Energy harvesting from human motion: exploiting swing and shock excitations

The large forces available upon heel-strike have motivated the development of several force-driven energy harvesting devices. The bending of piezoelectric materials attached to the shoe sole, both ceramics and polymer-based, was employed early on [3] leading to average power outputs of 1.8 mW and 1.1 mW respectively for a walking frequency of 1 Hz.

A generator using a lever and mechanical gears to translate the downward motion of the foot into a rotational motion coupled into a classical generator was also presented in [3]. While the device was rather large and heavy, it was able to generate an average power of 230 mW. A different approach employs the triboelectric effect, which is based upon materials of different electrochemical potential coming into contact, to generate maximum power outputs of up to 4.2 mW with a stacked structure which was pressed by a human palm [4]. Further force-driven devices can be found in [5–7].

Particularly concerning the acceleration impulses available upon heel-strike, there has been only limited work. In [8] a piezoelectric macro scale prototype is presented. A heavy cylindrical mass is set into motion when the foot is lifted to form an angle with the ground. Magnets attached to piezoelectric beams snap towards this mass when it comes into range and vibrate freely at their resonance frequency, when released. This large device was able to generate a maximum power output of 2.1 mW at an excitation of 2 Hz in a laboratory setup. A second device incorporates a shoe-mounted piezoelectric vibrating cantilever and was presented in [9]. In this device the mass attached to a piezoelectric cantilever is displaced when excited by the acceleration impulses induced by heel strike. The corresponding spring-mass system then starts to vibrate at its eigen-frequency. As a result, a classical damped response occurs at every heel-strike. A power output of about 14 μW was achieved when walking at normal speed. By means of a sensitivity analysis based on a numerical model optimal parameters were identified, which provide the largest power output. Using the optimum parameters a power output of 395 μW was predicted. In both cases described, the energy harvester mechanism is based on a frequency up-conversion technique.

In the case of linear swing-type harvesters a number of devices have been reported. The shoe-integrated prototype upon which parts of this work are based was presented in [10]. It consists of a single generating magnet that can swing freely within a PVC channel placed within the sole along the horizontal axis. Two coils are placed in precise positions in order to overlay the coils' voltage signals and double the output while requiring only one rectifying circuit. This device was able to generate average powers up to approximately 10.5 mW on a treadmill run at a velocity of 10 km h⁻¹.

A different device based on the magnet-in-channel setup was presented in [11]. Different configurations of the coils, channels and magnets were investigated, leading to an average power output of up to 14 mW at a walking velocity of two steps per second (1 Hz) for the best configuration found. However, this device did not use synchronized coil signals and would therefore require multiple rectifying circuits for more than one coil when used in a sensor system.

The acceleration-driven harvesters mentioned so far have the common problem of a large device size which greatly reduces their acceptability for an integration in shoes which in turn is hardly possible without altering the shoes appearance. As a consequence it is of utmost importance to reduce the device size and particularly the height of the harvesters while trying to reduce scaling effects and the loss of generated power due to down-scaling in size.

4.1.1. Introduction

For the miniaturized device a multi-coil configuration was chosen since a larger power output in contrast to a single coil design was expected. The magnets are concentrically placed in line separated by ferromagnetic steel spacers, creating an elongated stack as indicated in figure 3(a). Two neighboring magnets always show opposing polarization. The repulsive flux lines are therefore forced into the spacer and guided sideways as shown schematically in figure 3(b). This guarantees that each coil experiences several changes in direction of the magnetic flux within each step as several magnet-spacer sections pass by the coil. The coils are placed at equal intervals according to the distance between the magnets and connected in series. Because of this placement the magnets move through the coils simultaneously, i.e. every magnet enters a coil at the same time and with the same velocity. The alternating magnetic flux thus induces a voltage in every coil simultaneously, enabling the superposition of the voltage across the series connected coils, thereby reducing the requirements posed for the power management electronics, which in the simplest case can be a single rectifying circuit. Stopping magnets (SM) are introduced in order to prohibit the magnet stack from hitting the channel end at high velocities as this impact can clearly be felt in the shoe without cushioning and increases discomfort.

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4.1.2. System model

The system model (figure 4) follows the differential equation shown in (1). Apart from the real-world acceleration data, which is used as input to the system, a number of different forces acting upon the moving magnet are also considered.

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The friction forces between the magnet stack and the channel are calculated based on the weight of the magnet and the centripetal force built up during the swing motion of the foot, which acts as an additional normal force.

Air compression due to the air pushed in front of the magnet stack can be a highly limiting factor if no outlet is provided. In order to capture most of the magnetic flux within the coils, they are placed as closely to the magnets as possible. The channel is designed accordingly, leaving little space for air to pass by the magnet stack when it is moving. The model calculates the forces due to air compression by determining the volume change in the air pockets to the left and right of the magnet train at discrete time steps as the magnet moves. Thereupon one can estimate the exhaust velocity at the air outlet and the corresponding volume of air that is leaving the air pockets through the outlets. The differences in volume change between the air pockets and the corresponding differences in pressure can then be used to estimate the acting forces. Rubber stoppers were used in the fabricated setup and were modeled as a semi-elastic impact after first experiments showed that the influence of the SM on the moving magnet stack led to a greatly reduced range of motion.

As the magnet stack moves through the channel due to the external excitations, a voltage is induced in the surrounding coils and current flows through the coil windings. This current causes a magnetic field, which opposes the field of the magnet stack and thereby exerts a force on the magnets.

The equation of motion is given in (1) and considers the external acceleration input due to the foot motion ${{F}_{{\rm ext}}}$, the forces due to air compression ${{F}_{{\rm Air}}}\left( x,\dot{x} \right)$, friction forces ${{F}_{{\rm R}}}(\dot{x})$ and the electrical damping force ${{F}_{{\rm e}}}$

$$\begin{eqnarray}&&m\ddot{x}={{F}_{{\rm ext}}}-{{F}_{{\rm Air}}}\left( x,\dot{x} \right)-{{F}_{{\rm R}}}\left( {\dot{x}} \right)-{{F}_{{\rm e}}}\left( {\dot{x}} \right).\end{eqnarray} \tag{ 1 }$$

In order to determine the power generated in the coils and the electrical damping force, the spatial distribution of the magnetic flux density is calculated using FEM software. A steady-state axisymmetric problem is set up using the software FEMM. Asymptotic boundaries are defined at a distance of 2 cm from the magnet stack. The magnetic flux density is extracted from FEMM along the area corresponding to the coil area. The coupling coefficient is calculated using the FEM data according to equation (2), where k is the coupling coefficient, φ is the magnetic flux and x is the axis of motion:

$$\begin{eqnarray}&&k=-\frac{{\rm d}\varphi }{{\rm d}x}.\end{eqnarray} \tag{ 2 }$$

The coupling coefficient reaches its highest values between two magnets where a change in the flux direction occurs (figure 5). A more detailed description of the calculation of the coupling coefficient and consequently the generated voltage can be found in [12].

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The software model implemented in Matlab/Simulink calculates the motion of the magnet stack from the sum of the forces listed in equation (1). The curve representing the spatial distribution of the coupling coefficient is shifted in position along the x axis, thus modeling the motion of the magnetic field. As the coils are placed in predetermined places and with fixed spacing, each coil experiences a separate magnetic flux depending on its location and generates a voltage according to equation (3), where U_ind is the voltage induced in the coils, B is the magnetic flux density and A is the cross-sectional area of the coil:

$$\begin{eqnarray}\begin{array}{lllllllllllllll} {{U}_{{\rm ind}}} & = & -\frac{{\rm d}\varphi }{{\rm d}t}\;=-{{\left( \frac{{\rm d}A}{{\rm d}t}B+\frac{{\rm d}B}{{\rm d}t}A \right)}_{\left| A={\rm const}. \right.}} \\ {} & = & -\frac{{\rm d}B}{{\rm d}t}A\cdot \frac{{\rm d}x}{{\rm d}x}=-\frac{{\rm d}B}{{\rm d}x}A\cdot \frac{{\rm d}x}{{\rm d}t}=k\cdot \dot{x}. \\ \end{array}\end{eqnarray} \tag{ 3 }$$

The electrical damping force can be calculated using the coupling coefficient k and the current i induced in the coils according to equation (4):

$$\begin{eqnarray}&&{{F}_{{\rm e}}}=i\cdot k.\end{eqnarray} \tag{ 4 }$$

Each coil is divided into ten coil cells in order to represent the spatial extent of the coil more accurately. For each cell the value of the coupling coefficient at its location is determined, which improves the accuracy of the calculations. An optimum resistive load equal to the coil resistance (approximately 166 Ω) is used in the simulations.

4.1.3. Optimization

4.1.4. Implementation

Several difficulties were encountered during construction of the device. Gluing magnets together against the repulsive forces due to their opposing polarization proved very challenging. Several designs were investigated as shown in figure 6. The designs were simulated and the expected power output normalized to 100% for the best design is shown.

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The most practical design which uses ring-magnets and a supporting rod of non-ferromagnetic material in the free space at the center of the magnets shows a significant reduction in power output. Not only does this setup imply a reduced volume of active magnetic material but it also allows the magnetic field to partially short-circuit in the free space within the ring. This trade-off is acceptable for practical reasons, as it inherently allows the correct alignment of magnets and spacers with complete overlap. Additionally it facilitates the gluing process and especially when using a thread rod, the magnets can be held in place by screwing a nut onto either end of the rod. The fabricated prototype and its external placement on a shoe for characterization purposes are shown in figure 7.

In order to analyze the performance of the device under real conditions, several treadmill runs were performed. A linear accelerator table was used for brief testing of the swing-type harvesters, however its attainable accelerations are limited to approximately 1 m s⁻². Therefore the measured accelerations that occur during walking could not be replicated by other means than a treadmill.

As before, measurements were performed at four different motion speeds and for two runners of different body geometries. Figure 8 shows the measured power output of the harvester for runs performed on a treadmill and as a comparison for runs performed on the ground without a treadmill. It was reported earlier that with the transition from the abrupt motions of fast walking to the rather smooth motions of slow jogging, a decrease in power output can be observed [10]. This effect can be observed in figure 8 as well, where the curves do not show a steadily ascending slope. The fact that for runner 'KY' this drop in power output occurs at lower motion speeds than is the case with runner 'DH' is attributed to the walking style and the body geometry of the runners. Measurements were also performed at a reduced set of motion speeds for walking without a treadmill. While treadmill runs offer a certain level of reproducibility, some differences can be expected when compared to walking on the ground. First, on a treadmill one automatically makes alterations to the gait patterns in order to run smoothly. Second, the inherent spring-loaded characteristic of the treadmill causes the impact of the foot to be damped to a certain degree.

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At the slowest measured speed of 4 km h⁻¹ on a treadmill, the harvester was able to generate 0.34 mW and 0.46 mW for the two runners. At approximately the same speed on the ground, power outputs of 0.375 mW and 0.526 mW were achieved. It can also be noticed that the maximum achieved power output of 0.81 mW for 'ground walking' is measured at 5 km h⁻¹ and thereby at a speed 1 km h⁻¹ slower than on a treadmill, where a nearly identical power output of 0.84 mW is achieved at 6 km h⁻¹. It can therefore be assumed that the power output during normal walking without a treadmill is slightly larger than for treadmill runs, independent of the motion speed.

Figures 9(a) and (b) depict the measured voltage and power output respectively for approximately one step for runner KY at a speed of 6 km h⁻¹. It can be seen from the figures that each step shows two characteristic impulses corresponding to the two major motions of the foot (forward and backward movement). Each waveform is made up from a number of consecutive peaks, which represent the change in flux direction between the coils of the magnet stack. The total energy per step can be obtained by integrating the power over one such step and its two impulses.

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The previous sections show that the miniaturization of a swing-type harvester through means of parallelization can be achieved without the devices power output dropping into unfeasible ranges. However, it has to be kept in mind that with a maximum recorded average power output of 0.84 mW the reduction due to scaling effects is significant as compared to [10]. The volume scales quadratically with the radius and thus the mass of the magnet stack, which is the inertial mass of this system, was greatly reduced from approximately 50 g in [10] to 9.8 g in this work. Not only does this result in reduced inertia of the magnet stack, but it also results in a reduced magnitude of the magnetic field due to the smaller magnets and consequently in a reduced power output. In practical terms the reduction in size is a great advantage, as the device with a total height of 15 mm including the housing is now far easier to incorporate into shoes. With a total length of 70 mm including housing it can also be integrated into the heel section of a shoe and is not negatively affected by the bending of the front part of the sole during walking.

Concerning the modeling of the device, a complete match between simulation and measurement for all velocities has not been achieved so far. Figure 10 shows a comparison between the simulated and measured power outputs for both runners. Apart from differences caused due to the simple physics, errors are introduced by the discrete nature of the calculations performed, e.g. the magnetic flux density is calculated at fixed spatial intervals and used to determine a mean flux within each coil. The accuracy of this approximation depends on the step size. An increased resolution leads to a manifold increase in computing time as both the FEM simulation and Matlab have to perform an increased number of computations $({{t}_{{\rm calc}}}\sim {\rm resolutio}{{{\rm n}}^{2}})$. Concerning the optimization algorithm which calculates hundreds of designs, a balance has to be found between computing time and accuracy. Additionally, it is assumed that the speed-dependent effects of the system model require further improvement.

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Therefore future work clearly includes improvements to the reproduction of real-world physics within the system model and the approximations used in the model, which continually leads to a better match between simulation and measurements. The influence of the calculation resolution on the model accuracy is not considered in this work.

The model was limited in flexibility as it was designed to simulate a fixed number of coils equal to the number of flux transitions between magnets. If the algorithm calculated a design with 14 magnets, the number of coils in the simulation would be set to 13. To avoid this limitation a fully flexible model is being worked on, which can calculate designs where the number of coils is independent from the number of magnets. Further improvement through a new design in a new optimization run is expected.

As discussed for the swing-motion harvester, the usability of a device for energy harvesting from human motion depends strongly on its integration capability and thus on its size. Therefore, a strict constraint on the device size was also applied to the shock-excited energy harvester. For integration of the energy harvester into the heel of a shoe, the total height of the device must not exceed a limit of 20 mm. The width and length of the device were restricted to 40 mm and 60 mm, respectively. Applying these size constraints, an integration of the device into the heel of a shoe is feasible.

For converting the acceleration pulses into electrical energy an electromagnetic conversion mechanism was chosen. Due to the limited device height, the shock-excited energy harvester incorporates a magnetic circuit, which contains two air gaps. In this manner a reasonably flat design is achievable without losing too much volume for the active components (coil volume, magnet volume). A schematic diagram of the energy harvester structure (cross-section) including relevant design parameters is shown in figure 11(a). The total width of the structure W_total, which is equal to 33 mm, follows from the total device width (40 mm) less the thickness of the housing and some air gap on both sides. The gap between coil and magnet was chosen to be 0.5 mm. The width of the coil W_coil follows from the dimensions of W_sheet, W_mag and the gap between magnet and coil. The height of the back iron sheet H_sheet, which is equal to two times the height of the magnet H_mag, is limited by the maximum height of the device and the internal displacement amplitude z_max. There will be a trade-off between the parameters H_mag and z_max. A large magnet height will increase the magnetic volume and the seismic mass. However, this is at the expense of the internal displacement amplitude. A small internal displacement will induce impacts at the mechanical stoppers more often. The magnet height also depends on the availability of magnets with a particular height. In this first design, a magnet height of 5 mm was chosen resulting in a height of 10 mm for the back iron sheet. Considering a total device height of 20 mm and a thickness of the housing of 2 mm, the internal displacement amplitude yields to 3 mm. The following design parameters are still variable and must be optimized with respect to the power output: the width of the magnet W_mag, the width of the back iron sheet W_sheet and the outer diameter of the coil D_coil. The value for L_mag and L_sheet is equal to H_sheet. The inner diameter of the coil is 2 mm.

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The energy conversion structure of the shock-excited energy harvester is suspended using two pairs of magnets with opposite polarity. The outer suspension magnets are fixed within the housing (base and lid). The size of the magnets can be varied for adjusting the magnetic suspension force with respect to the excitation conditions. Larger or smaller magnets will change the stiffness in the system and thus the eigen-frequency can be varied.

For optimization of the variable design parameters a system model based on differential equations was developed and implemented in MATLAB/Simulink. A schematic diagram of the system model is shown in figure 11(b). The rotational motion of the cantilever arm is described by the following differential equation:

$$\begin{eqnarray}&&\;J\ddot{\varphi }=\;\mathop \sum \limits^{} {{M}_{i}}=\mathop \sum \limits^{} {{M}_{g}}+\mathop \sum \limits^{} {{M}_{{\rm ex}}}+{{M}_{{\rm d},{\rm e}}}+{{M}_{{\rm d},{\rm m}}}+{{M}_{{{F}_{{\rm m}}}}},\end{eqnarray} \tag{ 5 }$$

where $J\ddot{\varphi }$ is equal to the sum of all torsional moments in the system. The moments induced by weight are summarized as following:

$$\begin{eqnarray}&&\;\mathop \sum \limits^{} {{M}_{g}}=g\mathop \sum \limits^{} {{m}_{i}}{{r}_{i}}=g\cdot {{m}_{{\rm tot}}}\cdot {{L}_{{\rm eff}}}\cdot \;{\rm cos} \;\varphi ,\end{eqnarray} \tag{ 6 }$$

where g is the gravity of earth, m_tot is the total mass in the system and L_eff is the effective length with respect to the center of gravity of the total mass. The external excitation also generates torsional moments as described in equation (7):

$$\begin{eqnarray}&&\;\mathop \sum \limits^{} {{M}_{{\rm ex}}}=A\mathop \sum \limits^{} {{m}_{i}}{{r}_{i}}=A\cdot {{m}_{{\rm tot}}}\cdot {{L}_{{\rm eff}}}\cdot \;{\rm cos} \;\varphi ,\end{eqnarray} \tag{ 7 }$$

where A is the excitation acceleration. Further torsional moments are induced by the electrical damping force F_d,e and the mechanical damping force F_d,m. The associated moment arm is the distance ${{L}_{{\rm d}}}$. The general moment is given by:

$$\begin{eqnarray}&&{{M}_{{\rm d},j}}={{F}_{{\rm d},j}}\cdot {{L}_{{\rm d}}}.\end{eqnarray} \tag{ 8 }$$

The index j accounts for either electrical or mechanical damping forces. The electrical damping force F_d,e, which originates from the Lorentz force, results from the coupling factor C_F and the current i in the coil:

$$\begin{eqnarray}&&{{F}_{d,e}}={{C}_{{\rm F}}}\left( \varphi \right)\cdot i\left( \varphi ,\dot{\varphi } \right)={{d}_{{\rm e}}}(\varphi )\cdot \dot{\varphi }.\end{eqnarray} \tag{ 9 }$$

From equation (9) follows that the electrical damping force F_d,e can be represented by a velocity proportional damping element with the electrical damping coefficient:

$$\begin{eqnarray}&&{{d}_{{\rm e}}}={{C}_{{\rm F}}}\left( \varphi \right)\frac{{{u}_{{\rm ind}}}}{{{R}_{{\rm in}}}+{{R}_{L}}}\cdot \frac{1}{{\dot{\varphi }}}=\frac{{{C}_{{\rm F}}}{{\left( \varphi \right)}^{2}}}{{{R}_{{\rm in}}}+{{R}_{L}}}.\end{eqnarray} \tag{ 10 }$$

In the same way, the mechanical damping force F_d,m is proportional to the angular velocity with the mechanical damping coefficient d_m:

$$F_{d,m}=d_{{\rm m}}\cdot\dot{\varphi}. \tag{ 11 }$$

The mechanical damping coefficient was determined experimentally. The magnetic force F_m between the repulsive magnets changes with the variable in a nonlinear manner and introduces a stiffness into the system. The magnetic force hereby generates a torsional moment as following:

$$\begin{eqnarray}&&{{M}_{{{F}_{{\rm m}}}}}={{F}_{{\rm m}}}\left( \varphi \right)\cdot {{L}_{{{F}_{{\rm m}}}}}.\end{eqnarray} \tag{ 12 }$$

The magnetic force as a function of displacement angle was numerically calculated using the FE-method. The set of equations described above represents the model of the shock-excited energy harvester and was solved numerically.

The implementation of the shock-excited energy harvester is shown in figure 12 (the lid is removed). The rim of the housing is reinforced using steel bolts in order to increase the robustness of the device (figure 12(a)). The outer suspension magnets are accommodated in the base and the lid. Between the anchor and the active structure is enough space for a power management circuit. Figure 12(b) shows a side view of the energy harvester structure. The device was integrated into the sole of a shoe for characterization and testing.

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The shock-excited energy harvester was tested under realistic conditions on a treadmill. An example of the instantaneous voltage output during one step is depicted in figure 13(a). The overlaid acceleration signal shows an initial acceleration peak of about 18 g, which is caused by the heel-strike. The motion speed was 6 km h⁻¹. The highest voltage peak is about 5.8 V and corresponds to a power output peak of 46 mW (reached at the third peak in figure 13(b)). During one step the active structure of the shock-excited energy harvester oscillates with about 16 periods of oscillations until the voltage amplitude drops below 1 V. The decay of the voltage response seems to be a more or less linear characteristic. A second displacement event of the active structure occurs 0.65 s after the first impact. At this moment the foot is lifted from the ground. However, the power output from this event is rather small.

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Figure 14 shows the power output for two different test persons as a function of walking speed. In general the power output at a specific motion speed depends on the test subject. At a motion speed of 4 km h⁻¹ (slow walking) the power output is 1.25 mW for test person DH whereas just 1 mW is generated for test person KY. At motion speeds of 6 km h⁻¹ (fast walking) and 8 km h⁻¹ (slow jogging) a more significant difference in output power can be observed between the two test persons. Possible reasons are the differences in the walking style and in the physiognomy (e.g. weight of person, length of leg, etc) of the test persons. The maximum power output of ca. 3.5 mW appears for runner KY at a motion speed of 6 km h⁻¹ (figure 14(b)). At a motion speed of 10 km h⁻¹ the output power is just below 3 mW and is almost equal for both test persons. At this particular motion speed, the average of the acceleration peaks from heel-strike reaches up to 34 g. In addition to the treadmill runs, the power output was also measured for 'ground walking'. The maximum achieved power output was 4.13 mW at a motion speed of approximately 5 km h⁻¹.

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The simulation results obtained by the numerical model are also shown in figure 14. The power estimation is reasonably close to the experimental results. However, the drop in power output when the transition from the abrupt movements of fast walking to the smooth movements of slow jogging occurs is not apparent in the simulation data.