrations, controlled scanning spec
`trum vibrations, broadband vibrations, etc.
`0057. As will be discussed in greater detail below, in the
`illustrated embodiment, a bi-directional and symmetric non
`linear force is applied to a cantilever by orienting pairs of
`permanent magnets in a repelling and face-to-face orientation
`to one another along an axis of a cantilever, with one magnet
`disposed proximate an end of the cantilever and the other
`magnet disposed eitherona fixed support or proximate an end
`of a second cantilever disposed generally along the same axis
`as the other cantilever. It will be appreciated, however, that a
`non-linear force may be applied in other manners consistent
`with the invention. For example, other orientations of mag
`nets may be used, including orienting magnets in an attractive
`orientation, orienting magnets at other relative angles to one
`another and/or to the cantilever axis, or using multiple fixed
`and/or cantilever-mounted magnets. As one example, it may
`be desirable to utilize multiple fixed magnets on opposing
`sides of a cantilever to apply balanced attractive or repulsive
`forces to a cantilever-mounted magnet. It is believed that by
`applying non-linear forces bi-directionally and symmetri
`cally to a vibration element, dampening of the response of the
`vibration element at its resonant frequency is minimized.
`0.058 Turning now to the Drawings, wherein like numbers
`denote like parts throughout the several views, FIG. 1(a)
`illustrates an exemplary test set up for an energy scavenging
`device 10 incorporating as a linear vibration element a piezo
`electric cantilever 12. Device 10 is illustrated as disposed on
`a shaker table 14. Cantilever 12 is coupled at one end to a
`Support 16 that orients the cantilever in a generally horizontal
`orientation, or more generally in an orientation that is gener
`ally perpendicular to the vibration direction.
`0059. In this embodiment, cantilever 12 is subjected to a
`non-linear force taking the form of a magnetic force oriented
`along the cantilever axis, incorporating a pair of permanent
`magnets 18, 20 facing one another separated by a distance 11.
`By orienting the non-linear force along the cantileveraxis, the
`frequency response of the piezoelectric cantilever can be
`substantially altered in a way that provides an effective
`method to harvest off-resonance vibrations, without altering
`the resonant frequency of the cantilever or dampening the
`response at the resonant frequency. Instead, the response is
`broadened by the appearance of non-periodic oscillations
`outside of the resonance condition, thus improving the
`response to off-resonance vibrations, and increasing the out
`put of the piezoelectric cantilever for random or broadband
`vibration sources.
`
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`US 2011/0048133 A1
`
`Mar. 3, 2011
`
`0060. The following working examples illustrate various
`experiments and simulations performed using the basic con
`figuration illustrated in FIG. 1(a), as well as various modifi
`cations that may be made to Such a configuration to alter the
`energy scavenging capabilities of the device in different envi
`ronments. It will be appreciated that the invention is not
`limited to these particular modifications and configurations.
`Working Example 1
`Single and Double Cantilevers
`0061 A test set up configured in the manner illustrated
`above in connection with FIGS. 1(a) and 1(b) was con
`structed. Cantilever 12 was manufactured using commer
`cially available unimorph piezoelectric discs composed of an
`about 0.09 mm thick PZT layer deposited on an about 0.1 mm
`thick brass shim (APC International, MFT-50T-1.9A1). The
`disc was cut into an about 13 mm wide by about 50 mm long
`strip, and clamped at one end to produce an about 44 mm long
`cantilever. The PZT layer extended about 25 mm along the
`length of the cantilever, and the remainder was composed
`only of brass. The proof mass (including the magnet and an
`additional fixture that holds the magnet) weighed about 2.4
`gm, while the cantilever itself weighed about 0.8 gm. The
`electrical leads were soldered with thin lead wires (134 AWP.
`Vishay) to the top side of the PZT and the bottom side of the
`shim.
`0062) Vibration was generated by a shaker table 14 (Lab
`work ET-126) powered by an amplified sinusoidal wave using
`aYokogawa EG300 function generator and a Labwork Pa-13
`amplifier. A custom Labview data acquisition program was
`used to measure output Voltage from the cantilever beam.
`Magnets 18, 20 were implemented as about 4.8 mm diameter
`disc-shaped rare earth magnets (Radio Shack model
`64-1895), with one magnet 18 attached to the vibrating tip of
`cantilever 12, and the other magnet 20 attached directly to a
`vertical support 22 on the shaker table frame.
`0063. In all measurements, the shaker table acceleration
`was set to approximately 7 m/s, and the frequency swept
`from 0 to 30 Hz in 0.5 Hz steps. The voltage generated by the
`piezoelectric cantilever beam was rectified, and detected
`across a 22 uF capacitor and 1 MOhm resistor in parallel,
`using circuit 24 shown in FIG. 1(b). The resonance frequency
`of the cantilever beam with its proof mass was measured to be
`approximately 10.4HZ. The opposing magnet fitted at the free
`end of the cantilever Supplied a symmetrical, repulsive force
`about the balance of the cantilever during vibration. The
`horizontal separation between the magnets (designated by m)
`was adjusted to be approximately m3 mm. This separation
`was found to provide good compensation for the spring force,
`and minimized the effective restoring force near the equilib
`rium point.
`0064 FIG. 2(a) shows the output of the cantilever as a
`function of shaker table vibration frequency for the case
`where the opposing magnet is fixed to the shaker table. The
`results from two measurement runs in the coupled State are
`shown, together with the output of the cantilever measured in
`the uncoupled State. (This is obtained by removing the oppos
`ing magnet.) At the resonance frequency, the output of the
`cantilever exceeded 16 V. and the peak height, resonance
`frequency and line width are all approximately the same for
`the coupled and un-coupled states. On either side of the main
`resonance, however, there is additional output observed for
`the coupled cantilever, which is not observed in the uncoupled
`
`state. As can be seen from a comparison of the two coupled
`runs, the frequency distribution of the peaks is not completely
`reproducible, although there is a reproducibility in the overall
`pattern of the output. The motion of the cantilever in the off
`resonance condition is aperiodic.
`0065. Also measured was a double cantilever system, e.g.,
`as shown in FIG. 1 (c), in which the second magnet was
`connected to an opposing cantilever (having resonant fre
`quency higher than 60 Hz) rather than to a fixed point. In
`particular, unlike device 10 of FIG. 1(a). FIG. 1 (c) utilizes an
`energy scavenging device 30 incorporating dual cantilevers
`32, 33, with cantilever 32 implemented as a piezoelectric
`cantilever operating as a linear vibration element. Device 30
`is illustrated as disposed on a shaker table 34. Cantilever 32 is
`coupled at one end to a support 36 that orients the cantilever
`in a generally horizontal orientation, or more generally in an
`orientation that is generally perpendicular to the vibration
`direction. In this embodiment, cantilever 32 is subject