Energy harvesting using flexible piezoelectric materials from human walking motion: Theoretical analysis

Abstract

Human walking is a good energy source that can be harvested to support wearable devices. For one walking cycle, the muscles at each joint of human lower body consume tens of watts. The considerable amount of kinetic energy generated while walking can be turned to useful electric energy through energy transducers. In this article, we theoretically investigate energy harvesting from flexible piezoelectric materials attached to humans while walking. We focus on the hip, knee, and ankle motions of walking humans and analyze the frequency characteristic of the motions using Fourier series fitting. A model is utilized to predict the electrical responses from piezoelectric materials and the power harvested through load resistances. In particular, we estimate the harvested power from polyvinylidene fluoride and derive the contour maps with respect to the harvested power as a function of the load resistance and walking frequency. Moreover, we discuss the necessary mechanical power input required to deflect the energy harvester and the effects of the varied parameters.

Keywords

Energy harvesting piezoelectric material walking motion

Introduction

Recent developments in the area of energy harvesting have promoted scientific and technological advancements for self-powered devices (Elvin and Erturk, 2013; Kazmierski and Beeby, 2011; Priya and Inman, 2009). Electronic devices supported by integrated energy harvesters provide several benefits such as semi-permanent lifetime, reduced weight, and low maintenance (Sodano et al., 2005). These advantages are especially useful for systems in inaccessible areas. We can use various energy sources for harvesting energy in such environments, such as oceanic waves (Cha et al., 2015; Park et al., 2014), wind (Erturk et al., 2010; Myers et al., 2007), animal motions (Cha et al., 2013c, 2016; Shafer et al., 2012; Wu et al., 2014), and human activities (Delnavaz and Voix, 2014; Hwang et al., 2014; Renaud et al., 2009).

We need to integrate energy transducers into the harvesting systems to extract useful electric energy from the kinetic energy sources. Flexible smart materials, such as polyvinylidene fluoride (PVDF) (Kawai, 1969), macro-fiber composite (MFC) (Sodano et al., 2004), and ionic polymer metal composite (IPMC) (Jo et al., 2013; Shahinpoor and Kim, 2001), are under examination at present on account of their suitability for use as energy transducers because of the piezoelectric effect and low stiffness (Elvin and Erturk, 2013; Erturk and Inman, 2011). For example, in the work by Sodano et al. (2005), the possibility of charging a battery from ambient mechanical vibrations was experimentally demonstrated using MFC. An energy harvesting system with MFCs attached to a cantilever beam, which is excited by another MFC actuator, was presented by Yang et al. (2009). In the work by Erturk and Delporte (2011), the underwater energy harvesting capability of bimorph MFC cantilevers was experimentally validated. In the work by Cha et al. (2013a), energy harvesting from underwater base excitation of partially immersed MFC beams was investigated. In the work by Jiang et al. (2010), energy harvesting from PVDF cantilever with a magnetic mass was experimentally studied. In the work by Vatansever et al. (2011), the feasibility of energy generation from PVDF when subjected to various wind speeds and water droplets was evaluated. In the work by Farinholt et al. (2009), energies harvested by PVDF and IPMC for energy harvesting were compared. In the work by Tiwari and Kim (2010), thick IPMC disks were tested for energy harvesting. In the works by Aureli et al. (2010) and Anand et al. (2010), energy harvesting from the underwater flexural vibrations of an IPMC beam was demonstrated. In the work by Cha et al. (2013b), the underwater torsional vibrations of a patterned IPMC beam were used as a source of energy. In the work by Giacomello and Porfiri (2011), IPMCs mounted on heavy fluttering flags were utilized to harvest energy from steady water flow. In the work by Cellini et al. (2014), a turbine hosting multiple IPMCs for harvesting energy from flowing water was reported. While MFC has a higher electromechanical coupling than IPMC and PVDF, they are more flexible (Farinholt et al., 2009; Shen, 2009; Tiwari and Kim, 2013). In addition, IPMC is appropriate for usage in moist environment or underwater because its piezoelectric property degrades in dry environments.

Here, we study the theory of energy harvesting through flexible piezoelectric materials attached to humans while walking. Human motions have been utilized as energy sources for wearable energy harvesters (Delnavaz and Voix, 2014; Hwang et al., 2014; Renaud et al., 2009). For instance, in the work by Renaud et al. (2009), an energy harvester on a human limb was demonstrated. In the work by Delnavaz and Voix (2014), energy was harvested from the jaw movements of human using a piezoelectric chin strap. In the work by Hwang et al. (2014), a self-powered pacemaker that uses heartbeats was tested. Moreover, human walking is a good source of kinetic energy (Riemer and Shapiro, 2011). In the works by Kymissis et al. (1998) and Ylli et al. (2015), energy harvesting shoes that use the movement of feet while walking were introduced. In the works by Rome et al. (2005) and Granstrom et al. (2007), energy harvesting backpacks that utilize human walking were proposed. In the works by Donelan et al. (2008) and Pozzi and Zhu (2011), energy harvesting devices using direct knee motions made while walking were reported. A theoretical study about harvesting energy from walking and running using a resonant vibrational harvester was reported by Elvin and Elvin (2013). Most of these research works except Elvin and Elvin (2013) focused on the experimental demonstration and the specific case study of the energy harvested from human motions. As a result, the wider understanding of the energy harvesters under various conditions is insufficient. We focus on predicting the amount of energy harvested from human walking using integrated flexible piezoelectric materials. In particular, we analyze the motions of the lower human body during walking. The walking data in the work by Riemer and Shapiro (2011) are utilized to study the motions. The frequency characteristic of human walking is identified by determining the Fourier series of the data. We assume that the flexible piezoelectric materials are fully attached to the hip, knee, and ankle through a tight suit. The structure of the piezoelectric materials is considered as a beam deflected along with the radius of each joint. Additionally, we estimate the voltage output generated by the deformation of piezoelectric materials and human walking motions using an electromechanical model. In addition, we elucidate the effect of the shunting load resistance and walking frequency on the power harvested from piezoelectric materials while walking. Finally, we study the input mechanical power required to deflect the energy harvesters and power harvested for various electromechanical couplings and capacitances. The main contributions of this work from a methodological point of view are as follows: (1) analyzing the frequency characteristics of each joint in the lower human body while walking; (2) developing a simple model to investigate energy harvesting from human walking; (iii) providing insights into energy harvesting from human walking under a broad range of conditions.

This article is organized as follows. In section “Human walking motion,” we analyze human walking motion in terms of frequency characteristics. In section “Electrical response of piezoelectric material,” we introduce a model and predict the electrical responses from the piezoelectric materials attached to humans during walking. In section “Power transfer,” we analyze the power harvested from the piezoelectric materials during walking under various conditions. Finally, the conclusions are summarized in section “Conclusion.”

Human walking motion

Motion trajectory

The human walking motion is mainly focused on the movements of the lower body. In particular, the pitch movements of the hip, knee, and ankle joints contribute to the walking motion (Riemer and Shapiro, 2011). Figure 1 displays the trajectory of each joint angle $Θ$ of the lower body during one walking cycle $T$ (Riemer and Shapiro, 2011). The walking speed and frequency are $U = 1.3 m / s$ and $f = 1 / T = 0.9 Hz$ , respectively. Zero hip, knee, and ankle angles indicate the thigh at $90 \circ$ with the ground, full extension, and $90 \circ$ between the shank and the foot, respectively (Riemer and Shapiro, 2011). In other words, all zero angles mean that a human is in the vertical position.

We analyze the frequency characteristics of the motion trajectories by performing Fourier series fitting. The fitting uses the built-in “fit” function provided by MATLAB. In particular, we use the following equation for the fitting

a_{0} + \sum_{m = 1}^{n} a_{m} \sin (m ω t + b_{m}), n = 1, 2, \dots

(1)

where $ω = 2 π f$ .

The fitting results until $n = 6$ are displayed in Figure 1, and the coefficients $a_{0}$ and $a_{m}$ are shown in Tables 1 to 3. When we consider the fundamental harmonic, the values of coefficients of determination R² are 0.8554 (hip), 0.6688 (knee), and 0.2982 (ankle). Therefore, fitting results based on the fundamental harmonic are insufficient to describe the angle motions. However, the values of R² improve to 0.9648 (hip), 0.9788 (knee), and 0.8734 (ankle) when the second harmonics are included in the fitting. Although the value of R² for the ankle is under 0.9, the improvements show the importance of considering the second harmonic in the human walking motions. Additionally, the values of R² achieved by considering the fourth harmonic increase to 0.9957 (hip), 0.9973 (knee), and 0.9848 (ankle), and Figure 1 shows that fitting is sufficient to simulate all the angle motions. In the remaining parts, we use the fitting results with $n = 4$ to study theoretically and numerically the energy harvested from human walking. Figure 2 displays the angular velocities obtained by differentiating the fitted angles with $n = 4$ . The values of velocities correspond to the experimentally measured values by Riemer and Shapiro (2011).

Table 1.

Fourier fitting results from hip motion.

$n$	1	2	3	4	5	6
$a_{0}$	7.065	7.163	7.177	7.192	7.186	7.189
$a_{1}$	13.37	13.05	13.04	13.04	13.03	13.03
$a_{2}$	–	4.71	4.501	4.518	4.499	4.507
$a_{3}$	–	–	2.432	2.397	−2.363	2.366
$a_{4}$	–	–	–	−0.394	−0.429	−0.407
$a_{5}$	–	–	–	–	−0.659	−0.639
$a_{6}$	–	–	–	–	–	−0.265
R ²	0.8554	0.9648	0.9949	0.9957	0.9979	0.9983

The unit of $a$ is degree.

Table 2.

Fourier fitting results from knee motion.

$n$	1	2	3	4	5	6
$a_{0}$	22.83	23.18	23.34	23.26	23.27	23.25
$a_{1}$	25.85	24.38	24.57	24.45	24.44	24.47
$a_{2}$	–	17.95	17.48	17.42	17.48	17.48
$a_{3}$	–	–	−3.874	−3.786	3.774	3.826
$a_{4}$	–	–	–	−1.600	−1.699	−1.666
$a_{5}$	–	–	–	–	−0.496	0.378
$a_{6}$	–	–	–	–	–	−0.601
R ²	0.6688	0.9788	0.9947	0.9973	0.9975	0.9979

The unit of $a$ is degree.

Table 3.

Fourier fitting results from ankle motion.

$n$	1	2	3	4	5	6
$a_{0}$	−2.429	−1.633	−1.699	−1.813	−1.824	−1.817
$a_{1}$	−5.378	−5.343	−5.413	−5.585	−5.636	−5.575
$a_{2}$	–	−8.178	−7.982	−7.966	−8.000	−7.941
$a_{3}$	–	–	−2.335	−2.265	−2.215	−2.206
$a_{4}$	–	–	–	2.691	2.607	2.598
$a_{5}$	–	–	–	–	−0.497	−0.692
$a_{6}$	–	–	–	–	–	0.869
R ²	0.2982	0.8734	0.9197	0.9848	0.9871	0.9940

The unit of $a$ is degree.

Relationship between walking speed and frequency

The walking speed $U$ is estimated from the walking frequency $f$ using the empirical relationship in the works by Kuo (2001) and Bertram and Ruina (2001), that is

f = c U^{0.58}

(2)

where $c$ is an unknown constant. In addition, we note that the walking speed can be given by $U = fS$ , where $S$ is the stride length (Bertram and Ruina, 2001).

When we use the walking speed $U = 1.3 m / s$ and frequency $f = 0.9 Hz$ from Riemer and Shapiro (2011), we obtain $c = 0.773$ . Figure 3 displays the predicted walking speed for a range of walking frequencies from $0.5$ to $1.5 Hz$ . Here, the predicted walking speed is from $0.5$ to $3 m / s$ .

Electrical response of piezoelectric material

Modeling

Here, we assume that piezoelectric materials used as energy transducers are attached to the hip, knee, and ankle. For example, the energy transducers can be attached to the human body through a tight suit (see Proto et al., 2016). Typically, the piezoelectric materials have a beam structure that deflects along with the radius of the joint, as shown in Figure 4. The deflection until $ρ \tan (Θ)$ has the uniform curvature of $1 / ρ$ , and it has the uniform rotation of $\tan (Θ)$ after that point. Therefore, the beam deflection is

w (x, t) = {\begin{matrix} \frac{x^{2}}{2 ρ sgn (Θ (t))} & 0 \leq x < x_{1} (t) \\ \frac{x_{1}^{2} (t)}{2 ρ sgn (Θ (t))} + (x - x_{1} (t)) \tan (Θ (t)) & x_{1} (t) \leq x \leq L \end{matrix}

(3)

where $w$ is the beam deflection on the x-axis (length direction), $x_{1}$ is $ρ sgn (Θ (t)) \tan (Θ (t))$ , and $L$ is the length of the piezoelectric material. We mention that this model is based on the small deformation beam for simple modeling, though the rotation is not small.

The electrical response of piezoelectric materials is described by the relationship between the charge stored in the structure and the rotation of the beam as given by Maurini et al. (2006), Erturk and Inman (2009), and Cha et al. (2013a)

Q (t) = CV (t) + θ {\frac{\partial w (x, t)}{\partial x} |}_{x = 0}^{L}

(4)

where $Q$ is the stored charge, $C$ is the internal capacitance of the piezoelectric material, $V$ is the voltage between both the electrodes of the piezoelectric material, and $θ$ is the electromechanical coupling coefficient.

When the piezoelectric material is bonded to a substrate layer of the same size for a unimorph composite beam, the coupling coefficient of the piezoelectric material $θ$ is obtained using the following equation (Erturk and Inman, 2008)

θ = - \frac{Y_{p} d_{31} B}{2 h_{p}} (h_{c}^{2} - {(h_{c} - h_{p})}^{2})

(5)

where $Y_{p}$ is the Young’s modulus of the piezoelectric material, $Y_{s}$ is the Young’s modulus of the substrate layer, $d_{31}$ is the piezoelectric constant of the piezoelectric material, $B$ is the width of the piezoelectric material, $h_{p}$ is the thickness of the piezoelectric material, $h_{s}$ is the thickness of the substrate layer, and $h_{c} = (h_{p}^{2} + 2 (Y_{s} / Y_{p}) h_{p} h_{s} + (Y_{s} / Y_{p}) h_{s}^{2}) / (2 (h_{p} + (Y_{s} / Y_{p}) h_{s}))$ is the distance from the top of the piezoelectric material layer to the neutral axis.

When the piezoelectric material is open-circuited $(Q = 0)$ , the voltage is reduced to

V_{oc} (t) = - \frac{θ}{C} {\frac{\partial w (x, t)}{\partial x} |}_{x = 0}^{L}

(6)

Additionally, when the load resistance $R_{load}$ is connected to the piezoelectric material, the voltage at the load $V_{load}$ satisfies Ohm’s law

\frac{d Q (t)}{d t} = - \frac{V_{load} (t)}{R_{load}}

(7)

When the trajectory of the piezoelectric beam deflection is given by a mathematical function, the load voltage can be obtained by solving equations (4) and (7). Here, we numerically compute the load voltage using the built-in function “NDSolve” in Mathematica.

Additionally, when the deflection is a periodic function like human walking, we can predict the power transferred from the piezoelectric material $P_{load}$ to $R_{load}$ , that is

P_{load} = \frac{1}{T} \int_{0}^{T} \frac{V_{load}^{2} (t)}{R_{load}} d t

(8)

Open-circuit voltage

We assume that the piezoelectric beams attached to the hip, knee, and ankle are deformed along with the angular motions of each part during human walking, as shown in Figure 4. In the hypothesis, the rotation differences between the piezoelectric beams $d w (x) / d x |_{x = 0}^{L}$ are obtained from the tangent of the angles. Figure 5 shows the rotation differences computed using the fitting angles with $n = 4$ in Figure 1. We note that the rotation differences show the same trends with the angle motions.

Equation (6) and the data in Figure 5 can be used to predict the open-circuit voltages from the piezoelectric materials on the hip, knee, and ankle, as shown in Figure 6. Here, we select the material properties of PVDF produced by Measurement Specialties (www.meas-spec.com) as the piezoelectric and aluminum as the substrate, that is, $h_{p} = 0.000028 m$ , $Y_{p} = 3 GPa$ , mass density $m_{p} = 1780 kg / m^{3}$ , $d_{31} = - 23 pm / V$ , $h_{s} = 0.0001 m$ , $Y_{s} = 69 GPa$ , and $m_{s} = 2700 kg / m^{3}$ . The surface width was chosen as $B = 0.01 m$ , and the length was chosen as the semi-circumference, that is, $L = π ρ$ . The radii of the hip $(ρ = 0.08 m)$ , knee $(0.047 m)$ , and ankle $(0.035 m)$ refer to the data of bitrochanteric, knee, ankle diameters, respectively, in the work by Heinz et al. (2003). The capacitances obtained using the size are $C = 9.55 nF$ at hip, $5.61 nF$ at knee, and $4.18 nF$ at ankle. Using equation (5), the coupling coefficient $θ$ is calculated as $43.6 nJ / V$ . We note that the voltages have opposite phase with respect to the angles. Moreover, the peak voltage of the knee is approximately $17 V$ , while the peaks of the voltages of the hip and ankle are less than $4 V$ .

Load voltage

When the piezoelectric beams are shunted to the load resistances, we predict the voltage outputs using the model in the subsection “Modeling.” In this section, we investigate the variations in the load voltages obtained by varying the load resistance and walking frequency.

Varied load resistance

Figure 7 displays the load voltages for load resistances from $100 k$ to $1 G Ω$ . When the load resistances are $100 k$ and $1 M Ω$ , the levels of the load voltages are significantly less than that of the others. The load voltages at $R_{load} = 100 M and 1 G Ω$ are similar with opposite phase angles, similar to the open-circuit voltages. Interestingly, the voltage at $R_{load} = 10 M Ω$ has the shape of a mid-step between the angular velocity and angle. We note that the peak of the load voltage saturates after the peak increases with the load resistance until $R_{load} = 100 M Ω$ .

Varied frequency

We assume that walking motion at normal walking speed has the same trajectory when the walking frequency is varied (see, for example, Liu et al., 2008). By changing $f$ in equation (1) and using the fitting data in Tables 1 to 3, we simulate the walking motion in the walking frequency range of 0.5–1.5 Hz. Figure 8 displays the load voltages at $R_{load} = 10 M Ω$ obtained by varying the walking frequency. As the walking frequency increases, the peak voltage increases, and the shape is more similar to the angle with an opposite sign.

Power transfer

We can estimate the power transferred from the piezoelectrics to the load using the voltage predicted from the load resistance and equation (8). In this section, the result of the harvested power is shown as a function of the load resistance and walking frequency. Additionally, we discuss the necessary mechanical power input required to deflect the energy harvester and the effects of the electromechanical coupling coefficient and capacitance.

Harvested power

Figure 9 illustrates the results of the transferred power computed as a function of the walking frequency and shunting load resistance. We comment that the power depends on both the frequency of the walking motion and the value of the load resistance, corresponding to the results of other piezoelectric energy harvesters (Erturk and Inman, 2011). Moreover, for each frequency of walking motion, there is an optimal value of the resistance, which decreases slightly with the walking frequency. For a fixed load resistance, the transferred power increases with the frequency. The optimal harvested power is of the order of $0.1 μ W$ on the hip and ankle and $1 μ W$ on the knee, which are comparable with experimental findings in the work by Proto et al. (2016). Also, the order of the harvested power is enough to support a self-powered watch, which consumes sub-microwatt (www.seiko-cleanenergy.com). In addition, the harvested power is maximized for load resistances of the order of $10 M Ω$ . In particular, the optimal load resistances at $1 Hz$ are approximately $14 M Ω$ on the hip, $18 M Ω$ on the knee, and $18 M Ω$ on the ankle. The optimal load resistance on the hip roughly corresponds to the matching impedance magnitude of the fundamental harmonic of the piezoelectric materials, $| 1 / ω C | = 17 M Ω$ , while the optimal value on the ankle matches the magnitude of the impedance of the second harmonic, $| 1 / 2 ω C | = 19 M Ω$ . The optimal load resistance on the knee is between both the matching impedance magnitudes of the fundamental and second harmonics (14–28 MΩ). These are attributed to the different frequency characteristics of the hip, knee, and ankle. While the fundamental harmonic dominates for the hip (see Table 1), the effect of the second harmonic on the knee and ankle is bigger than that on the hip, see Tables 2 and 3.

Input mechanical power

We calculate the power input $P_{mec}$ using Euler–Bernoulli beam theory (Meirovitch, 2001) to offer further insight into the power required to deflect the piezoelectric composites in the system. Specifically, by multiplying the beam equation with the total beam velocity $\partial w (x, t) / \partial t$ , integrating from $0$ to $L$ , and computing the time average in the vibration period $T$ , we obtain

P_{mec} = \frac{1}{T} \int_{0}^{T} \int_{0}^{L} (K \frac{\partial^{4} w (x, t)}{\partial x^{4}} + B (m_{p} h_{p} + m_{s} h_{s}) \frac{\partial^{2} w (x, t)}{\partial t^{2}}) \frac{\partial w (x, t)}{\partial t} d x d t

(9)

where $K$ is the bending stiffness.

Figure 10 reports the obtained mechanical power input as a function of the frequency. Notably, the power input is in the range of 0.01–1 mW and monotonically increases with the frequency. Knee needs the greatest power input because of its large deflection. While the hip produces the smallest harvested power, the input power is the same as that produced by the knee. We also note that results depicted in Figures 9 and 10 indicate that the power harvested using the piezoelectric composites is of the order of 0.1% of input power. Furthermore, it is noteworthy that the additional power input by the energy harvester is insignificant to humans because the muscles at each joint of the body consume several tens of watts during the walking cycle (Riemer and Shapiro, 2011).

Effect of coupling coefficient and capacitance

In Figures 11 and 12, we report the power harvested at a frequency of $0.9 Hz$ and the load resistance matched to the second harmonic as a function of the electromechanical coupling coefficient and capacitance in order to study the harvested power of the piezoelectric composites at varied parameters. Here, the reference value $θ_{0}$ is selected as $43.6 nJ / V$ , and $C_{0}$ is $9.55 nF$ at the hip, $5.61 nF$ at the knee, and $4.18 nF$ at the ankle. The parameters are varied from half to twice the reference values. Increasing the coupling coefficient increases the harvested power. For example, at $θ / θ_{0} = 2$ , the harvested power becomes 250% of the value attained for $0.5$ . However, the harvested power decreases smoothly when the capacitance increases. Based on this analysis, we expect a larger harvested power from the piezoelectric composites with higher electromechanical coupling and lower capacitance.

Conclusion

In this article, we have theoretically studied about harvesting the energy generated while walking using piezoelectric materials. We used data related to the walking motion of the lower body (hip, knee, and ankle) of a human from Riemer and Shapiro (2011) and analyzed the motion through Fourier series. We used the analyzed motion data and predicted the power harvested from the motion using a model of piezoelectric materials. In the model, the voltage generated using piezoelectric materials is related to the rotation of the structure, and we assumed that the piezoelectric structures are deformed along with the motion of each part during walking. In addition, we considered the case of load resistance shunted to piezoelectric materials and calculated the power transferred from the piezoelectric materials to the load resistances. Finally, we derived contour maps with respect to the power harvested from walking as a function of the load resistance and the walking frequency.

The results in the article highlight the importance of the second harmonic of the walking frequency in humans. The finding was confirmed by the result of the optimal load resistance required to maximize the power harvested from piezoelectric materials. In addition, we have noted that the frequency characteristic of each body part is different in spite of the same walking cycle. Specifically, the effect of the fundamental harmonic dominates in the hip, the second harmonic part is strong in the ankle, and both the effects are comparable in the knee. With respect to the electrical response, we showed that the shape of the open-circuit voltage is the same as that of the opposite phase of the angle. However, the voltage for small load resistance has a shape similar to that of the angular velocity with the opposite sign. This result also presents the possibility of sensing the human walking motion using piezoelectric materials.

This study suggests future studies on the demonstration of energy harvesters based on flexible smart materials using human walking motion. In addition, it presents a theoretical energy guideline for supporting wearable devices using energy harvesters, although we have analyzed the ideal cases. For example, if we use MFC as an energy transducer for this application, we can expect that the harvested power and necessary mechanical power input increase because of larger electromechanical coupling and stiffness than PVDF.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the KIST flagship program (Project No. 2E27200).

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