Kinetic energy harvesting from human walking and running using a magnetic levitation energy harvester

Accepted Manuscript Title: Kinetic Energy Harvesting from Human Walking and Running usinga Magnetic Levitation Energy Harvester Author: D.F. Berdy D.J. Valentino D. Peroulis PII: DOI: Reference:

S0924-4247(14)00512-3 http://dx.doi.org/doi:10.1016/j.sna.2014.12.006 SNA 8988

To appear in:

Sensors and Actuators A

Received date: Revised date: Accepted date:

17-8-2014 1-12-2014 6-12-2014

Please cite this article as: D.F. Berdy, D.J. Valentino, D. Peroulis, Kinetic Energy Harvesting from Human Walking and Running usinga Magnetic Levitation Energy Harvester, Sensors & Actuators: A. Physical (2014), http://dx.doi.org/10.1016/j.sna.2014.12.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

- First experimental study of an electromagnetic vibration energy harvester on human participants while walking and running on a treadmill - Optimized device damping to allow the device to operate at 50% lower acceleration input

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- average of 342 μW power output when placed on a person walking at 6 mph

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- average of 71 μW power output when placed on a person walking at 3 mph

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Kinetic Energy Harvesting from Human Walking and Running using a Magnetic Levitation Energy Harvester D. F. Berdya,b,, D. J. Valentinoc , D. Peroulisa,b,d a School

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of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA b Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA c LANDAUER, Inc, Glenwood, IL, 60425, USA d School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA

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Abstract

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For the first time, the power output of an electromagnetic magnetic levitation vibration energy harvester was studied when placed on 10 human participants while walking and running on a treadmill from 2 mph (3.2 km/hr) to up to 7 mph (11.3 km/hr). The power generated from the device when participants walked at 3 mph (4.8 km/hr) averaged 71 µW. When running at 6 mph, the power increased to 342 µW. The testing on participants revealed that due to unique gaits and body structure, acceleration spectrum and damping can vary significantly between participants. Taller participants had a lower step frequency and therefore lower frequency acceleration content, signifying that a single design may not be optimal for all participants. Additionally, the estimated damping force varied largely between participants, from 3 to 8 mN. To minimize the effects of damping, the paper studies the effect of angle of attachment and damping reduction techniques using low friction materials and a guide rail system, which improve power output by over 50% when compared to the sub-optimal design.

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Keywords: electromagnetic, vibration, energy harvesting, magnetic levitation, walking, running

1. Introduction

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Developments in wireless and low power portable electronics have led to new applications for wearable electronics in consumer products and healthcare monitoring [1, 2]. A drawback of current electronics is that battery lifetime is limited. To alleviate this problem, researchers have focused on developing devices to harvest energy from human motion and vibrations during daily activities such as walking [3]. Harvesting and converting ambient energy into electrical energy is of great interest because it can extend battery life or completely replace batteries. In vibration (or kinetic) energy harvesting, mechanical kinetic energy is converted into useful electrical energy by utilizing piezoelectric [4–6], electromagnetic [7, 8], electrostatic [9, 10], or magnetostrictive [11] transduction mechanisms. One device well-suited for converting human kinetic energy is a magnetic levitation energy harvester [12–20]. This device can achieve a very low resonant frequency, which is ideal for converting human kinetic energy into useful electric energy because human kinetic energy is concentrated at frequencies below 10 Hz. An additional advantage of the device is that there is no physical spring, thus leading to a long lifetime because the physical spring is the most common point of failure. In this paper, we measure, for the first time, the power output of a magnetic levitation vibration energy harvester on human

Email addresses: [email protected] (D. F. Berdy), [email protected] (D. J. Valentino), [email protected] (D. Peroulis) Preprint submitted to Sensors and Actuators A: Physical

participants while they walk and run on a treadmill. A potential issue with magnetic levitation energy harvesters is damping of the levitating magnet due to the guide box or guiding system design. The damping likely increases in a real world application, where the energy harvester may not always be vertical and perfectly aligned with the excitation force due to different body types, gait style, and variation in device attachment. Therefore, before testing on human participants, we explore techniques to reduce damping by implementing designs with different guide rail systems and materials. 2. Magnetic Levitation Energy Harvester A diagram of the magnetic levitation vibration energy harvester is shown in Fig. 1. The energy harvester consists of a levitating magnet, fixed magnets, guide box and coil. The polarity of the magnets are arranged so the levitating magnet experiences a repulsive force due to the fixed magnets. In the diagram, fixed magnets are only shown on the bottom of the box, but they could also be added to both top and bottom ends of the box. When the box experiences an acceleration, the levitating magnet oscillates in the guide box. Ideally, the frequency of the acceleration on the guide box matches the resonant frequency of the device to maximize mass movement and thus maximize power output. As the levitating magnet moves through the coil wrapped around the box, a voltage is induced on the coil, producing a current that flows into an attached electrical load. The design and optimization of the energy harvester has been presented previously [21]. The initial design was and made December 12, 2014

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1.15 mm

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Figure 2: Diagram of design dimensions of the levitating energy harvester [21].

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Table 1: Final design dimensions and values of energy harvester

Dimension hb Ll × wl × hl Lf × wf × hf Ls Zc hc m J

Two main factors are explored in this paper to improve device performance by reducing parasitic damping: box cross section and box material. First, two box cross sections are studied to determine their effect on performance. The cross sections are shown in Fig. 3 and consist of a box with a guide rail and without a guide rail. The guide rail is a 0.5 mm radius extrusion that runs the height of the box. In the box without the rail, the corners were removed so that the radius of the corners due to limitations of the machining process would not block the magnet from moving. The purpose of the guide rails is to minimize the contact area of the box with the levitating magnet. Qualitatively, it is expected that the box with guide rails will achieve a lower damping because there is less friction on the levitating magnet. Experimentally, we observe this in Section 4. In addition to the box cross section, the box material is also studied. Coefficients of friction vary between materials, therefore material choice affects damping because the levitating mass is in contact with the box. The box material is limited to electrical insulators because conductive materials would induce eddy currents in the box, thus significantly increasing damping. In this paper, we study boxes made of acrylic and Polytetrafluoroethylene (PTFE, also commonly known as Teflon). Due to the lower coefficient of friction of Teflon, it is expected to have a reduced damping and thus higher power output. A third effect studied is the angle of attachment of the device. In real world applications, the device may not always be aligned perfectly with gravity or with the excitation force. Therefore, in this paper, we study how the device attachment angle effects power output and damping. Furthermore, we demonstrate that implementing the damping reduction techniques makes device performance less dependent on the angle of attachment.

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Figure 1: Diagram of levitating block magnet vibration energy harvester [21].

Value (mm) 35 mm 25.4 mm × 3.175 mm × 12.7 mm 3.175 mm × 3.175 mm × 1.6 mm 14 mm -2.5 mm 4 mm 7.7 grams 1.3 Tesla

from an acrylic box with Neodymium permanent magnets and achieved a measured power output of 410 µW at 0.1 g, 6.7 Hz acceleration in a package less than 30 mm × 10 mm × 40 mm, for a normalized power density of 7000 µWcm−3 g−2 . The device dimensions were limited due to the application requirements. The designed dimensions of the energy harvester are shown in Fig. 2 along with the values for each dimension in Table 1. The coil has 1000 turns. In the table, m is the mass of the levitating magnet and J is the strength of the magnets.

3. Energy Harvester Model The model of the energy harvester was developed in [14] and [21]. The differential equation of the model was obtained by summing the forces on the levitating magnet with the equation: h i m¨z(t)+ ce (z(t)) + c p z˙(t)+F Fric −Fmag (z(t))+mg = −m¨y(t) (1) 2

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Acrylic with guide rail

Teflon with guide rail

Figure 4: Fabricated devices, from left to right: acrylic box without guide rail, acrylic box with guide rail, PTFE box with guide rail.

Accel.

where m is the levitating magnet mass, ce (z(t)) is the electrical damping, c p is the parasitic viscous damping coefficient, F Fric is parasitic dry friction damping, Fmag (z(t)) is the the magnetic force, g is gravity, y(t) is the displacement of the device frame due to external forces, and z(t) is the displacement of the mass relative to the device frame. In this equation, both viscous and dry friction (Coulomb) damping are shown. In most literature, only viscous damping has been modeled, but it is likely that both occur in this type of device because the magnet can make contact with the box causing friction. Previously we found the damping mechanism to be dominated by dry friction damping [21], although it is likely that there is also a viscous contribution. The dry friction was modeled using:

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Figure 5: Device placed vertically (left) and at an angle of 30◦ (right).

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adjusted to apply the stated acceleration in the direction of the device. For example, when the device was vertical, at 0.1 g excitation, 0.1 g was actually applied in the direction of the levitating magnet; but when the device was at an angle, only 0.1cos(30), or 0.087 g, was applied in the direction of the levitating magnet. First, the open circuit ringdown waveform was captured for each device in every mounting configuration. The ringdown test was performed by pulling the magnet to the top of the box and releasing it to ring down within the box. The model and measurement results of the ringdown waveform are shown in Fig. 6. It was found that the measured device frequency was about 0.3 Hz higher than the model’s prediction, due to the shaker’s internal magnet and deviation in the device dimensions and material properties. The damping force was found by fitting the model ringdown with the measured ringdown waveform. Next, a load resistor was attached to the device and the RMS power was found. To find the optimal frequency of operation, the power versus resistance was measured for several frequencies around the resonant frequency. The frequency which achieved the peak power was selected. The plot of power versus resistance for 0.1 g acceleration at the optimal frequency for each device at each angle is shown in Fig. 7. Similar measurements were performed for 0.075 g and the optimal results are listed in Table 2. The table shows the maximum output power for each device under each operating condition. Additionally, the power output for the devices was measured for accelerations from 0.05 g to 0.2 g, with the results plotted in Fig. 8.

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where z˙(t) is the velocity of the levitating magnet and Fd is the magnitude of the dry friction damping force. The model in equation (1) can be solved using a time step model in Simulink. In the model, the magnetic force and the magnetic flux through the coil were calculated based on analytic equations [22, 23]. The damping is dependent upon the type and shape of the materials, thus the devices were fabricated in order to better estimate the damping. 4. Experimental Results on Electrodynamic Shaker

The fabricated devices are shown in Fig 4. Three different boxes were made: acrylic box without guide rail, acrylic box with guide rail, and Teflon box with guide rail. The boxes were machined using computer numeric control (CNC) machining from the respective materials. All dimensions are the same for each box, as shown in Table 1 and the 1000-turn coil was wrapped using 42 AWG (63.5 µm diameter) wire with a resistance of 450 Ω. The magnets are grade N42 Neodymium magnets. The device was tested on a TIRA TV 51120 electrodynamic shaker with an ADXL203 accelerometer attached to measure the applied acceleration. Three different mounting configurations were tested: vertical, 15◦ angle offset, and 30◦ angle offset. The mounting for vertical and 30◦ angle offsets are shown in Fig. 5. As shown in the figure, the acceleration was always applied in the same direction relative to the mounting platform. It was not applied in the direction of the device, but at an angle to the device. Also, the amplitude of acceleration was not

5. Discussion of Electrodynamic Shaker Results The open circuit ringdown waveforms in Fig. 6 illustrate the modeled damping (Fd ) for each configuration. The graphs show that the acrylic device with guide rail has lower damping than the device without the guide rail. In fact, the damping force (Fd ) was reduced by almost 50%. Additionally, changing the material to Teflon further reduced damping as was expected due to its lower coefficient of friction. Therefore, in order to optimize the device performance, it is recommended that the designer reduce the levitating magnet contact area with the box while also 3

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Figure 6: Measurement and model results of open circuit voltage ringdown waveform for all three devices while mounted: (a) vertically, (b) at a 15◦ angle, and (c) at a 30◦ angle.

Table 2: Summary of measurement results

Accel. (g) 0.1 0.1 0.1 0.075 0.075 0.075 0.1 0.1 0.1 0.075 0.075 0.075 0.1 0.1 0.1 0.075 0.075 0.075

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Angle Vertical Vertical Vertical Vertical Vertical Vertical 15◦ 15◦ 15◦ 15◦ 15◦ 15◦ 30◦ 30◦ 30◦ 30◦ 30◦ 30◦

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Device Acrylic, no rail Acrylic, with rail Teflon, with rail Acrylic, no rail Acrylic, with rail Teflon, with rail Acrylic, no rail Acrylic, with rail Teflon, with rail Acrylic, no rail Acrylic, with rail Teflon, with rail Acrylic, no rail Acrylic, with rail Teflon, with rail Acrylic, no rail Acrylic, with rail Teflon, with rail

Freq. (Hz) 6.7 (meas.) 6.7 (meas.) 6.7 (meas.) 6.7 (meas.) 6.7 (meas.) 6.7 (meas.) 6.6 (meas.) 6.6 (meas.) 6.6 (meas.) 6.6 (meas.) 6.6 (meas.) 6.6 (meas.) 6.1 (meas.) 6.1 (meas.) 6.1 (meas.) 6.1 (meas.) 6.1 (meas.) 6.1 (meas.)

Max Power (µW) 327 410 392 202 304 326 243 322 363 ∼0 138 235 ∼0 ∼0 147 ∼0 ∼0 73

double when moving from a 15◦ to 30◦ angle.

using a low friction material such as Teflon. The main drawbacks of Teflon are that it is generally more expensive and not as easy to manufacture compared to other plastics.

In Fig. 7(a), the power output is limited by the levitating magnet displacement limit. As seen in the figure, the power reaches a peak point and then abruptly begins to decrease. This is because the levitating magnet displacement is limited by the height of the box. This displacement limit only allows the levitating magnet to move 10 mm from the box center. If the box height were increased, the power output could be increased, but the application requirements do not allow an increase in box height. The other option would be to decrease the levitat-

As the device is placed at an angle, the damping increases as shown by the ringdown waveforms. Stepping from 15◦ angle to 30◦ angle, the friction force (Fd ) approximately doubles. In theory, the friction force is proportional to the sine of the angle. Therefore, this doubling in friction force makes mathematical sense, because for 15◦ , the sin(15) is 0.26 and for 30◦ , the sin(30) is 0.5, meaning that the force should approximately 4

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Figure 7: Measurement and model results of AC RMS power at 0.1 g excitation for all three devices while mounted: (a) vertically, (b) at a 15◦ angle, and (c) at a 30◦ angle.

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Figure 8: Measured optimal power versus acceleration amplitude with devices at (a) vertical, (b) 15◦ angle and (c) 30◦ angle

ing magnet height, but this would reduce the levitating magnet mass, resulting in reduced power output at lower acceleration amplitudes or when the device is placed at an angle. Based on the vertical measurement results summarized in Table 2, the acrylic device with guide rail outperformed the device without the guide rail. At 0.1 g the device without the guide rail produced 327 µW while with the guide rail it produced 410 µW (a 25% improvement). At 0.075 g the improvement was more pronounced, resulting in a 50% increase in power. The power output of the acrylic and Teflon devices with rail were similar at 410 µW and 392 µW, respectively, when vertical. They have similar power output because the estimated damping force on these devices is similar at 0.001 and 0.0008 Newtons, respectively. Additionally, the displacement of the levitating magnet is limited by the box height, and therefore the

power output is limited. The results show that the acrylic device has slightly higher power output, but their powers are close enough that the difference can be attributed to fabrication and measurement tolerance. As seen in Table 2, the difference in power becomes more pronounced at 0.075 g, with 304 and 326 µW, for acrylic and Teflon with the rail, respectively. As the acceleration decreases the damping has more of an effect on the acrylic device. At an angle of 15◦ , as shown in Fig. 7(b), the Teflon device shows a larger improvement over the acrylic devices. The Teflon device achieved 13% higher power than the acrylic with guide rail at 0.1 g, and 70% higher power at 0.075 g. The use of Teflon versus acrylic has a large effect at an angle because friction forces become stronger due to the larger normal force. At the 30◦ angle in Fig. 7(c), the only device that had some power 5

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output was the Teflon device because the static friction could not be overcome by the excitation force in both of the acrylic devices. To determine when the devices overcame static friction and began to operate, they were tested at several different acceleration levels as shown in Fig. 8. The devices produced power at every level when vertically mounted, and became saturated at 0.15 and 0.2 g acceleration levels. Even at 0.1 g the levitating magnet reached the displacement limitation. While at a 15◦ angle, the devices overcame static friction between 0.05 and 0.1 g acceleration. Eventually as the acceleration level increased to 0.15 and 0.2 g, all the devices reached the same power output because the power output became saturated due to the displacement limit imposed by the box height. At a 30◦ angle, the devices again did not operate at 0.05 g, and only the Teflon device operated at 0.075, 0.1, and 0.15 g. Eventually at 0.2 g, the acrylic devices overcame the static friction and began to operate. In Fig. 7, as the angle increases, the optimal operating frequency decreases. This is because when the device is at an angle, the force of gravity acting on the levitating magnet is reduced. With a reduction in the effective force of gravity, the levitating magnet’s static equilibrium point moves higher in the box. If the equilibrium point changes, the spring constant and thus resonant frequency also change due to the nonlinear nature of the spring. This explains why, when the angle increases from 0◦ to 30◦ angle, the measured optimal frequency changes from 6.7 Hz to 6.1 Hz. The results in Table 2 and Fig. 7 show that the power output of the Teflon device with the rail varied less with the angle of the device placement. Comparing the devices, the Teflon power output was reduced by 7% moving from vertical to 15◦ angle, whereas the acrylic device with the rail was reduced by 21%, and acrylic without the rail was reduced by 26%. Considering the 30◦ angle measurements, the Teflon power output only reduced by 63% compared to vertical, whereas the acrylic devices have no power output. This result is important to the human testing because it verifies that the Teflon device’s power output is less dependent on the mounting of the device on the human participants.

Accelerometer

Measured Acceleration Direction

Energy Harvester

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Data Acquisition Hardware

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(protected with Kapton tape)

Figure 9: Vest with energy harvester and data acquisition hardware.

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the device, as shown in Fig. 9, then it was placed inside a plastic name badge holder along with an ADXL335 accelerometer to measure the applied acceleration. Only the acceleration along the levitating magnet’s movement direction was recorded. The name badge holder with energy harvester and accelerometer were attached to a vest that also contained wireless batterypowered data acquisition hardware, as shown by a dashed outline in Fig. 9. The vest was fitted on human subjects while they walked on a treadmill.

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6.2. Optimal Load Resistance

6. Testing on Human Subjects

The testing in this section was performed under the approval and guidance of Purdue University’s Institutional Review Board (IRB). All procedures were followed according to the testing protocol approved by the IRB. The testing was completed at Purdue’s Recreational Sports Center under the supervision of the staff at the center.

In this study, the AC RMS power across a load resistor attached to the energy harvester was measured. Therefore, before beginning the experiments on the treadmill, the approximate optimal load resistance was found. To determine the optimal load resistance, one participant walked at a normal pace of about 3 to 3.5 mph (4.8 to 5.6 km/hr) for 30 seconds with several different load resistances attached. The test was repeated 3 times for each load resistance value. The results are shown in Fig. 10. The solid line connects the average value of the 3 different data points. The optimal resistance was about 680 Ω. In the remaining tests, a 1000 Ω load was used instead of 680 Ω. In previous tests of the device using the electrodynamic shaker, the optimal resistance was between 1000 and 2000 Ω, as seen in Fig 7. Considering that the frequency and acceleration applied to the energy harvester varies based on each individual’s walking style, 1000 Ω was selected because the penalty for choosing a lower than optimal load resistance is more severe than choosing one that is higher than the optimal resistance. 6.3. Procedure for Testing Power Output With the load resistance set to 1000 Ω, the device was tested on human participants while they walked and ran on a treadmill. The vest containing the energy harvester, accelerometer and data acquisition hardware was fitted to the participant. The treadmill speed started at 2 mph (3.2 km/hr) and the participant was asked to walk for 1 minute while data was collected. The data included the energy harvester voltage (with load resistor attached), and the acceleration in the direction the levitating magnet moves. After 2 mph (3.2 km/hr), the speed was increased by

6.1. Test Setup Based upon the experimental results of the different devices on the electrodynamic shaker, the Teflon device was selected to test on human participants due to its lower damping and the ability to operate at lower acceleration levels. To protect the device, especially the coil, Kapton tape was wrapped around 6

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P a r tic ip a n t 2 ( 3 m p h )

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M e a s u re m e n ts A v e r a g e o f d a ta p o in ts

S te p F re q . 1 .8 8 H z R

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P o w e r ( µW )

R

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(a) Acceleration waveform where ‘L’ indicates strike attributed to left foot and ‘R’ indicates strike attributed to right foot

0.5 mph (0.8 km/hr) increments until 4 mph, then the increment increased to 1 mph (1.6 km/hr). The participant was asked to go up to whatever speed they felt comfortable at, but no more than 7 mph (11.3 km/hr). A total of 8 participants had a maximum speed of 7 mph (11.3 km/hr) while 2 had a maximum speed of 6 mph (9.7 km/hr). In addition to collecting the voltage and acceleration, the point at which each participant switched from a walking gait to a jogging/running gait was noted. The device was tested on 10 participants, 6 male and 4 female. The weight of the participants was 144±36 pounds (65.5±16.5 kg). The age of the participants was 25±5 years. The height of the participants was 5 feet 7 inches ± 5 inches (171±13 cm). In this paper, the analysis focuses on walking, because this is the more common daily operating condition. According to the participants in this study, most said that 3 mph was a comfortable walking speed. This agrees with previous studies, such as in [24], which report that comfortable walking speeds for men and women in their 20’s is approximately 3.1 mph (5 km/hr).

P a r tic ip a n t 2 ( 3 m p h )

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Figure 10: RMS power harvested across various load resistors.

0 .2 0

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(b) FFT of acceleration

Figure 11: Measured acceleration waveform and FFT for participant at 3 mph (4.8 km/hr).

The acceleration waveform was input into the Simulink model [21] and the voltage across the 1000 Ω resistor was found. The measured voltage and modeled voltage across the load are shown in Fig. 12(a) for one participant while walking at 3 mph (4.8 km/hr). To estimate the damping force, the parasitic damping force magnitude (Fd ) was swept in the model to minimize the root mean square error between the measured and modeled voltages. A plot of the RMS error between measured and modeled voltages is shown in Fig. 13, with the minimum RMS error at a damping of 0.0035 Newtons.

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6.4. Human Testing Results A typical acceleration waveform and its fourier transform (FFT) are shown in Fig. 11 for one participant while walking at 3 mph (4.8 km/hr). On the acceleration waveform, the footsteps are seen as sharp peaks in the waveform at a frequency of 1.88 Hz. On the plot, ‘L’ indicates a left foot strike and ‘R’ indicates a right foot strike. Every other peak on the waveform has slightly lower amplitude, indicating that for one foot (assumed to be the left foot in the graph) the acceleration observed by the accelerometer is lower than for the other foot. The lower acceleration observed when the left foot strikes is because the accelerometer and energy harvester are offset slightly towards the right side of the person’s chest, so higher acceleration is observed for the right foot impacts. This is a non-ideal effect seen in the acceleration spectrum at 1 Hz. The main acceleration components are the ‘step frequency’ at around 2 Hz along with its higher harmonics. In this section, the term harmonics refers to harmonics of the step frequency, since its amplitude dominates. For example, the 1st harmonic is at about 2 Hz and the 2nd harmonic is at about 4 Hz.

The FFT of the voltage waveform is shown in Fig. 12(b). According to the measurements of the device on the electrodynamic shaker, the resonant frequency was between 6 and 7 Hz. This value, however, depends on how the device is positioned, because resonant frequency varies with the angle towards gravity and the damping. As seen in the voltage FFT, the maximum voltage amplitude occurs close to 6 Hz, which is closest to the device resonant frequency. Several other peaks corresponding to the harmonics in the acceleration spectrum are also visible. Since the 3rd harmonic of the step frequency is closest to the 7

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V o lta g e ( M e a s u r e d , P 2 , 3 m p h ) V o lta g e ( M o d e l, F d = 0 .0 0 3 5 )

0 .1 4

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Figure 13: RMS error between modeled and measured voltage waveform for different values of modeled damping.

V o lta g e ( M e a s u r e d , P 2 , 3 m p h ) V o lta g e ( M o d e l, F d = 0 .0 0 3 5 )

0

0 .0 0 6

D a m p in g F o r c e ( F d )

(a) Energy harvester voltage waveform (with 1000 Ω load)

E n e r g y H a r v e s te r V o lta g e ( V )

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E n e r g y H a r v e s te r V o lta g e ( V )

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(b) FFT of energy harvester voltage

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Figure 12: Measured and modeled voltage waveform and FFT for participant at 3 mph (4.8 km/hr).

3 0 7

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Figure 14: RMS power harvested for various walking/running speeds.

of 86 µW. As observed in Fig. 14 by the large standard deviation, there was a relatively large variation in the amount of power harvested between participants. This variation was due to the fact that individuals have a unique gait, and varying mounting angle. Individual gait styles vary significantly enough that some researchers have been able to uniquely identify a person based on their gait [25] using stride length and cadence, which is related to step frequency. The uniqueness of gait is observed in our measurement results as different acceleration spectra. For example, a plot of the step frequency as a function of walking speed is shown in Fig. 15. In most cases, the step frequency varies by about 0.2 Hz, or 10% variation. Another interesting way to plot step frequency is versus participant height, as shown for 3 mph in Fig. 16. The general trend shows that shorter participants have higher step frequency, which can be explained by their shorter stride length, requiring more steps for a given speed compared to taller participants. Focusing on 3 mph (4.8 km/hr) and looking at the frequencies and accelerations of the harmonics provides more insight

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resonant frequency and has sufficiently high amplitude, it plays an important role in the power output as observed by the voltage spectrum. The highest amplitude acceleration is the step frequency observed close to 2 Hz, as shown in Fig. 11. Ideally, the energy harvester should be designed to operate at this frequency, but this was not feasible. Due to application requirements, the device dimensions were limited to less than 30 mm × 10 mm × 40 mm, and therefore the energy harvester resonant frequency could not be designed lower than about 6 Hz due to significant displacement limitation constraints [21]. The RMS power across the 1000 Ω load was found for each participant at each speed and is shown in Fig. 14. The plot shows the mean value from all participants with the standard deviation shown by error bars. At 3 mph, the average power was 71 µW with a standard deviation of 30 µW. Between 4 and 5 mph, there is a large jump observed because this was when most of the participants switched from a walking gait to a running gait, which resulted in higher accelerations. When running at 6 mph, the power increased to 342 µW with a standard deviation 8

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0 .3 0

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Figure 15: Step frequency as a function of walking/running speed.

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Figure 17: Amplitude of harmonics for participants walking at 3 mph (4.8 km/hr).

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Figure 16: Step frequency as a function of participant height at 3 mph (4.8 km/hr).

into the large variation in power output. The acceleration amplitude and frequency of the first 5 harmonics of the step frequency are shown in Fig. 17 and Fig. 18. The amplitude of the 3rd harmonic, which is close to the resonant frequency, has a mean value of 0.057 g, but has a standard deviation of 0.019, or 33% of the mean. Additionally, the frequency of the 3rd harmonic has a mean of 5.77 Hz and standard deviation of 0.36 Hz, or 6% variation. With such large variation in acceleration and frequency, it is expected that the power will vary quite significantly. To determine whether a relation exists in power versus 3rd harmonic frequency and acceleration, different participant’s power at 3 mph (4.8 km/hr) versus 3rd harmonic frequency is shown in Fig. 19. The size of the circle in the plot indicates the magnitude of the 3rd harmonic’s acceleration, where larger size indicates a larger acceleration amplitude. The 3rd harmonic amplitude and estimated damping are also listed by each point. The plot generally shows that for participants with a higher 3rd harmonic frequency, the power output is higher, likely because it is approaching the device resonant frequency. As was intuitively expected, the results indicate that the power output of the

1

2

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H a r m o n ic

Figure 18: Frequency of harmonics for participants walking at 3 mph (4.8 km/hr).

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energy harvester is heavily dependent upon how close the harmonic is to the device resonant frequency, indicating that when designing the device, the resonant frequency should be matched to a harmonic with high acceleration amplitude. Some discrepancies are observed in Fig. 19, most notably P9 and P8. The acceleration of P9 is the highest observed out of all of the points, while the estimated damping is the lowest. Therefore, we would expect its power output to be significantly higher, especially compared to P1. One reason for the discrepancy is that there are likely additional un-modeled damping effects, because the damping is not a constant value and varies as the person’s body moves in all three dimensions, thus forcing the levitating magnet into the sidewall of the box. For example, based on observation, some participant’s shoulders moved forward and backwards more than other participants. This movement in the shoulders could potentially cause a significant increase in damping because the levitating magnet is being forced into the sidewall. Additionally the angle of the device mounting is not known and can vary between participants. Another factor not taken into account in Fig. 19 is the acceleration of the other peaks. As observed in Fig. 12(b), the volt9

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Table 3: Summary of results at 3 mph (4.8 km/hr)

RMS Power, Model (µW) 121.8 85.7 61.3 39.1 124.2 32.3 51.5 62.7 105 101.7 78.5±33.7

1 2 0 P 1

us

F d = 0 .0 0 4 5 A c c e l = 0 .0 3 8

1 0 0

8 0

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F d = 0 .0 0 4 A c c e l = 0 .0 3 5

P 9

F d = 0 .0 0 3 A c c e l = 0 .0 9 1

P 3

F d = 0 .0 0 5 5 A c c e l = 0 .0 4 5

6 0 P 7

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R M S P o w e r ( µW )

P 1 0

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F d = 0 .0 0 5 5 A c c e l = 0 .0 5 7

4 0

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5 .6 rd

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H a r m o n ic F r e q u e n c y ( H z )

7. Conclusion

ed

3

M

P 4

F d = 0 .0 0 4 5 P 6 A c c e l = 0 .0 3 6 F d = 0 .0 0 8 A c c e l = 0 .0 7 4

2 0

% Error 8.3 0.5 10.9 26.1 16.4 20.0 4.1 23.9 24.1 9.9 14.4±9.0

information can be used to create several designs for varying heights by slightly changing the device resonant frequency. Future studies should include many more participants with more widely varying body types and heights to determine how accurately body type (height, weight, gender, etc.) determine gait frequency and acceleration. Additionally, future studies should capture 3-axis acceleration in order to compare lateral accelerations, which could give more information about relative damping between participants. By including 3-axis accelerations, the model fidelity and accuracy can be improved by modeling the dynamic damping induced on the levitating magnet by lateral forces exerted by lateral body movements.

P 5

F d = 0 .0 0 4 A c c e l = 0 .0 7 4

RMS Power, Meas. (µW) 112.5 85.3 68.8 31 106.7 26.9 53.7 50.6 84.6 92.5 71.4±30.1

ip t

RMS Voltage Error 0.086 0.071 0.078 0.082 0.099 0.070 0.075 0.089 0.138 0.085 0.087±0.020

Fd 0.004 0.0035 0.0055 0.0045 0.0045 0.008 0.005 0.0055 0.003 0.004 0.0048±0.0014

cr

Participant P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Avg.±Std. Dev.:

Figure 19: Power versus 3rd harmonic frequency with 3rd harmonic acceleration amplitude shown as size of point for participants at 3 mph (4.8 km/hr).

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pt

age consists of several harmonics and is not simply composed of the 3rd harmonic, although this appears to be dominant at 3 mph. The other peaks do play a role in the power harvested and we cannot simply compare power output to the 3rd harmonic amplitude and frequency. A summary of the modeling and measurement results for 3 mph (4.8 km/hr) are shown in Table 3. The table shows the modeled damping where the minimum RMS voltage error occurred, the simulated RMS power based on the estimated damping and measured acceleration waveform, the measured RMS power, and the error between the modeled and measured power. The modeled and measured power on average deviate by 14%. This deviation is likely due to the unmodeled effect of variable damping and variable resonant frequency due to variation in gait and angle of the device while on the participant. Some error can also be attributed to the variation in material properties and dimensions along with measurement errors. As has been observed in other fields, the uniqueness of individual gaits plays an important role in device performance. Therefore, it may be beneficial to tailor the device to an individual. From a mass production point of view, this may be difficult and costly to accomplish, however, as was observed in Fig. 16, the step frequency has some relation to a person’s height. This

In this work, we have experimentally studied and compared several designs to optimize power output from a magnetic levitation vibration energy harvester and tested the optimal device on human subjects. When tested on 10 participants while walking at 3 mph, the power output averaged 71 µW with a standard deviation of 30 µW. When running at 6 mph, the power increased to 342 µW with a standard deviation of 86 µW. The model in this paper predicted the power on average within 14% of the measured power output. The measurement results show that the variation in power generated is relatively significant due to the variation in walking and running gait styles as well as the angle of attachment of the device. For example, when mounted at an angle of 30◦ on an electrodynamic shaker, the power reduced by 63% compared to vertically mounted due to increased damping. However, due to device optimization, the power output of the optimized device was less sensitive to the angle of mounting. Finally, as was intuitively expected and is indicated by the measurement results, the power output of the device is heavily influenced by the harmonic closest to the resonant frequency. Thus, the energy harvester resonant frequency should be designed as close as possible to a high amplitude harmonic in the acceleration spectrum. Acknowledgments This work was supported in part by a grant from LANDAUER Inc (Glenwood, IL, U.S.A.). The authors would like to

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thank Birck Nanotechnology Center, Herrick laboratories, and Professor Jeffrey Rhoads at Purdue for support in fabrication and testing of the devices, and all the study participants for taking time to participate in this study. Finally, the authors want to thank the staff at Purdue’s Recreational Sports Complex for the use of their facilities and the wonderful support throughout the study.

[20] A. R. M. Foisal, C. Hong, G.-S. Chung, Multi-frequency electromagnetic energy harvester using a magnetic spring cantilever, Sensors and Actuators A: Physical 182 (2012) 106–113. [21] D. F. Berdy, D. J. Valentino, D. Peroulis, Design and optimization of magnetically sprung block magnet vibration energy harvester, Sensors and Actuators A: Physical. [22] G. Akoun, J.-P. Yonnet, 3D analytical calculation of the forces exerted between two cuboidal magnets, IEEE Transactions on Magnetics 20 (5) (1984) 1962–1964. [23] R. Ravaud, G. Lemarquand, Magnetic field produced by a parallelepipedic magnet of various and uniform polarization, Progress In Electromagnetics Research 98 (2009) 207–219. [24] R. W. Bohannon, Comfortable and maximum walking speed of adults aged 20-79 years: reference values and determinants., Age and ageing 26 (1) (1997) 15–9. [25] C. BenAbdelkader, R. Cutler, L. Davis, Stride and cadence as a biometric in automatic person identification and verification, in: Proceedings of Fifth IEEE International Conference on Automatic Face Gesture Recognition, IEEE, 2002, pp. 372–377.

Biography

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[1] S. Lam Po Tang, Recent developments in flexible wearable electronics for monitoring applications, Transactions of the Institute of Measurement and Control 29 (3-4) (2007) 283–300. [2] B. Lo, S. Thiemjarus, R. King, G. Yang, Body sensor network-a wireless sensor platform for pervasive healthcare monitoring, . . . Conference on Pervasive . . . (2005) 77–80. [3] P. Mitcheson, E. Yeatman, G. Rao, A. Holmes, T. Green, Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices, Proceedings of the IEEE 96 (9) (2008) 1457–1486. [4] S. Roundy, P. K. Wright, A piezoelectric vibration based generator for wireless electronics, Smart Mater. and Struct. 13 (5) (2004) 1131–1142. [5] A. Erturk, D. J. Inman, An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations, Smart Materials and Structures 18 (2) (2009) 025009. [6] D. F. Berdy, P. Srisungsitthisunti, B. Jung, X. Xu, J. F. Rhoads, D. Peroulis, Low-frequency meandering piezoelectric vibration energy harvester., IEEE transactions on ultrasonics, ferroelectrics, and frequency control 59 (5) (2012) 846–58. [7] C. Williams, R. Yates, Analysis of a micro-electric generator for microsystems, Proceedings of the International Solid-State Sensors and Actuators Conference - TRANSDUCERS ’95 44 (0) (1995) 369–372. [8] S. P. Beeby, R. N. Torah, M. J. Tudor, P. Glynne-Jones, T. O’Donnell, C. R. Saha, S. Roy, A micro electromagnetic generator for vibration energy harvesting, J. Micromech. Microeng. 17 (7) (2007) 1257–1265. [9] S. Roundy, P. Wright, J. Rabaey, A study of low level vibrations as a power source for wireless sensor nodes, Computer Communications 26 (2003) 1131–1144. [10] S. Meninger, J. Mur-Miranda, R. Amirtharajah, a. Chandrakasan, J. Lang, Vibration-to-electric energy conversion, IEEE Transactions on Very Large Scale Integration (VLSI) Systems 9 (1) (2001) 64–76. [11] L. Wang, F. G. Yuan, Vibration energy harvesting by magnetostrictive material, Smart Materials and Structures 17 (4) (2008) 045009. [12] K. Sun, G. Q. Liu, X. Y. Xu, Nonlinear Resonant Generator for Harvesting Energy from Human Wrist Vertical Shaking, Applied Mechanics and Materials 128-129 (2011) 923–927. [13] C. Saha, T. ODonnell, N. Wang, P. McCloskey, Electromagnetic generator for harvesting energy from human motion, Sensors and Actuators A: Physical 147 (1) (2008) 248–253. [14] P. Constantinou, P. H. Mellor, P. D. Wilcox, A Magnetically Sprung Generator for Energy Harvesting Applications, IEEE/ASME Transactions on Mechatronics 17 (3) (2012) 415–424. [15] X. Yang, B. Zhang, J. Li, Y. Wang, Model and Experimental Research on an Electromagnetic Vibration-Powered Generator With Annular Permanent Magnet Spring, IEEE Transactions on Applied Superconductivity 22 (3) (2012) 5201504–5201504. [16] A. R. M. Foisal, B.-C. Lee, G.-S. Chung, Fabrication and performance optimization of an AA size electromagnetic energy harvester using magnetic spring, 2011 IEEE SENSORS Proceedings (2011) 1125–1128. [17] P. Constantinou, P. Mellor, P. Wilcox, A Model of a Magnetically Sprung Vibration Generator for Power Harvesting Applications, in: 2007 IEEE International Electric Machines & Drives Conference, IEEE, 2007, pp. 725–730. [18] E. Dallago, M. Marchesi, G. Venchi, Analytical Model of a Vibrating Electromagnetic Harvester Considering Nonlinear Effects, IEEE Transactions on Power Electronics 25 (8) (2010) 1989–1997. [19] B. Mann, N. Sims, Energy harvesting from the nonlinear oscillations of magnetic levitation, Journal of Sound and Vibration 319 (1-2) (2009) 515–530.

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References

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David F. Berdy received his B.S. degree in computer engineering from Rose-Hulman Institute of Technology, Terre Haute, IN, in 2008. He is currently pursuing his Ph.D in electrical engineering in the School of Electrical and Computer Engineering at Purdue University, West Lafayette. His research interests include energy harvesting, MEMS transducers and their applications. Daniel J. Valentino received his Ph.D. in Biomedical Physics from the University of California at Los Angeles in 1990. He was an Associate Professor of Radiology at UCLA, a founding member of the Biomedical Engineering Program at UCLA, and a founding member of the NIH-funded Center for Computational Biology. At UCLA, his research interests included imaging informatics, image processing and image databases for neuroimaging, and computational fluid dynamics for brain vascular mapping. He was the PI or co-PI on several large NIH-funded program project grants, and grants from the NSF and state of California. He is the author of over 200 peer-reviewed papers. He was the Chief Technology Officer for iCRco, Inc, where he led the research and development of new imaging devices, image processing algorithms, and image data management systems. He is currently the Vice President of Technology & Innovation for LANDAUER, Inc, where he leads the research and development of innovative new radiation detection systems and products. Dimitrios Peroulis received his Ph.D. in Electrical Engineering from the University of Michigan at Ann Arbor in 2003. He has been with Purdue University since August 2003 where he is currently leading a group of graduate students on a variety of research projects in the areas of RF MEMS, sensing and power harvesting applications as well as RFID sensors for the health monitoring of sensitive equipment. He has been a PI or a co-PI in numerous projects funded by government agencies and industry in these areas. He is currently a key contributor in two DARPA projects at Purdue focusing on 1) very high quality (Q>1,000) RF tunable filters in mobile form factors (DARPA Analog Spectral Processing Program, Phases I, II and III) and on 2) developing comprehensive characterization methods and models for understanding the viscoelasticity/creep phenomena in high-power RF MEMS devices (DARPA M/NEMS S&T Fundamentals Program, Phases I and II). Furthermore, he is leading the experimental program on the Center for the Prediction of Reliability, Integrity and Survivability of Microsystems (PRISM) funded by the National Nuclear Security Administration. In addition, he is heading the development of the

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MEMS technology in a U.S. Navy project (Marines) funded under the Technology Insertion Program for Savings (TIPS) program focused on harsh-environment wireless micro-sensors for the health monitoring of aircraft engines. He has over 130 refereed journal and conference publications in the areas of microwave integrated circuits, sensors and antennas. He received the National Science Foundation CAREER award in 2008. His students have received numerous student paper awards and other student research-based scholarships. He is a Purdue University Faculty Scholar and has also received eight teaching awards including the 2010 HKN C. Holmes MacDonald Outstanding Teaching Award and the 2010 Charles B. Murphy award, which is Purdue University’s highest undergraduate teaching honor.

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