Looped energy harvester for human motion

The system consists of a magnetic ball moving freely inside a circular tore. Several independent coils are wrapped along the loop (figure 1). When the system is carried by a person during a physical activity, the magnetic ball moves freely inside the loop and induces electrical currents inside the coils. These outputs are rectified separately and driven to a common charge. A peripheral band (or 'rail') of soft ferromagnetic material is encircling the device (the role of this practical tip is explained in section 2.3).

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2.2.1. Model

First, we propose a brief theoretical approach to estimate the potential of this toroidal format to harvest energy from human mechanical excitations. We consider a general 2D model of an inertial system with an eccentric mass $m$ pivoting around a central axis at a distance ${r}_{d}$ (which in our case corresponds to the radius of the closed trajectory of the ball). The self-rotation of the magnetic ball is not considered here. The model parameters are illustrated in figure 2. In the reference frame of the generator (with the relative coordinate system $\mathop{{e}_{x}}\limits^{\longrightarrow},\mathop{{e}_{y}}\limits^{\longrightarrow}$), the position of the moving mass is defined by an angular parameter $\theta .$

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The device is assumed to be attached 'vertically' to a limb of the user and undergoes an 'in-plane' excitation, characterized by an acceleration ${a}_{x}\,\mathop{{e}_{x}}\limits^{\longrightarrow}+{a}_{y}\,\mathop{{e}_{y}}\limits^{\longrightarrow}$ and a rotational acceleration $\ddot{\varphi }\mathop{{e}_{z}}\limits^{\longrightarrow};$ for instance, a subject is running with the device attached to the side of his arm (figure 2). The inertial forces trigger the free motion of the magnetic mass, which can be described using Newton' second law (1):

$$\begin{eqnarray}\ddot{\theta } & = & -\displaystyle \frac{1}{{\rm{m}}}({{\rm{c}}}_{{\rm{e}}}+{{\rm{c}}}_{{\rm{m}}})\dot{\theta }+\displaystyle \frac{1}{{{\rm{r}}}_{{\rm{d}}}}({{\rm{a}}}_{{\rm{x}}}\,\sin (\theta )\,-{{\rm{a}}}_{{\rm{y}}}\,\cos (\theta ))\\ & & +\displaystyle \frac{{\rm{g}}}{{{\rm{r}}}_{{\rm{d}}}}\,\sin (\theta +\varphi )-\ddot{\varphi }\end{eqnarray} \tag{ 1 }$$

φ is the rotation angle between $\mathop{{e}_{x}}\limits^{\longrightarrow}$ and the vertical direction $\mathop{{e}_{g}}\limits^{\longrightarrow},$ ${a}_{x}$ and ${a}_{y}$ are the acceleration components expressed in the relative ($\mathop{{e}_{x}}\limits^{\longrightarrow},\mathop{{e}_{y}}\limits^{\longrightarrow}$) coordinate system and $g=9.81\,{\rm{m}}.{{\rm{s}}}^{-2}$ is gravity. ${c}_{e}$ and ${c}_{m}$ are the electromechanical and mechanical damping coefficients, which are arbitrarily considered constant in this theoretical study. The instantaneous electrical power ${p}_{e}\,$ extracted from the kinetic energy of the moving mass by the electromechanical damping is:

$$\begin{eqnarray}&&{{\rm{p}}}_{{\rm{e}}}={{\rm{c}}}_{{\rm{e}}}\,{({{\rm{r}}}_{{\rm{d}}}\dot{\theta })}^{2}\end{eqnarray} \tag{ 2 }$$

2.2.2. Simulation from an experimental 'running' input data

Using a 9-axis motion sensor (InvenSense MPU-9250) attached to the upper arm, we recorded both acceleration components ${a}_{x},$ ${a}_{y}$ (figure 3(a)) and rotational speed $\dot{\varphi }$ (figure 3(b)) of the limb while the person was running on a treadmill at 8 km h⁻¹. Interestingly, the rotational measurement shows an asymmetric form, which suggests that the 'upward' swing (corresponding to the negative peaks) plays an important motor role in the running gait. With this experimental input, the previous model was implemented on Matlab Simulink and the output power of the generator was simulated. The moving mass (m = 2 g) and the mechanical damping coefficient (${c}_{m}$ = 0.01 N.s/m) were kept constant.

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First the influence of the radius ${r}_{d}$ of the device was examined (figure 3(c)). For each point, the value of electrical damping ${c}_{e}$ was determined so as to maximize the average output power. The results suggest that a few milliwatts can be generated from this 'running'-type excitation, for a radius of the device greater than 1 cm, and increase with the radius. This was expected because of the rotational component of the excitation, $\ddot{\varphi },$ is unaffected by the radius ${r}_{d}$ (see equation (1)), while the electrical power remains dependent on this parameter (expression (2)). The power density relative to the volume of the toroidal device decreases from 230 μW.cm⁻³ to 130 μW.cm⁻³ (the volume $V$ considered for these values is $V=2\pi {r}_{d}S,$ with a tore section $S$ set to 1.33 cm²).

The impact of the electrical damping was also evaluated, for three different generator radiuses (figure 3(d)). This simulation revealed that smaller device radiuses require greater levels of electrical damping to reach the maximum power. This observation is important since the magnetic mass here is small (2 g), which limits the damping levels achievable. On the other hand, the output power seems less dependent on the electrical damping for smaller device radiuses, which can be an advantage considering that this parameter is difficult to control experimentally due to the self- rotation of the magnetic ball.

While performing preliminary experiments with this concept of generator, it was observed that the electromechanical damping coefficient—and thus the electrical power—were very limited with the elementary device (i.e. without the additional ferromagnetic 'rail'). We propose here to explain this effect and show how the implementation of a ferromagnetic rail offers a solution, using a finite element method approach (performed on COMSOL). A simplified static situation is considered, involving only one coil and neglecting the curvature of the device (figure 4(a)). The parameters are illustrated in figure 4(b): the ball moves along the y-axis, its magnetic polar axis is assumed in the xy plane and defined by angle $\beta .$ For the numerical values, we consider an 8 mm-diameter N38 magnetic ball (2 g mass), a 1000-turns coil and a 1.55 mm × 0.2 mm ferromagnetic band placed at x = 8 mm (these parameters are the same as for the prototype, see table 1 hereafter). Examples of the magnetic field densities $B$ produced by the magnetic ball and the coil are illustrated in figures 4(c) and (d), respectively. The geomagnetic field, which is in the order of a few 10⁻⁵ T, is neglected in this study.

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2.3.1. Magnetic flux gradient inside the coil

As stated by Faraday's laws, induction is linked to the time variation of the magnetic flux inside the coil. Here, this variation is the consequence of both the displacement and the rotation of the ball. The value of the magnetic flux averaged over the volume of the coil is plotted in figure 5. The electrical damping coefficient ${c}_{e}$ is proportional to the square of the instantaneous gradient of this flux [30]. Depending on the signs of the respective variations of the displacement $d$ and the magnetic orientation $\beta ,$ the sum of the two contributions can either add-up or compensate each other. For example, the ball rolling away from the coil will cause an oscillating magnetic flux inside the coil with a decreasing amplitude.

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Although the addition of soft ferromagnetic parts in inductive generators usually aims at channeling the magnetic flux inside the coils and thus increase the electromechanical coupling [29], given the reduced dimensions of the soft ferromagnetic medium here (the 'rail'), its influence on the magnetic flux density inside the coil is insignificant.

2.3.2. Electromagnetic torque

During the motion of the ball, induced current in the coil produces an opposing magnetic field which slows down the moving magnet. It also applies a magnetic torque, ${\tau }_{\mathrm{coil}},$ which triggers the self-rotation of the ball. We evaluated the amplitude of this torque as a function of the instantaneous magnetic orientation $\beta$ of the ball and the electrical current I in the coil (figure 6(a)). The torque is proportional to the induced current in the coil, and has different effects depending on the relative motion of the ball. For example, if the magnetic ball is sliding away from the coil, the coil will generate an attractive magnetic field to oppose the motion of the ball. The stable orientation of the latter, defined by ${\tau }_{\mathrm{coil}}=0$ and $\partial {\tau }_{\mathrm{coil}}/\partial \beta \lt 0,$ will be $\beta =90^\circ$ or $\beta =-90^\circ ,$ depending of the sign of the induced current in the coil. On the contrary, if the magnetic ball is sliding towards the coil, the magnetic field produced by the induced current in the coil will be repulsive: the only stable orientation is the induction-less one, i.e. $\beta =0^\circ \,[180^\circ ].$

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In any case, the induced self-rotation of the magnetic ball tends to limit the magnetic flux variation inside the coil, in accordance with Lenz's law. To counteract this issue, the magnetic orientation of the ball shall be imposed by other effects than this electromagnetic torque.

2.3.3. Ferromagnetic torque

2.3.4. Friction torque

The last component that must be taken into account is the mechanical 'rolling' torque resulting from the friction between the casing and the ball during its motion. As an approximation, it may be evaluated using the Coulomb friction model. Considering the normal force $\vec{N}$ applied on the ball by the inner wall of the tube and using the same motion model parameters detailed in section 1, the norm of this force (3) can be expressed from the equation of motion projected on the radial direction. If the peripheral ferromagnetic rail is present, the radial attraction force ${F}_{\mathrm{fer}}\,\mathop{{e}_{r}}\limits^{\longrightarrow}$ it applies to the magnetic ball is compensated by the wall.

$$\begin{eqnarray}{\rm{N}} & = & \vec{{\rm{N}}}\cdot \mathop{{{\rm{e}}}_{{\rm{r}}}}\limits^{\longrightarrow}=-{\rm{mr}}{(\dot{\theta }+\dot{\varphi })}^{2}+{\rm{m}}({{\rm{a}}}_{{\rm{x}}}\,\cos (\theta )\\ & & \,+{a}_{{\rm{y}}}\,\sin (\theta )+{\rm{g}}\,\cos (\theta +\varphi ))-{{\rm{F}}}_{{\rm{fer}}}\end{eqnarray} \tag{ 3 }$$

with:

$$\begin{eqnarray*}&&\left\{\begin{array}{l}{{\rm{F}}}_{{\rm{fer}}}=0\,{\rm{without}}\,{\rm{ferromagnetic}}\,{\rm{rail}}\\ {{\rm{F}}}_{{\rm{fer}}}=-{\left.\displaystyle \frac{{{\rm{dW}}}_{{\rm{mag}}}}{{\rm{dr}}}\right|}_{{\rm{r}}={{\rm{r}}}_{{\rm{d}}}}\,{\rm{with}}\,{\rm{ferromagnetic}}\,{\rm{rail}}\end{array}\right.\end{eqnarray*}$$

In Coulomb friction model, the maximum tangential force applicable by the wall to the ball is $| T| =\mu \times | N| ,$ μ being the coefficient of friction. Considering the radius of the magnetic ball ${r}_{\mathrm{ball}},$ the amplitude of the friction torque is then:

$$\begin{eqnarray}&&| {\tau }_{{\rm{friction}}}| ={{\rm{r}}}_{{\rm{ball}}}\cdot | {\rm{T}}| ={{\rm{r}}}_{{\rm{ball}}}\cdot \mu \cdot | {\rm{N}}| \end{eqnarray} \tag{ 4 }$$

The coefficient of friction between the magnetic ball and a plastic wall was estimated experimentally to μ ≈ 0.2. Using Simulink and the ferromagnetic attraction force calculated by FEM, the average value for the normal wall force $N$ was estimated to be 0.05 N or 0.35 N, without or with the ferromagnetic band respectively. The corresponding values for the friction torque are 4.10⁻⁵ N.m and 2.8 10⁻⁴ N.m.

2.3.5. Resulting torque—advantages of the ferromagnetic rail

The self-rotation of the ball follows equation (5). ${I}_{z}=\tfrac{2}{5}m\,{r}_{\mathrm{ball}}^{2}$ = $1.3\,{10}^{-8}\,\mathrm{kg}.{{\rm{m}}}^{2}\,$is the moment of inertia of the ball.

$$\begin{eqnarray}&&{{\rm{I}}}_{{\rm{z}}}\,\ddot{\beta }={\tau }_{{\rm{friction}}}+{\tau }_{{\rm{coil}}}(+{\tau }_{{\rm{fer}}.})\end{eqnarray} \tag{ 5 }$$

Without the ferromagnetic rail, the electromechanical torque is higher than the friction torque for induced currents of few mA only. In that case, the electrical damping of the device is limited, and the ball is often sliding which increases the mechanical losses. On the other hand, the friction torque becomes a lot higher when the ferromagnetic part is present; adding the 'static' torque generated by the latter, the influence of the induction-limiting torque from the coils is therefore reduced, and the electrical damping is strengthened (at the cost of some static friction). Besides, depending on the instantaneous intensity of the mechanical excitation applied to the device and the dimensions of the ferromagnetic rail, the ball is often rolling which reduces the mechanical losses. By promoting the rolling behavior, the ferromagnetic rail therefore offers a dual advantage.

A prototype was built with a ${r}_{d}=2.5\,{\rm{cm}}$ radius trajectory. The body was manufactured in plastic, and the 1000-turns coils were made on a winding machine (figure 7(a)). The dimensions of the ferromagnetic rail were chosen in order to increase the 'natural' rolling of the magnetic ball sufficiently to overcome the electromagnetic torque, as explained previously. Prototype parameters are detailed in table 1. The signals of the independent coils were rectified separately with voltage doubling circuits, the outputs of which were placed in parallel (figure 7(b)). We used BAS70-04 diodes, with a forward voltage drop of 410 mV at 1 mA.

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The moving magnet was one N38 NdFeB ball (Ø8 mm, m = 2 g, B_r = 1.24 T). The mechanical (parasitic) damping coefficient ${c}_{m}$ was estimated to be in the 0.005–0.01 N.s/m range from the oscillations of the ball in a free fall experiment (i.e. in open-circuit, without the ferromagnetic band). A value for the average electromechanical coupling ${c}_{e}$ was also determined by inducing a forced cycling motion of the ball (at a fixed velocity ${v}_{\mathrm{ball}}$) and measuring the average dissipated electrical power ${P}_{e,\mathrm{ave}},$ according to expression (6):

$$\begin{eqnarray}&&{{\rm{c}}}_{{\rm{e}}}\approx \displaystyle \frac{{{\rm{P}}}_{{\rm{e}},{\rm{ave}}}}{{{\rm{v}}}_{{\rm{ball}}}^{2}}\end{eqnarray} \tag{ 6 }$$

Without the ferromagnetic rail, this value was evaluated at c_e = 0.007 N.s/m, which is very low given the 2 g magnetic mass and the 1000-turns coils. It is in particular insufficient regarding the optimal value (0.05 N.s/m) suggested by the previous simulations of the system. After attaching the ferromagnetic rail to the device, the electrical damping coefficient was estimated to about c_e = 0.04 N.s/m, which is closer to the optimal value estimated for this device dimensions (see figure 3(d), with ${r}_{d}=2.5\,{\rm{cm}}$).

We tested the performance of the device while it was carried by a person running on a treadmill. The average electrical power received by the two resistive loads (${{\rm{R}}}_{1}={{\rm{R}}}_{2}={{\rm{R}}}_{{\rm{coils}}}=200\,{\rm{\Omega }}$) was measured during 50 s samples.

First, the relevance of the added ferromagnetic strip was verified (figure 8(a)). The device was attached to the arm, and the average power received by the resistive loads was measured for running speeds between 4 km h⁻¹ (very slow) and 8 km h⁻¹ (moderate). The load power of the elementary device varies from 0.5 mW to 0.8 mW, while it ranges from 1.8 mW to 4.8 mW after adding the ferromagnetic band. These last values are consistent with the preliminary simulation (which announced 4.2 mW at 8 km h⁻¹ for the 2.5 cm radius system). The form of the electrical current in the two resistive loads for the device with the ferromagnetic rail (at 8 km h⁻¹) is displayed in figure 8(b). It shows current 'packets' occurring with a frequency of about 2.5 Hz. They are triggered by the step impacts and swing accelerations, happening at this same frequency, which overcome the static friction.

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Different generator locations on the body were tested, revealing significant performance differences between them (figure 8(c)). We exposed in a previous study [23] that the upper body was well benefiting from impacts from both feet during the run, while only half were felt in the legs. The 'upper arm' and 'wrist' positions get mechanical energy from these steps 'shocks', as well as the important limbs 'swing' accelerations. They thus yield the best output powers (between 2 and 5 mW). It is worth noticing that the generator worn on the wrist produces more than 3 mW even at the lowest running speeds. The foot area is also quite relevant because of the important 'swing' amplitude. The two tested orientations of the generator (vertically on the ankle, and horizontally on top of the shoe) showed similar results, from 0.5 to 2.5 mW. However, placing the device around the thigh (for example in the pocket) was not conclusive, with a maximum of 0.6 mW generated at 8 km h⁻¹. This could be expected since both 'swing' and 'shocks' are reduced at this position. The system was finally tested during the walk (at 4 km h⁻¹). This activity is mechanically far less energetic than running, and therefore the output powers were only of a few 100 s μW.

These output powers up to 4.8 mW obtained from the 'running' activity are satisfying given the small moving mass (m = 2 g). Indeed, state-of-the art inertial energy harvesters for human motion with comparable moving mass values usually generate sub-mW outputs [17, 20, 25, 26]. This performance underlines the relevance of the 'looped' device format combined with the rolling moving mass. The power density of the device is in the average, up to 220 μW.cm⁻³ relatively to the 21 cm³ volume of the whole loop. The best inductive generators in the literature exhibited power densities over 500 μW.cm⁻³ [22, 23], obtained from resonant structures.

To improve the power density, we considered a 'half' device, with extremal foam bumpers (figure 9(a)). The output powers of this configuration are close with those of the full device at the lowest running speeds, as about 2 mW were produced when the device was worn on the arm. At higher speeds however, the motion amplitude limitation decreases the output, and a maximum of 3 mW only was produced at 8 km h⁻¹ (figure 9(b)). The related power densities are only slightly better, up to 280 μW cm⁻³ (figure 9(c)).

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Besides the use of the ferromagnetic rail, another solution to keep the electrical damping at a sufficient level is to block the self-rotation of the moving magnetic part. We considered a magnetic 'train' of two magnetic balls separated by a curving spacer (figure 10(a)). The interaction between the balls keeps the magnetic polarization of the moving ensemble constant along the trajectory. From the free-fall experiment, the mechanical damping coefficient associated with this configuration was c_m = 0.05–0.1 N.s/m, which is ten times the value obtained for the single moving ball. The use of solid or liquid lubricants was tested, but did not permit to lower this value significantly. Because of it, the output power of the system (carried on the arm) was importantly weakened (between 0.8 mW and 1 mW, see figure 10(c)), despite the greater moving mass (m = 4 g). Although the performance may be improved by using the low-friction materials for the inner wall of the tube and the surface of the magnetic balls, these results suggest that ability to roll of the previous single ball is an important factor to decrease the friction losses.

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The fixed magnetization orientation enables using two moving magnetic ensembles placed in a repulsive configuration, as illustrated in figure 10(b). However appealing in terms of additional mechanical input, this concept was eventually not conclusive experimentally, as shown by the weak output power (figure 10(c)). A first explanation that could be advanced is that the repulsive force between the two magnet trains effectively limits their respective motion range and subsequently the achievable velocities and power output. However, as observed with the 'half-device' (Variant 1), the reduced motion range should not have been that much of an issue, at least for the lowest running speeds. Yet, we observe that the output power with the two moving 'trains' at 4 km h⁻¹ is only half of what was obtained in the single moving 'train' situation. Therefore, the main explanation for this weak electrical performance lies probably in the mechanical losses. The two magnetic parts interact not only in terms of angular repulsion, but also in terms of torque: the two magnetic dipoles try to rotate to reach a stable magnetic alignment. This interaction increases the mechanical friction with the walls furthermore.

Many applications of energy harvesters require an intermediate storage unit, at least to provide a steady voltage source. The full-loop device with a single magnetic ball (m = 2 g) and the peripheral ferromagnetic rail was tested to recharge a 2.4 V NiMH battery (RS Pro, 80 mAh). For this experiment, the outputs of the rectifying circuits were connected to two 1 mF capacitors, in parallel with the battery (figure 11(a)). The power transferred to the cell was calculated from the average current it received during the experiment, i.e. $\langle {{\rm{P}}}_{{\rm{cell}}}\rangle =\,2.4{\rm{V}}\times \langle {\rm{i}}\rangle .$ This current was measured by monitoring the voltage across a 50 Ω resistance that was connected in series with the battery. The generator was placed on the side of the upper arm. The average charging power increased from 1.5 mW to 2.8 mW, for running speeds from 4 to 8 km h⁻¹ (figure 11(b)).

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The looped generator was finally tested with a Wireless Sensor Node (WSN) to validate the whole energy harvesting chain. This WSN was made of an nRF51 System-on-Chip with a Bluetooth Low Energy stack (Nordic Semiconductor) and an ADXL363 3-axis acceleration and temperature sensor (Analog Devices), which are both ultra-low power consumption devices (figure 12(a)). The measured power consumption of this node at a 20 Hz operating frequency was 1.2 mW. Compared to the previous cell charging experiment, the device can produce enough power to recharge a battery and fuel the WSN at the same time, which is interesting given the variations of intensity of human activity: the stored extra power may be used during low-activity periods.

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We verified that the direct power supply of the WSN was possible. A low-power Schmitt trigger was placed at the output, set to close a PMOS switch as soon as the voltage on the buffer capacitor reaches 3.3 V, and to open it when it falls below 2.5 V (figure 12(b)). This configuration solves the issue of the large power consumption of microcontrollers under 1 V. The good operation of the WSN, sending data at 20 Hz was validated. Figure 12(c) shows a screenshot of the receiving smartphone displaying the measured 3-axes acceleration during the test.