U.S. patent application number 14/468825 was filed with the patent office on 2015-03-26 for high energy density vibration energy harvesting device with high-mu material.
This patent application is currently assigned to NORTHEASTERN UNIVERSITY. The applicant listed for this patent is Northeastern University. Invention is credited to Nian-Xiang SUN.
Application Number | 20150084443 14/468825 |
Document ID | / |
Family ID | 48171653 |
Filed Date | 2015-03-26 |
United States Patent
Application |
20150084443 |
Kind Code |
A1 |
SUN; Nian-Xiang |
March 26, 2015 |
HIGH ENERGY DENSITY VIBRATION ENERGY HARVESTING DEVICE WITH HIGH-MU
MATERIAL
Abstract
The present disclosure describes a vibration energy harvester
with increased output power density. The vibration energy harvester
has two magnetic solenoids, each with cores that include multiple
layers of high permeability materials. The two magnetic solenoids
are fixed at two sides of a movably supported hard magnetic core,
such as a magnet pair with anti-parallel magnetization, which
produces a spatially inhomogeneous bias magnetic field for
switching the flux inside the solenoids during vibration of the
magnetic core. An output voltage of 2.52 V and a power density
20.84 mW/cm3 at 42 Hz, with a half peak working bandwidth of 6
Hz.
Inventors: |
SUN; Nian-Xiang;
(Winchester, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Northeastern University |
Boston |
MA |
US |
|
|
Assignee: |
NORTHEASTERN UNIVERSITY
Boston
MA
|
Family ID: |
48171653 |
Appl. No.: |
14/468825 |
Filed: |
August 26, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
13554263 |
Jul 20, 2012 |
8816540 |
|
|
14468825 |
|
|
|
|
61510781 |
Jul 22, 2011 |
|
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Current U.S.
Class: |
310/25 |
Current CPC
Class: |
H02K 35/02 20130101;
H02K 35/02 20130101; H02K 2213/03 20130101; H02K 7/1876
20130101 |
Class at
Publication: |
310/25 |
International
Class: |
H02K 35/02 20060101
H02K035/02 |
Claims
1. An energy harvesting device, comprising: a first and second
solenoid, each solenoid comprising (a) a wire coil wrapped around
(b) a high permeability core with two or more layers, and the first
and second solenoid being disposed along a first path; and a
magnetic core: disposed between the first and second solenoid such
that the first solenoid is mounted on a first side of the magnetic
core, and the second solenoid is mounted on a second side of the
magnetic core; and mounted on a support such that the magnetic core
can vibrate along a second path that intersects the first path,
vibration of the magnetic core inducing a flux change in the first
and second solenoids.
2. The energy harvesting device of claim 1, wherein the magnetic
core comprises a first magnet.
3. The energy harvesting device of claim 2, wherein the magnetic
core comprises a second magnet disposed above the first magnet such
that the first magnet and second magnet have anti-parallel
moments.
4. The energy harvesting device of claim 1, wherein the support
comprises a spring.
5. The energy harvesting device of claim 4, wherein the spring
comprises a circular cross-section.
6. The energy harvesting device of claim 4, wherein the spring has
a resonance frequency of 42 Hz.
7. The energy harvesting device of claim 6, wherein vibration of
the magnetic core achieves a power output density of 20.84
mW/cm.sup.3.
8. The energy harvesting device of claim 1, wherein each high
permeability core is a 28-layer core, each layer comprising
dimensions 2 cm.times.2 cm.times.0.002 inch.
9. The energy harvesting device of claim 8, wherein the magnetic
core comprises a second magnet, and the first and second magnets
are SmCo magnets with dimensions 2.2 cm.times.1.3 cm.times.0.2
cm.
10. The energy harvesting device of claim 9, wherein a total volume
of the energy harvesting device is 6.44 cm.times.3.25 cm x1.4 cm
=29.3 cm.sup.3.
11. The energy harvesting device of claim 1, wherein the first
solenoid, the second solenoid, and the support are mounted to a
base such that the first path is substantially parallel to the
base, and the second path is substantially perpendicular to the
base.
12. The energy harvesting device of claim 1, wherein the first and
second solenoids comprise a same size.
13. The energy harvesting device of claim 12, wherein the first and
second solenoids comprise a same shape.
14. The energy harvesting device of claim 12, further comprising
joining the first and second solenoids in series to double a
voltage of the energy harvesting device.
15. In an energy harvesting device, comprising (1) a first and
second solenoid, each solenoid comprising (a) a wire coil wrapped
around (b) a high permeability core with two or more layers, and
the first and second solenoid being disposed along a first path,
and (2) a magnetic core disposed between the first and second
solenoid such that the first solenoid is mounted on a first side of
the first magnet, and the second solenoid is mounted on a second
side of the first magnet, the magnetic core being mounted on a
support such that the magnetic core can vibrate along a second path
that is orthogonal to the first path, a method comprising:
vibrating the magnetic core along the second path to induce a flux
change in the first and second solenoids.
16. The method of claim 15, further comprising: vibrating the
magnetic core at 42 Hz; and generating an output power of 610.62
mW.
Description
CROSS REFERENCES TO RELATED APPLICATIONS
[0001] This application is a continuation of and claims the benefit
of and priority under 35 U.S.C. .sctn.119(e) to U.S. patent
application Ser. No. 13/554,263, filed on Jul. 20, 2012, and
entitled"High Energy Density Vibration Energy Harvesting Device
with High-mu Material," and to U.S. Provisional Application No.
61/510,781, filed on Jul. 22, 2011, and entitled "High Energy
Density Vibration Energy Harvesting Device with High-mu Material,"
the disclosures of which are hereby incorporated herein by
reference in their entirety.
FIELD OF THE INVENTION
[0002] The present disclosure relates generally to high energy
density vibration energy harvesting devices with high-mu
materials.
BACKGROUND
[0003] Vibration energy harvesting technologies are developing
rapidly, showing great potential in many different applications.
For example, miniature vibration energy harvesters are often used
for applications such as autonomous sensors and system on chip
applications. Most applications use one of four major vibration
energy harvesting mechanisms, including electromagnetic,
electrostatic, magnetoelastic, and piezoelectric mechanisms.
However, such vibration energy harvesters achieve different output
powers and energy densities. For example, piezoelectric-based
vibration energy harvesters often demonstrate a much higher energy
density than other counterpart mechanisms, reaching
.about.6mW/cm.sup.3. Specifically, some piezoelectric bare beam
based vibration energy harvesters can generate a power of 6.63
mW/cm.sup.3. Because of this, piezoelectric-based vibration energy
harvesters are often more widely used than other forms of vibration
energy harvesters. However, they can suffer from narrow bandwidth
(or a limited operating frequency range of 2-5% of the center
operating frequency), degraded polarization after prolonged use,
and/or the negative side-effects caused by a brittle
cantilever.
SUMMARY
[0004] In one aspect, an energy harvesting device, includes a first
and second solenoid, each solenoid including (a) a wire coil
wrapped around (b) a high permeability core with two or more
layers, and the first and second solenoid being disposed along a
first path, and a magnetic core: disposed between the first and
second solenoid such that the first solenoid is mounted on a first
side of the magnetic core, and the second solenoid is mounted on a
second side of the magnetic core, and mounted on a support such
that the magnetic core can vibrate along a second path that
intersects the first path, vibration of the magnetic core inducing
a flux change in the first and second solenoids.
[0005] In one aspect, in an energy harvesting device, including (1)
a first and second solenoid, each solenoid including (a) a wire
coil wrapped around (b) a high permeability core with two or more
layers, and the first and second solenoid being disposed along a
first path, and (2) a magnetic core disposed between the first and
second solenoid such that the first solenoid is mounted on a first
side of the first magnet, and the second solenoid is mounted on a
second side of the first magnet, the magnetic core being mounted on
a support such that the magnetic core can vibrate along a second
path that is orthogonal to the first path, a method includes
vibrating the magnetic core along the second path to induce a flux
change in the first and second solenoids.
[0006] In one or more embodiments, the magnetic core includes a
first magnet.
[0007] In one or more embodiments, the magnetic core includes a
second magnet disposed above the first magnet such that the first
magnet and second magnet have anti-parallel moments.
[0008] In one or more embodiments, the support includes a
spring.
[0009] In one or more embodiments, the spring includes a circular
cross-section.
[0010] In one or more embodiments, the spring has a resonance
frequency of 42 Hz.
[0011] In one or more embodiments, vibration of the magnetic core
achieves a power output density of 20.84 mW/cm.sup.3.
[0012] In one or more embodiments, each high permeability core is a
28-layer core, each layer including dimensions 2 cm.times.2
cm.times.0.002 inch.
[0013] In one or more embodiments, the magnetic core includes a
second magnet, and the first and second magnets are SmCo magnets
with dimensions 2.2 cm.times.1.3 cm.times.0.2 cm.
[0014] In one or more embodiments, a total volume of the energy
harvesting device is 6.44 cm.times.3.25 cm.times.1.4 cm=29.3
cm.sup.3.
[0015] In one or more embodiments, the first solenoid, the second
solenoid, and the support are mounted to a base such that the first
path is substantially parallel to the base, and the second path is
substantially perpendicular to the base.
[0016] In one or more embodiments, the first and second solenoids
include a same size.
[0017] In one or more embodiments, the first and second solenoids
include a same shape.
[0018] In one or more embodiments, the first and second solenoids
are joined in series to double a voltage of the energy harvesting
device.
[0019] In one or more embodiments, the magnetic core is vibrated at
42 Hz, and an output power of 610.62 mW is generated.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] The above and other objects and advantages of the present
invention will be apparent upon consideration of the following
detailed description, taken in conjunction with the accompanying
drawings, in which like reference characters refer to like parts
throughout, and in which:
[0021] FIG. 1 is a table that lists different comparison metrics
for various vibrating energy harvesting mechanisms in accordance
with certain embodiments;
[0022] FIG. 2A is a schematic of an energy harvesting device in
accordance with certain embodiments;
[0023] FIG. 2B is a schematic of the energy harvesting device of
FIG. 2A with its magnetic core in an upper position in accordance
with certain embodiments;
[0024] FIG. 3A is a top-view image of an energy harvesting device
in accordance with certain embodiments;
[0025] FIG. 3B is a side-view image of the energy harvesting device
of FIG. 3A in accordance with certain embodiments;
[0026] FIG. 4 is a graph of open circuit voltage (V) of the energy
harvesting device of FIGS. 3A-3B over time (s) using three
different springs in accordance with certain embodiments;
[0027] FIG. 5 is a graph of the output power (mW) of the energy
harvesting device achieved using the three springs graphed in FIG.
4 in accordance with certain embodiments; and
[0028] FIG. 6 is a graph of the power density (mW/cm.sup.3) of the
energy harvesting device based on the frequency (Hz) of the support
in accordance with certain embodiments.
DETAILED DESCRIPTION OF THE INVENTION
[0029] The present disclosure provides for magnetic-based vibration
energy harvesters that achieve a high energy density by using high
permeability magnetic materials. While a piezoelectric bare beam
based vibration energy harvester can generate a power energy
density of 6.63 mW/cm.sup.3, theoretically the magnetostatic energy
density (1/2.mu.H.sup.2) in high permeability magnetic materials is
10.sup.5-10.sup.6 times that of the electrostatic energy density
(1/2.epsilon.E.sup.2) in piezoelectrics. Such magnetic-based
vibration energy harvesters can achieve, for example, a energy
density greater than 20 mW/cm.sup.3 (e.g., with an acceleration of
5 g), which is over 3 times the energy density of known vibration
energy harvesters.
[0030] Before describing in detail the particular components of
magnetic-based vibration energy harvesters, in some embodiments the
vibration energy harvesters include two fixed solenoids. Each
solenoid has a multi-layer high permeability solenoid core. A
vibrating magnetic core is disposed between the two fixed
solenoids. The multilayer high permeability solenoid cores lead to
significantly increased flux change in the solenoid within one
period of vibration of the magnetic core than other such devices,
without increasing the total volume of the device. In addition, the
two solenoids at both sides of the vibrating magnet(s) make full
use of the spatially inhomogeneous bias magnetic fields at both
sides of the magnets, leading to doubled power output, and a
dramatically enhanced power density than previous energy
harvesters.
[0031] FIG. 1 is a table 100 that shows metrics of comparison among
various vibrating energy harvesting mechanisms. The
mechanisms/products include electrostatic, magnetoelectric,
piezoelectric, magnetoelectric sensor based, magnetostrictive,
perpetuum, KCF (from KCF Technologies of State College, Pa.), and
high permeability (High-.mu. (1.sup.st gen), and High-.mu.
(2.sup.nd gen)) material-based energy harvesting devices. The
metrics of comparison include the central frequency f.sub.center,
measured in Hz; acceleration "a," measured in g (9.8 m/s.sup.2);
P.sub.max, the maximum output power of the device, measured in mW;
and power density, measured in mW/cm.sup.3. As shown in table 100,
the 2.sup.nd generation high-.mu. vibration energy harvester (e.g.,
which includes two fixed solenoids with multi-layer high
permeability cores, and a vibrating magnetic core, as described
herein) has the largest output power density of 20.84 for an
f.sub.center of 42 Hz. Such a power density is over three times
larger than the widely used piezoelectric device. Further, the
performance of the High-.mu. (2.sup.nd gen) device is greater than
that of the High-.mu. (1.sup.st gen) device (e.g., upwards of
10.times. the flux change of the High-.mu. (1.sup.st gen) device).
The High-.mu. (2.sup.nd gen) device uses two stationary solenoids
with thicker multi-layer high-.mu. magnetic core materials (e.g.,
20 layers of material), which allows a greater flux change to be
induced in one vibration of the magnetic core. In contrast, the
High-.mu. (1.sup.st gen) device has a single vibrating solenoid,
and therefore the solenoid core can not be thick, resulting in less
flux change.
[0032] FIG. 2A is a schematic of an energy harvesting device 200 in
accordance with certain embodiments. The energy harvesting device
200 includes a first solenoid 202A and a second solenoid 202B
(indicated by respective dotted rectangles for ease of reference,
and collectively referred to herein as solenoids 202). Each
solenoid 202 can include a wire coil (204A, 204B) wrapped around a
multi-layer high permeability (high-.mu.) core (206A, 206B). The
energy harvesting device 200 includes a magnetic core 208, which is
disposed between solenoid 202A and solenoid 202B. Solenoid 202A is
mounted to the base 220 on the left side of the magnetic core 208
via mount 210A, and solenoid 202B is mounted to the base 220 on the
right side of the magnetic core 208 via mount 210B. The magnetic
core 208 is mounted to the base 220 via support 212 such that the
magnetic core 208 can vibrate between the solenoids 202. While two
solenoids 202 are shown in device 200, any number of solenoids can
be used for a particular energy harvesting device (e.g., 1, 3,
etc.). Further, the configuration shown in FIG. 2A is intended to
be exemplary only, and is not intended to be limiting. One of skill
can appreciate that other variations of energy harvesting devices
can be engineered according to the principles described herein
without departing from the spirit of the description.
[0033] In some embodiments, the solenoids 202 are manufactured to
have the same size (e.g., the same three dimensional size) and/or
shape (e.g., the same number of layers in the cores 206A, 206B, and
the same number of coil layers for each coil 204A, 204B, the same
number of rotations around the core per coil layer, and/or the
like). In some embodiments, the multi-layer high permeability cores
(206A, 206B) are formed of multiple layers of a non-oriented 80%
nickel-iron-molybdenum alloy, which offers extremely high
permeability. The material can be fabricated using hydrogen
annealing to maximize permeability. In some embodiments, the high
permeability materials are foils provided by The MuShield.RTM.
Company of Londonderry, N.H. (e.g., foil with thicknesses of
0.002'', 0.004'', 0.006'', and/or 0.010''). Any high permeability
magnetic materials can be used as the magnetic core for the energy
harvester to achieve similar harvester performance. (e.g., ferrite
or other inductor core materials).
[0034] The magnetic core 208 includes magnets 214 and 216. Magnet
214 is disposed above the magnet 216 such that the magnets have
anti-parallel moments (e.g., the North (N) pole of magnet 214 is
disposed above the South (S) pole of magnet 216, and the South (S)
pole of magnet 214 is disposed above the North (N) pole of magnet
216). The magnets 214, 216 are joined by joining portion 218 (e.g.,
which can be made from a magnetic or a non-magnetic material). In
some embodiments, the support 212 is a spring (e.g., with a
circular cross-section, a square cross-section, and/or the like).
While the magnetic core 208 is shown with two magnets 214 and 216,
the magnetic core can include any number of magnets. For example,
in some embodiments, the magnetic core 208 includes one magnet, or
three or more magnets. Further, the magnets can be arranged in
other ways than with anti-parallel moments. For example, the
magnets can be oriented such that the same moments are aligned
(e.g., N above N, and S above S). As another example, the magnets
can be partially crossed, such that they do not completely overlap
with eachother (e.g., to form an "X" shape).
[0035] Vibration of magnetic core 208 creates a voltage V across
the solenoids 202. As the pair of magnets 214, 216 vibrate up and
down, the magnetic field lines inside each solenoid 202 change
direction periodically, inducing a large magnetic flux change (M)
in both solenoids 202. The magnetostatic coupling between the
solenoids 202 and the time varying inhomogeneous bias magnetic
field results in a nonlinear oscillation and a complete magnetic
flux reversal in the solenoids 202. The presence of the multi-layer
highly permeable cores dramatically increase the magnitude of
magnetic flux inside the coils of the solenoids 202. The induced
voltage can be doubled to form voltage V by connecting the two
solenoids in series.
[0036] FIG. 2B is a schematic of the energy harvesting device 200
of FIG. 2A with the magnetic core 208 in an upper position. As
shown in FIGS. 2A-2B, the solenoids 202 are disposed along first
path 250. In some embodiments, the first path 250 is substantially
horizontal to the surface plane of the base 220. Magnetic core 208
can vibrate along a second path 252 that intersects (e.g., is
orthogonal to) the first path 250. In some embodiments, the second
path 252 is substantially perpendicular to the surface plane of
base 220. As shown by arrows 254A, 254B, vibration of the magnetic
core along path 252 induces a flux change in the solenoids 202
(e.g., arrows 254A, 254B point to the right in FIG. 2B, compared to
the arrows in FIG. 2A which point left, due to the movement of the
magnetic core 208 to an upward position along the path 252. The
mass of the hard magnetic core 208, the stiffness of the supporting
spring, and/or the magnetostatic coupling between the solenoids 202
and/or hard magnetic core 208 can determine the resonance vibration
frequency and the output voltage of the energy harvester.
[0037] While paths 250, 252 are shown as straight paths in FIG. 2B,
in some embodiments the paths are nonlinear paths. For example, an
equivalent stand-alone spring-mass system becomes a nonlinear
oscillation system once introduced into the energy harvesting
device 200 due to the magnetostatic coupling between the solenoids
202 and the hard magnetic core 208. This nonlinear effect can be
explained, for example, from a potential energy point of view. The
elastic potential energy of a stand-alone spring-mass system is a
well-know linear relationship, with only one minimum value, which
happens when the mass passes the equilibrium position in the
middle. In contrast, the magnetostatic potential energy has two
identical minimum values due to the coupling between the magnet(s)
and solenoids, which appear when the magnet(s) move a short
distance up or down from the equilibrium position in the middle. As
a result, the superposition of two different types of potential
energy make a nonlinear relationship, leading to a wider
oscillation frequency range.
[0038] In some embodiments, the total induced voltage of the energy
harvesting device equals the integral over the whole solenoid,
because the magnetic field magnitude varies along the axis. The
open circuit voltage, V, can be expressed by Equation (1):
V = 2 .PHI. ( t ) t = 2 .intg. { H [ x , y ( t ) ] + 4 .pi. M [ x ,
y ( x , t ) ] } A N t = 2 .intg. 4 .pi. M [ x , y ( x , t ) ] A N t
, ( 1 ) ##EQU00001##
where: d.phi.(t)=the magnetic flux change over time; dt=time;
H[x,y(t)]=the magnetic field H at time t, at the spatial position
defined by the point (x (along the length of the solenoid), y
(along the direction the vibrating magnetic core travels));
M[x,y(x,t)]=magnetization M as a function of time t at coordinates
x, y(x,t); A=the total cross section area of the multilayer cores
of the solenoids; and dN=the number of loops in the infinitesimal
length unit of the solenoid, which can be calculated according to
Equation (2):
dN=N.sub.Ldx/d.sub.w. (2)
where: N.sub.L=the number of loop layers of the coil; dx=the
position x along the length of the solenoid; and d.sub.w=the copper
wire diameter.
[0039] Hence, the maximum output power P.sub.max, which happens
when the load impedance equals the conjugate of the output
impedance of the solenoid coil R.sub.coil, is defined by Equation
(3):
P max = ( V 2 ) 2 R coil = 16 S R coil ( A ' .pi. N L d w ) 2 (
.intg. 0 L { M [ x , y ( x , t ) ] t } x ) 2 , ( 3 )
##EQU00002##
where: R.sub.coil=the resistance of the solenoid; S=the number of
layers in each core; A'=the cross section area of one layer of the
core; L=the length of the solenoid; and d.sub.w=the diameter d of
the wire w.
[0040] Equation (3) shows that the output power P.sub.max increases
as the vibration frequency increases (e.g., if all other parameters
are kept constant). In some examples, when using the same source
power, the amplitude decreases if the frequency increases.
Moreover, at a particular frequency, the output power P.sub.max can
depend on the total magnetic flux change in the solenoid, in one
oscillation period, which is directly related to the permeability
.mu. of the magnetic cores. Therefore, multi-layer soft magnetic
beams with a high permeability constitute excellent candidates for
the solenoid cores. In some embodiments, a multilayer structure of
magnetic material generates a much larger flux change than a single
layer, as shown in FIG. 1 by the High-.mu. (1.sup.st gen) device,
which among other differences, uses a single layer core.
[0041] In some embodiments, the magnetic coupling between the fixed
solenoids 202 with multi-layer highly permeable cores, and the time
varying bias magnetic field generated by the vibrating magnetic
core 208 results in a large magnetic flux reversal and maximized
flux change in the solenoids 202, leading to a high maximum power
of 610.62 mW, and a maximum power density of 20.84 mW/cm.sup.3 at a
frequency of 42 Hz.
[0042] FIG. 3A is a top-view image of an exemplary energy
harvesting device 300, and FIG. 3B is a side-view image of the
exemplary energy harvesting device 300 of FIG. 3A. The device 300
includes solenoids 302A, 302B, each with a copper wire coil 304A,
304B formed around the core, and wrapping 306A, 306B made of a thin
insulator (e.g., teflon, paper, etc.) to hold the respective copper
wire coil 304A, 304B in place about the core. In this example, each
solenoid 302A, 302B core is a 28-layer high permeability
MuShield.RTM. material, with dimensions 2 cm.times.2 cm.times.0.002
inch for each layer. In some embodiments, the copper wire coils
304A, 304B are made of copper wire (e.g., with a diameter of 1 mm
or 40 mils). In some embodiments, the copper wires include 2-5
layers of copper coils, and each layer includes 20-50 turns around
the core. The coil resistance of each solenoid 302A, 302B is 1.3
Ohm. Each solenoid 302A, 302B is held in place by a mount 308A,
308B made of a dielectric material (e.g., acrylic, or other
insulator material). In some embodiments, the copper wires are
coated with a thin insulator.
[0043] The magnetic core 310 includes two SmCo hard magnets 312,
314 with dimensions 2.2 cm.times.1.3 cm.times.0.2 cm. The two
magnets 312, 314 are joined by a non-magnetic spacer to produce a
fringing field that is coupled to the solenoids on the two ends of
the hard magnets. The magnetic core 310 is mounted on spring 320,
which has a circular cross-section. The magnetic core 310 can
vibrate within the area formed by the mount 308A, 308B and supports
316, 318. In this example, the device 300 is powered by a vibrating
stage that is driven by an audio power amplifier, and its
mechanical movement is monitored by an accelerometer. The voltage
output of the harvester 300 in the time domain is monitored by a
digital oscilloscope. Total volume of the energy harvester is 6.44
cm.times.3.25 cm.times.1.4 cm=29.3 cm.sup.3, which includes the
solenoids 302A, 302B, the magnetic core 310 and the gap between the
solenoids 302A, 302B and the magnetic core 310.
[0044] FIG. 4 is a graph 400 of measured open circuit voltage (V)
of the energy harvesting device 300 of FIGS. 3A-3B over time (s)
using three different springs in accordance with certain
embodiments. Each spring has a different resonance frequency:
spring #1 has a resonance frequency of 27 Hz, spring #2 has a
resonance frequency of 33 Hz, and spring #3 has a resonance
frequency of 42 Hz. For the first spring #1, the peak voltage is
1.18 V for an acceleration of 2 g (where g=9.8 m/s.sup.2), and the
maximum output power on a 2.6 Ohm load is 133.88 mW. For the second
spring #2, the peak voltage is 1.64 V for acceleration of 3 g,
resulting in a maximum output power of 258.62 mW on a 2.6 Ohm load.
For the third spring #3, the maximum induced voltage is 2.52 V for
an acceleration of 5 g, with the corresponding power 610.62 mW on a
2.6 Ohm load. Increasing acceleration values were applied to
maintain the same source vibration amplitude. Considering that the
total practical volume of the device is 29.3 cm.sup.3, this device
demonstrated excellent performance with the maximum power density
of 20.84 mW/cm.sup.3 at 42 Hz. Graph 400 demonstrates that a higher
resonance frequency leads to a larger output power.
[0045] The Q factor of the harvester at 42 Hz was 16, which was
obtained from the decay curve of output voltage when turning off
the source. Almost the entire device damping is generated from the
mechanical collision between the spring supported magnetic core and
the solenoid supports. Therefore, other crafting techniques that
reduce this mechanical collision could achieve a much higher Q
factor while using a much lower input force or acceleration (e.g.,
by designing the magnetic core such that it floats along a rail, to
include bearings to reduce the friction against the surrounding
supports, to include a material that reduces the friction between
the magnetic core and the surrounding supports, etc.). A simple
relation between frequency and power can be derived from Equation
(3), as shown below in Equation (4), if all other parameters kept
constant:
P.sub.max.about.(.DELTA.M/.DELTA.T).sup.2.about.f.sup.2 (4)
where: .DELTA.M is the flux change per period; .DELTA.T the period;
and f is the frequency.
[0046] Measured test results confirm the parabolic curve fitting,
as shown in FIG. 5, which is a graph 500 of the output power (mW)
of the energy harvesting device achieved for the different
frequencies (Hz) of the three springs graphed in FIG. 4. In some
embodiments, the vibration energy harvester design can accommodate
different vibrating frequencies of the environment by changing the
spring that is connected to the magnetic core. For example, a
larger vibration frequency of the environment (for a particular
application) can induce a higher output power if matched with a
spring with an appropriate resonance frequency. In some examples,
if the vibration amplitude of the testing stage is kept the same,
the output power and power density are proportional to the second
power of the vibration frequency. If P.sub.max.about.f.sup.2 can be
extrapolated to higher frequencies, a higher output power density
can be achieved while maintaining a constant amplitude.
[0047] FIG. 6 is a graph 600 of the power density (mW/cm.sup.3) of
the energy harvesting device based on the frequency (Hz). Graph 600
shows that the output power demonstrates a sagging rise before 42
Hz, which achieves a maximum output of 610.62 mW, and then rapidly
declines afterwards. The asymmetrical curve can be caused by the
nonlinear oscillation, which can increase the mechanical damping as
the frequency ascends. The half-power bandwidth of the device with
spring #3 was measured to be 6 Hz, or .about.15% of the central
frequency, which is much higher than the typical 2-5% bandwidth of
typical piezoelectric cantilever-based energy harvesters.
[0048] Upon review of the description and embodiments of the
present invention, those skilled in the art will understand that
modifications and equivalent substitutions may be performed in
carrying out the invention without departing from the essence of
the invention. Thus, the invention is not meant to be limiting by
the embodiments described explicitly above, and is limited only by
the claims which follow.
* * * * *