Harvesting biomechanical energy in the walking by shoe based on liquid metal magnetohydrodynamics

Abstract

A liquid metal magnetohydrodynamics generation system (LMMGS) was proposed and demonstrated in this paper for collecting parasitic power in shoe while walking. Unlike the conventional shoe-mounted human power harvesters that use solid coil and gear mechanism, the proposed system employs liquid metal (Ga₆₂In₂₅Sn₁₃) as energy carrier, where no moving part is requested in magnetohydrodynamics generators (MHGs). While walking with the LMMGS, the foot alternately presses the two liquid metal pumps (LMPs) which are respectively placed in the front and rear of the sole. As a result, the liquid metal in the LMPs (LMP I and II) is extruded and flows through the MHGs (MHG I and II) in which electricity is produced. For a comparison, three types of LMMGSs (LMMGS A, B and C) were built where all the parts are the same except for the LMPs. Furthermore, performances of these LMMGSs with different volume of injected liquid metal were tested respectively. Experimental results reveal that both the output voltage and power of the LMMGS increase with the volume of injected liquid metal and the size of the LMPs. In addition, a maximum output power of 80 mW is obtained by the LMMGS C with an efficiency of approximately 1.3%. Given its advantages of no side effect, light weight, small size and reliability, The LMMGS is well-suited for powering the wearable and implantable micro/nano device, such as wearable sensors, drug pumps and so on.

Keywords

human energy harvesting / liquid metal / wearable magnetohydrodynamics generator / parasitic power in shoe

Introduction

Over the last few years, with the power consumption requirements for electronic products decreasing gradually, human power is becoming a promising option for powering the electronic products, which has been drawing a growing attention. In fact, human body could be a huge renewable energy source. According to former research, approximately 133.9 W of energy was generated by kinetic energy from an adult [1]. Besides, to generate electricity over long duration, many researches on human power have been conducted to harvest energy from everyday activities, such as walking. Until now, various human power generators have been proposed to capture human power during walking. Kymissis et al. proposed a magnetic generator in shoe which can produce an average of 250 mW electricity during standard walk [2]. Based on the analysis of the power output of hip, knee and ankle while walking, Donelan and his colleague [3-6] built and tested a knee-mounted harvester (1.6 kg) which can produce approximately 5 watts of electricity by two sets of such devices while walking. Rome et al. [7] developed a backpack mounted generator which could generate 7.4 watts by carrying 20-30 kg of load. Saha et al. [8] designed an electromagnetic generator for human motion energy harvesting which was used to power body worn sensors or electronics devices. Their experimental results showed that electricity power produced by such generator was between 300 µW and 2.5 mW.

Although a lot of magnetic generators have been proposed to successfully harvest human power during walking, some problems still require to be solved such as too much weight, high friction loss, and short life span etc. In order to meet these requirements, a type of shoe-mounted human power harvester-liquid metal magnetohydrodynamics generation system (LMMGS) was proposed and realized in this paper. Unlike most of the conventional magnetic generators with solid coil and gear mechanism, the LMMGS has no rotary part and transmission component, making it much lighter and more reliable. Moreover, performances of the LMMGS are tested and discussed. Experimental results demonstrate that this generation system is highly feasible. Based on its many unique characteristics, the LMMGS is very helpful to power personal services such as tracker, GPS, bluetooth, etc. in the future.

Theoretical analysis

Structure of LMMGS

The structure of the LMMGS is shown in Fig. 1. From Fig. 1(b) it can be seen that the LMMGS is comprised of two liquid metal pumps (LMPs: LMP I and II), two magnetohydrodynamics generators (MHGs: MHG I and II), two check valves (Check valve I and II), and two connecting pipes (Connecting pipe I and II). As the driving part, the LMPs are analogous to liquid pumps, which can pump the liquid metal in the LMMGS when they are pressed. Figure 1(a) shows the installation location of the LMMGS in shoe. In Fig. 1(a), it can be found that parts of the LMMGS are inlayed into the sole except the LMPs which are set on the surface of the sole. To be specific, LMP I and II are installed in the front and rear of the sole, respectively. One end of LMP I is connected to MHG II while the other is connected to Check valve I. In addition, MHG I is connected to one end of LMP II while Check valve II is connected to the other. Furthermore, Connecting pipe I is used to connect Check valve I and MHG I, whereas Connecting pipe II is employed to connect Check valve II and MHG II.

Figure 2 illustrates the working principle of the LMMGS while walking. In Fig. 2(a), when the forefoot presses LMP I first, the liquid metal in LMP I will be extruded and first flow through Check valve I then MHG I, and finally arrive at LMP II, where MHG I will generate electricity. In Fig. 2(b), with the orthocenter of human body moving to the heel, LMP II is pressed; and consequently, the liquid metal in LMP II will be extruded and first flow through Check valve II then MHG II, and finally arrive at LMP I. In this process, MHG II will produce electricity. In this way, MHG I and II in the LMMGS will work alternately during the time the forefoot strikes on LMP I while the heel off LMP II or the heel strikes on LMP II while the forefoot off LMP I. Figure 2(c) denotes the force on the LMPs and flow direction of the liquid metal in the LMMGS while walking. From Fig. 2(c), it can be observed that once LMP I or II is pressed, the liquid metal will flow counter-clockwise in the LMMGS, under the function of the check valves.

MHGs are the core unit in the LMMGS, where electricity will be produced when the liquid metal flows through it. A MHG is composed of an inlet, a generator body, two electrodes, two magnets, a magnetic flux conductor, and an outlet. The structure of the MHG is depicted in Fig. 3. Two magnets are inlayed into the upper and lower surface of the generator body respectively. Two electrodes are set in the left and right sides of the generator body. The inlet is set in the front side of the generator body while the outlet is set in the back. When the liquid metal goes through the inlet into the generator body, it will cut the magnetic induction lines produced by the two magnets, and electricity will be conducted by two electrodes in the direction perpendicular to the magnetic field and flow direction. Here, the magnetic flux conductor, which surrounds the faces of the generator body except the front and back ones, is used to conduct the magnetic flux, thus a close loop magnetic circuit would be formed and an enhanced magnetic field strength would be made.

Performance analysis of LMMGS

The volume flow of the liquid metal in the LMMGS is dependent on the volume of the LMP and the frequency of walking, which can be defined as

(1)\stackrel{•}{Q}=Q_{\mathrm{P}}\times f_{\mathrm{W}}\times n,

where \stackrel{•}{Q} is the volume flow of the liquid metal, Q_{\mathrm{P}} is the volume of LMP, f_{\mathrm{W}} is the frequency of walking, n is the volume percentage of injected liquid metal in the LMMGS. Therefore, the flow velocity of the liquid metal in the MHG is

(2)v_{\mathrm{G}}={\displaystyle \frac{\stackrel{•}{Q}}{S_{\mathrm{G}}}},

where v_{\mathrm{G}} is the flow velocity of the liquid metal in the MHG, S_G is the cross sectional area of the MHG. Thus, the output voltage of the MHG is described as

(3)E=BL{v}_{\mathrm{G}},

where E is the output voltage of the MHG, B is the magnetic induction intensity, L is the distance between two electrodes in the MHG. Under the result of combining Eqs. (1), (2) and (3), the output voltage of the MHG can be rewritten as

(4)E=BL\times {\displaystyle \frac{Q_{\mathrm{P}}\times f_{\mathrm{W}}\times n}{S_{\mathrm{G}}}}.

For the experimental prototype, B=0.945 T, L=0.01 m, S_{\mathrm{G}}=\mathrm{0.01}\times \mathrm{0.001}=\mathrm{1}\times {\mathrm{10}}^{-\mathrm{5}}{\mathrm{m}}^{\mathrm{2}}, and f_w=1.16 Hz. In addition, limited by the space of shoe, the range of Q_{\mathrm{P}} falls between 11615 mm³ and 26564 mm³. Furthermore, the value of n is from 60% to 90%. So Eq. (4) can be rewritten as

(5)\begin{array}{l}E=\mathrm{1096}\times Q_{\mathrm{P}}\times n,\hfill \\ (\mathrm{1.1615}\times {\mathrm{10}}^{-\mathrm{5}}\le Q_{\mathrm{P}}\le \mathrm{2.6564}\times {\mathrm{10}}^{-\mathrm{5}},\mathrm{60}\%\le n\le \mathrm{90}\%).\hfill \end{array}

From Eq. (5) it can be seen that the output voltage of the MHG is proportional to the product of Q_{\mathrm{P}} and n, when the parameters of the MHG and walking frequency are fixed. In order to denote the relationship among them vividly, changes of output voltage with the volume of the LMP and n can be illustrated in Fig. 4. From Fig. 4, it can be found that the output voltage increases with Q_{\mathrm{P}} and n when Q_{\mathrm{P}} is from 1.1615×10^-5 m³ to 2.6564×10^-5 m³ and n is from 60% to 90%. Moreover, the maximum voltage value is from 20 mV to 25 mV, when Q_{\mathrm{P}} and n are in the permitted scale.

Experiment

Experimental prototype

The photograph of the experimental prototype is illustrated in Fig. 5. The length of the prototype is 235 mm, and the maximal width is 65 mm. In this experiment, the LMPs and connecting pipes are realized by silicone tubes. The Check valves are made of plastic, model OCV518CVN. In the MHG, the materials for each part are as follows: Both of the two magnets are made of NdFeB (neodymium iron boron); The two electrodes are made of copper; The generator body is made of organic glass. The magnetic flux conductor is 2Cr13. During the test, the voltage value is measured by an Agilent data acquisition system, model 34970A, USA. While mass data is measured by an electronic scale with a measuring range of 1 kg.

In this study, three kinds of LMMGSs were built, which are LMMGS A, B and C, respectively. Among them, the output voltage and power of LMMGS A and B were mainly compared with different volume percentages of injected liquid metal. In LMMGS A and B, all the parts are the same except for the LMPs. Among the same parts, dimensions of Connecting pipe I in the two LMMGSs is 6.8×9×8 mm (inner diameter × outer diameter × length), while Connecting pipe II is 6.8×9×10 mm. The LMPs in the LMMGSs are demonstrated in Tables 1 and 2 respectively, from which, it is easy to figure out that the LMPs in LMMGS B are larger than those in LMMGS A.

In addition, the total system volume of LMMGS A and B is measured. The volume percentage of the injected liquid metal in the total volume of the LMMGS which is tested in this paper is 60%, 70%, 80% and 90%, respectively. So the volume of the injected liquid metal can be calculated based on the system volume of the LMMGS. Finally, the mass of the injected liquid metal is gained by multiplying the calculated volume of the injected liquid metal and liquid metal density which is 5910 kg/m³ in the experiment [9]. In addition, the mass of LMMGS A without liquid metal weighs 170 g, while that of LMMGS B is 180g, as denoted in Tables 3 and 4 respectively.

Experimental results

In this experiment, the performances of the LMMGSs were tested by a test subject of 45 kg while walking at approximately 1.16 Hz. Figure 6 displays the changes of open-circuit voltage of LMMGS A when the volume of the injected liquid metal is 60% (Fig. 6(a)), 70% (Fig. 6(b)), 80% (Fig. 6(c)) and 90% (Fig. 6(d)) of the total system volume respectively. In Figs. 6(a), (b), (c), and (d), the peak value of the open-circuit voltage of MHG I and MHG II appears alternately, which is aligned with the movement that the forefoot and the heel press LMP I and II alternately while walking. Additionally, comparing with the output voltage values in Fig. 6(a), (b), (c) and (d), it can be found that the output voltage of LMMGS A increases with the volume of the injected liquid metal when such volume is less than 90% of the total volume of LMMGS A. In Fig.6, a maximum open-circuit voltage of 12.5 mV is gained when the injected liquid metal takes up 90% of the total system volume.

When a 0.01 Ω resistance is employed as a load for each MHG electrical circuit in the LMMGS, the output power changes are exhibited in Fig. 7. To be specific, Fig. 7(a), (b), (c) and (d) illustrates that the output power changes with time when the volume percentages of the injected liquid metal are 60% (Fig. 7(a)), 70% (Fig. 7(b)), 80% (Fig. 7(c)) and 90% (Fig. 7(d)) respectively. From Figs. 7(a), (b), (c) and (d), it can be observed that the peak value of the output power of MHG I and MHG II appears alternately. In addition, the maximum value of the output power increases with the volume percentage of the injected liquid metal. An approximate power of 10mW as the maximum output power is obtained, when the volume percentage of the injected liquid metal is 90% in LMMGS A with a load of 0.01 Ω.

Changes of open-circuit voltage with time in LMMGS B when the volume percentages of the injected liquid metal are 60%, 70%, 80% and 90% are denoted in Figs. 8(a), (b), (c) and (d) respectively. The peak value of the open-circuit voltage of MHG I and MHG II also appears alternately in LMMGS B. Meanwhile, the open-circuit voltage also increases with the volume percentages of the injected liquid metal. And the maximum open-circuit voltage in LMMGS B is also gained when the volume of the injected liquid metal is 90% of the total volume of LMMGS B. Besides, a comparison of Fig. 6 and 8 indicates that when the volume percentage of the injected liquid metal is the same, the maximum of the open-circuit voltage in LMMGS B is lager than that in LMMGS A. For example, the maximum open-circuit voltage in LMMGS A is 7.5 mV which is smaller than 16.1 mV in LMMGS B, when the volume percentage of the injected liquid metal is 60%. This demonstrates that the open-circuit voltage of LMMGS increases with the size of the LMPs, because other parts in LMMGS A and B are the same except the LMPs.

The output power of LMMGS B is also tested when two 0.01 Ω loads are connected to MHG I and MHG II of LMMGS B respectively. Changes of output power of LMMGS B with 0.01 Ω load are presented in Fig. 9 when the volume percentages of the injected liquid metal are 60% (Fig. 9(a)), 70% (Fig. 9(b)), 80% (Fig. 9(c)) and 90% (Fig. 9(d)) respectively. The maximum value of output power from MHG I and MHG II also arises alternately. Meanwhile, the output power increases with the volume percentages of the injected liquid metal. Furthermore, comparing the results in Fig. 7 with those in Fig. 9, it can be noticed that the output power of LMMGS B is larger than that of LMMGS A, when the volume percentage of the injected liquid metal is the same. So, like the open-circuit voltage, it can be seen that the output power increases with the size of the LMPs in the LMMGS as well.

The experimental data in Figs. 6, 7, 8 and 9 show that the open-circuit voltage of the liquid metal increases with the inner diameter of the LMPs when the percentage of the injected liquid metal, as well as the output power of the LMMGS, is identical. Therefore, based on the analysis above, the optimized LMMGS C was developed by increasing the inner diameter of the LMP to the maximum permissible value for shoe in this paper. The dimensions of the LMPs in LMMGS C are listed in Table 5, while the other parts of LMMGS C are identical with those of LMMGS A and B. The mass of LMMGS C without liquid metal was measured as 181 g. In addition, when the volume percentage of the injected liquid metal is 90%, changes of the open-circuit voltage of LMMGS C, as well as the output power when two 0.01 Ω loads are connected to each MHG in LMMGS C, is revealed in Fig. 10. From Fig. 10 it can be see that the peak value of the open-circuit voltage and output power also appear alternately, and they are larger than those in LMMGS A and B when the volume percentage of the injected liquid metal is 90%. To be specific, a maximum output voltage of 22.5 mV, as well as the maximum output power of 40 mW, is gained in LMMGS C with a total system mass of 336.92 g.

In addition, the experimentally measured data conforms to the theoretical prediction. On the one hand, the open-circuit voltage and output power increase with the size of LMPs as well as the volume percentage of the injected liquid metal. On the other hand, the experimental value of the open-circuit voltage is in the scale of theoretical calculation. Therefore, the LMMGS is developed successfully.

Discussion

The dimensionless parameter of Cost of Harvesting (COH) was first introduced to evaluate the additional metabolic power in watts required to generate 1 W electricity power by Donelan et al. [6]. They defined COH is

(6)\mathrm{C}\mathrm{O}\mathrm{H}={\displaystyle \frac{\mathrm{\Delta }\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}}{\mathrm{\Delta }\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{d}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{e}\mathrm{f}\mathrm{f}\times \mathrm{m}\mathrm{u}\mathrm{s}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{e}\mathrm{f}\mathrm{f}}},

where device eff is the conversion efficiency of kinematical energy to electricity power, muscle eff’ is the conversion efficiency of metabolic power to kinematical energy. To the LMMGS proposed in this paper, the COH can be expressed as

(7)\mathrm{C}\mathrm{O}\mathrm{H}={\displaystyle \frac{\mathrm{1}}{{\eta }_{\mathrm{d}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{c}\mathrm{e}}{\eta }_{\mathrm{m}\mathrm{u}\mathrm{s}\mathrm{c}\mathrm{l}\mathrm{e}}}},

where {\eta }_{\mathrm{d}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{c}\mathrm{e}} is the efficiency of the LMMGS, {\eta }_{\mathrm{m}\mathrm{u}\mathrm{s}\mathrm{c}\mathrm{l}\mathrm{e}} is the efficiency of muscle. Furthermore, the efficiency of the LMMGS can be described as

(8){\eta }_{\mathrm{d}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{c}\mathrm{e}}={\displaystyle \frac{p}{mg{d}_{\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{r}}{f}_{\mathrm{W}}}},

where p is the output power of the LMMGS, m is the weight of the user, g is the local acceleration of gravity, d_{\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{r}} is the inner diameter of the LMP. As Eq. (8) shows the efficiency of the LMMGS is determined by the walking frequency, the weight of the user and the inner diameter of the LMP. For LMMGS C, the inner diameter of the LMP is 12 mm, the maximum output power is approximately 80 mW, the weight of test subject is 45 kg and the walking frequency is 1.16 Hz. So the efficiency of LMMGS C can be calculated as

(9){\eta }_{\mathrm{L}\mathrm{M}\mathrm{M}\mathrm{G}\mathrm{S}\mathrm{C}}=\mathrm{1.3}\%.

When muscle’s peak efficiency which is approximately 25% [10] is available, the COH of the LMMGS can be revised as

(10)\mathrm{C}\mathrm{O}{\mathrm{H}}_{\mathrm{L}\mathrm{M}\mathrm{M}\mathrm{G}\mathrm{S}\mathrm{C}}=\mathrm{308.}

From Eq. (10) it can be obtained that if 1 watt of electricity is generated by LMMGS C, 308 watts of metabolic power is needed. Although the output power of the LMMGS is larger than the tube magnetic generator [8] and lighter than the conventional shoe-mounted and knee-mounted magnetic generators [2, 6], the efficiency of the LMMGS is low. So research on optimization and improvement for the LMMGS is still required in the future, which should mainly focus on reducing the flow resistance of the liquid metal in the LMMGS, improving the performance of the MHG and even changing the shape of the LMP.

Conclusion

In this paper, based on liquid metal (Ga₆₂In₂₅Sn₁₃), a new shoe-mounted LMMGS is developed successfully. The LMMGS, which is built to harvest human power to support wearable mobile electronic devices, mainly consists of two LMPs, two MHGs, two check valves and two connecting pipes. Performances of three types of LMMGS (LMMGS A, B and C) are tested in the conceptual experiment. According to the measured results, the open-circuit voltage and output power of the LMMGS increase with the size of the LMPs when the volume percentage of the injected liquid metal is fixed. Meanwhile, for the same LMMGS, the open-circuit voltage and output power increase with the volume percentage of the injected liquid metal. In addition, the maximum output voltage of 22.5 mV and a maximum output power of 80 mW are obtained in LMMGS C with an efficiency of 1.3%, when the volume percentage of the injected liquid metal is 90%. Although the feasibility of LMMGS is demonstrated, improving work to obtain the best energy output is still needed in the future.

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