nonlinear energy harvesting technology and its applications

Nonlinear Energy Harvesting Technology

and Its Applications

Wang Wei （王炜）

Department of Mechanics

Tianjin University

http://bbs.okhere.net/UploadFile/2005-6/200567153252192.gif

http://bbs.okhere.net/UploadFile/2005-6/200567153252192.gif

• Introduction

• Nonlinear Energy Harvesting Technology

• Applications

• Summary

Outline

2

Background & Key Issues--The rise of the Internet of Things (IoTs)

Substantial increase in usage of IoT edge devices

23 billion battery powered IoT devices in 2025

Periodic charging Life-limited Environmental pollution

Battery

Introduction-Energy Harvesting

Find energy from

the environment

3

Hydro


Solar Wind

Radio Wave

Ambient/waste

energyElectricity Applications

Vibration

Wearable DevicesIndustrial field4

• Light energy (solar energy form sunlight or lamps)

• Thermal energy (human body, industry)

• Radio frequency energy (electromagnetic spectrum, antennas)

• Kinetic energy (motion, vibration, rotation, linear movement)

• Chemical/biological energy (osmose, diffusion, radioisotopes)

• Atmospheric energy (gravity changes, pressure changes etc.)

• Hydro energy (kinetic energy from water)


Electromagnetic

Electrostatic

Piezoelectric

Triboelectric

5


Electromagnetic

Electrostatic

Piezoelectric

Triboelectric

1. How to improve the efficiency of the harvester?

2. Where to use the energy harvesting technology?

Nonlinear energy harvesting

Frequency matching between the harvester and ambient vibrations can be difficult

Linear Nonlinear(narrow operating bandwidth) (larger range of input frequencies)

3. Frequency up-conversion technique

1. Multi-stable nonlinearity

2. Nonlinear force

Nonlinearity


Nonlinear

3. Frequency up-conversion technique

1. Multi-stable nonlinearity

2. Nonlinear force Wider frequency range

Large volume voltage

Nonlinear force Frequency up-conversion Multi-stability

7

Technique Advantages Disadvantages

Monostable • Increased bandwidth when compared with equivalent

linear systems for harmonic excitations

• Frequency for peak response can be shifted away from

the resonant frequency

• Poor performance for random excitations

Bistable • Improved performance for random excitations

• Interwell dynamics result in high amplitude responses

• Interwell oscillations require high excitation

levels

• Design requires prior knowledge of

excitation levels

Tri-stable • Shallower wells than bistable harvester

• Interwell dynamics can be triggered more easily

• More complex configuration and layout


8


B.P. Mann (2008)

(Magnetic levitation)

David A. W. Barton(2010)

(Nonlinear magnetic force + Bistable structure)

ZHIMING LIN (2016)

(Multimodal Nonlinear Magnet)

Williams et al. (2001)

(Membrane structure)

Kluger (2015)

(Cantilever-surface contact)Neiss (2014)

(Tunable + bistable nonlinear structure)

Soliman MSM (2008)

Stopper

(Frequency up-conversion)

Piecewise restoring force

9

Quin-stable（5）

Nonlinear Energy Harvesting Technology – innovation architectures

Multi-stable nonlinearity-- Realization of Tri/Quin-stable nonlinearity

Tri-stable（3）

1. Magnet

2. Stopper

( )

0

m bMZ Z KZ V F Z Z

V V Z

5 3 9 5

12 7 15 9

3.324 10 6.870 10 3.929 10

8.541 10 6.144 10

rF Z Z Z

Z Z

5 3 3

5 3 9 5

3

13 7 16 9

8.245 2.228 10 8 10

44.691 9.601 10 6.553 108 10

1.693 10 1.353 10

r

Z Z Z

F Z Z ZZ

Z x

Tri-stable Quin-stable

The Quin-stable harvester has piecewise-nonlinear restoring force

1. Shallower potential wells

2. Lower excitation threshold

for interwell motion

AIP Advance, 2017

10


1. The QEH has a higher power density, at least 1.7 times higher than

that of the TEH all over its effective bandwidth.

2. The effective bandwidth of the QEH is more desirable than that of

the conventional TEH under the same excitation.

3. The QEH shows promise in low-intensity vibration environment

because of the low energy required to excite the harvesting system to

a high-energy motion orbit.

Multi-stable nonlinearity-- Realization of Tri/Quin-stable nonlinearity1. Magnet

2. Stopper

11


Low-frequency wideband vibration energy harvesting by

using frequency up-conversion and quin-stable nonlinearity

1. Magnet

2. Multi-beams

( 2 ) ( 2 ) 2

d d

d g d g g

mz c z k z mb z d

mz c c z k k z k d mb z d

Piecewise-nonlinear restoring force

5 3 3

2 6 3 10 5

3

13 7 16 9

23.08 4.982 10 9 10

2.517 10 4.869 10 3.093 109 10

7.662 10 6.090 10

r

z z z

F z z zz

z z

MSSP, 2019

12

35 times more powerthan the conventionalcounterpart


Low-frequency wideband vibration energy harvesting by

using frequency up-conversion and quin-stable nonlinearity

1. Magnet

2. Multi-beams

1. By utilizing interwell motions in coupled vibration period, the

defection of generating beam can be easily enlarged to generate

significant amount of output power, i.e., 35 times more power than its

conventional counterpart, within its entire operating bandwidth.

2. The soften effect induced by magnetic force in IQEH could broaden its

operating bandwidth to lower frequencies.

MSSP, 2019

13


Quad-stability using nonlinearity and frequency

up-conversion by cantilever-surface contact

1. Magnet

2. Cantilever-surface contact

The mono-stable to the quad-stable, depending on the combination of the distance parameters (d and h).

MSSP, 2017

14


Quad-stability using nonlinearity and frequency

up-conversion by cantilever-surface contact

1. Magnet

2. Cantilever-surface contact

By utilizing large-amplitude inter-well motions, the cantilever-

surface contact can make the piezoelectric cantilever to generate

significant amount of output power, i.e., 4.2 times more power

than its linear counterpart under a low-intensity vibration.

Meanwhile, the quad-stable nonlinearity can broaden the

operating bandwidth of the harvester to low frequency range.

MSSP, 2017

15


Bistable Electromagnetic Vibration Energy Harvester 1. A bistable membrane energy harvester

2. Nonlinear Galerkin method for the higher-order

nonlinearities.

q t q t q t G q t q t q t F t2 2 3 2 31 2

1 1 1 1 1 1 1 11 11 1 11 1 11 1 1( ) 2 ( ) ( ) ( ) ( ) ( ) cos

2 21st

2 2 3 2 2

1 1 1 1 1 1 1 11 11 1 12 11 1 2 22 11 1 2

2 2 2 3 12 11 21 1 2 12 21 1 2 22 21 2 11 1 21 2

2 3 2211 1 11 12 1 2

( ) 2 ( ) ( ) [ ( ) 2 ( ) ( ) ( ) ( )]

[ ( ) ( ) 2 ( ) ( ) ( )] [ ( ) ( )]2

[ ( ) 3 ( ) ( )2

q t q t q t G q t q t q t q t q t

G q t q t q t q t q t q t q t

q t q t q t

2 2 3

12 11 22 1 2 21 22 2 1

2 2 3 2 2

2 2 2 2 2 2 1 11 12 1 12 12 1 2 22 12 1 2

2 2 2 3 12 11 22 1 2 12 22 1 2 22 22 2 12 1

(2 ) ( ) ( ) ( )] cos

( ) 2 ( ) ( ) [ ( ) 2 ( ) ( ) ( ) ( )]

[ ( ) ( ) 2 ( ) ( ) ( )] [ (2

q t q t q t F t

q t q t q t G q t q t q t q t q t

G q t q t q t q t q t q t

22 2

3 2 2 2 2 3211 12 1 12 22 1 2 12 11 22 1 2 22 2 2

) ( )]

[ ( ) 3 ( ) ( ) (2 ) ( ) ( ) ( )] cos2

q t

q t q t q t q t q t q t F t

2nd

Galerkin method Nonlinear Galerkin method 2 1

) [ )]( (q t f q t

Mechanical model of the EH 16


Nonlinear Galerkin method 2 1

) [ )]( (q t f q t

Bistable Electromagnetic Vibration Energy Harvester 1. A bistable membrane energy harvester

2. Nonlinear Galerkin method for the higher-order

nonlinearities.

F t q t q t G q tq t

G G q t

3 3

2 1 12 1 2 11 12 1 1 11 12 12 2 2 2 2 2

2 1 12 12 2 12 11 22 1 22 2 11 22 1

2 cos ( ) ( ) 2 ( )( )

2 4 [2 ( ) 2 ] ( )

SODF equation is very large and complex Efficient approachStrong nonlinearity

17

Nonlinear Energy Harvesting Technology - Analytical method

Dynamic Frequency Method Construct analytical periodic solutions for the strongly nonlinear systems

Harmonic balance method (HB)

Dynamic Frequency component

2

0 1 2( ) ( , ),u u f u f u u 2

cos ( cos sin )N

n n

n

u b a t a n t b n t

1,0

1,0 1,0 1,1

cos ,

( )sin , ( ) ( ).k

i

ii

u b a t

u a t t t p t

1,0 1,

1

( ) ( )k

i

ii

t p t

2 2 2

0 1 2 3

1 1( ) ( , ) ( )

2 2u E u f u udt f u u udt f t udt

Energy equation

1,0 1,0

1,0

2

1,0

Step 1: balance the constant term

Step 2 : balance the term of sin cos

Step 3 : balance the term

S

,

,

of cos

Step 4 : balance the term of sin ,

te m

,

p 5 : balance the ter of remaining terms.

t or t t

t

t

Only need to balance at most five terms in each order to

find those unknown variables for the periodic solutions 18

Nonlinear Energy Harvesting Technology - Analytical method

,

2 4 5

2 4 5

2 3 2

0 3 0 1 2,1( ( + ) cos)u u u u u u u u F t

Dynamic Frequency Method Construct analytical periodic solutions for the strongly nonlinear systems

Runge-Kutta method (red solid line),

the first order dynamic frequency method (black dotted line),

the second order dynamic frequency method (blue dashed line)

Parameter identification of nonlinear system

( ( ), ( )k kx x

19

The analytical expression is fitted with the value sets from

phase coordinates measured in periodic oscillation of the

nonlinear systems, and the unknown parameters are

identified with the interior-reflective Newton method.

Nonlinear Energy Harvesting Technology – Data driven method

Parameter identification of nonlinear system and its energy harvester applicationParameter identification

Find the phase coordinates

Dynamic Frequency method

least-squares method

( ( ), ( )k kx x

( ( ), ( ))k kx t x t

2 2

1 1

[ ( ) ( )]N N

k k k

k k

R R x t x

Acta Mechanica Sinica, 202020

A Local Sparse Screening Identification Algorithm(LSSI) Extracting nonlinear governing equations from noisy data


Sparse identification nonlinear dynamics algorithm (SINDy) Local linear embedding (LLE)

Most physical systems have only a few relevant terms to

define the dynamics, which made governing equations

sparse in high-dimensional nonlinear function space.

Dimensionality reduction

+ Noisy data handling

CMES, 2020

21


A Local Sparse Screening Identification Algorithm(LSSI)

Obtain the initial variable: the measurement data x

(1) Find the neighbor parameter K for each sample point

(3) Calculate the reconstruction weights matrix ijw

(2) Calculate Linear reconstruction of data X

1. Acquire clean time series

2. Construct basic function ( ( ), ) t tX

3. Solve sparse coefficients Ξ with sparse regression

Choose the optimal solution using the MES method

Determine the optimal governing equation

= Θ( , )t ΞX X

2

| | | | | | | |

Θ( , ) = 1 sin( ) cos( ) sin( ) cos( )

| | | | | | | |

jppt t t ωt ωt

X X X X

= arg min ( ) Θ( ( ), )R

t - t tΞ

Ξ ΞX X

2

( ) Θ( ( ), ) ,1

MES t t tM= - ΞX X

= Ξ 1 2 nξ ξ … ξ

CMES, 2020

22

Basis functions


A Local Sparse Screening Identification Algorithm(LSSI)

The results show that the new algorithm

improves the ability of noise immunity and

optimal parameters identification provides a

desired foundation for nonlinear analyses.

2 2 3 2

0 1 2 1 2 0+ + (( + ) + ( + )) = cos(Ω )0x ω x ε α x α x x β β x εF t

Table 6: Multiple solutions of the experimental

dataset

Ξ 1 x x 3x 2x x cos( )21.4t

1S -0.7702 -1.069×103 -15.8780 9.6068×107 5.8747×107 1.0458

17S 0 411.4801 -6.4302 -9.0418×107 -9.3898×106 0.3983

95S 0 524.2199 3.6873 -3.6366×108 -9.0408×106 0.2940

CMES, 2020

23

Developed an all-in-one on-rotor electromagnetic EH

Nonlinear Energy Harvesting Technology – Applications

On-rotor electromagnetic energy harvester

With the design of the counterweight, the coils and

magnets can perform relative motion which can

produce induced voltage in the coils.

The proposed harvester (a) Charging a 3.7V

250mAh Lithium battery, (b) supplying the smart

watch, temp/humidity, calculator and LEDs (c)

powering a commercial Bluetooth sensor.

The harvester can be simplified into a friction pendulum

2 2 2 2 2

0 sin mc ml T ml cΩ ml gr l

Kinetic Energy of Rotation

24

counterweight


Yang, 2012

(Self-Powered Magnetic Sensor Based on a Triboelectric Nanogenerator)

Wearable Devices

Flexibility

Lightweight

Easy processing

Great performance

Triboelectric Nanogenerator （TENG）

25


A low-frequency, broadband and tri-hybrid energy harvester with septuple-stable nonlinearity-enhanced mechanical frequency up-conversion mechanism for powering portable electronics Nano Energy, 2019

26

(a) the magnetic spring force

(b) the restoring force of the piezoelectric units

Experimental setup of the electrodynamic shaker test



27


1. Enhance the output performance of the

frequency up-conversion via inter-well

motions

2. Offer a wide and highly efficient

operating bandwidth at low acceleration

via the combination of resonant inter-well

oscillation behavior and non-resonant

behavior.


28

Summary

Challenges

Multi degrees of freedom system

Power harvesting circuit

New material

Methodologies

Promising technique to power electronic devices

Wide frequency range and increase power output

Energy harvesting + Health Monitoring

MDOF

SMFE(synchronized magnetic flux extraction)

TENG(Triboelectric nanogenerator)

(Rim-mounted tire pressure monitoring system)

29

Publications

1. Parameter identification of nonlinear system via a dynamic frequency approach and its energy harvester application[J].

Acta Mechanica Sinica, 2020, 36(3): 606-617.

2. A low-frequency, broadband and tri-hybrid energy harvester with septuple-stable nonlinearity-enhanced mechanical

frequency up-conversion mechanism for powering portable electronics [J]. Nano Energy, 2019, 64.

3. A nonlinear multi-stable piezomagnetoelastic harvester array for low-intensity, low-frequency, and broadband

vibrations[J]. Mechanical Systems and Signal Processing, 2019, 112: 87-102.

4. Dynamic modeling and structural optimization of a bistable electromagnetic vibration energy harvester [J]. Energies,

2019, 12(12).

5. Optimization of galloping piezoelectric energy harvester with v-shaped groove in low wind speed [J]. Energies, 2019,

24(12).

6. A low-frequency, wideband quad-stable energy harvester using combined nonlinearity and frequency up-conversion by

cantilever-surface contact [J]. Mechanical Systems and Signal Processing, 2018, 112: 305-318.

7. Low-frequency wideband vibration energy harvesting by using frequency up-conversion and quin-stable nonlinearity [J].

Journal of Sound and Vibration, 2017, 399: 169-181. 30

1. The National Natural Science Foundation of China, The strongly nonlinear dynamic analysis and

structure optimization of a membrane type vibration energy harvester, 11772218, 2018.01-2021.12

2. The National Natural Science Foundation of China, Study on the complex dynamics of piezoelectric

vibration energy harvesters with strongly nonlinear coupled arrays, 11872044，2019.01-2022.12

3. China-UK NSFC-RS Joint Project, Development of an innovative hybrid piezo-electromagnetic energy

harvester for self-powered monitoring system of railway vehicles, 11911530177, 2019.01-2021.03

4. Tianjin Research Program of Application Foundation and Advanced Technology, The

methodologies to research the key issues in designing a kind of electromagnetic vibration energy

harvester basing on the strongly nonlinear oscillation method, 17JCYBJC18900. 2017.04-2020.03

Funds

31

Research Group

Wang Wei

Wang Zhixia Liu Cheng

Li Jiacheng Liang SinanDing Bei Li Mingyu

Zhao Kaiyuan Oliver

32

Thank You!

Q & A

Email: [email protected]

Wechat:

33


Multi-stable nonlinearity-- Realization of Multi-stable nonlinearity1. Magnetic

2. More Stopper

1

( )

0

c r b

p

mz F F v mz t

C v vR z

3

1 3 1

3 9

1 3 9 1 2

3 2 1

1 3 2 1 3

r

n

n

a z a z z z

F b z b z b z z z z

p z p z p z z z

Piecewise-nonlinear restoring force34


Multi-stable nonlinearity-- Realization of Multi-stable nonlinearity1. Magnetic

2. More Stopper

35

nonlinear energy harvesting technology and its applications

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