The present disclosure relates generally to methods and apparatus for converting mechanical energy into electrical energy, and in particular to systems and methods for converting electromotive forces to electrical energy.
This section introduces aspects that may help facilitate a better understanding of the disclosure. Accordingly, these statements are to be read in this light and are not to be understood as admissions about what is or is not prior art.
With the advent of wearable electronics and sensors in recent years, the ambient energy from human motion kinetic energy has become a large area of interest. The implementation of effective energy harvesting in low power wireless applications has led to long device operating lifetimes. Many different approaches have been taken for kinetic energy harvesting, the two most dominant being piezoelectric and electromagnetic.
Devices exist that convert vibration energy into electrical energy. However, such devices to date are not efficient enough to warrant widespread use, such as, for example, to power portable electronic devices or supplementally charge a battery.
For example, U.S. Pat. No. 7,009,315 discloses an apparatus for converting vibration energy into electric power which electrically converts vibration energy produced when a power system is working. The apparatus includes a bar magnet unit and a coil unit helically wound around the magnet unit. The device also uses a damping spring positioned between the magnet unit and the coil unit for holding the magnet unit at the helically neutral position of the coil unit during non-vibration and for attenuating the transmission of vibration to the coil unit during vibration. The device obtains electrical power by picking up a current flowing to the winding of the coil unit responsive to a change in the magnetic field generated when the vibration produced in the power system causes the magnet unit to move reciprocally along the helical axis of the coil unit. The device however, is constrained to movement along one or two linear axes, as illustrated for example, in FIGS. 1-4 of the '315 patent.
The use of fixed magnets to provide spring force eliminates the use of a physical spring, one of the most likely components to fail in a mechanical spring-damper system. There are also no wires attached directly to the moving mass, further eliminating another fault condition. Levitating magnet energy harvesters utilize Faraday's law of induction which states that a changing magnetic flux through a coil will result in an induced electromotive force. This EMF can be attached to a load and used to power an external system. These magnetic levitation harvesters have shown success in many different applications, ranging from wrist shaking to vehicle suspension.
One of the main difficulties with all previously presented levitating magnet energy harvesters has been their limited degrees of freedom and their high resonant frequencies. They have been limited to only one orientation for proper or ideal operation. If the harvester is tilted at an angle or rotated within the ideal orientation, harvester output can become greatly limited or eliminated. Researchers have developed devices that respond in this way as a consequence of having a free magnet that is free to move in one dimension only. Devices that have achieved rotation independence have done so without the capability of harvesting low frequency vibrations less than 10 Hz, as is needed for human walking energy harvesting. Other researchers have developed rotation independent energy harvesters but with resonant frequencies of 25 Hz and 370 Hz, respectively. Yet other researchers have developed energy harvesters with a resonant frequency of 10 Hz was developed by Moss et al., but their device is not rotation independent in its performance.
The limitation of the harvester rotation presents issues when the harvester may be worn, and the wearer is not careful to attach the device a proper rotation. Given the desire to use these harvesters in wearable electronics, it is expected that the device will rotate and be held at different angles. Clip-on devices will likely be clipped at angles and often even upside down, rendering 1-dimensional harvesters inoperable. Furthermore, while human walking has a predominant vertical acceleration force, there are also horizontal vibrations which are not utilized in these limited harvesters.
As a consequence of the constraint, the ability to generate electricity is limited to certain types of vibration and orientation. Therefore, there is an unmet need for a novel kinetic energy to electrical energy converter that is capable of taking advantage of two dimensional degrees of freedom and which can generate electrical energy based on frequencies associated with human walking.
A kinetic energy to electrical energy converter is disclosed. The converter includes a housing defining a cavity having a circumference and covers enclosing the cavity. The converter also includes at least one fixedly supported perimeter magnet disposed about the circumference. The converter further includes at least one magnetically levitating center magnet magnetically influenced by the at least one fixedly supported magnet, disposed in the cavity and limited to substantially a two dimensional movement by the covers. Furthermore, the converter includes at least one coil fixedly supported with respect to the fixedly supported perimeter magnet. Movements of the at least one center magnet is configured to generate an electrical current in the at least one coil.
A method of converting kinetic energy to electrical energy is also disclosed. The method includes providing a fixedly supported perimeter magnet disposed in a housing defining a cavity having a circumference and covers enclosing the cavity. The method also includes levitating at least one center magnet magnetically influenced by the at least one fixedly supported magnet, disposed in the cavity and limited to substantially a two dimensional movement by the covers. The method further includes providing at least one coil fixedly supported with respect to the fixedly supported perimeter magnet. Furthermore, the method includes generating an electrical current in the at least one coil in response to movements of the at least one center magnet.
For the purposes of promoting an understanding of the principles of the present disclosure, reference will now be made to the embodiments illustrated in the drawings, and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of this disclosure is thereby intended.
The levitating magnetic energy harvester presented is capable of harvesting energy from ambient vibrations in two dimensions along the harvester's plane of operation, thereby allowing the energy harvester to be rotated at any angle and will not suffer from performance degradation. The presented harvester has been tuned to an 8.2 Hz resonant frequency, making it capable of harvesting energy from the higher harmonic frequencies of human step frequencies.
Referring to
The fixed magnet 14 in this embodiment is a ring-shaped cylindrical magnet having and south magnetic poles at top and bottom sides thereof. In an alternate embodiment, discussed below, the ring magnet can be replaced by a number of small cylindrical magnets all of which are disposed similarly, e.g., with north poles facing up and south poles facing down. The levitating magnet 12 is suspended or levitated in a position in the interior of the ring-shaped fixed magnet 14, and includes a north top pole and a south bottom pole to align in the same orientation as the north and south poles of the outer fixed magnet 14. Thus, the inner floating or levitating magnet 12 is repelled on all sides within a plane A (not shown, but one which crosses the center of the floating magnet 12 as well as the outer magnet) in which the magnets 12 and 14 reside. The housing or other constraint on vertical movement of the levitating magnet 12 prevents the levitating magnet 12 from being expelled from the plane A (not shown), and preferably from flipping.
It will be appreciated that while the opposing magnetic forces generally hold the levitating magnet 12 in the center of the ring formed by the fixed magnet 14 in plane A (not shown), movement of the converter 10, and particularly the fixed magnet 14, such as by vibration or other kinetic energy, will cause temporary displacement of the levitating magnet 12 within the ring formed by the fixed magnet 14, because the magnetic forces act as springs. After the initial movement, the magnetic forces will tend to move the levitating magnet 12 back to substantially a center position of the ring formed by the fixed magnet 14. Because the levitating magnet 12 moves with respect to the fixed magnet 14, it also moves with respect to the housing (not shown).
The coils 16 are positioned to harvest energy from movements in multiple directions. To this end, the coils are preferably in a fixed relationship with respect to either the housing (not shown), and thereby the fixed magnet 14, or with respect to the levitating magnet 12. Thus, movement of the magnet 12 with respect to the fixed magnet 14 causes a change in flux in one or more of the coils 16, which imparts a voltage across the one or more coils 16. The coils 16 can also have some ferrite core to concentrate flux and improve performance.
The device of
Not only may energy be harvested from the current components IG1, IG2, IG3, and IG4, but also movement in general may be detected, and the direction of movement may he detected. For example, movement of the housing including the outer magnet 14 towards the upper left of the page will cause temporary movement of the inner magnet 12 toward the lower right coil 16, which may cause a unique induced voltage or current distribution among the coils (e.g., unique signature of currents IG1, IG2, IG3, and IG4). This unique distribution can be analyzed and the direction of movement identified.
Referring to
In the embodiment of
In any of the above embodiments of
Referring to
A schematic view of the kinetic energy to electrical energy converter is shown in
Many factors are involved in the design of the energy harvester dimensions and configuration. Due to the desire for full 2-dimensional functionality, symmetry in a circular design is preferential. A sufficient number of perimeter magnets are then required to ensure minimal variation in harvester output due to rotation. Minimal has been defined as a maximum 0.5 Hz variation in resonant frequency with harvester rotation. The magnet force also needs to be sufficient such that the center magnet does not hit sidewalls at appreciable accelerations.
One coil of N turns is z-positioned above the free moving center magnet on one side of the energy harvester. Due to Faraday's law of induction, the changing magnetic flux through this coil will result in an induced EMF. The coil output may then be attached to a load and electrical energy may be harvested from the motion of the center magnet. The inductance of the coil can be roughly estimated using air core coil inductance calculators to be about 50 μH. With a frequency of 10 Hz, this is an impedance of 3Ω, or about less than 1% of the coil resistance.
A low resonant frequency is desired such that the harvester can be used in human walking kinetic energy harvesting applications. Dominant step frequency of human walking falls at around 2-3 Hz. Due to the inherently inverse relationship between resonant frequency and harvester size, obtaining a resonant frequency in the 2-3 Hz range would require a large harvester, excluding it from wearable electronics applications. For this reason, wearable energy harvesters to date are designed to have a resonant frequency matching one of the higher harmonics of the dominant step frequencies, around 6-8 Hz.
The energy harvester may be modeled mechanically as a mass-spring-damper system, as illustrated in
As shown in
wherein, Fmag is the fixed magnet force,
The electromagnetic damping force Fem is the force that acts to resist the magnet's motion near the coil. It is caused by the magnetic field that the coil generates as current is induced by the changing flux of the moving magnet. This force is responsible for the energy from the magnet's motion that is being harvested. The instantaneous power delivered to the coil and load as a function of coil open circuit voltage Voc, coil flux ΦB, load resistance Rload, and coil resistance Rcoil is
The instantaneous power input from Fem acting against the magnet's motion is
P
in
=F
em
p′(t) (2b)
By conserving energy,
The derivative dΦB/dp is the displacement-derivative of magnetic flux through the coil, a parameter calculated in Section 3.3. It depends on p(t) and is a function determined by the coil placement and magnet characteristics (strength and dimensions). Therefore, Fem is a function of p(t) and p′(t) as shown in Eq. 2. The quantity −mq″(t) is the pseudo-force felt by the magnet due to the acceleration of the casing. Finally, −mg is the force of gravity.
The fixed perimeter cuboidal magnets and the center free moving disk magnet impart a repellant force upon one another. Many different methods and solutions for determining the force between different types and shapes of permanent magnets exist. Some of these methods are semi-analytical or completely numerical and could be used interchangeably, but an analytical solution was sought after in this work. The analytical solution exists for the force between cuboidal magnets. For this reason, the center magnet was modeled as a cuboidal magnet with volume equal to that of the cylindrical magnet used in measurements. This simplification introduces error, but good agreement with the model and experimental measurements shows that the error is minimal.
The force on the center magnet due to fixed perimeter mag-nets was calculated iteratively and then summed. In each case, the center free moving magnet and the fixed perimeter magnet were modeled as a pair of “magnetically charged” parallel plates with σ and σ′ charge, respectively. Since both magnets are the same grade (N42 neodymium), σ=σ′. The coordinates for the pair of cuboidal magnets is demonstrated in
Where μ0 is the permeability of free space.
r=√{square root over ((α+X−x)2+(β+Y−y)2+y2)} (3b)
The pair of magnets have magnetizations J and J′, and they are related to the magnetic charges densities by
σ={right arrow over (J)}·{right arrow over (n)} (4a)
Assuming that {right arrow over (J)} and {right arrow over (n)} are parallel leaves
σ=J and σ′=J′ (4b)
The gradient of the interaction energy is taken to determine the force between the cuboidal magnets. This expression is given by
for force vector components Fx, Fy, and Fz, respectively:
with
u(i,j)=α+(−1)jA−(−1)ia (7a)
v(k,l)=β+(−1)lB−(−1)kb (7b)
w(p,q)=γ+(−1)qC−(−1)pc (7c)
r(u,v,w)=√{square root over (u2+v2+w2)} (7d)
For this analysis, only the y direction force Fy is needed due to symmetry. This force is calculated at discrete y coordinates reachable by the free moving center magnet (x=0). This is done for each perimeter magnet and the Fy forces are then summed, giving the total vertical force on the center magnet as a function of y coordinate. Given that all the magnets are centered on the same x-y plane, and no z displacement is possible, Fz is zero.
When the device is held upright, gravity pulls the center magnet to an equilibrium point y0 where mg=Fy. At this point, the displacement-derivative of Fy can approximate the resonant frequency of the center magnet by Eq. (8b).
A cylindrical magnet with axial magnetization may be modeled as a cylindrical coil of equal diameter and height with azimuthal surface current equal to J, and its magnetic field can then be deter-mined analytically. The coordinate system for the cylindrical magnetic field calculations is shown in
The magnet moves at a z-offset beneath the coil. As the change in magnetic field through the coil results in the induced EMF, the only magnetic field component of interest is the Bz. B runs tangential to the coil surface and Bφ is zero. The expression for Bz above the magnet is split into two regions of interest; the region above the magnet within the radius of the magnet, and the region above the magnet outside the radius of the magnet. These are respectively given by
where F(a; b; c; d) is the Gaussian hypergeometric function, and B∞ is the B-field intensity that would be inside a solenoid of equal diameter and surface current, but of infinite length.
B∞=μ0J (10)
In computer modeling, the summations are finite, and an adequate upper bound for n must be used. Such an adequate value can be determined by comparing the discontinuous values of Bz/B∞ for both expressions at their joining point p=a. The discrepancy is large with small n upper bounds less than 5 (at n=5, 2.3% discrepancy). An n upper bound of 10 is sufficient to close this discrepancy to less than 0.1%. The simulation in this work uses an n upper bound of 50, to ensure accuracy with reasonable simulation times. Once the magnetic field z-component Bz can be known for any point above the magnet, where the coil will be, then the magnetic flux φB can be calculated with
ΦB=∫∫SBrdA (11)
where S is the total surface enclosed by each loop of the coil. This general form of the equation accounts for the multiple loops of wire, and is necessary since Bz will vary along the different heights and diameters of the turns of the coil. The magnetic flux φB will be a function of magnet position p(t), and the coil voltage will be the derivative
This voltage will be distributed across the coil resistance and the load resistance in series.
The radius of the coil in the presented harvester was chosen so that the edge of the coil is at the same level as the equilibrium point of the center magnet. This is due to there being maximum change in flux through the coil when the magnet is crossing the coil edge. Therefore, the inner and outer radii of the coil were chosen to be 8.5 mm and 12.5 mm, respectively. With the coordinate system shown in
The magnetic flux through the coil was calculated numerically. First, Bz was calculated at discrete values as a function of and z. Then, the magnetic flux φB through the coil's 1200 turns of varying radii and heights was found by numerical integration to approximate Eq. (11), as a function of the y coordinate of the center magnet.
A MATLAB/SIMULINK model has been developed to aid in optimizing energy harvester design. The model implements the equations in the previous subsections to simulate the center magnet's motion in response to an external excitation of choice. This in turn allows the model to simulate power delivery to a load of choice. The model for the presented harvester was constructed using the derived parameters shown in
The equilibrium point y0 is determined in the model to be at y=−6.2 mm. Using Eq. (8b), this yields a resonant frequency of 8.15 Hz.
A Simulink time step model simulates the energy harvester operation by solving Eqs. (2), (2d), and (12). Through this time step model, several values are calculated. Of importance is the induced voltage in the coil, named hereafter as the open circuit voltage,
where φB is the total flux through the coil (the number of turns has been accounted for). From here, load voltage can be determined with coil resistance Rcoil, and load resistance Rload by
The instantaneous and average power delivered to the load, respectively, are
The model finds the average power delivered to the load for the given parameters of the simulation, such as vibration profile, center magnet starting position, and harvester rotation.
An initial modeling test to perform is the ring down test. With the harvester held upright and with no external excitation, the center magnet is brought to a specific height, and then quickly released. The result is a damped, undriven oscillator. The test is shown in
To determine the best combination of Ff and cp, one can calculate the error between modeled and measured results of the discrete data sets of the two ringdown tests above.
The logarithm is taken twice in order to facilitate locating the minimum value of error on a contour plot error as a function of Ff and cp is shown in
A look at the good agreement in
With a versatile model in place, a few important optimization simulations can be produced. These simulations provide an important insight in what direction to take towards an optimal design, while reducing the need for excessive prototyping. The following simulations rely on a couple important parameters that are both modeled and measured, and are shown in Section 4. These include the optimum load for power transfer, 1700Ω, and the optimum excitation frequency, 8.2 Hz. It should also be noted that while the model is capable of simulating with a pure sinusoidal external excitation, better agreement was observed by inputting the accelerometer waveform from the shaker that was used to con-duct measurements on the presented harvester. These simulations therefore use the accelerometer data from said shaker as excitation input. The following examples show some of the optimization capabilities that the model can realize.
Using the presented harvester's dimensions and perimeter mag-net count of 12, a simulation to optimize the diameter and location of the coil can be generated. This simulation assumes the number of turns in the coil remains 1200, and that the coil is only moved up or down, along the y axis, on the harvester casing. Additionally, this optimization is while the harvester is under an 8.2 Hz, 0.2 g excitation. Different optimizations may be reached for different excitations.
The simulation from
If the coil is instead held constant, so that its parameters are as those of the presented harvester, then a simulation to optimize the dimensions of the harvester, and the number of perimeter magnets can be generated. This is shown for an excitation frequency of 8.2 Hz in
The model can be further configured to optimize more than two parameters at a time, however, figures can't clearly demonstrate this. Mainly, the optimization techniques shown are to display the versatile nature of the model, and that an optimization process can be created to design a device that is best suited for a particular purpose. This is done by identifying a few desired characteristics for the device, such as resonant frequency, size constraint, optimum load size, etc. Then, an optimization model can be used to determine the remaining design parameters, such as number of perimeter magnets, radius to perimeter magnets, coil location and size, even center and perimeter magnet strength and mass.
A few tests are performed using the presented harvester in order to determine its power output, as well as its agreement with the model for model validation. A load sweep test determines the optimum load for maximum power transfer when the harvester is subjected to an external excitation of 8.2 Hz and 9.0 Hz, with a maximum acceleration of 0.1 g.
The test, results of which are shown in
A frequency sweep determines what frequency excitation leads to the greatest power delivery to the load. This test is done at 0.1 g and 0.2 g maximum acceleration to introduce measurement variation.
The test, results of which are shown in
The tests were performed with a rectifying circuitry 230 that is shown in
Lastly, an acceleration sweep test is shown in
The harvester's rotation independence to power output, is also demonstrated. While the harvester exhibits nearly uniform response as a function of rotation in the x-y plane, the discrete nature of the perimeter magnets results in a periodic change in response as the harvester is rotated. Due to the symmetric arrangement of the perimeter magnets, the response is repeated periodically every 360/n° of rotation, for n equally spaced and symmetrically positioned perimeter magnets. For the 12 perimeter magnet configuration presented, the response of the harvester is periodic every 30° of rotation. The resonant frequencies for a full rotation of the harvester are shown in
The measured power output can also be shown to remain fairly constant as a function of device rotation. This is shown in
In the general theory of operation, the levitating non-fixed magnet is suspended in position by the fixed magnet(s). Either the levitating magnet can be surrounded by the fixed magnets (
Those skilled in the art will recognize that numerous modifications can be made to the specific implementations described above. The implementations should not be limited to the particular limitations described. Other implementations may be possible.
The present U.S. patent application is related to and claims the priority benefit of U.S. Provisional Patent Application Ser. No. 62/094,003, filed Dec. 18, 2014, the contents of which is hereby incorporated by reference in its entirety into this disclosure.
Number | Date | Country | |
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62094003 | Dec 2014 | US |