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Bistable broadband hybrid generator for ultralow-frequency rectilinear motion
Nano Energy 65 (2019) 103973
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Full paper
Bistable broadband hybrid generator for ultralow-frequency rectilinear motion ⁎,1
Huaxia Deng
T
, Jingchang Ye1, Yu Du1, Jin Zhang, Mengchao Ma, Xiang Zhong
School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, Anhui, 230009, People's Republic of China
ARTICLE INFO
ABSTRACT
Keywords: Energy harvesting Nonlinear Low frequency Broadband Linear generator
In the natural environment, rectilinear motions normally take the form of low-frequency and broadband vibrations. This poses problems for devices aimed at harvesting energy from these motions, since conventional linear electromagnetic generators are inefficient under such conditions. Here we present a bistable triboelectric linear generator (BTLG) with nonlinear characteristics for low-frequency and broadband energy harvesting. In this device, a nonlinear structure is used to achieve the bistable contact–separation motion to widen the working bandwidth as well as enhance the energy harvesting efficiency in low-frequency range. Piezoelectric components are also used in the device without increasing the complexity of the structure, which can compensate for the defects that the contact-separation mode triboelectric nanogenerator cannot work at a small amplitude. Experiments show that a 10 µ F capacitor can be charged to 0.12 V in 60 s at an ultralow frequency of 0.1 Hz. The frequency bandwidth of the BTLG is greatly broadened to 441% compared with a linear device. The proposed BTLG is capable of harvesting mechanical energy at low frequency with large working bandwidth, thus providing a effective method for energy harvesting of ambient low-frequency rectilinear motions.
1. Introduction As a form of vibrational motion, reciprocating rectilinear motion occurs widely, for example in the form of ocean waves [1–8], vibration of suspension systems [9–13], and human walking [14–20]. Typically, this type of vibration is low-frequency, broadband, and extensively distributed. Harvesting of the mechanical energy of rectilinear motion [21], such as blue energy and human kinetic energy [22], by linear generators has the potential to supply power for a range of applications, for example distributed sensors [23–25] and the Internet of Things [26–29]. However, in the case of ambient rectilinear motions, their generally low frequency and broadband characteristics mean that electromagnetic linear generators are not suitable [30,31]. Electromagnetic generation (EMG) is based on the induction effect represented by the first term of Maxwell's displacement current, namely, the time derivative of the electric field. Because of this, EMG performs well at high frequencies (>50 Hz) [31], but cannot effectively harvest mechanical energy at low frequencies such as those of ocean waves, which are mostly concentrated below 10 Hz [32]. Therefore, much work has been done on increasing the power generation efficiency of electromagnetic linear generators for harvesting wave energy by incorporating a speed increaser in the generator system [33–37].
The second term of Maxwell's displacement current is related to the polarization of a material medium [30]. It is this term that determines the fundamental characteristics of a triboelectric nanogenerator (TENG) [38–41] and gives it an excellent energy harvesting capability in the low-frequency range [42]. The superior power generation performance of TENGs has already been applied to energy harvesting of low-frequency rectilinear motion and, in particular, Wang's team have done much work on the preparation and application of TENGs [6,7,17,20,27,30,31,42–46]. A wavy Kapton film, triggered by footsteps, can effectively harvest the energy of low-frequency rectilinear motion of the human body, providing enough power to light up 104 LEDs simultaneously, and this approach can harvest vibrational energy at 5 Hz [43]. A mesh-based structure containing a small rolling ball has been designed to collect distributed wave energy [44]. It generates 1.15 MW of energy per square kilometer of sea area, but can only be used on the ocean surface. A contact–separation-type TENG can effectively respond to input vibration frequency at 2 Hz. Supported by four springs, it has the advantages of simple structure and high output power [45]. A spring-based second-order linear system is used for TENG, which can improve its low-frequency performance by up to 10 times [47]. Even so, as a second-order linear system, its effective working band is near the resonant frequency.
Corresponding author. E-mail address: [email protected] (H. Deng). 1 Huaxia Deng, Jingchang Ye, and Yu Du contributed equally to this work. ⁎
https://doi.org/10.1016/j.nanoen.2019.103973 Received 28 June 2019; Received in revised form 28 July 2019; Accepted 1 August 2019 Available online 12 August 2019 2211-2855/ © 2019 Elsevier Ltd. All rights reserved.
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The TENG-based energy harvesters developed to date are based mainly on linear dynamical systems, which principally work near the resonance frequency. An effective way to broaden the working frequency band is through bistable vibrational energy harvesting [48,49] based on nonlinear dynamical systems [50,51]. Classical bistable energy harvesting utilizes magnetically coupled cantilever beams to harvest broadband vibrational energy [52,53]. In the case of a synergetic poly-stable beam array, using the magnetic repulsion between different beams, the working bandwidth is broadened by a factor of 41 compared with a linear beam array [52]. To collect broadband vibrational energy with low intensity, a seesaw-type approach has been proposed to overcome the potential barrier and enhance nonlinear energy harvesting performance [53]. However, beam-type energy harvesters usually use their own bending vibrations to generate electricity [54], and this approach is difficult to apply to TENGs working on contact–separation mode. Therefore, it is necessary to design a bistable structure that is suitable for the contact–separation motion of traditional TENGs. Here, we present a bistable triboelectric linear generator (BTLG) with nonlinear characteristics and capable of achieving bistable-type contact–separation motion, with the aim of resolving the difficulty in harvesting energy from low-frequency reciprocating rectilinear motions. Furthermore, piezoelectric components are also used in this device to compensate for the inapplicability of contact-separation mode TENGs in small amplitudes without increasing the complexity of the original device structure. We show the details of the device how to work. The bistability and low-frequency adaptability of this device are proved by a theoretical analysis. Direct-drive experiments under excitations of 0.1–12 Hz reveal the generating capability of this device at ultralow frequencies. Inertial-force swept experiments comparing the BTLG with a corresponding linear device verify its high efficiency of energy harvesting and broadband characteristics. The experiment under constant frequency excitation of inertial force further demonstrates the superiority of the BTLG while operating in a bistable state. In addition, the practicality of this device is proved by practical environmental experiments.
A. The magnet B and the shaft are together able to perform one-dimensional linear reciprocating motion. The center of the cross leaf spring is fixed to the shaft, and the four ends of the spring are constrained by the simple support of the shell. The position at which the cross leaf spring is attached to the shaft is such that the magnets A and B are in the same horizontal plane when the gravitational force on the shaft (and on other components mounted on the shaft) and the elastic force of the cross leaf spring are balanced with each other. In this situation, the displacement z of the shaft is defined as zero. During reciprocating motion, owing to the repulsive force between the permanent magnets and the restoring force of the cross leaf spring, the movable shaft undergoes nonlinear bistable motion under broadband excitation. In Fig. 1 b, the piezoelectric components are attached to the clamping ends of the cross leaf spring near the center shaft. The reciprocating rectilinear motion of the central shaft drives the deformation of the cross leaf spring as well as the PVDF piezoelectric films, thus generating electrical energy. Fig. 2 shows the mechanism of the contact-separating triboelectric nanogenerator in the device. The contact-separation movement between the nitrile baffle and the triboelectric components is driven by the reciprocating motion of the central shaft. The electrical energy generated by the triboelectric components and the piezoelectric components is harvested and stored by subsequent capture circuits. A cycle of electricity generation process is illustrated in Fig. 2. First, nitrile baffle is not in contact with PDMS and therefore has no charge exchange. External excitation causes the PDMS to contact the nitrile baffle and generates positive triboelectric charges on the nitrile side and negative charges on the PDMS side. Then the two materials are separated by the restoring force. In order to counteract the electric field generated by the triboelectric charge, electrons are transferred from the copper electrode to the aluminum alloy electrode. As the distance of separation increases, the electrostatic field generated by the triboelectric charge is completely counteract. When the excitation causes the two materials to approach again, the balance of electric field is broken, which cause electrons to transfer from the aluminum electrons to the copper electrode. Triboelectric components and piezoelectric components play different roles under different conditions of excitation. When the amplitude of external excitation is sufficient, the harvested energy of the BTLG is mainly generated by the triboelectric components, while the output of the piezoelectric components only occupies lesser proportions. On the contrary, when the external excitation amplitude is too small to ensure realization of contact-separation motion of the triboelectric components, the piezoelectric elements, rather than the
2. Design and mechanism As shown in Fig. 1 a, the BTLG consists of a movable center shaft, two nitrile baffle, two annular permanent magnets A and B, a cross leaf spring, triboelectric components, piezoelectric components, and an aluminum alloy shell. The annular permanent magnet B is fixed on the shaft and is repelled by the externally fixed annular permanent magnet
Fig. 1. Schematic illustration of the structure and working principle of the BTLG. (a) Schematic of the BTLG and its two stable states; (b) Schematic of the power generation by the piezoelectric components in the BTLG; (c) Magnetic dipole model; (d) Potential energy function. 2
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Fig. 2. The mechanism of the TENG in the BTLG.(a)Initial state. (b) Contact with each other, the nitrile baffle and the triboelectric components generate charge. (c) Separation, electrode electron transfer. (d) The transfer of electrons balances the electric field. (e) Approaching, the electrons are transferred again.
triboelectric ones, plays a leading role in the output of the BTLG. This kind of nonlinear generator is suitable for various energy of rectilinear motion, examples being the vibration energy under the action of inertial force and the kinetic energy of reciprocating rectilinear motions under the direct pull of the external force. Fig. 3 shows two application examples of such nonlinear generators. As shown in Fig. 3a, by installing the BTLGs into a car suspension system, the vibrational energy of car body can be collected in real time and supplied to electrical systems, thereby reducing consumption of fossil energy. Blue energy of the sea, harvested by a linear generator array placed underwater in Fig. 3b, is capable of providing power supply for human's daily use on a island. The realization of bistable motion under inertial force requires that the device have bistable characteristics. To understand the nonlinear bistable characteristics of the BTLG, we adopt a magnetic dipole model [55]. We analyze the force on the movable shaft in a magnetic field and the potential energy function of the device. The magnetic dipole model for the annular permanent magnets A and B is shown in Fig. 1c. The magnet A is considered to be composed of infinitesimal micro-elements a, each with magnetic moment ma . We analyze the force on each microelement to calculate the total force on the magnet A. The horizontal distance between magnetic dipole a and magnetic dipole B, with the latter having magnetic moment mB , is denoted by x, and the vertical distance is equal to the displacement of the center shaft, denoted by z. The vector from dipole a to dipole B is denoted by r . The magnetic flux density produced by magnetic dipole a at magnetic dipole B is
BaB =
µ0 4
ma r , |r|3
magnetization intensity vector of a, A, and B, respectively. Va , VA , and VB are the volume of a, A, and B, respectively. is the gradient operator, where i and k are the unit vectors in the x and z directions, respectively. The magnetic force between dipoles a and B is
FaB =
(2)
( BaB mB).
The magnetic force between magnets A and B is the sum of the forces between all the elements a and magnet B. The micro-element forces cancel each other out in the horizontal direction, while those in the vertical direction are superimposed on each other. Thus, the magnetic force between magnets A and B is
FAB =
FaB =
3µ 0 |MA ||MB |VA VB z (3x 2 2z 2 ) k. 4 (x 2 + z 2) 7/2
(3)
The magnetic potential energy between a and B is
UaB =
BaB mB =
µ 0 |MA ||MB |dVA VB (x 2 4 (x 2 + z 2 )5/2
2z 2 )
.
(4)
Correspondingly, the magnetic potential energy between A and B is
UAB =
UaB =
µ 0 |MA ||MB |VA VB (x 2 4 (x 2 + z 2)5/2
2z 2) (5)
The elastic potential energy of the cross leaf spring is
Ue =
1 k eq z 2, 2
(6)
where k eq is the equivalent stiffness of the spring. Therefore, the total potential energy is
(1)
where the permeability of the vacuum µ 0 = 4 × 10 H/m. The magnetic moment of dipole a, A and B is ma = Ma Va = MA dVA , mA = MA VA , and mB = MB VB , respectively. Ma , MA , and MB are the
U = UAB + Ue =
7
µ 0 |MA ||MB |VA VB (x 2 4 (x 2 + z 2 )5/2
2z 2 )
+
1 keq z 2 2
(7)
Substitution of the parameters of the BTLG into the expression (7)
Fig. 3. Two examples of the application of BTLGs: (a) Car suspension energy harvesting; (b) Energy harvesting array pulled by buoys on the sea. 3
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gives the potential energy U as a function of displacement z as shown in Fig. 1d, according to which the proposed BTLG has two stable equilibrium states with corresponding displacements z = 0.01 m and 0.01 m, thus proving the bistable characteristics of the device. Inter-well motion across the two potential wells helps to increase the amplitude of the device at non-resonant frequencies, thereby broadening the working frequency band. The amplification of the amplitude not only increases the amount of deformation of the cross leaf spring, thereby increasing the output voltage of the piezoelectric components, but also contributes to the realization of the contact-separation motion, thus enhancing the power generation of the triboelectric components. The triboelectric components generate electricity by reciprocating contact–separation motion with the nitrile baffle. The motion of the center shaft is no longer simple harmonic motion, but rather a kind of shock vibration, which we like to think of as being analogous to a triangular motion in which the dependence of displacement x on time t can be expressed as follows:
2At / T , 2At / T ,
x (t ) =
0
t T /2
T /2, t 0,
3.1. Low-frequency response For the direct-drive mode of the device, the device can work as long as it has external driving force. The working bandwidth of the device is almost equal to the power generation bandwidth of the material itself. The electric energy that can be harvested is the main factor determining the application of the device. Low-frequency experiments can be used to illustrate the power generation characteristics of the BTLG at low frequencies, under conditions similar to those found when harvesting ocean wave energy. To achieve this type of vibration, we fixed the device on the vibrating table with its central shaft attached to a metal bracket on the base, which is the direct-drive mode of this device. In the experiment, the peak-to-peak excitation of the vibrating table was 20 mm and the excitation frequencies applied were 2, 4, 6, 8, 10, and 12 Hz. The power output from the BTLG was used to charge a 10 µ F electrolytic capacitor, and the capacitor voltage was measured by a digital multimeter. In addition, we used a mechanical tensile stretcher (MTS) for ultralow-frequency experiments at frequencies below 1 Hz (see Supplementary Fig. 2). The experimental results are shown in Fig. 4. At excitation frequencies of 2, 4, 6, 8, 10, and 12 Hz, the voltage of the capacitor charged by the BTLG reached 0.71, 1.35, 2.29, 3.27, 4.67, and 5.80 V, respectively, after a time of 20 s. The device is also capable of generating an effective amount of electricity under excitation at ultralow frequencies below 1 Hz: under excitation by the MTS at 0.2 Hz, the device charged the 10 µ F capacitor to 0.248 V in 60 s. In addition, the charging results of the capacitor after removing the piezoelectric components is shown in Fig. 4c and d. Compared with the former, the charging voltage of the capacitor drops by 1.5, 1.28, 1.05, 0.79, 0.47, and 0.21 V at the excitation frequencies of 2, 4, 6, 8, 10, and 12 Hz, respectively. Under excitation by the MTS at 0.2 Hz, the device without piezoelectric components charged the 10 µ F capacitor to 0.11 V in 60 s. As the charging process continues, the voltage of the capacitor will continue to increase until it is close to the peak open-circuit voltage of the BTLG, whereas the voltage of a capacitor charged by an EMG will be restricted to a fairly low value owing to the low output voltage of EMGs under low-frequency excitation. EMGs are therefore unsuitable for harvesting energy from low-frequency excitations [31]. In contrast, the bistable linear generator with triboelectric and piezoelectric components presented here is able to efficiently harvest energy at ultralow frequencies.
(8)
where A is the peak displacement and T is the period of vibration. To analyze the frequency characteristics, we compute the Fourier series representation of x (t ) ,
x (t ) = a 0 +
(an cos n
0t
+ bn sin n
0 t ).
n= 1
(9)
For x (t ) as given by the expression (8), we have bn = 0 , a0 = A/2, and
an =
4A/(n ) 2 , n = 1,3,5, …, 0 n = 2,4,6, …,
(10)
and so
x (t ) =
A 2
4A 2
n = 1,3,5, …
1 2n cos t . n2 T
(11)
The amplitude of the Nth harmonic component is then
An =
an2 + bn2 =
A/2, n = 0, A/(n ) 2, n = 1,3,5, …, 0, n = 2,4,6, ….
(12)
The energy of mechanical vibration is proportional to the square of the amplitude. From (12), the amplitudes of the DC component and the first-harmonic component are much larger than the amplitude of the high-frequency harmonic component. Therefore, the mechanical energy of this form of motion is concentrated mainly in the low-frequency band below the fundamental frequency, indicating that the BTLG is indeed suitable for ultralow-frequency vibrational energy harvesting.
3.2. Broadband frequency response The device mainly relies on its own inertial force to move in the inertia-drive mode, which corresponds to the conditions encountered in applications to vehicle suspensions. In this mode, the working bandwidth, related to the structural resonant frequency, and the output power density are two important factors for evaluating the power generation performance of the device. To study the bandwidth of the device in the inertia-drive mode, we carried out an inertial-force frequency-sweep test. We again compared the BTLG with the LTLG under the same excitation conditions. We fixed the device at the center of the vibrating table and added mass blocks to the unconstrained central shaft. Fig. 5 presents the results for the frequency-domain performances of the BTLG and LTLG under a peak-to-peak excitation of 8 mm, with the excitation frequency f swept from 3 to 13 Hz at a frequency rise rate of 0.2 Hz/s. It can be seen from Fig. 5a that the center shaft displacement of the LTLG reached a peak of 20 mm between 4.9 and 6.6 Hz, and from Fig. 5b that the open-circuit voltage of the piezoelectric components also reached a peak value (of 20 V) in this range. Fig. 5c and d shows that the peak open-circuit voltages of the triboelectric components on the lower and upper surfaces were 22.1 and 8.0 V, respectively. In the case of the BTLG, there was large-amplitude inter-well motion within a wide frequency band from 4.2 to 11.7 Hz, with a peak amplitude of
3. Experiment To verify the theoretical analysis and the high energy-harvesting efficiency of the device at low frequencies, the BTLG was tested under various low-frequency conditions. The characteristics of the device at low frequencies were determined in three different experiments examining the low-frequency response, bistable vibration, and broadband frequency response, respectively. In the experiments, the device has two working modes due to its structural characteristic. One is a directdrive mode that the center shaft is driven directly by external forces, such as the applications in the ocean. The other is inertia-drive mode, which the reciprocating rectilinear motion of the center shaft is accomplished through the inertial force of itself, such as the applications of suspension system. Our experimental system includes a vibrating table and its controller, a computer, a DC stabilized power supply, a digital multimeter, a laser displacement sensor, and a resistance box(see Supplementary Fig. 1). 4
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Fig. 4. Voltage of 10 µ F capacitor charged by the BTLG: (a) Low frequency (>1 Hz); (b) Ultralow frequency (<1 Hz); (c) Low frequency without piezoelectric components (>1 Hz); (d) Ultralow frequency without piezoelectric components (<1 Hz).
20 mm (Fig. 5a). The peak open-circuit voltages of the triboelectric components on the lower and upper surfaces were 50.5 and 24.4 V, respectively (Fig. 5c and d). The observations indicate that the LTLG has a resonance frequency point in the frequency between 4.9 and 6.6 Hz, which greatly increases the amplitude of the LTLG. In other frequency ranges, the voltage of the piezoelectric components decreases, and the triboelectric components not work because the amplitude is insufficient to complete the contact-separation movement. The working frequency bandwidth of BTLG has been broadened due to the bistable characteristics. In order to quantitatively compare the working bandwidth of LTLG and BTLG in the inertia-drive mode, the effective working bands, defined as the frequency bands corresponding to full-stroke motion, are
indicated in orange in Fig. 5a. For the BTLG the working bandwidth at low frequencies was very much wider than that of the LTLG (to 441%). By virtue of the inter-well motion in the BTLG, the displacement of the center shaft and the open-circuit voltages of the piezoelectric components and the triboelectric components were all greatly enhanced compared with the LTLG (to 229% in the case of the open-circuit voltage of the triboelectric components). The optimum power density is used to evaluate the effect of this nonlinear approach to improving electricity generation performance. The basic output of the PDMS and PVDF needs to be determined to obtain the optimum power. Basic output, including output voltage, output current (Fig. 6a and c) and power (Fig. 6b and d) of the two materials, was measured under an excitation with constant frequency Fig. 5. Results of inertial-force frequency-sweep test under 8 mm peak-to-peak excitation at 3–13 Hz sweep frequency: (a) Center shaft displacement; (b) Open-circuit voltage of piezoelectric components; (c) Open-circuit voltage of triboelectric components on the lower surface (PDMS 1); (d) Open-circuit voltage of triboelectric components on the upper surface (PDMS 2).
5
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Fig. 6. Basic output of two materials and power densities of BTLG and LTLG at optimum resistance. (a) Output voltage and output current of PDMS under different resistance values; (b) The power of PDMS at different resistance values; (c) Output voltage and output current of PVDF under different resistance values; (d) The power of PVDF at different resistance values; (e) The power density of BTLG under inertial-force swept excitation from 3 to 13 Hz; (f) The power density of LTLG under inertial-force swept excitation from 3 to 13 Hz.
(7.2 Hz) and peak-to-peak value (8 mm). The output voltage and current of the two materials of interest was measured by changing the resistance of the resistance box. The optimum resistance of the materials was determined by obtaining the maximum output power. We found that the maximum output power was achieved when the resistance was 10 M . Benefiting greatly from the nonlinear bistable structure, the nonresonant vibration of the BTLG are increased in the process of frequency-sweep test. During this process, the BTLG vibrates with large amplitudes for most of the time, while the LTLG exhibits obvious vibration only near its resonant frequency (see Supplementary Movie 1 and Movie 2). These experimental phenomena reveal the reason for the increase in displacements as well as voltages at non-resonant frequencies. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.nanoen.2019.103973. The power density can be calculated by formula Pd = U 2/(RV ) , while U, R, and V are output voltage, load resistance, and effective volume of the device, respectively. In this device, the optimal power density can be obtained by selecting 10 M load resistance. The
optimum power density responses are plotted in Fig. 6e and f. The opencircuit voltage of the BTLG was higher than that of the LTLG for frequencies within the ranges 3–5.2 Hz and 7–11.5 Hz. It is obvious that the high power bandwidth of the BTLG 13 Hz was 203% of that of the LTLG. It is noteworthy that the optimum power density of the BTLG was 877.8 mW/m3, which is 83% higher than that of the LTLG (480.2 mW/ m3). The nonlinear system clearly enhances the electricity generation performance of the harvester under low excitation levels and broadens the working bandwidth for large-amplitude vibrations at low frequencies. 3.3. Bistable vibration Theoretical analysis has revealed the bistable characteristics of the BTLG in the inertia-drive mode. Bistable vibration, also known as interwell motion, is capable of increasing the amplitude of vibration of the central shaft of the device, thus further enhancing its power generation efficiency. An inertial-force fixed-frequency experiment was used to confirm this theoretical analysis. We compared the performance BTLG with that of the corresponding linear device (LTLG, i.e., the BTLG 6
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Fig. 7. Results of inertial-force fixed-frequency experiment under 10 mm peak-to-peak-value excitation: (a) Center shaft displacement; (b) Open-circuit voltage of piezoelectric components; (c) Open-circuit voltage of triboelectric components on the lower surface (PDMS 1); (d) Open-circuit voltage of triboelectric components on the upper surface (PDMS 2).
Supplementary video related to this article can be found at https:// doi.org/10.1016/j.nanoen.2019.103973. Experiments have shown that the device can effectively generate electrical energy at low frequencies, even at ultralow frequencies below 1 Hz. This low-frequency power generation characteristic is especially suitable for energy harvesting of low-frequency vibrations, such as ocean wave energy. Under excitation by an inertial force, the working frequency band of the device is wider than in the case of a linear system, and, obviously, this also increases the energy harvesting efficiency. The capability of power generation is greatly improved by working in a bistable state, especially for the triboelectric components. The bistable motion increases the amplitude of the device at low frequencies, allowing the triboelectric components to come into contact and separate from the nitrile baffle, thereby greatly increasing the overall output. Fig. 8. BTLG installed on a bicycle to collect vibrational energy during cycling.
3.4. Practical environmental experiment
without the annular permanent magnet A) under the same excitation conditions. We determined the behavior of the displacement and the open-circuit voltages of the triboelectric components and the piezoelectric components. The excitation frequency f of the vibrating table was 7.2 Hz, and the excitation peak-to-peak value A was 10 mm. As shown in Fig. 7a, the center shaft displacement amplitude of the BTLG reached 20.0 mm, and the shaft underwent contact–separation bistable motion, whereas the corresponding amplitude of the LTLG was only 11.5 mm. Fig. 7a shows clearly that the contact–separation bistable motion was a triangular motion, which is consistent with the theoretical analysis. As can be seen from Fig. 7b, the peak open-circuit voltage of the piezoelectric components of the BTLG was 18.5 V, and that of the LTLG was 11.8 V. Thus, the open-circuit voltage of the piezoelectric components of the BTLG was 157% of that of the LTLG. The triboelectric components on the upper and lower surfaces of the LTLG cannot generate electricity: the vibration peaks are insufficient for them to come into contact, and hence the open-circuit voltage of these components is zero. In contrast, as can be seen from Fig. 7c and d, the open-circuit voltage of the triboelectric components of the BTLG reached 138.0 V because the nonlinear structure increased the amplitude of vibration of the device. And the output power of the BLTG is increased such that it becomes capable of lighting up 36 series-connected LEDs (see Supplementary Movie 3).
In order to prove that the designed BTLG is able to collect the lowfrequency vibrational energy in the practical environment, we use a bicycle to provide random excitation for the device, as shown in Fig. 8. We chose a piece of undulant meadowland to provide low-frequency vibrational excitation for the BTLG under the conditions of riding and pushing, respectively. We measured the vibration data of the riding and pushing process (see Supplementary S4, S5 and S6), which proved that this environmental drive is a low-frequency vibration. Under both experimental conditions, BTLG is capable of lighting up 36 series-connected LEDs (see Supplementary Movie 4 and Movie 5), which proves the prospect of practical applications of this design. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.nanoen.2019.103973. 4. Conclusion A bistable triboelectric linear generator with nonlinear characteristics, suitable for broadband energy harvesting in the low-frequency range, has been proposed. Without increasing the structural complexity, the piezoelectric components is used to compensate for the defects that the contact-separation mode triboelectric nanogenerator cannot work at small amplitudes. Theoretical analysis has revealed that the device has bistable characteristics and that the energy of the 7
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bistable contact–separation motion is concentrated within the first harmonic component. Driven directly by low-frequency tension, the device is capable of efficiently generating electrical energy. Even under excitation at an ultralow frequency of 0.1 Hz, the device can charge a 10 µ F capacitor to 0.12 V within 60 s. Under swept excitation, the opencircuit voltage of the piezoelectric components is increased to 157%, with that of the triboelectric components reaching 138 V. With the proposed BTLG, the working bandwidth is widened to 441% compared with the linear device. The bistable vibration significantly improves electricity generation performance at low frequencies. This contact–separation bistable structural design, with ultralow operating frequency and wide working bandwidth, has potential for a variety of practical low-frequency energy harvesting applications, providing a welcome boost for the development of compact and efficient rectilinear motion energy harvesters.
[17] [18] [19] [20] [21] [22]
Acknowledgment
[23]
The authors appreciate the support of the National Natural Science Foundation of China (Grant Nos. 11872167, 51575156, 51675156, 51775164, and 51705122), the Fundamental Research Funds for the Central Universities (Grant Nos. JZ2017HGPA0165 and PA2017GDQT0024, and Natural Science Foundation of Anhui Province (1908085J15).
[24] [25] [26]
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.nanoen.2019.103973.
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Yu Du received his B.S. degree from the College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2015, and M.S. degree from the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, China, in 2019. He is going to study for a Ph.D. degree in the School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His current research interests include energy harvesting, triboelectric nanogenerator, and mechanical analysis.
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Jin Zhang received his B.E. degree from Hefei University of Technology, Hefei, China, in 2005. He received his M.S. and Ph.D. degrees from Tianjin University, Tianjin, China, in 2007 and 2010, respectively. He has been an associate professor at the School of Instrument Science and Optoelectronics Engineering, Hefei University of Technology since 2012. His current research interests include optical measurement technology and vibration testing. Dr. Zhang is a member of Youth Committee of China Instrument and Control Society.
Mengchao Ma received his Ph.D. degree from the University of Science and Technology of China, Hefei, China, in 2014. He is currently an associate professor in the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology. His current research interests include artificial compound eye, structured-light measurement, and dynamic testing.
Huaxia Deng received his B.E. and M.S. degrees from the University of Science and Technology of China, Hefei, China, in 2004 and 2007, respectively, and the Ph.D. degree from the University of Liverpool, Liverpool, U.K., in 2011. He has been the Hungshan Young Scholar Professor with the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, since 2012. His current research interests include smart materials and vibration control. He is the Review Editor of the journal Frontiers in Smart Materials.
Xiang Zhong received his B.S. degree from the School of the measurement and control technology and instrument, Tianjin University, Tianjin, China, in 2008, and the Ph.D. degree in optical engineering from Beihang University, Beijing, China, in 2016. He is currently a lecturer in the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology. His current research interests include optical fiber sensing and dynamic testing.
Jingchang Ye received his B.S. degree from the School of the mechanical and electronic engineering, Wuhan University of Technology, Wuhan, China, in 2017. He is currently a postgraduate student in the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, China. His current research interests include energy harvesting, electric circuit design, and mechanical design.
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Full paper
Bistable broadband hybrid generator for ultralow-frequency rectilinear motion ⁎,1
Huaxia Deng
T
, Jingchang Ye1, Yu Du1, Jin Zhang, Mengchao Ma, Xiang Zhong
School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, Anhui, 230009, People's Republic of China
ARTICLE INFO
ABSTRACT
Keywords: Energy harvesting Nonlinear Low frequency Broadband Linear generator
In the natural environment, rectilinear motions normally take the form of low-frequency and broadband vibrations. This poses problems for devices aimed at harvesting energy from these motions, since conventional linear electromagnetic generators are inefficient under such conditions. Here we present a bistable triboelectric linear generator (BTLG) with nonlinear characteristics for low-frequency and broadband energy harvesting. In this device, a nonlinear structure is used to achieve the bistable contact–separation motion to widen the working bandwidth as well as enhance the energy harvesting efficiency in low-frequency range. Piezoelectric components are also used in the device without increasing the complexity of the structure, which can compensate for the defects that the contact-separation mode triboelectric nanogenerator cannot work at a small amplitude. Experiments show that a 10 µ F capacitor can be charged to 0.12 V in 60 s at an ultralow frequency of 0.1 Hz. The frequency bandwidth of the BTLG is greatly broadened to 441% compared with a linear device. The proposed BTLG is capable of harvesting mechanical energy at low frequency with large working bandwidth, thus providing a effective method for energy harvesting of ambient low-frequency rectilinear motions.
1. Introduction As a form of vibrational motion, reciprocating rectilinear motion occurs widely, for example in the form of ocean waves [1–8], vibration of suspension systems [9–13], and human walking [14–20]. Typically, this type of vibration is low-frequency, broadband, and extensively distributed. Harvesting of the mechanical energy of rectilinear motion [21], such as blue energy and human kinetic energy [22], by linear generators has the potential to supply power for a range of applications, for example distributed sensors [23–25] and the Internet of Things [26–29]. However, in the case of ambient rectilinear motions, their generally low frequency and broadband characteristics mean that electromagnetic linear generators are not suitable [30,31]. Electromagnetic generation (EMG) is based on the induction effect represented by the first term of Maxwell's displacement current, namely, the time derivative of the electric field. Because of this, EMG performs well at high frequencies (>50 Hz) [31], but cannot effectively harvest mechanical energy at low frequencies such as those of ocean waves, which are mostly concentrated below 10 Hz [32]. Therefore, much work has been done on increasing the power generation efficiency of electromagnetic linear generators for harvesting wave energy by incorporating a speed increaser in the generator system [33–37].
The second term of Maxwell's displacement current is related to the polarization of a material medium [30]. It is this term that determines the fundamental characteristics of a triboelectric nanogenerator (TENG) [38–41] and gives it an excellent energy harvesting capability in the low-frequency range [42]. The superior power generation performance of TENGs has already been applied to energy harvesting of low-frequency rectilinear motion and, in particular, Wang's team have done much work on the preparation and application of TENGs [6,7,17,20,27,30,31,42–46]. A wavy Kapton film, triggered by footsteps, can effectively harvest the energy of low-frequency rectilinear motion of the human body, providing enough power to light up 104 LEDs simultaneously, and this approach can harvest vibrational energy at 5 Hz [43]. A mesh-based structure containing a small rolling ball has been designed to collect distributed wave energy [44]. It generates 1.15 MW of energy per square kilometer of sea area, but can only be used on the ocean surface. A contact–separation-type TENG can effectively respond to input vibration frequency at 2 Hz. Supported by four springs, it has the advantages of simple structure and high output power [45]. A spring-based second-order linear system is used for TENG, which can improve its low-frequency performance by up to 10 times [47]. Even so, as a second-order linear system, its effective working band is near the resonant frequency.
Corresponding author. E-mail address: [email protected] (H. Deng). 1 Huaxia Deng, Jingchang Ye, and Yu Du contributed equally to this work. ⁎
https://doi.org/10.1016/j.nanoen.2019.103973 Received 28 June 2019; Received in revised form 28 July 2019; Accepted 1 August 2019 Available online 12 August 2019 2211-2855/ © 2019 Elsevier Ltd. All rights reserved.
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The TENG-based energy harvesters developed to date are based mainly on linear dynamical systems, which principally work near the resonance frequency. An effective way to broaden the working frequency band is through bistable vibrational energy harvesting [48,49] based on nonlinear dynamical systems [50,51]. Classical bistable energy harvesting utilizes magnetically coupled cantilever beams to harvest broadband vibrational energy [52,53]. In the case of a synergetic poly-stable beam array, using the magnetic repulsion between different beams, the working bandwidth is broadened by a factor of 41 compared with a linear beam array [52]. To collect broadband vibrational energy with low intensity, a seesaw-type approach has been proposed to overcome the potential barrier and enhance nonlinear energy harvesting performance [53]. However, beam-type energy harvesters usually use their own bending vibrations to generate electricity [54], and this approach is difficult to apply to TENGs working on contact–separation mode. Therefore, it is necessary to design a bistable structure that is suitable for the contact–separation motion of traditional TENGs. Here, we present a bistable triboelectric linear generator (BTLG) with nonlinear characteristics and capable of achieving bistable-type contact–separation motion, with the aim of resolving the difficulty in harvesting energy from low-frequency reciprocating rectilinear motions. Furthermore, piezoelectric components are also used in this device to compensate for the inapplicability of contact-separation mode TENGs in small amplitudes without increasing the complexity of the original device structure. We show the details of the device how to work. The bistability and low-frequency adaptability of this device are proved by a theoretical analysis. Direct-drive experiments under excitations of 0.1–12 Hz reveal the generating capability of this device at ultralow frequencies. Inertial-force swept experiments comparing the BTLG with a corresponding linear device verify its high efficiency of energy harvesting and broadband characteristics. The experiment under constant frequency excitation of inertial force further demonstrates the superiority of the BTLG while operating in a bistable state. In addition, the practicality of this device is proved by practical environmental experiments.
A. The magnet B and the shaft are together able to perform one-dimensional linear reciprocating motion. The center of the cross leaf spring is fixed to the shaft, and the four ends of the spring are constrained by the simple support of the shell. The position at which the cross leaf spring is attached to the shaft is such that the magnets A and B are in the same horizontal plane when the gravitational force on the shaft (and on other components mounted on the shaft) and the elastic force of the cross leaf spring are balanced with each other. In this situation, the displacement z of the shaft is defined as zero. During reciprocating motion, owing to the repulsive force between the permanent magnets and the restoring force of the cross leaf spring, the movable shaft undergoes nonlinear bistable motion under broadband excitation. In Fig. 1 b, the piezoelectric components are attached to the clamping ends of the cross leaf spring near the center shaft. The reciprocating rectilinear motion of the central shaft drives the deformation of the cross leaf spring as well as the PVDF piezoelectric films, thus generating electrical energy. Fig. 2 shows the mechanism of the contact-separating triboelectric nanogenerator in the device. The contact-separation movement between the nitrile baffle and the triboelectric components is driven by the reciprocating motion of the central shaft. The electrical energy generated by the triboelectric components and the piezoelectric components is harvested and stored by subsequent capture circuits. A cycle of electricity generation process is illustrated in Fig. 2. First, nitrile baffle is not in contact with PDMS and therefore has no charge exchange. External excitation causes the PDMS to contact the nitrile baffle and generates positive triboelectric charges on the nitrile side and negative charges on the PDMS side. Then the two materials are separated by the restoring force. In order to counteract the electric field generated by the triboelectric charge, electrons are transferred from the copper electrode to the aluminum alloy electrode. As the distance of separation increases, the electrostatic field generated by the triboelectric charge is completely counteract. When the excitation causes the two materials to approach again, the balance of electric field is broken, which cause electrons to transfer from the aluminum electrons to the copper electrode. Triboelectric components and piezoelectric components play different roles under different conditions of excitation. When the amplitude of external excitation is sufficient, the harvested energy of the BTLG is mainly generated by the triboelectric components, while the output of the piezoelectric components only occupies lesser proportions. On the contrary, when the external excitation amplitude is too small to ensure realization of contact-separation motion of the triboelectric components, the piezoelectric elements, rather than the
2. Design and mechanism As shown in Fig. 1 a, the BTLG consists of a movable center shaft, two nitrile baffle, two annular permanent magnets A and B, a cross leaf spring, triboelectric components, piezoelectric components, and an aluminum alloy shell. The annular permanent magnet B is fixed on the shaft and is repelled by the externally fixed annular permanent magnet
Fig. 1. Schematic illustration of the structure and working principle of the BTLG. (a) Schematic of the BTLG and its two stable states; (b) Schematic of the power generation by the piezoelectric components in the BTLG; (c) Magnetic dipole model; (d) Potential energy function. 2
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Fig. 2. The mechanism of the TENG in the BTLG.(a)Initial state. (b) Contact with each other, the nitrile baffle and the triboelectric components generate charge. (c) Separation, electrode electron transfer. (d) The transfer of electrons balances the electric field. (e) Approaching, the electrons are transferred again.
triboelectric ones, plays a leading role in the output of the BTLG. This kind of nonlinear generator is suitable for various energy of rectilinear motion, examples being the vibration energy under the action of inertial force and the kinetic energy of reciprocating rectilinear motions under the direct pull of the external force. Fig. 3 shows two application examples of such nonlinear generators. As shown in Fig. 3a, by installing the BTLGs into a car suspension system, the vibrational energy of car body can be collected in real time and supplied to electrical systems, thereby reducing consumption of fossil energy. Blue energy of the sea, harvested by a linear generator array placed underwater in Fig. 3b, is capable of providing power supply for human's daily use on a island. The realization of bistable motion under inertial force requires that the device have bistable characteristics. To understand the nonlinear bistable characteristics of the BTLG, we adopt a magnetic dipole model [55]. We analyze the force on the movable shaft in a magnetic field and the potential energy function of the device. The magnetic dipole model for the annular permanent magnets A and B is shown in Fig. 1c. The magnet A is considered to be composed of infinitesimal micro-elements a, each with magnetic moment ma . We analyze the force on each microelement to calculate the total force on the magnet A. The horizontal distance between magnetic dipole a and magnetic dipole B, with the latter having magnetic moment mB , is denoted by x, and the vertical distance is equal to the displacement of the center shaft, denoted by z. The vector from dipole a to dipole B is denoted by r . The magnetic flux density produced by magnetic dipole a at magnetic dipole B is
BaB =
µ0 4
ma r , |r|3
magnetization intensity vector of a, A, and B, respectively. Va , VA , and VB are the volume of a, A, and B, respectively. is the gradient operator, where i and k are the unit vectors in the x and z directions, respectively. The magnetic force between dipoles a and B is
FaB =
(2)
( BaB mB).
The magnetic force between magnets A and B is the sum of the forces between all the elements a and magnet B. The micro-element forces cancel each other out in the horizontal direction, while those in the vertical direction are superimposed on each other. Thus, the magnetic force between magnets A and B is
FAB =
FaB =
3µ 0 |MA ||MB |VA VB z (3x 2 2z 2 ) k. 4 (x 2 + z 2) 7/2
(3)
The magnetic potential energy between a and B is
UaB =
BaB mB =
µ 0 |MA ||MB |dVA VB (x 2 4 (x 2 + z 2 )5/2
2z 2 )
.
(4)
Correspondingly, the magnetic potential energy between A and B is
UAB =
UaB =
µ 0 |MA ||MB |VA VB (x 2 4 (x 2 + z 2)5/2
2z 2) (5)
The elastic potential energy of the cross leaf spring is
Ue =
1 k eq z 2, 2
(6)
where k eq is the equivalent stiffness of the spring. Therefore, the total potential energy is
(1)
where the permeability of the vacuum µ 0 = 4 × 10 H/m. The magnetic moment of dipole a, A and B is ma = Ma Va = MA dVA , mA = MA VA , and mB = MB VB , respectively. Ma , MA , and MB are the
U = UAB + Ue =
7
µ 0 |MA ||MB |VA VB (x 2 4 (x 2 + z 2 )5/2
2z 2 )
+
1 keq z 2 2
(7)
Substitution of the parameters of the BTLG into the expression (7)
Fig. 3. Two examples of the application of BTLGs: (a) Car suspension energy harvesting; (b) Energy harvesting array pulled by buoys on the sea. 3
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gives the potential energy U as a function of displacement z as shown in Fig. 1d, according to which the proposed BTLG has two stable equilibrium states with corresponding displacements z = 0.01 m and 0.01 m, thus proving the bistable characteristics of the device. Inter-well motion across the two potential wells helps to increase the amplitude of the device at non-resonant frequencies, thereby broadening the working frequency band. The amplification of the amplitude not only increases the amount of deformation of the cross leaf spring, thereby increasing the output voltage of the piezoelectric components, but also contributes to the realization of the contact-separation motion, thus enhancing the power generation of the triboelectric components. The triboelectric components generate electricity by reciprocating contact–separation motion with the nitrile baffle. The motion of the center shaft is no longer simple harmonic motion, but rather a kind of shock vibration, which we like to think of as being analogous to a triangular motion in which the dependence of displacement x on time t can be expressed as follows:
2At / T , 2At / T ,
x (t ) =
0
t T /2
T /2, t 0,
3.1. Low-frequency response For the direct-drive mode of the device, the device can work as long as it has external driving force. The working bandwidth of the device is almost equal to the power generation bandwidth of the material itself. The electric energy that can be harvested is the main factor determining the application of the device. Low-frequency experiments can be used to illustrate the power generation characteristics of the BTLG at low frequencies, under conditions similar to those found when harvesting ocean wave energy. To achieve this type of vibration, we fixed the device on the vibrating table with its central shaft attached to a metal bracket on the base, which is the direct-drive mode of this device. In the experiment, the peak-to-peak excitation of the vibrating table was 20 mm and the excitation frequencies applied were 2, 4, 6, 8, 10, and 12 Hz. The power output from the BTLG was used to charge a 10 µ F electrolytic capacitor, and the capacitor voltage was measured by a digital multimeter. In addition, we used a mechanical tensile stretcher (MTS) for ultralow-frequency experiments at frequencies below 1 Hz (see Supplementary Fig. 2). The experimental results are shown in Fig. 4. At excitation frequencies of 2, 4, 6, 8, 10, and 12 Hz, the voltage of the capacitor charged by the BTLG reached 0.71, 1.35, 2.29, 3.27, 4.67, and 5.80 V, respectively, after a time of 20 s. The device is also capable of generating an effective amount of electricity under excitation at ultralow frequencies below 1 Hz: under excitation by the MTS at 0.2 Hz, the device charged the 10 µ F capacitor to 0.248 V in 60 s. In addition, the charging results of the capacitor after removing the piezoelectric components is shown in Fig. 4c and d. Compared with the former, the charging voltage of the capacitor drops by 1.5, 1.28, 1.05, 0.79, 0.47, and 0.21 V at the excitation frequencies of 2, 4, 6, 8, 10, and 12 Hz, respectively. Under excitation by the MTS at 0.2 Hz, the device without piezoelectric components charged the 10 µ F capacitor to 0.11 V in 60 s. As the charging process continues, the voltage of the capacitor will continue to increase until it is close to the peak open-circuit voltage of the BTLG, whereas the voltage of a capacitor charged by an EMG will be restricted to a fairly low value owing to the low output voltage of EMGs under low-frequency excitation. EMGs are therefore unsuitable for harvesting energy from low-frequency excitations [31]. In contrast, the bistable linear generator with triboelectric and piezoelectric components presented here is able to efficiently harvest energy at ultralow frequencies.
(8)
where A is the peak displacement and T is the period of vibration. To analyze the frequency characteristics, we compute the Fourier series representation of x (t ) ,
x (t ) = a 0 +
(an cos n
0t
+ bn sin n
0 t ).
n= 1
(9)
For x (t ) as given by the expression (8), we have bn = 0 , a0 = A/2, and
an =
4A/(n ) 2 , n = 1,3,5, …, 0 n = 2,4,6, …,
(10)
and so
x (t ) =
A 2
4A 2
n = 1,3,5, …
1 2n cos t . n2 T
(11)
The amplitude of the Nth harmonic component is then
An =
an2 + bn2 =
A/2, n = 0, A/(n ) 2, n = 1,3,5, …, 0, n = 2,4,6, ….
(12)
The energy of mechanical vibration is proportional to the square of the amplitude. From (12), the amplitudes of the DC component and the first-harmonic component are much larger than the amplitude of the high-frequency harmonic component. Therefore, the mechanical energy of this form of motion is concentrated mainly in the low-frequency band below the fundamental frequency, indicating that the BTLG is indeed suitable for ultralow-frequency vibrational energy harvesting.
3.2. Broadband frequency response The device mainly relies on its own inertial force to move in the inertia-drive mode, which corresponds to the conditions encountered in applications to vehicle suspensions. In this mode, the working bandwidth, related to the structural resonant frequency, and the output power density are two important factors for evaluating the power generation performance of the device. To study the bandwidth of the device in the inertia-drive mode, we carried out an inertial-force frequency-sweep test. We again compared the BTLG with the LTLG under the same excitation conditions. We fixed the device at the center of the vibrating table and added mass blocks to the unconstrained central shaft. Fig. 5 presents the results for the frequency-domain performances of the BTLG and LTLG under a peak-to-peak excitation of 8 mm, with the excitation frequency f swept from 3 to 13 Hz at a frequency rise rate of 0.2 Hz/s. It can be seen from Fig. 5a that the center shaft displacement of the LTLG reached a peak of 20 mm between 4.9 and 6.6 Hz, and from Fig. 5b that the open-circuit voltage of the piezoelectric components also reached a peak value (of 20 V) in this range. Fig. 5c and d shows that the peak open-circuit voltages of the triboelectric components on the lower and upper surfaces were 22.1 and 8.0 V, respectively. In the case of the BTLG, there was large-amplitude inter-well motion within a wide frequency band from 4.2 to 11.7 Hz, with a peak amplitude of
3. Experiment To verify the theoretical analysis and the high energy-harvesting efficiency of the device at low frequencies, the BTLG was tested under various low-frequency conditions. The characteristics of the device at low frequencies were determined in three different experiments examining the low-frequency response, bistable vibration, and broadband frequency response, respectively. In the experiments, the device has two working modes due to its structural characteristic. One is a directdrive mode that the center shaft is driven directly by external forces, such as the applications in the ocean. The other is inertia-drive mode, which the reciprocating rectilinear motion of the center shaft is accomplished through the inertial force of itself, such as the applications of suspension system. Our experimental system includes a vibrating table and its controller, a computer, a DC stabilized power supply, a digital multimeter, a laser displacement sensor, and a resistance box(see Supplementary Fig. 1). 4
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Fig. 4. Voltage of 10 µ F capacitor charged by the BTLG: (a) Low frequency (>1 Hz); (b) Ultralow frequency (<1 Hz); (c) Low frequency without piezoelectric components (>1 Hz); (d) Ultralow frequency without piezoelectric components (<1 Hz).
20 mm (Fig. 5a). The peak open-circuit voltages of the triboelectric components on the lower and upper surfaces were 50.5 and 24.4 V, respectively (Fig. 5c and d). The observations indicate that the LTLG has a resonance frequency point in the frequency between 4.9 and 6.6 Hz, which greatly increases the amplitude of the LTLG. In other frequency ranges, the voltage of the piezoelectric components decreases, and the triboelectric components not work because the amplitude is insufficient to complete the contact-separation movement. The working frequency bandwidth of BTLG has been broadened due to the bistable characteristics. In order to quantitatively compare the working bandwidth of LTLG and BTLG in the inertia-drive mode, the effective working bands, defined as the frequency bands corresponding to full-stroke motion, are
indicated in orange in Fig. 5a. For the BTLG the working bandwidth at low frequencies was very much wider than that of the LTLG (to 441%). By virtue of the inter-well motion in the BTLG, the displacement of the center shaft and the open-circuit voltages of the piezoelectric components and the triboelectric components were all greatly enhanced compared with the LTLG (to 229% in the case of the open-circuit voltage of the triboelectric components). The optimum power density is used to evaluate the effect of this nonlinear approach to improving electricity generation performance. The basic output of the PDMS and PVDF needs to be determined to obtain the optimum power. Basic output, including output voltage, output current (Fig. 6a and c) and power (Fig. 6b and d) of the two materials, was measured under an excitation with constant frequency Fig. 5. Results of inertial-force frequency-sweep test under 8 mm peak-to-peak excitation at 3–13 Hz sweep frequency: (a) Center shaft displacement; (b) Open-circuit voltage of piezoelectric components; (c) Open-circuit voltage of triboelectric components on the lower surface (PDMS 1); (d) Open-circuit voltage of triboelectric components on the upper surface (PDMS 2).
5
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Fig. 6. Basic output of two materials and power densities of BTLG and LTLG at optimum resistance. (a) Output voltage and output current of PDMS under different resistance values; (b) The power of PDMS at different resistance values; (c) Output voltage and output current of PVDF under different resistance values; (d) The power of PVDF at different resistance values; (e) The power density of BTLG under inertial-force swept excitation from 3 to 13 Hz; (f) The power density of LTLG under inertial-force swept excitation from 3 to 13 Hz.
(7.2 Hz) and peak-to-peak value (8 mm). The output voltage and current of the two materials of interest was measured by changing the resistance of the resistance box. The optimum resistance of the materials was determined by obtaining the maximum output power. We found that the maximum output power was achieved when the resistance was 10 M . Benefiting greatly from the nonlinear bistable structure, the nonresonant vibration of the BTLG are increased in the process of frequency-sweep test. During this process, the BTLG vibrates with large amplitudes for most of the time, while the LTLG exhibits obvious vibration only near its resonant frequency (see Supplementary Movie 1 and Movie 2). These experimental phenomena reveal the reason for the increase in displacements as well as voltages at non-resonant frequencies. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.nanoen.2019.103973. The power density can be calculated by formula Pd = U 2/(RV ) , while U, R, and V are output voltage, load resistance, and effective volume of the device, respectively. In this device, the optimal power density can be obtained by selecting 10 M load resistance. The
optimum power density responses are plotted in Fig. 6e and f. The opencircuit voltage of the BTLG was higher than that of the LTLG for frequencies within the ranges 3–5.2 Hz and 7–11.5 Hz. It is obvious that the high power bandwidth of the BTLG 13 Hz was 203% of that of the LTLG. It is noteworthy that the optimum power density of the BTLG was 877.8 mW/m3, which is 83% higher than that of the LTLG (480.2 mW/ m3). The nonlinear system clearly enhances the electricity generation performance of the harvester under low excitation levels and broadens the working bandwidth for large-amplitude vibrations at low frequencies. 3.3. Bistable vibration Theoretical analysis has revealed the bistable characteristics of the BTLG in the inertia-drive mode. Bistable vibration, also known as interwell motion, is capable of increasing the amplitude of vibration of the central shaft of the device, thus further enhancing its power generation efficiency. An inertial-force fixed-frequency experiment was used to confirm this theoretical analysis. We compared the performance BTLG with that of the corresponding linear device (LTLG, i.e., the BTLG 6
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Fig. 7. Results of inertial-force fixed-frequency experiment under 10 mm peak-to-peak-value excitation: (a) Center shaft displacement; (b) Open-circuit voltage of piezoelectric components; (c) Open-circuit voltage of triboelectric components on the lower surface (PDMS 1); (d) Open-circuit voltage of triboelectric components on the upper surface (PDMS 2).
Supplementary video related to this article can be found at https:// doi.org/10.1016/j.nanoen.2019.103973. Experiments have shown that the device can effectively generate electrical energy at low frequencies, even at ultralow frequencies below 1 Hz. This low-frequency power generation characteristic is especially suitable for energy harvesting of low-frequency vibrations, such as ocean wave energy. Under excitation by an inertial force, the working frequency band of the device is wider than in the case of a linear system, and, obviously, this also increases the energy harvesting efficiency. The capability of power generation is greatly improved by working in a bistable state, especially for the triboelectric components. The bistable motion increases the amplitude of the device at low frequencies, allowing the triboelectric components to come into contact and separate from the nitrile baffle, thereby greatly increasing the overall output. Fig. 8. BTLG installed on a bicycle to collect vibrational energy during cycling.
3.4. Practical environmental experiment
without the annular permanent magnet A) under the same excitation conditions. We determined the behavior of the displacement and the open-circuit voltages of the triboelectric components and the piezoelectric components. The excitation frequency f of the vibrating table was 7.2 Hz, and the excitation peak-to-peak value A was 10 mm. As shown in Fig. 7a, the center shaft displacement amplitude of the BTLG reached 20.0 mm, and the shaft underwent contact–separation bistable motion, whereas the corresponding amplitude of the LTLG was only 11.5 mm. Fig. 7a shows clearly that the contact–separation bistable motion was a triangular motion, which is consistent with the theoretical analysis. As can be seen from Fig. 7b, the peak open-circuit voltage of the piezoelectric components of the BTLG was 18.5 V, and that of the LTLG was 11.8 V. Thus, the open-circuit voltage of the piezoelectric components of the BTLG was 157% of that of the LTLG. The triboelectric components on the upper and lower surfaces of the LTLG cannot generate electricity: the vibration peaks are insufficient for them to come into contact, and hence the open-circuit voltage of these components is zero. In contrast, as can be seen from Fig. 7c and d, the open-circuit voltage of the triboelectric components of the BTLG reached 138.0 V because the nonlinear structure increased the amplitude of vibration of the device. And the output power of the BLTG is increased such that it becomes capable of lighting up 36 series-connected LEDs (see Supplementary Movie 3).
In order to prove that the designed BTLG is able to collect the lowfrequency vibrational energy in the practical environment, we use a bicycle to provide random excitation for the device, as shown in Fig. 8. We chose a piece of undulant meadowland to provide low-frequency vibrational excitation for the BTLG under the conditions of riding and pushing, respectively. We measured the vibration data of the riding and pushing process (see Supplementary S4, S5 and S6), which proved that this environmental drive is a low-frequency vibration. Under both experimental conditions, BTLG is capable of lighting up 36 series-connected LEDs (see Supplementary Movie 4 and Movie 5), which proves the prospect of practical applications of this design. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.nanoen.2019.103973. 4. Conclusion A bistable triboelectric linear generator with nonlinear characteristics, suitable for broadband energy harvesting in the low-frequency range, has been proposed. Without increasing the structural complexity, the piezoelectric components is used to compensate for the defects that the contact-separation mode triboelectric nanogenerator cannot work at small amplitudes. Theoretical analysis has revealed that the device has bistable characteristics and that the energy of the 7
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bistable contact–separation motion is concentrated within the first harmonic component. Driven directly by low-frequency tension, the device is capable of efficiently generating electrical energy. Even under excitation at an ultralow frequency of 0.1 Hz, the device can charge a 10 µ F capacitor to 0.12 V within 60 s. Under swept excitation, the opencircuit voltage of the piezoelectric components is increased to 157%, with that of the triboelectric components reaching 138 V. With the proposed BTLG, the working bandwidth is widened to 441% compared with the linear device. The bistable vibration significantly improves electricity generation performance at low frequencies. This contact–separation bistable structural design, with ultralow operating frequency and wide working bandwidth, has potential for a variety of practical low-frequency energy harvesting applications, providing a welcome boost for the development of compact and efficient rectilinear motion energy harvesters.
[17] [18] [19] [20] [21] [22]
Acknowledgment
[23]
The authors appreciate the support of the National Natural Science Foundation of China (Grant Nos. 11872167, 51575156, 51675156, 51775164, and 51705122), the Fundamental Research Funds for the Central Universities (Grant Nos. JZ2017HGPA0165 and PA2017GDQT0024, and Natural Science Foundation of Anhui Province (1908085J15).
[24] [25] [26]
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.nanoen.2019.103973.
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Yu Du received his B.S. degree from the College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2015, and M.S. degree from the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, China, in 2019. He is going to study for a Ph.D. degree in the School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His current research interests include energy harvesting, triboelectric nanogenerator, and mechanical analysis.
from mechanical triggering/vibration and water waves, ACS Nano 8 (2014) 7405–7412, https://doi.org/10.1021/nn502618f. J. Chen, J. Yang, Z. Li, X. Fan, Y. Zi, Q. Jing, H. Guo, Z. Wen, K.C. Pradel, S. Niu, Z.L. Wang, Networks of triboelectric nanogenerators for harvesting water wave energy: a potential approach toward blue energy, ACS Nano 9 (2015) 3324–3331, https://doi.org/10.1021/acsnano.5b00534. G. Zhu, Z.-H. Lin, Q. Jing, P. Bai, C. Pan, Y. Yang, Y. Zhou, Z.L. Wang, Toward largescale energy harvesting by a nanoparticle-enhanced triboelectric nanogenerator, Nano Lett. 13 (2013) 847–853, https://doi.org/10.1021/nl4001053. X. Wen, Y. Su, Y. Yang, H. Zhang, Z.L. Wang, Applicability of triboelectric generator over a wide range of temperature, Nano Energy (2014) 150–156, https://doi.org/ 10.1016/j.nanoen.2014.01.001. C. Wu, R. Liu, J. Wang, Y. Zi, L. Lin, Z.L. Wang, A spring-based resonance coupling for hugely enhancing the performance of triboelectric nanogenerators for harvesting low-frequency vibration energy, Nano Energy 32 (2017) 287–293, https:// doi.org/10.1016/j.nanoen.2016.12.061. A. Erturk, J. Hoffmann, D.J. Inman, A piezomagnetoelastic structure for broadband vibration energy harvesting, Appl. Phys. Lett. 94 (2009) 254102, https://doi.org/ 10.1063/1.3159815. F. Cottone, H. Vocca, L. Gammaitoni, Nonlinear energy harvesting, Phys. Rev. Lett. 102 (2009) 080601, , https://doi.org/10.1103/PhysRevLett.102.080601. T. Yildirim, M.H. Ghayesh, W. Li, G. Alici, A review on performance enhancement techniques for ambient vibration energy harvesters, Renew. Sustain. Energy Rev. 71 (2017) 435–449, https://doi.org/10.1016/j.rser.2016.12.073. M.G. Tehrani, S.J. Elliott, Extending the dynamic range of an energy harvester using nonlinear damping, J. Sound Vib. 333 (2014) 623–629, https://doi.org/10.1016/j. jsv.2013.09.035. H. Deng, Y. Du, Z. Wang, J. Ye, J. Zhang, M. Ma, X. Zhong, Poly-stable energy harvesting based on synergetic multistable vibration, Commun. Phys. 2 (2019) 21, https://doi.org/10.1038/s42005-019-0117-9. H. Deng, Z. Wang, Y. Du, J. Zhang, M. Ma, X. Zhong, A seesaw-type approach for enhancing nonlinear energy harvesting, Appl. Phys. Lett. 112 (2018) 231902, https://doi.org/10.1063/1.5032307. H. Deng, Y. Du, Z. Wang, J. Zhang, M. Ma, X. Zhong, A multimodal and multidirectional vibrational energy harvester using a double-branched beam, Appl. Phys. Lett. 112 (2018) 231901, https://doi.org/10.1063/1.5024567. H. Deng, Z. Wang, Y. Du, J. Zhang, M. Ma, X. Zhong, A compact and flexible nonbeam-type vibrational energy harvesting device with bistable characteristics, IEEE ASME Trans. Mechatron. 24 (2019) 282–292, https://doi.org/10.1109/ TMECH.2019.2891289.
Jin Zhang received his B.E. degree from Hefei University of Technology, Hefei, China, in 2005. He received his M.S. and Ph.D. degrees from Tianjin University, Tianjin, China, in 2007 and 2010, respectively. He has been an associate professor at the School of Instrument Science and Optoelectronics Engineering, Hefei University of Technology since 2012. His current research interests include optical measurement technology and vibration testing. Dr. Zhang is a member of Youth Committee of China Instrument and Control Society.
Mengchao Ma received his Ph.D. degree from the University of Science and Technology of China, Hefei, China, in 2014. He is currently an associate professor in the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology. His current research interests include artificial compound eye, structured-light measurement, and dynamic testing.
Huaxia Deng received his B.E. and M.S. degrees from the University of Science and Technology of China, Hefei, China, in 2004 and 2007, respectively, and the Ph.D. degree from the University of Liverpool, Liverpool, U.K., in 2011. He has been the Hungshan Young Scholar Professor with the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, since 2012. His current research interests include smart materials and vibration control. He is the Review Editor of the journal Frontiers in Smart Materials.
Xiang Zhong received his B.S. degree from the School of the measurement and control technology and instrument, Tianjin University, Tianjin, China, in 2008, and the Ph.D. degree in optical engineering from Beihang University, Beijing, China, in 2016. He is currently a lecturer in the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology. His current research interests include optical fiber sensing and dynamic testing.
Jingchang Ye received his B.S. degree from the School of the mechanical and electronic engineering, Wuhan University of Technology, Wuhan, China, in 2017. He is currently a postgraduate student in the School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, China. His current research interests include energy harvesting, electric circuit design, and mechanical design.
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