Journal Pre-proof

Bistable broadband hybrid generator for ultralow-frequency rectilinear motion

Huaxia Deng, Jingchang Ye, Yu Du, Jin Zhang, Mengchao Ma, Xiang Zhong

PII: S2211-2855(19)30680-9

DOI: https://doi.org/10.1016/j.nanoen.2019.103973

Reference: NANOEN 103973

To appear in: Nano Energy

Received Date: 28 June 2019

Revised Date: 28 July 2019

Accepted Date: 1 August 2019

Please cite this article as: H. Deng, J. Ye, Y. Du, J. Zhang, M. Ma, X. Zhong, Bistable broadband hybridgenerator for ultralow-frequency rectilinear motion, Nano Energy (2019), doi: https://doi.org/10.1016/j.nanoen.2019.103973.

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Center shaft

Cross leaf

springPDMS

Nitrile baffle

Annular permanent

magnet

PVDFShell

Triboelectric

Piezoelectric

Bistable broadband hybrid generator for ultralow-frequency rectilinear motion

Huaxia Deng, Jingchang Ye, Yu Du, Jin Zhang, Mengchao Ma, and Xiang Zhong

School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, Anhui, 230009, People’s Republic of China. E-mail:(hxdeng@hfut.edu.cn).

Abstract

In the natural environment, rectilinear motions normally take the form of low-frequency and broadband vibrations. This posesproblems for devices aimed at harvesting energy from these motions, since conventional linear electromagnetic generators areinefficient under such conditions. Here we present a bistable triboelectric linear generator (BTLG) with nonlinear characteristicsfor 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 forthe defects that the contact-separation mode triboelectric nanogenerator cannot work at a small amplitude. Experiments show thata 10 µF capacitor can be charged to 0.12 V in 60 s at an ultralow frequency of 0.1 Hz. The frequency bandwidth of the BTLGis greatly broadened to 441% compared with a linear device. The proposed BTLG is capable of harvesting mechanical energy atlow frequency with large working bandwidth, thus providing a effective method for energy harvesting of ambient low-frequencyrectilinear motions.

Keywords: Energy harvesting, Nonlinear, Low frequency, Broadband, Linear generator

1. Introduction

As a form of vibrational motion, reciprocating rectilin-ear motion occurs widely, for example in the form of oceanwaves [1–8], vibration of suspension systems [9–13], and hu-man walking [14–20]. Typically, this type of vibration is low-frequency, broadband, and extensively distributed. Harvestingof the mechanical energy of rectilinear motion[21], such asblue energy and human kinetic energy [22], by linear genera-tors has the potential to supply power for a range of applica-tions, for example distributed sensors [23–25] and the Internetof Things [26–29]. However, in the case of ambient rectilin-ear motions, their generally low frequency and broadband char-acteristics mean that electromagnetic linear generators are notsuitable [30, 31].

Electromagnetic generation (EMG) is based on the inductioneffect represented by the first term of Maxwell’s displacementcurrent, namely, the time derivative of the electric field. Be-cause of this, EMG performs well at high frequencies (>50 Hz)[31], but cannot effectively harvest mechanical energy at lowfrequencies such as those of ocean waves, which are mostlyconcentrated below 10 Hz [32]. Therefore, much work has beendone on increasing the power generation efficiency of electro-magnetic linear generators for harvesting wave energy by in-corporating a speed increaser in the generator system [33–37].

The second term of Maxwell’s displacement current is re-lated to the polarization of a material medium [30]. It is this

1Huaxia Deng, Jingchang Ye, and Yu Du contributed equally to this work.2Corresponding authors: Huaxia Deng (hxdeng@hfut.edu.cn).

term that determines the fundamental characteristics of a tribo-electric nanogenerator (TENG)[38–41] and gives it an excellentenergy harvesting capability in the low-frequency range [42].The superior power generation performance of TENGs has al-ready been applied to energy harvesting of low-frequency rec-tilinear motion and, in particular, Wang’s team have done muchwork 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 rectilinearmotion of the human body, providing enough power to light up104 LEDs simultaneously, and this approach can harvest vibra-tional energy at 5 Hz[43]. A mesh-based structure containing asmall rolling ball has been designed to collect distributed waveenergy [44]. It generates 1.15 MW of energy per square kilo-meter of sea area, but can only be used on the ocean surface. Acontact–separation-type TENG can effectively respond to inputvibration frequency at 2Hz. Supported by four springs, it hasthe 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 10times[47]. Even so, as a second-order linear system, its effectiveworking band is near the resonant frequency.

The TENG-based energy harvesters developed to date arebased mainly on linear dynamical systems, which principallywork near the resonance frequency. An effective way to broadenthe working frequency band is through bistable vibrational en-ergy harvesting [48, 49] based on nonlinear dynamical systems[50, 51]. Classical bistable energy harvesting utilizes magneti-cally coupled cantilever beams to harvest broadband vibrationalenergy [52, 53]. In the case of a synergetic poly-stable beam

Preprint submitted to Nano Energy August 6, 2019

PVDFShell

Center shaft

PDMS2

PDMS1 Nitrile baffle

Cross leaf spring

Annular permanent

magnet A

Annular permanent

magnet B

PVDF

Stable equilibrium state 1

Stable equilibrium state 2

a

Electric energy

Electric energy

b Power generation components at

small amplitude

A

B

xz

a

am

bm

r

c d

Figure 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 powergeneration by the piezoelectric components in the BTLG; (c) Magnetic dipole model; (d) Potential energy function.

array, using the magnetic repulsion between different beams,the working bandwidth is broadened by a factor of 41 com-pared with a linear beam array.[52] To collect broadband vibra-tional energy with low intensity, a seesaw-type approach hasbeen proposed to overcome the potential barrier and enhancenonlinear energy harvesting performance.[53] However, beam-type energy harvesters usually use their own bending vibrationsto generate electricity [54], and this approach is difficult to ap-ply to TENGs working on contact–separation mode. Therefore,it is necessary to design a bistable structure that is suitable forthe contact–separation motion of traditional TENGs.

Here, we present a bistable triboelectric linear generator(BTLG) with nonlinear characteristics and capable of achiev-ing bistable-type contact–separation motion, with the aim of re-solving the difficulty in harvesting energy from low-frequencyreciprocating rectilinear motions. Furthermore, piezoelectriccomponents are used in the device, which compensates for thedefects that the contact-separated triboelectric nanogenerator insmall amplitude without increasing the complexity of the orig-inal device structure. We show the details of the device howto work. The bistability and low-frequency adaptability of thisdevice are proved by a theoretical analysis. Direct-drive exper-iments under excitations of 0.1–12 Hz reveal the generatingcapability of this device at ultralow frequencies. Inertial-forceswept experiments comparing the BTLG with a correspondinglinear device verify its high efficiency of energy harvesting andbroadband characteristics. The experiment under constant fre-quency excitation of inertial force further demonstrates the su-periority of the BTLG while operating in a bistable state. Inaddition, the practicality of this device is proved by practicalenvironmental experiments.

2. Design and mechanism

As shown in Fig. 1 a, the BTLG consists of a movable centershaft, two nitrile baffle, two annular permanent magnets A andB, a cross leaf spring, triboelectric components, piezoelectriccomponents, and an aluminum alloy shell. The annular perma-nent magnet B is fixed on the shaft and is repelled by the exter-nally fixed annular permanent magnet A. The magnet B and theshaft are together able to perform one-dimensional linear recip-rocating motion. The center of the cross leaf spring is fixed tothe shaft, and the four ends of the spring are constrained by thesimple support of the shell. The position at which the cross leafspring is attached to the shaft is such that the magnets A andB are in the same horizontal plane when the gravitational forceon the shaft (and on other components mounted on the shaft)and the elastic force of the cross leaf spring are balanced witheach other. In this situation, the displacement z of the shaft isdefined as zero. During reciprocating motion, owing to the re-pulsive force between the permanent magnets and the restoringforce of the cross leaf spring, the movable shaft undergoes non-linear bistable motion under broadband excitation. In Fig. 1 b,the piezoelectric components are attached to the clamping endsof the cross leaf spring near the center shaft. The reciprocatingrectilinear motion of the central shaft drives the deformation ofthe cross leaf spring as well as the PVDF piezoelectric films,thus generating electrical energy.

Fig. 2 shows the mechanism of the contact-separating tri-boelectric nanogenerator in the device. The contact-separationmovement between the nitrile baffle and the triboelectric com-ponents is driven by the reciprocating motion of the centralshaft. The electrical energy generated by the triboelectric com-ponents and the piezoelectric components is harvested andstored by subsequent capture circuits. A cycle of electricitygeneration process is illustrated in Figure 2. First, nitrile baffleis not in contact with PDMS and therefore has no charge ex-

2

i

iReleasing

Pressing

Pressed

Released

Primary power generation

components at large amplitude

Nitrile

PDMSCopper

PDMS

Aluminum alloy

a b c

e

Wire

d

Figure 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.

change. External excitation causes the PDMS to contact the ni-trile baffle and generates positive triboelectric charges on the ni-trile side and negative charges on the PDMS side. Then the twomaterials are separated by the restoring force. In order to coun-teract the electric field generated by the triboelectric charge,electrons are transferred from the copper electrode to the alu-minum alloy electrode. As the distance of separation increases,the electrostatic field generated by the triboelectric charge iscompletely counteract. When the excitation causes the two ma-terials to approach again, the balance of electric field is broken,which cause electrons to transfer from the aluminum electronsto the copper electrode.

Triboelectric components and piezoelectric components playdifferent roles under different conditions of excitation. Whenthe amplitude of external excitation is sufficient, the harvestedenergy of the BTLG is mainly generated by the triboelectriccomponents, while the output of the piezoelectric componentsonly occupies lesser proportions. On the contrary, when the ex-ternal excitation amplitude is too small to ensure realization ofcontact-separation motion of the triboelectric components, thepiezoelectric elements, rather than the triboelectric ones, playsa leading role in the output of the BTLG.

Figure 3: Two examples of the application of BTLGs: (a) car suspension energyharvesting; (b) energy harvesting array pulled by buoys on the sea.

This kind of nonlinear generator is suitable for various en-ergy of rectilinear motion, examples being the vibration energy

under the action of inertial force and the kinetic energy of recip-rocating rectilinear motions under the direct pull of the externalforce. Fig. 3 shows two application examples of such nonlin-ear generators. As shown in Fig. 3a, by installing the BTLGsinto a car suspension system, the vibrational energy of car bodycan be collected in real time and supplied to electrical systems,thereby reducing consumption of fossil energy. Blue energy ofthe sea, harvested by a linear generator array placed underwaterin Fig. 3b, is capable of providing power supply for human’sdaily use on a island.

The realization of bistable motion under inertial force re-quires that the device have bistable characteristics. To under-stand the nonlinear bistable characteristics of the BTLG, weadopt a magnetic dipole model [55]. We analyze the force onthe movable shaft in a magnetic field and the potential energyfunction of the device. The magnetic dipole model for the an-nular permanent magnets A and B is shown in Fig. 1c. Themagnet A is considered to be composed of infinitesimal micro-elements a, each with magnetic moment ma. We analyze theforce on each micro-element to calculate the total force on themagnet A. The horizontal distance between magnetic dipole aand magnetic dipole B, with the latter having magnetic momentmB, is denoted by x, and the vertical distance is equal to thedisplacement of the center shaft, denoted by z. The vector fromdipole a to dipole B is denoted by r.

The magnetic flux density produced by magnetic dipole a atmagnetic dipole B is

BaB = −µ0

4π∇

ma · r|r|3

, (1)

where the permeability of the vacuum µ0 = 4π × 10−7 H/m.The magnetic moment of dipole a, A and B is ma = MaVa =

MAdVA, mA = MAVA, and mB = MBVB, respectively. Ma,MA, and MB are the magnetization intensity vector of a, A, andB, respectively. Va, VA, and VB are the volume of a, A, and B,

3

respectively. ∇ = (∂/∂x) i + (∂/∂z) k 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 = −∇(−BaB ·mB). (2)

The magnetic force between magnets A and B is the sum ofthe 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 eachother. Thus, the magnetic force between magnets A and B is

FAB =

∫FaB =

3µ0 |MA| |MB|VAVB

4πz(3x2 − 2z2)

(x2 + z2)7/2 k. (3)

The magnetic potential energy between a and B is

UaB = −BaB ·mB =µ0 |MA| |MB| dVA VB(x2 − 2z2)

4π(x2 + z2)5/2 . (4)

Correspondingly, the magnetic potential energy between A andB is

UAB =

∫UaB =

µ0 |MA| |MB|VAVB

(x2 − 2z2

)4π

(x2 + z2)5/2 (5)

The elastic potential energy of the cross leaf spring is

Ue = 12 keqz2, (6)

where keq is the equivalent stiffness of the spring. Therefore, thetotal potential energy is

U=UAB + Ue=µ0 |MA| |MB|VAVB

(x2 − 2z2

)4π

(x2 + z2)5/2 +

12

keqz2 (7)

Substitution of the parameters of the BTLG into the expres-sion (7) gives the potential energy U as a function of displace-ment z as shown in Fig. 1d, according to which the proposedBTLG has two stable equilibrium states with corresponding dis-placements z = 0.01 m and −0.01 m, thus proving the bistablecharacteristics of the device. Inter-well motion across the twopotential wells helps to increase the amplitude of the deviceat non-resonant frequencies, thereby broadening the workingfrequency band. The amplification of the amplitude not onlyincreases the amount of deformation of the cross leaf spring,thereby increasing the output voltage of the piezoelectric com-ponents, but also contributes to the realization of the contact-separation motion, thus enhancing the power generation of thetriboelectric components. The triboelectric components gener-ate electricity by reciprocating contact–separation motion withthe nitrile baffle. The motion of the center shaft is no longersimple harmonic motion, but rather a kind of shock vibration,which we like to think of as being analogous to a triangular mo-tion in which the dependence of displacement x on time t canbe expressed as follows:

x(t) =

2At/T, 0 ≤ t ≤ T/2,−2At/T, −T/2 ≤ t ≤ 0,

(8)

where A is the peak displacement and T is the period of vibra-tion. To analyze the frequency characteristics, we compute theFourier series representation of x(t),

x(t) = a0 +

∞∑n=1

(an cos nω0t + bn sin nω0t). (9)

For x(t) as given by the expression (8), we have bn = 0, a0 =

A/2, and

an =

−4A/(nπ)2, n = 1, 3, 5, . . . ,0 n = 2, 4, 6, . . . ,

(10)

and so

x(t) =A2−

4Aπ2

∑n=1,3,5,...

1n2 cos

(2nπT

t). (11)

The amplitude of the Nth harmonic component is then

An =

√a2

n + b2n =

A/2, n = 0,A/(nπ)2, n = 1, 3, 5, . . . ,0, n = 2, 4, 6, . . . .

(12)

The energy of mechanical vibration is proportional to thesquare of the amplitude. From (12), the amplitudes of the DCcomponent and the first-harmonic component are much largerthan the amplitude of the high-frequency harmonic component.Therefore, the mechanical energy of this form of motion is con-centrated mainly in the low-frequency band below the funda-mental frequency, indicating that the BTLG is indeed suitablefor ultralow-frequency vibrational energy harvesting.

3. Experiment

To verify the theoretical analysis and the high energy-harvesting efficiency of the device at low frequencies, theBTLG was tested under various low-frequency conditions. Thecharacteristics of the device at low frequencies were determinedin three different experiments examining the low-frequency re-sponse, bistable vibration, and broadband frequency response,respectively. In the experiments, the device has two workingmodes due to its structural characteristic. One is a direct-drivemode that the center shaft is driven directly by external forces,such as the applications in the ocean. The other is inertia-drivemode, which the reciprocating rectilinear motion of the centershaft is accomplished through the inertial force of itself, such asthe applications of suspension system. Our experimental systemincludes a vibrating table and its controller, a computer, a DCstabilized power supply, a digital multimeter, a laser displace-ment sensor, and a resistance box(see Supplementary Figure 1).

3.1. Low-frequency responseFor the direct-drive mode of the device, the device can work

as long as it has external driving force. The working bandwidthof the device is almost equal to the power generation bandwidthof the material itself. The electric energy that can be harvestedis the main factor determining the application of the device.

4

Low-frequency experiments can be used to illustrate the powergeneration characteristics of the BTLG at low frequencies, un-der conditions similar to those found when harvesting oceanwave energy. To achieve this type of vibration, we fixed the de-vice on the vibrating table with its central shaft attached to ametal bracket on the base, which is the direct-drive mode ofthis device. In the experiment, the peak-to-peak excitation ofthe vibrating table was 20 mm and the excitation frequenciesapplied were 2, 4, 6, 8, 10, and 12 Hz. The power output fromthe BTLG was used to charge a 10 µF electrolytic capacitor,and the capacitor voltage was measured by a digital multimeter.In addition, we used an mechanical tensile stretcher (MTS) forultralow-frequency experiments at frequencies below 1 Hz(seeSupplementary Figure 2).

The experimental results are shown in Fig. 4. At excitationfrequencies of 2, 4, 6, 8, 10, and 12 Hz, the voltage of the capac-itor 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 alsocapable of generating an effective amount of electricity underexcitation at ultralow frequencies below 1 Hz: under excitationby the MTS at 0.2 Hz, the device charged the 10 µF capacitorto 0.248 V in 60 s. In addition, the charging results of the ca-pacitor after removing the piezoelectric components is shownin Fig. 4c and Fig. 4d. Compared with the former, the chargingvoltage of the capacitor drops by 1.5, 1.28, 1.05, 0.79, 0.47, and0.21 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 devicewithout piezoelectric components charged the 10 µF capacitorto 0.11 V in 60 s. As the charging process continues, the volt-age of the capacitor will continue to increase until it is close tothe peak open-circuit voltage of the BTLG, whereas the voltageof a capacitor charged by an EMG will be restricted to a fairlylow value owing to the low output voltage of EMGs under low-frequency excitation. EMGs are therefore unsuitable for har-vesting energy from low-frequency excitations [31]. In contrast,the bistable linear generator with triboelectric and piezoelectriccomponents presented here is able to efficiently harvest energyat ultralow frequencies.

0 5 1 0 1 5 2 00

2

4

6

8

0 1 0 2 0 3 0 4 0 5 0 6 00 . 0

0 . 1

0 . 2

0 . 3

0 5 1 0 1 5 2 00

2

4

6

8

0 1 0 2 0 3 0 4 0 5 0 6 00 . 0

0 . 1

0 . 2

0 . 3

Voltag

e v (V

)

T i m e t ( s )

2 H z 4 H z 6 H z 8 H z 1 0 H z 1 2 H z

0

2 0

8 0

1 8 0

3 2 0

Electr

ic ener

gy W(

µJ)

0 . 1 H z 0 . 1 5 H z 0 . 2 H z

Voltag

e v (V

)

T i m e t ( s )

0 . 1 H z 0 . 1 5 H z 0 . 2 H z

0

0 . 0 5

0 . 2

0 . 4 5

Electr

ic ener

gy W(

µJ)

dc

ba

2 H z 4 H z 6 H z 8 H z 1 0 H z 1 2 H z

Voltag

e v (V

)

T i m e t ( s )0

2 0

8 0

1 8 0

3 2 0

Electr

ic ener

gy W(

µJ)

Voltag

e v (V

)

T i m e t ( s )0

0 . 0 5

0 . 2

0 . 4 5

Electr

ic ener

gy W(

µJ)

Figure 4: Voltage of 10 µF capacitor charged by the BTLG: (a) low frequency(>1 Hz); (b) ultralow frequency (<1 Hz); (c) low frequency without triboelectriccomponents (>1 Hz); (d) ultralow frequency without triboelectric components(<1 Hz).

3.2. Broadband frequency response

The device mainly relies on its own inertial force to move inthe inertia-drive mode, which corresponds to the conditions en-countered in applications to vehicle suspensions. In this mode,the working bandwidth, related to the structural resonant fre-quency, and the output power density are two important fac-tors for evaluating the power generation performance of the de-vice. To study the bandwidth of the device in the inertia-drivemode, we carried out an inertial-force frequency-sweep test. Weagain compared the BTLG with the LTLG under the same ex-citation conditions. We fixed the device at the center of the vi-brating table and added mass blocks to the unconstrained cen-tral shaft. Fig. 5 presents the results for the frequency-domainperformances of the BTLG and LTLG under a peak-to-peak ex-citation of 8 mm, with the excitation frequency f swept from 3to 13 Hz at a frequency rise rate of 0.2 Hz/s.

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 3 0- 2 0- 1 0

01 02 03 0

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 3 0- 2 0- 1 0

01 02 03 0

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 6 0- 4 0- 2 0

02 04 06 0

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 6 0- 4 0- 2 0

02 04 06 0

B T L G

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 3 0- 2 0- 1 0

01 02 03 0 L T L G

Displa

cement

z (mm

)

Voltag

e v (V

)Vo

ltage v

(V)

Displa

cement

z (mm

)

B T L G

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 3 0- 2 0- 1 0

01 02 03 0

d

c

aF r e q u e n c y f ( H z )

b

F r e q u e n c y f ( H z )F r e q u e n c y f ( H z )

F r e q u e n c y f ( H z )F r e q u e n c y f ( H z )

F r e q u e n c y f ( H z )

F r e q u e n c y f ( H z )F r e q u e n c y f ( H z )

Voltag

e v (V

)

Voltag

e v (V

)

Voltag

e v (V

)Vo

ltage v

(V)

F r e q u e n c y f ( H z )

L T L G

B T L G

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 6 0- 4 0- 2 0

02 04 06 0 L T L G

B T L G

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3- 6 0- 4 0- 2 0

02 04 06 0

L T L G

Figure 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 voltageof triboelectric components on the lower surface; (d) open-circuit voltage oftriboelectric components on the upper surface.

It can be seen from Fig. 5a that the center shaft displacementof 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 piezoelec-tric components also reached a peak value (of 20 V) in thisrange. Figs. 5c and 5d show that the peak open-circuit voltagesof the triboelectric components on the lower and upper surfaceswere 22.1 and 8.0 V, respectively. In the case of the BTLG,there was large-amplitude inter-well motion within a wide fre-quency band from 4.2 to 11.7 Hz, with a peak amplitude of20 mm (Fig. 5a). The peak open-circuit voltages of the tribo-electric components on the lower and upper surfaces were 50.5and 24.4 V, respectively (Figs. 5c and Fig. 5d). The observa-tions indicate that the LTLG has a resonance frequency point inthe frequency between 4.9 and 6.6 Hz, which greatly increasesthe amplitude of the LTLG. In other frequency ranges, the volt-age of the piezoelectric components decreases, and the tribo-electric components not work because the amplitude is insuffi-

5

cient to complete the contact-separation movement. The work-ing frequency bandwidth of BTLG has been broadened due tothe bistable characteristics.

In order to quantitatively compare the working bandwidth ofLTLG and BTLG in the inertia-drive mode, the effective work-ing bands, defined as the frequency bands corresponding to full-stroke motion, are indicated in orange in Fig. 5a. For the BTLGthe working bandwidth at low frequencies was very much widerthan that of the LTLG (to 441%). By virtue of the inter-well mo-tion in the BTLG, the displacement of the center shaft and theopen-circuit voltages of the piezoelectric components and thetriboelectric components were all greatly enhanced comparedwith the LTLG (to 229% in the case of the open-circuit voltageof the triboelectric components).

1 0 - 3 1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 1 0 30

3 06 09 0

1 2 01 5 0

1 0 - 3 1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 1 0 31 0 - 1

1 0 0

1 0 1

1 0 2

1 0 3

1 0 - 3 1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 1 0 30

5

1 0

1 5

2 0

1 0 - 3 1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 1 0 31 0 - 2

1 0 - 1

1 0 0

1 0 1

1 0 2

Voltag

e v (V

)

0

5

1 0

1 5

2 0

Curre

nt i (µ

A)

R e s i s t a n c e R ( M Ω )

P D M S

Powe

r P (µ

W)

R e s i s t a n c e R ( M Ω )

Voltag

e v (V

)

024681 0

Curre

nt i (µ

A)

R e s i s t a n c e R ( M Ω )

f

e

dc

ba

P V D F

Powe

r P (µ

W)

R e s i s t a n c e R ( M Ω )

3 4 5 6 7 8 9 1 0 1 1 1 2 1 30

2 0 04 0 06 0 08 0 0

1 0 0 0 B T L G

Powe

r Pd (m

W/m3 )

F r e q u e n c y f ( H z )

3 4 5 6 7 8 9 1 0 1 1 1 2 1 30

2 0 04 0 06 0 08 0 0

1 0 0 0 L T L G

Powe

r Pd (m

W/m3 )

F r e q u e n c y f ( H z )

Figure 6: Basic output of two materials and power density of BTLG and LTLGat optimum resistance. (a) Output voltage and output current of PDMS underdifferent resistance values; (b) The power of PDMS at different resistance val-ues; (c) Output voltage and output current of PVDF under different resistancevalues; (d) The power of PVDF at different resistance values; (e) The powerdensity of BTLG under inertial-force swept excitation from 3 to 13 Hz; (f) Thepower density of LTLG under inertial-force swept excitation from 3 to 13 Hz.

The optimum power density is used to evaluate the effectof this nonlinear approach to improving electricity generationperformance. The basic output of the PDMS and PVDF needsto be determined to obtain the optimum power. Basic output,including output voltage, output current (Figs. 6a and c) andpower (Figs. 6b and d) of the two materials, was measured un-der an excitation with constant frequency (7.2Hz) and peak-to-peak value (8 mm). The output voltage and current of the twomaterials of interest was measured by changing the resistanceof the resistance box. The optimum resistance of the materials

was determined by obtaining the maximum output power. Wefound that the maximum output power was achieved when theresistance was 10 MΩ.

Benefiting greatly from the nonlinear bistable structure, thenon-resonant vibration of the BTLG are increased in the pro-cess of frequency-sweep test. During this process, the BTLGvibrates with large amplitudes for most of the time, while theLTLG exhibits obvious vibration only near its resonant fre-quency (see Supplementary Movie 1 and Movie 2). These ex-perimental phenomena reveal the reason for the increase in dis-placements as well as voltages at non-resonant frequencies.

The power density can be calculated by formula Pd =

U2/(RV), while U, R, and V are output voltage, load resis-tance, and effective volume of the device, respectively. In thisdevice, the optimal power density can be obtained by selecting10 MΩ load resistance. The optimum power density responsesare plotted in Fig. 6e and f. The open-circuit voltage of theBTLG was higher than that of the LTLG for frequencies withinthe ranges 3–5.2 Hz and 7–11.5 Hz. It is obvious that the highpower bandwidth of the BTLG 13 Hz was 203% of that of theLTLG. It is noteworthy that the optimum power density of theBTLG was 877.8 mW/m3, which is 83% higher than that of theLTLG (480.2 mW/m3). The nonlinear system clearly enhancesthe electricity generation performance of the harvester underlow excitation levels and broadens the working bandwidth forlarge-amplitude vibrations at low frequencies.

3.3. Bistable vibrationTheoretical analysis has revealed the bistable characteristics

of the BTLG in the inertia-drive mode. Bistable vibration, alsoknown as inter-well motion, is capable of increasing the am-plitude of vibration of the central shaft of the device, thus fur-ther enhancing its power generation efficiency. An inertial-forcefixed-frequency experiment was used to confirm this theoreticalanalysis. We compared the performance BTLG with that of thecorresponding linear device (LTLG, i.e., the BTLG without theannular permanent magnet A) under the same excitation condi-tions. We determined the behavior of the displacement and theopen-circuit voltages of the triboelectric components and thepiezoelectric components. The excitation frequency f of the vi-brating table was 7.2 Hz, and the excitation peak-to-peak valueA was 10 mm.

As shown in Fig. 7a, the center shaft displacement ampli-tude of the BTLG reached 20.0 mm, and the shaft underwentcontact–separation bistable motion, whereas the correspond-ing amplitude of the LTLG was only 11.5 mm. Fig. 7a showsclearly that the contact–separation bistable motion was a tri-angular motion, which is consistent with the theoretical analy-sis. As can be seen from Fig. 7b, the peak open-circuit voltageof the piezoelectric components of the BTLG was 18.5 V, andthat of the LTLG was 11.8 V. Thus, the open-circuit voltage ofthe piezoelectric components of the BTLG was 157% of thatof the LTLG. The triboelectric components on the upper andlower surfaces of the LTLG cannot generate electricity: the vi-bration peaks are insufficient for them to come into contact, andhence the open-circuit voltage of these components is zero. Incontrast, as can be seen from Figs. 7c and 7d, the open-circuit

6

0 5 1 0 1 5 2 0 2 5 3 0- 3 0- 2 0- 1 0

01 02 03 0

Displa

cement

z (mm

)

T i m e t ( s )0 . 7 1 . 0 1 . 3 - 3 0

- 1 5

0

1 5

3 0 B T L G L T L G

0 5 1 0 1 5 2 0 2 5 3 0- 3 0- 2 0- 1 0

01 02 03 0

Voltag

e U (V

)T i m e t ( s )

1 . 1 1 . 3 1 . 5 1 . 7 1 . 9 - 3 0

- 1 5

0

1 5

3 0 B T L G L T L G

0 5 1 0 1 5 2 0 2 5 3 0- 1 8 0- 1 2 0- 6 0

06 0

1 2 01 8 0 d

b

c

T i m e t ( s )

a

Voltag

e U (V

)

T i m e t ( s )6 . 3 6 . 6 6 . 9 - 1 8 0

- 1 2 0- 6 006 01 2 01 8 0 B T L G

L T L G

0 5 1 0 1 5 2 0 2 5 3 0- 1 8 0- 1 2 0- 6 0

06 0

1 2 01 8 0

Voltag

e U (V

)

T i m e t ( s )8 . 1 8 . 3 8 . 5 8 . 7 8 . 9 - 1 8 0

- 1 2 0- 6 006 01 2 01 8 0 B T L G

L T L G

Figure 7: Results of inertial-force fixed-frequency experiment under 10 mmpeak-to-peak excitation: (a) center shaft displacement; (b) open-circuit voltageof piezoelectric components; (c) open-circuit voltage of triboelectric compo-nents on the lower surface; (d) open-circuit voltage of triboelectric componentson the upper surface.

voltage of the triboelectric components of the BTLG reached138.0 V because the nonlinear structure increased the ampli-tude of vibration of the device. And the output power of theBLTG is increased such that it becomes capable of lighting up36 series-connected LEDs (see Supplementary Movie 3).

Experiments have shown that the device can effectively gen-erate electrical energy at low frequencies, even at ultralow fre-quencies below 1 Hz. This low-frequency power generationcharacteristic is especially suitable for energy harvesting oflow-frequency vibrations, such as ocean wave energy. Underexcitation by an inertial force, the working frequency band ofthe device is wider than in the case of a linear system, and, ob-viously, this also increases the energy harvesting efficiency. Thecapability of power generation is greatly improved by workingin a bistable state, especially for the triboelectric components.The bistable motion increases the amplitude of the device atlow frequencies, allowing the triboelectric components to comeinto contact and separate from the nitrile baffle, thereby greatlyincreasing the overall output.

3.4. Practical environmental experiment

In order to prove that the designed BTLG is able to collect thelow-frequency vibrational energy in the practical environment,we use a bicycle to provide random excitation for the device, asshown in Fig. 8. We chose a piece of undulant meadowland toprovide low-frequency vibrational excitation for the BTLG un-der the conditions of riding and pushing, respectively. We mea-sured the vibration data of the riding and pushing process (seeSupplementary S4, S5 and S6), which proved that this environ-mental drive is a low-frequency vibration. Under both experi-mental 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 de-sign.

Figure 8: BTLG installed on a bicycle to collect vibrational energy during cy-cling.

4. Conclusion

A bistable triboelectric linear generator with nonlinear char-acteristics, suitable for broadband energy harvesting in the low-frequency range, has been proposed. Without increasing thestructural complexity, the piezoelectric components is used tocompensate for the defects that the contact-separation mode tri-boelectric nanogenerator cannot work at the small amplitudes.Theoretical analysis has revealed that the device has bistablecharacteristics and that the energy of the bistable contact–separation motion is concentrated within the first harmoniccomponent. Driven directly by low-frequency tension, the de-vice is capable of efficiently generating electrical energy. Evenunder excitation at an ultralow frequency of 0.1 Hz, the devicecan charge a 10 µF capacitor to 0.12 V within 60 s. Under sweptexcitation, the open-circuit voltage of the piezoelectric compo-nents is increased to 157%, with that of the triboelectric com-ponents reaching 138 V. With the proposed BTLG, the work-ing bandwidth is widened to 441% compared with the lineardevice. The bistable vibration significantly improves electric-ity generation performance at low frequencies. This contact–separation bistable structural design, with ultralow operatingfrequency and wide working bandwidth, has potential for a va-riety of practical low-frequency energy harvesting applications,providing a welcome boost to the development of compact andefficient rectilinear motion energy harvesters.

Acknowledgment

The authors appreciate the support of the National Nat-ural Science Foundation of China (Grant Nos. 11872167,51575156, 51675156, 51775164, and 51705122), the Funda-mental Research Funds for the Central Universities (Grant Nos.JZ2017HGPA0165 and PA2017GDQT0024, and Natural Sci-ence Foundation of Anhui Province(1908085J15).

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Huaxia Deng received his B.E. andM.S. degrees from the University of Sci-ence and Technology of China, Hefei,China, in 2004 and 2007, respectively,and the Ph.D. degree from the Universityof Liverpool, Liverpool, U.K., in 2011.

He has been the Hungshan YoungScholar Professor with the School of In-strument Science and Opto-electronics

Engineering, Hefei University of Technology, Hefei, since2012. His current research interests include smart materials andvibration control.

He is the Review Editor of the journal Frontiers in SmartMaterials.

Jingchang Ye received his B.S. de-gree from the School of the mechanicaland electronic engineering, Wuhan Uni-versity of Technology, Wuhan, China, in2017.

He is currently a postgraduate stu-dent in the School of Instrument Scienceand Opto-electronics Engineering, HefeiUniversity of Technology, Hefei, China.His current research interests include en-

ergy harvesting, electric circuit design, and mechanical design.Yu Du received his B.S. degree from

the College of Aerospace Engineering,Nanjing University of Aeronautics andAstronautics, Nanjing, China, in 2015,and M.S. degree from the School of In-strument Science and Opto-electronicsEngineering, Hefei University of Tech-nology, Hefei, China, in 2019.

He is going to study for a Ph.D. de-gree in the School of Electronic Informa-

tion and Electrical Engineering, Shanghai Jiao Tong University,Shanghai, China. His current research interests include energyharvesting, triboelectric nanogenerator, and mechanical analy-sis.

Jin Zhang received his B.E. degreefrom Hefei University of Technology,Hefei, China, in 2005. He received hisM.S. and Ph.D. degrees from TianjinUniversity, Tianjin, China, in 2007 and2010, respectively.

He has been an associate professorat the School of Instrument Scienceand Opto-electronics Engineering, HefeiUniversity of Technology since 2012.

His current research interests include optical measurementtechnology and vibration testing.

Dr. Zhang is a member of Youth Committee of China Instru-ment and Control Society.

Mengchao Ma received his Ph.D. de-gree from the University of Science andTechnology of China, Hefei, China, in2014.

He is currently an associate profes-sor in the School of Instrument Sci-ence and Opto-electronics Engineering,Hefei University of Technology. His cur-rent research interests include artificialcompound eye, structured-light measure-

ment, and dynamic testing.Xiang Zhong received his B.S. degree

from the School of the measurement andcontrol technology and instrument, Tian-jin University, Tianjin, China, in 2008,and the Ph.D. degree in optical engi-neering from Beihang University, Bei-jing, China, in 2016.

He is currently a lecturer in theSchool of Instrument Science and Opto-electronics Engineering, Hefei Univer-

sity of Technology. His current research interests include op-tical fiber sensing and dynamic testing.

9

1.We realized nonlinear bistable contact–separation type TENGs for the first time,

which widen the working bandwidth of the device to 441%.

2.A generator is proposed to harvest the energy of rectilinear motion in ultralow

frequencies below 1 Hz, even at 0.1Hz.

3. The design of hybrid power generation, which compensate the defects that contact-

separation TENG cannot work in the small amplitude with piezoelectric components.

4. Two modes of work for energy harvesting under different environmental vibration

conditions.