論文 / 著書情報
Article / Book Information
題目(和文)
Title(English)

Design and Development of Vibration Energy Harvesters using TunedMass Systems for Bridge Structures

著者(和文)

竹谷晃一

Author(English)

Kouichi Takeya

出典(和文)

学位:博士(工学),学位授与機関:東京工業大学,
報告番号:甲第10481号,
授与年月日:2017年3月26日,
学位の種別:課程博士,
審査員:佐々木 栄一,廣瀬 壮一,WIJEYEWICKREMA ANIL,北詰 昌樹,岩波 光保,小林 裕介

Citation(English)

Degree:Doctor (Engineering),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第10481号,
Conferred date:2017/3/26,
Degree Type:Course doctor,
Examiner:,,,,,

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Tokyo Institute Research Repository)

Doctoral Dissertation

Design and Development of Vibration
Energy Harvesters using Tuned-Mass Systems
for Bridge Structures

Tokyo Institute of Technology
Department of Civil Engineering
Supervised by Eiichi SASAKI

Kouichi TAKEYAi

Contents

List of Figures ................................................................................................................... v
List of Tables ................................................................................................................... xi
Acknowledgements .......................................................................................................... xii
Abstract............................................................................................................................. 1
1. Introduction ................................................................................................................... 1
1.1.

Background .......................................................................................................... 2

1.2.

Purpose and Objectives ......................................................................................... 4

1.3.

Related Research .................................................................................................. 4

2. Investigation on Characteristics of Electro-Mechanical Systems .................................... 13
2.1.

Overview ........................................................................................................... 14

2.2.

Theoretical Explanation of Single-Mass and Dual-Mass Systems .......................... 15

2.2.1.

Single-Mass Vibration Energy Harvesters .................................................... 15

2.2.2.

Dual-Mass Vibration Energy Harvesters ...................................................... 18

2.3.

Comparison between Single-Mass and Dual-Mass Systems .................................. 19

2.4.

Summary ............................................................................................................ 20

3. Proposal of Tuning Design Method ............................................................................... 31
3.1.

Overview ........................................................................................................... 32

3.2.

Effect of Parameters on Energy Harvesting in Dual-Mass Systems ....................... 32

3.3.

Multi-Physics Parameter Design Method for Power Generation ............................ 35

3.4.

Multi-Physics Parameter Design Method for Energy Storage ................................ 37

3.5.

Summary ............................................................................................................ 39

4. Trial Applications of TMG to an Actual Bridge ............................................................. 49
4.1.

Overview ........................................................................................................... 50

4.2.

Target Power Generation and Application Procedure ........................................... 50

4.3.

Target Vibration Frequency and Installation location ........................................... 51ii

4.3.1.

Detection of Natural Vibration Frequency of the Trial Bridge....................... 52

4.3.2.

Decision of the TMG Installation Location .................................................. 52

4.4.

Modal Mass and Damping ................................................................................... 53

4.4.1.

Modal Equivalent Masses ............................................................................ 53

4.4.2.

Modal Damping Ratio ................................................................................. 54

4.5.

Determination of Characteristics of TMG ............................................................ 54

4.5.1.

Mechanical Damping Characteristics of TMG .............................................. 54

4.5.2.

Mechanical Coil Spring Characteristics of TMG .......................................... 55

4.5.3.

Electric Characteristics of Power Generator ................................................. 55

4.5.4.

Electromotive Force Coefficient: k emf ........................................................... 56

4.5.5.

DC Resistance of the Internal Coil: r ........................................................... 56

4.5.6.

Inductance of the Internal Coil: L ................................................................ 57

4.6.

Parameter Design ............................................................................................... 57

4.7.

Application of TMG to the Trial Bridge .............................................................. 58

4.7.1.

Experiment for Power Generation ................................................................ 58

4.7.1.1. Target Frequency of 14.2 Hz.................................................................... 59
4.7.1.2. Target Frequency of 6.1 Hz ..................................................................... 59
4.7.2.

Experiment for Charging Batteries using Harvested Energy .......................... 59

4.7.2.1. Target Frequency of 14.2Hz ..................................................................... 60
4.7.2.2. Target Frequency of 6.1 Hz ..................................................................... 61
4.7.3.

Efficiency of Power Generation ................................................................... 62

4.7.4.

Vibration Energy ........................................................................................ 62

4.8.

Summary ............................................................................................................ 63

5. Efficiency Enhancement of Power Generators for Energy Harvesting ............................. 85
5.1.

Overview ........................................................................................................... 86

5.2.

Design Concept .................................................................................................. 87

5.2.1.

Analysis Model ........................................................................................... 87

5.2.1.1. Analysis Accuracy and Analysis Time...................................................... 87
5.2.2.

Target Design Parameters ............................................................................ 89

5.2.2.1. Electromotive Force Coefficient .............................................................. 89
5.2.2.2. Maximum Electric Damping Coefficient .................................................. 90
5.2.2.3. Magnetic Spring Force Effect .................................................................. 91

iii

5.3.

Design of Power Generator ................................................................................. 91

5.3.1.

Parameter Design Method of Power Generator ............................................. 92

5.3.2.

Iteration Procedure ..................................................................................... 93

5.3.3.

Design of Power Generator ......................................................................... 93

5.4.

Experimental Evaluation ..................................................................................... 94

5.4.1.

Electromotive Force Coefficient k emf ............................................................ 94

5.4.2.

Dynamic Friction Force .............................................................................. 95

5.4.3.

Magnetic Spring ......................................................................................... 96

5.4.4.

Design of TMG ........................................................................................... 96

5.5.

Summary ............................................................................................................ 97

6. Proposal of Uses of the Developed Energy Harvesting System ..................................... 110
6.1.

Overview ......................................................................................................... 111

6.2.

Application of TMG Systems ............................................................................ 111
6.2.1.

6.3.

Target Power for Monitoring Systems of Bridge Structures ..................... 111

Experimental Application of TMG Systems for Health monitoring systems of Bridge

Structures .................................................................................................................. 113
6.3.1.

Experiment for Power Generation .............................................................. 113

6.3.2.

Application TMG to A Monitoring System of Bridge Structure ................... 113

6.3.3.

Evaluation of Energy Harvesting in Long-Term Uses ................................. 115

6.4.

Summary .......................................................................................................... 117

7. Conclusions ............................................................................................................... 124
Recommendations .......................................................................................................... 128
References ..................................................................................................................... 129

iv

List of Figures

Chapter 1: Introduction
Figure 1.1: Configuration for a power generator consisted of a ball screw ················· 11
Figure 1.2: Configuration for a transverse flux linear motor (TFLM) with full
permanent magnet ···································································· 11
Figure 1.3: Configuration for an electromagnetic power generator using a coil andmagnet array ·········································································· 11
Figure 1.4: Flow of this dissertation ····························································· 12

Chapter 2: Investigation on Characteristics of Electro-Mechanical Systems
Figure 2.1: Analysis model of single mass systems ············································ 22
Figure 2.2: Electric circuit ········································································ 22
Figure 2.3: Harvesting power Wmax response of single mass systems with various
electric damping ratios (0 ≤ ζe ≤ 5) ················································ 23

Figure 2.4: Bridge vibration displacement Xmax response of single mass systems

with various electric damping ratios (0 ≤ ζe ≤ 5) ································· 23

Figure 2.5: Harvesting power Wmax response of single mass systems in different

electric damping ratios (ζe = 0.01, 0.03, 0.05) ···································· 24
Figure 2.6: Bridge vibration displacement Xmax response of single mass systems
with different electric damping ratios (ζe = 0.01, 0.03, 0.05) ··················· 24
Figure 2.7: Analysis model of dual-mass systems ·············································· 25
Figure 2.8: Harvesting power Wmax responses of dual-mass systems with various
electric damping ratios (0 ≤ ζe ≤ 5) ················································ 26

Figure 2.9: Bridge vibration amplitude Xmax responses of dual-mass systems withvarious electric damping ratios (0 ≤ ζe ≤ 5) ······································· 26v

Figure 2.10: Harvesting power Wmax responses of dual-mass systems with different
electric damping ratios (ζe = 0.01, 0.03, 0.05) ···································· 27
Figure 2.11: Bridge vibration amplitude Xmax responses of dual-mass systems withdifferent electric damping ratios (ζe = 0.01, 0.03, 0.05) ························· 27
Figure 2.12: Harvesting power responses of single-mass systems with different
frequency ratio ········································································ 28
Figure 2.13: Harvesting power responses of dual-mass systems with different
frequency ratio ········································································ 28
Figure 2.14: Vibration amplitude responses of single-mass systems with different
frequency ratio ········································································ 29
Figure 2.15: Vibration amplitude responses of dual-mass systems with different
frequency ratio ········································································ 29
Figure 2.16: Tuning of harvesting power responses of dual-mass systems withsecond mass ratio and frequency ratio ············································· 30
Figure 2.17: Vibration amplitude responses of dual-mass systems with second mass
ratio and frequency ratio ···························································· 30

Chapter 3: Proposal of Tuning Design Method
Figure 3.1(a): Energy flow model of bridge-TMG system ······································ 41
Figure 3.1(b): Energy flow of TMG with a dual-mass system on the bridge ················· 41
Figure 3.2: Distribution of harvesting power responses of the dual-mass system forvarious combinations of γ2 and 𝜁𝜁𝑒𝑒 ·················································· 42

Figure 3.3: Harvesting power responses of the dual-mass system for different

combinations of γ2 and 𝜁𝜁𝑒𝑒 ··························································· 42

Figure 3.4: Distribution of harvesting power responses of the dual-mass system forvarious combinations of 𝛾𝛾1 and 𝜇𝜇2 ·················································· 43

Figure 3.5: Harvesting power responses of the dual-mass system for different

combinations of 𝛾𝛾1 and 𝜇𝜇2 ··························································· 43

Figure 3.6: Objective and constraint functions of the proposed parameter design
method and frequency responses of power generation in dimensionlessform ···················································································· 44
Figure 3.7: Flow of the multi-physics parameters design method ···························· 45viFigure 3.8(a): 3D view of distribution of amplitude of 𝑊𝑊 with variations of threedesign parameters γ1 , γ2 and ζe ··················································· 46(b): 2D view of distribution of amplitude of 𝑊𝑊 with variations of threedesign parameters γ1 , γ2 and ζe ···················································· 46

Figure 3.9: Electric circuit for charging························································· 47
Figure 3.10: Flow of the multi-physics parameters tuning method for energy storage ······ 47
Figure 3.11(a): 3D view of distribution of amplitude of Wrms under variations of
three design parameters γ1 , γ2 and Br ·········································· 48(b): 2D view of distribution of amplitude of Wrms under variations of
three design parameters γ1 , γ2 and Br ··········································· 48

Chapter 4: Trial Application of TMG to an Actual Bridge
Figure 4.1: Flow of the study on application of TMG ········································· 65
Figure 4.2: Trial bridge and installation location of TMG and accelerometers ············· 65
Figure 4.3: Frequency spectrum of acceleration of bridge ···································· 66
Figure 4.4(a): Bridge vibration mode at 1.5 Hz ·················································· 66(b): Bridge vibration mode at 3 Hz ···················································· 66(c): Bridge vibration mode at 6 Hz ···················································· 67(d): Bridge vibration mode at 9 Hz ···················································· 67(e): Bridge vibration mode at 12 Hz ·················································· 67
Figure 4.5: N-degree of freedom model in i-order modal vibration ·························· 68
Figure 4.6: Developed TMG and the electromagnetic power generator ······················ 68
Figure 4.7: Analysis model of TMG and bridge system ······································· 69
Figure 4.8: Setup of TMG on an excitation machine ··········································· 70
Figure 4.9: Electric circuit for power generation ··············································· 71
Figure 4.10: Electric circuit for evaluation of DC resistance of the internal coil ofthe power generator ·································································· 71
Figure 4.11: Electric circuit for evaluation of self-inductance of the internal coil ofthe power generation ································································· 71
Figure 4.12: Electric circuit model used in the experiment ····································· 72
Figure 4.13: Generated electric energy and traffic per hour(target frequency: 14.2 Hz) ························································· 73vii

Figure 4.14: Generated electric energy and traffic per hour(target frequency: 6.1 Hz) ·························································· 73
Figure 4.15: Charging circuit ······································································ 74
Figure 4.16(a): Setup of the charging circuit with a super capacitor array used in
the experiment ···································································· 75
Figure 4.16(b): Discharge characteristic curve of the super capacitor array ·················· 75
Figure 4.17: Storage electric energy and hourly traffic (target frequency: 14 Hz) ··········· 76
Figure 4.18: Storage electric energy and hourly traffic (target frequency: 6.1 Hz) ·········· 76
Figure 4.19: Generated voltage by TMG ························································· 77
Figure 4.20: Bridge acceleration measured at 18m from the bridge start at the
installation location of TMG ························································ 77
Figure 4.21: Generated power by TMG ··························································· 78
Figure 4.22: Energy flow in the bridge-TMG vibration system ································ 78
Figure 4.23: Energy flow of each vibration mode in the TMG-bridge vibration system························································································· 79
Figure 4.24: Summation of band-pass filters that was used in the modal analysis ofenergy flows ·········································································· 81
Figure 4.25(a): Hourly traffic of large vehicles between 8 th and 9 th November 2014········ 82(b): Hourly distribution of bridge vibration energy between 8 th and 9 thNovember 2014 ··································································· 82(c): Distribution of total bridge vibration energy between 8 th and 9 thNovember 2014 ··································································· 82
Figure 4.26(a): Hourly traffic of large vehicles between 25 th to 26 th November 2014 ······ 83(b): Hourly distribution of bridge vibration energy between 25 th to 26 th
November 2014 ··································································· 83(c): Distribution of total bridge vibration energy between 25 th to 26 th
November 2014 ··································································· 83
Figure 4.27(a): Hourly traffic of large vehicle between 17 th to 18 th November 2015········ 84(b): Hourly distribution of bridge vibration energy between 17 th to 18 th
November 2015 ··································································· 84(c): Distribution of total bridge vibration energy between 17 th to 18 th
November 2015 ··································································· 84

viii

Chapter 5: Efficiency Enhancement of Power Generators for Energy Harvesting
Figure 5.1: A model electromagnetic power generator ········································ 98
Figure 5.2: Analysis model of power generator with 2D axial symmetric model ··········· 98
Figure 5.3: Nonlinear characteristic of relative permeability of yokes (steel: SS400)························································································· 99
Figure 5.4(a): Entire view of the analysis model ··············································· 100(b): A closer view of the analysis model ············································ 100(c): Entire view of the moving part and the fixed part of the analysis model ··· 100
Figure 5.5: Element division of the most accurate Finite Element model ·················· 101
Figure 5.6: Finite Element model of a power generator ······································ 101
Figure 5.7: Relationship between analysis accuracy for voltage generation andrelative tolerance of various FE models ·········································· 102
Figure 5.8: Relationship between analysis time and relative tolerance of various FEmodels ················································································ 102
Figure 5.9: Relationship between analysis accuracy and relative tolerance in thecase of two different absolute tolerances ········································· 103
Figure 5.10: Relationship between analysis time and relative tolerance in the case of
two different absolute tolerances ·················································· 103
Figure 5.11: Electromotive force coefficients verses displacement for various
combination of parameters for multi-objective functions ······················· 105
Figure 5.12: Power generator and equipment of experimental evaluation test using an
excitation machine ·································································· 106
Figure 5.13: Displacement applied to the moving part, velocity of the moving part,and induced voltage signal of the power generator in the experimental
evaluation test ······································································· 106
Figure 5.14: Electromotive force coefficients of displacement in the experimental
evaluation test ······································································· 107
Figure 5.15: Relationship between force and position of the moving part of the power
generator ············································································· 107
Figure 5.16: Relationship between friction force and position of the moving part ofthe power generator in the experimental evaluation test ························ 108
Figure 5.17: Relationship between magnetic spring force and position of the movingixpart of the power generator in the experimental evaluation test ··············· 108
Figure 5.18: Analysis model of bridge-TMG system using nonlinear characteristicsof the developed power generator and friction forces ··························· 109

Chapter 6: Proposal of Uses of the Developed Energy Harvesting System
Figure 6.1: Example of health monitoring device (wireless data transmission, 3-axis
MEMS accelerometers, voltage sensor, temperature and humidity
sensors) ··············································································· 117
Figure 6.2: Experimental result of the hourly harvested energy from bridge
vibrations of the trial bridge ······················································· 118
Figure 6.3: Charging circuit using lithium-ion batteries and schottky barrier diodes(SBD) ················································································· 119
Figure 6.4: Comparison of voltage drop of lithium-ion batteries and a super
capacitor ·············································································· 119
Figure 6.5: Proposed continuous health monitoring system suppling harvested
energy ················································································ 120
Figure 6.6: Battery voltage – time with supplying electricity to the monitoring
system ················································································ 120
Figure 6.7: Evaluation of harvested energy (numerical analysis) ··························· 121
Figure 6.8: Evaluation procedure of long-term electric energy harvesting ················· 121
Figure 6.9: Evaluation of long-term electric energy harvesting based on the
numerical analysis··································································· 122xList of Tables
Chapter 4: Trial Application of TMG to an Actual Bridge
Table 4.1:

Natural frequency in each vibration mode of bridge and equivalent massat installation location of TMG ··················································· 68

Table 4.2:

Tuning parameters for 14.2 Hz vibration mode ··································· 71

Table 4.3:

Tuning parameters for 6.1 Hz vibration mode ···································· 71

Table 4.4:

Power consumption of general monitoring devices of bridge
structures and power supply ratio by TMG ···································· 74

Chapter 5: Efficiency Enhancement of Power Generators for Energy Harvesting
Table 5.1: Relative permeability of each material of the power generator, magnetic
flux density of the neodymium magnet, and coil turns for Finite Element
Analysis ·············································································· 99
Table 5.2: Initial value of dimensional parameters of the power generator andlimitations ············································································· 104
Table 5.3: Two different design objective functions F opt and the identified
dimensional parameters of the power generator ··································· 104
Table 5.4: Designed dimensional parameters of the power generator ······················· 105

Chapter 6: Proposal of Uses of the Developed Energy Harvesting System
Table 6.1: Required energy for monitoring plans ·············································· 117
Table 6.2: P arameters of the analysis model of Bridge – TMG system ·····················118
Table 6.3: Unit energy harvesting per large vehicle and evaluated long-term
harvested energy (average in 5 weeks) ············································· 122
Table 6.4: Evaluation of power supply in each monitoring plan ····························· 122xiAcknowledgements

I wish to express my deepest gratitude to my supervisor, Associate Professor Eiichi
Sasaki for his very kind supports, advices and encouragements. I am thankful for his
aspiring guidance, invaluably constructive criticisms and friendly advices during the
research work. A special gratitude I give to Professor Chitoshi Miki for his very kind
supports, stimulating suggestions and encouragement.
I wish to express my gratitude to Associate Professor Yusuke Kobayashi, Dr.
Atsushi Tanabe and Dr. Hisatada Suganuma for his accurate advice and kindencouragements. I am sincerely grateful to them for their truthful and constructive
views on a number of issues related to this research. I would like also to thank sincerely
Assistant Professor Hiroshi Tamura for his kind support, very friendly advices andencouragements.
Furthermore, I would like to mention about the support by NEXCO Co., LTD. My
research works were financial supported by NEXCO Co., LTD. Furthermore, themember of NEXCO Co. gave me useful information and suggestions. Especially, I
would like to thank Mr. Osafune, Mr. Kanno and Mr. Iwabuki. I would also like tomention about the support by E-stir Co. LTD., Scraft Co. LTD. and ITM Co. LTD. In
order to develop electro-mechanical systems, I had technical help from them.
Especially, I would like to thank Mr. Akazawa from E-stir Co., LTD., Mr. Hagiuda and
Mr. Kato from Scraft Co. LTD. And Mr. Kataoka from ITM Co., LTD. I wish to express
my gratitude to Mr. Kato, Mr. Hiyama, Mr. Hasegawa and Mr. Itami from Tokkyokiki
Co., LTD. I would also like to thank to Mr. Nagoya and Mr. Arita from Subaru Co.,LTD and President Sonobe from Sinwa-technos for their help of field experiments.
A special thanks goes to Ms. Ishihara and Ms. Hamada for her support in nonresearch field. They helped many office works. I would like to great thank PhD.

xii

students Ms. Akutsu for her kind advice. She gave me useful view and remarks of myresearch works. It was good experience for me to help her research work. I learned
many things from assisting her work and discussion with her. I wish to thank ourlaboratory members, Mr. Ando and Mr. Iizuka. It was good experience for me to help
their research works. Mr. Itami friendly came to help my field experiment. PhD.
student Mr. Natdanai gave me advices on my research works, and experiments. It wasgood experience for me to discuss on our research works with PhD. students Mr. Caoand Ms. Tuttipongsawat, Mr. Tominaga, Mr. Ota and Mr. Mishima.
I wish to special great thank Ms. Scorupski for her advice about my research work
and English. She gave me useful view and remarks of my research works. Furthermore,
I would like to thank our graduated laboratory members, Mr. Umekawa, Mr. Navicus,
Mr. Ueda, Mr. Kanamori and Mr. Ebisawa for their kind help and friendship. Especially,
I learned many things from assisting their research work and discussion with them.
Finally, I would like to thank to my parents Ms. Akiko and Mr. Shinichi Takeya
and my grandfather Mr. Shoji Takeya for their long support and understanding.

xiii

Abstract

A method to harvest bridge vibration energy has been proposed in this paper using
a tuned mass damper system, named hereafter Tuned Mass Generator (TMG). To
harvest and make use of the unused reserve of bridge vibration energy the
aforementioned damper system absorbs, a linear electromagnetic power generator has
been applied. The benefits of using dual-mass systems over single-mass systems for
power generation have been clarified according to the theory of vibrations. TMG
parameters have been determined considering multi-physics parameters, and TMG has
been tuned using a newly proposed parameter design method. Theoretical andnumerical analysis results have found that for effective energy harvesting, it isessential that TMG has robustness against uncertainties in bridge vibrations and tuning
errors, and TMG has demonstrated this feature when it was applied to an actual bridge.
In addition, the design procedure of the TMG system, including the health monitoring
system, has been proposed and the ability for continuous health monitoring has been
demonstrated.

Keywords: bridge vibration; energy harvesting; tuned mass damper;
electromagnetic power generator, efficiency.

1

Chapter 1
Introduction

Abstract .
Vibration-based energy harvesting has been studied in various fields and one
area of growing interest is the potential for this harvested vibration energy tosupply electric power to wireless sensing devices, or other intelligent systems,
for the health monitoring of bridges. An energy harvester, using a tuned dualmass damper system and electromagnetic power generator, named hereafter
Tuned Mass Generator (TMG), has subsequently been proposed.

11.1. Background
The importance of managing aging infrastructure has become of great concern inrecent years, hence it is urgently required that effective maintenance management of
infrastructures is established. One useful method is to monitor the dynamic behaviorof structures, especially the vibrations of bridge structures [1-6]. However, due to thecritical problem of continuous power supply required for monitoring, effective
maintenance management has yet to be achieved. To supply electric power tomonitoring sensing devices, vibration-based energy harvesting has become one area ofgrowing interest and has been studied in various fields [7-9]. There is also the prospectfor harvesting energy from large scale structures [10-17].
To date, tuned mass damper or shock absorbing damper systems [18-20] have beenstudied to control bridge vibration which causes damage or noise. Considering thesestudies, tuned mass damper systems could, in particular, satisfactorily control bridge
vibration when an ideal dynamic balance is achieved between its mass, springs anddampers [21-27]. If a power generator (or transducer) replaced the damper in a tuned
mass damper system and could successfully absorb bridge vibration energy, it would
have the capacity to harvest energy and control bridge vibration simultaneously.
However, one problem of harvesting energy from bridge vibration is that the natural
frequency of bridges is generally much lower than the mechanical vibrations whichhave so far been the main target of energy harvesting.
In recent years, harvesting energy from low frequency vibrations [13] or supplying
harvested energy to monitoring systems has been studied using building model
structures [14], yet the amplitude of the target vibration in these cases is much higher
than that of bridge vibration. In the case of bridge structures, the damping effect ofelectric power generators decrease in low frequency ranges, and as a result, theefficiency of energy harvesting or vibration control decreases. One solution to thisproblem could be to apply high performance power generators with large electric
damping.
Many types of transduction mechanisms have already been developed to increase
the efficiency of power generation, such as electromagnetic power generators using
ferromagnetic devices [7,12,28-31], piezoelectric power generators using piezoelectric2ceramics [32-34], or even electrets [35-39]. Among these many new developments,
electromagnetic power generators can, in particular, generate high electric power andproduce large damping forces; it is thus considered that high performanceelectromagnetic power generators can produce enough electric damping for harvestingenergy from even low frequency bridge vibrations [40-43]. However, the power
generation level obtained from bridge vibrations has been around micro-watt to milliwatt and is not still satisfied to monitor dynamic behavior of bridge structures.
Another problem concerning harvesting energy from bridge vibration is that thenatural frequency of bridges is uncertain due to many factors, including traffic
conditions and temperature [4,44-51]. However, the performance of tuned mass damper
systems is highly sensitive, and can drop with the slightest change in frequency when
the forced excitation frequency is near the effective frequency. In other words, tuned
mass damper systems have a narrow target frequency range, and have low robustness
against changes in vibration frequency [52].
One approach that has been proposed to reduce this sensitivity is to apply muchhigher damping than theoretically designed [53]. However, increasing the damping
reduces the performance of tuned mass dampers, and vice versa, hence various
parameter design methods have been proposed depending on the desired peak value ofdisplacement for a given bridge [54-56]. There are parameter design methods thatconsider how the balance between robustness and the peak value of displacement canbe adjusted through evaluation functions or band width parameters, and using multiple
tuned mass dampers to improve this balance has also been investigated [57-65]. Still,further investigation is required to implement these various design parameters, due tothe limitations of weight and accuracy when assembling these tuned mass dampers,
including tuning errors, and these factors have been considered in this study. A further
difficulty of the aforementioned parameter design methods is that they have beendeveloped considering vibration control only; hence they cannot be applied directly toenergy harvesting. In several studies, tuning methods for energy harvesting were
proposed considering mechanical systems and electric circuits of energy harvesters[66,67]. Yet, these methods were found to be insufficient for efficient energy
harvesting, since the performance of electromagnetic transducers should also be
designed considering harvested energy from vibration of bridge structures.

3

1.2. Purpose and Objectives
To solve the aforementioned difficulties surrounding the energy harvesting frombridge structural vibrations, and achieve continuous health monitoring systems ofbridges, the purpose of this study is to design and develop an efficient energy harvester
to capture energy from vibrations of bridge structures. To achieve the purpose, anenergy harvester using a tuned mass system and electromagnetic power generator (ortransducer) is developed, named hereafter Tuned Mass Generator (TMG), which canthen lead to continuous health monitoring systems of bridge structures. To be specific,
efficiency enhancement of the TMG system is considered to achieve the energy
harvesting from low frequency and uncertain bridge vibrations. To satisfy the aim ofenergy harvesting to obtain various required electricity for health monitoring such as
dynamic behavior of bridge structures, efficient electromechanical structure design of
TMG is required and maximum power generation should be higher than one watt, in
brief, watt order. To achieve the aforementioned purpose, the following research
objectives are considered.
I.

Investigation of the structural characteristics of energy harvesters

II. Proposal of a parameter design method for effective energy harvesting
III. Evaluation of the applicability of TMG to an existing bridge
IV. Enhancement of a power generators efficiency
V. Development of a TMG system that includes a health monitoring system of bridge
structures

1.3. Related Research
1.3.1. Health monitoring for Bridge Structures
Aging of infrastructure including bridges has rapidly progressed over the past
decade [68], and so the importance of infrastructure management has become of great4

importance. Moreover, it is vital to recognize the condition of structures as soon as
possible when abnormal events such as earthquakes occur. However, due to the decline
in engineers and the limitation of available finance, sufficient inspection andmaintenance methods have become difficult to carry out. To solve the aforementioned
problems surrounding infrastructure, it is urgent to construct an effective maintenancemanagement method to supplement the inspections that are being carried out byengineers.
One constructive maintenance management method is to monitor the dynamic
behavior of structures, especially the vibrations of bridge structures, and so far various
studies have been carried out [1-3]. Bridge structures are greatly affected by various
dynamic traffic loads, such as heavy vehicles. Miki et al. [4] has established amonitoring system for the dynamic behavior of bridge structures such as by using
accelerometers and displacement sensors. In addition, long-term operation of themonitoring system was carried out to inspect abnormalities in bridge structures andtraffic conditions of large vehicles, and to detect damages quickly after disasters.
Fukada et al. [5] carried out long-term monitoring of structural dynamic behaviors ofa bridge to inspect the dynamic stress of the bridge girders and the total weight oftrucks typically crossing a bridge.
As identified in these researches, the importance of health monitoring systems ofbridge structures has been demonstrated, in particular, the long-term monitoring ofdynamic structural behaviors. However, due to the critical problem of supplying
continuous power to monitoring systems, the long-term health monitoring of bridge
structures is currently limited. Nonetheless, vibration-based energy harvesting has thepotential for using the harvested vibration energy to supply electric power for thehealth monitoring of bridges [8].

1.3.2. Structural Design of Energy Harvester
Environmental vibration power generation is performed by converting mechanicalenergy from vibrations into electric energy using a power generator. The conversion
efficiency highly depends on the power generation system and the vibration conditions.
Among the various conversion systems, such as electromagnetic power generators
using ferromagnetic devices [7,12,29-31], piezoelectric power generators using5

piezoelectric ceramics [32-34], or even electrets [35-38], piezoelectric andelectromagnetic devices have an advantage of higher electrical power generation withsimple implementation. Arroyo et al. investigated piezoelectric and electromagnetic
vibration energy harvesters using normalized models [69]. Three parameters wereconsidered in the normalized models, namely the coupling coefficient, loss coefficientand mechanical quality factor. Based on the findings in experiments and a theoretical
study regarding piezoelectric and electromagnetic generators, it was determined that
although electromagnetic generators demonstrate high resistive losses, this iscompensated by high coupling coefficients. In addition, it was notably shown that thepower density of an electromagnetic generator does not decrease in proportion to its
volume as it is commonly observed. However, the power generation obtained is still
low for efficient energy harvesting from vibrations of bridge structures.
Most researches on energy harvesting have been focused on vibration
characterized by frequencies above 10Hz and below milli-watt power [7-17]. In
contrast, the fundamental vibration frequency of large-scale structures, such as highrise buildings or bridges, is typically around 1Hz. Since large-scale energy is expectedin these vibrating structures [70,71], power generators to harvest this vibration energy
must be capable of extracting large power from low-frequency and low-velocity
oscillations.
Cassidy et al. proposed an electromagnetic power generator for harvesting energy
from large structures such as high-rise buildings or bridges [72]. To obtain large power
generation, a ball screw coupled with a permanent-magnet synchronous machine wasused in the proposed power generator (Figure 1.1). To evaluate this devices energy
harvesting capability, impedance matching theory [73-75] was used, and the ability of
harvesting energy was experimentally demonstrated. Although large power generation
could be obtained, large power losses were also distinguished.
Other approaches to obtain large power generation density include using theTransverse Flux Linear Motor, namely TFLM (Figure 1.2) [76], or using a magnet
array [77]. TFLM is a type of linear motor with high power per volume since themagnetic circuit is separated from the electric circuit, and high thrust force density is
obtained due to flux concentration [78-84]. To acquire higher power per volume,
Hoang et al. considered several types of TFLM devices with various configurations of6

the permanent magnet using the equivalent magnetic circuit network method [76].
However, disadvantages of TFLM such as mechanical loss including cogging andefficiency, and power factor, should also be considered.
Tang et al. proposed a new type of electromagnetic power generator with highpower density by putting strong rare-earth magnet arrays in alternating directions andusing high-magnetic-conductive casing (figure 1.3) [77]. However, throughexperiment it was shown that the maximum damping capacity obtained included large
mechanical loss.
To obtain large power generation density, kinematic devices, such as a crank, camor ball screw, are generally required in electromagnetic power generators. However,
the mechanical transmission loss in these kinematic devices cause a reduction in
efficiency of electric power generation and the power generator also becomes larger insize. In addition, although the power density increases, the more permanent magnets
that are used, the lower the efficiency and the higher the cost.
Akazawa et al. [40-43] proposed a new type of free-piston linear electromagnetic
power generator to attain high efficiency and a compact design. Linear systems haveadvantages such as low mechanical loss. In particular, the free-piston linear electric
power generator has advantages not only for low mechanical loss but also highefficiency power generation. In addition, the volume of strong rare-earth magnets inthe power generators can be reduced using the free-piston linear power generator
system. Although the proposed device was originally designed for stirring engine
systems, this technology could improve the efficiency of harvesting energy fromstructural vibrations due to its compact design and ability to obtain high power
efficiency.

1.3.3. Tuned Mass Systems for Bridge Vibrations
Among tuned mass systems, tuned mass dampers could, in particular, satisfactorily
control vibrations when an ideal dynamic balance is achieved between its mass, springsand dampers [21-23,27]. If a power generator replaced the damper in a tuned massdamper system and could successfully absorb bridge vibration energy, it would havethe capacity to harvest energy and control bridge vibration simultaneously. Zhu et al.
[85] proposed an application of electromagnetic power generators, namely EM

7dampers, for both vibration damping and energy harvesting in buildings. Theoreticaland experimental studies of linear EM dampers was presented. Based on the results,
EM dampers replaced traditional viscous fluid dampers for vibration mitigation oflightly damped and flexible structures, such as high-rise buildings. Zuo et al. [66,67]
modeled two energy harvesters with tuned mass damper systems, single-mass and dualmass systems, and concluded that dual-mass systems provide greater power generation
with an increase in electrical damping if the energy harvester is under forced
excitation, or base displacement excitation is applied. However, in the case of energy
harvesting from vibrations of bridge structures, the forced excitation is from traffic
vibrations and not a forced excitation directly applied to the energy harvester. In
addition, since vibration characteristics of bridge structures depend on vibration
amplitude, it is considered that the vibration characteristics, in small vibration
amplitudes such as a micro-tremor and in large vibration amplitudes such as traffic oflarge vehicles or earthquakes, significantly differ [48,49]. Consequently, it is difficult
to achieve effective vibration control on real bridges in addition to harvesting energy.
For the above reasons, an effective model and practical design method for bridge
vibration energy harvesting has yet to be established.

1.3.4. Monitoring System of Bridge Structures using Energy Harvesting
A prototype monitoring system using a piezoelectric device and an electric circuit
was developed and examined at an existing bridge by Yoshida et al. [8,9]. The aim was
to obtain electricity from train-induced vibrations of the actual bridge. Not only wereadvantageous shapes and materials of piezoelectric power generators examined,
electric circuits, for effectively harvesting energy from train load induced vibrationsof bridge structures was also examined. The generated electric power when trains passthrough the bridge was demonstrated. In addition, based on the experimental results, aprototype monitoring system was proposed. The prototype system demonstrated
measured and transmitted data five times with the power generated from bridge
vibrations induced by a train composed of ten cars, and the train received thistransmitted data wirelessly. Yoshida’s study demonstrated that it is possible to harvest
electricity from railway bridge vibrations and transmit small monitoring data
wirelessly.

8

Although vibration-based energy harvesting for supplying electric power tostructural health monitoring systems is of growing interest, generated voltage signals
have yet to be practically used. Yamaguchi et al. [11] developed a new passive typevibration velocity sensor by using the power generation characteristics of vibrated
electret. Based on the findings in a numerical simulation, a vibration velocity sensor
using an electret electrode structure was proposed. As a basic experimental result, a
relationship between generated voltage per unit velocity and frequency was obtained
as transfer functions for converting voltage signals to velocities. Finally, experimentsof voltage signal responses from vibration of an existing bridge were carried out toexamine the applicability of the proposed sensors. Yamaguchi’s study demonstrated a
new use of energy harvesting from vibrations of bridge structures.

1.4. Outline of this Dissertation
The research objectives are discussed in the five main chapters respectively as
outlined below (Figure 1.4).

Chapter 1.

Introduction

Background, related research, purpose and objectives were discussed.

Chapter 2.

Investigation on Characteristics of Electro-Mechanical Systems

In order to develop an advantageous design of energy harvesters for vibrations ofbridge structures, electro-mechanical characteristics of a Tuned Mass Generator(TMG) were investigated. Advantages of dual-mass systems over single-masssystems were evaluated for power generation from vibrations of bridge structures.

Chapter 3.

Proposal of Tuning Design Method

The tuning design method of TMG for efficient energy harvesting of vibrations
from bridge structures has been proposed. Based on parametric studies, the effectof parameters on robustness regarding frequency change and tuning errors wasdetermined.

9Chapter 4.

Trial Applications of TMG to an Actual Bridge

TMG was designed and developed for application on an actual bridge. The
characteristics of power generation from bridge vibrations were investigated anddiscussed.

Chapter 5.

Efficiency Enhancement of Power Generators for Energy Harvesting

In order to improve the applicability of TMG, electromechanical structure of apower generator for efficient energy harvesting was considered and developed.

Chapter 6.

Proposal of Uses of the Developed Energy Harvesting System

Based on the findings in the previous chapters, a practical use of TMG for
monitoring systems of bridge structures has been proposed and its capability isexperimentally verified.

Chapter 7.

Conclusion and Recommendations

The results of each chapter are summarized in this chapter. Based on the findings
obtained in this study, recommendations for an efficient energy harvesting systemand practical use of the developed TMG are proposed.

10Figure 1.1

Configuration for a power generator consisted of a ball screw

Figure 1.2

Configuration for a transverse flux linear motor (TFLM) withfull permanent magnet

Figure 1.3

Configuration for an electromagnetic power generator using acoil and magnet array11

1. Introduction
2. Investigation on Characteristics of Electro-Mechanical Systems
 Tuned Mass Systems for Energy
Harvesting

3. Proposal of Tuning Design Method
5. Efficiency Enhancement ofPower Generator for Energy
Harvesting Parametric Study on Efficiency andRobustness

4. Trial Applications of TMG to an
Actual Bridge

 Efficiency Enhancement using
knowledge Obtained in theExperiment on the Trial Bridge

 Energy Harvesting and Charging

6. Proposal of Usage of the Developed Energy Harvesting System
 Simulation of Energy Harvesting A Monitoring System using
Harvested Energy

7. Conclusion and Recommendations

Figure 1.4

Flow of this dissertation

12

Chapter 2
Investigation on Characteristics of ElectroMechanical Systems

Abstract .
In this chapter, advantages of dual-mass systems over single-mass systems for
power generation from vibrations of bridge structures have been theoreticallyinvestigated. Results from the theoretical study show that for effectively using
harvested energy for charging, it is essential to consider the robustness againstchanges in the electric damping, and dual-mass systems were found tosuccessfully demonstrate this ability. Moreover, it was found that dual-masssystems have advantages over single-mass systems for robustness against
tuning errors and changes in natural frequencies of bridges.

132.1. Overview
To date, tuned mass damper systems have been found to satisfactorily control
bridge vibration when an ideal dynamic balance is achieved between its mass, springsand dampers. If the damper in a tuned mass damper system was replaced with anelectromagnetic power generator and could successfully absorb bridge vibrationenergy, it would have the capacity to harvest energy. However, one problem of
harvesting energy from bridge vibration is that the natural frequency of bridges isgenerally much lower than the mechanical vibrations which have so far been the main
target of energy harvesting. Another factor to be considered is that large-scale energy
is expected in vibrating bridge structures [72,73], and so energy harvesters should becapable of extracting large power from low-frequency and low-velocity oscillations.
Zuo et al. [66,67] modeled two energy harvesters with tuned mass systems, namely
a single-mass and a dual-mass system, and concluded that dual-mass systems provide
greater power generation with an increase of electric damping if the energy harvester
is under forced excitation, or base displacement excitation is applied. However, in thecase of harvesting energy from bridge vibrations, the forced excitation is from traffic
vibrations and is thus not a forced excitation that is directly applied to the energy
harvester. It is therefore still controversial as to whether a single-mass system or adual-mass system is more efficient for harvesting energy from bridge vibrations. Dueto the above reasons, an effective structural system to harvest energy from vibrationsof bridge structures has yet to be established.
In this chapter, characteristics of electro-mechanical systems of an energy
harvester for vibration of bridge structures has been investigated when using both
single-mass and dual-mass systems. It was concluded that an energy harvester using a
tuned dual-mass system was more advantageous and this system along with anelectromagnetic power generator, named hereafter Tuned Mass Generator (TMG), has
subsequently been proposed. In addition, the characteristics of TMG have beentheoretically explained to investigate how TMG can achieve greater power generationfrom vibrations of bridge structures.

14

2.2. Theoretical Explanation of Single-Mass and Dual-Mass
Systems

2.2.1. Single-Mass Vibration Energy Harvesters
Figure 2.1 shows a single-mass vibration energy harvester, where mass m1 isconnected to the bridge mass M with spring k1 and an electromagnetic power generator
is installed. F(t) is the excitation force, Fe (t) is the damping force by theelectromagnetic power generator. Bridge mass M is connected to the base with anequivalent spring K and a damping coefficient CM . x(t) and X(t) express thedisplacement of the mass m1 and the bridge mass M. As shown in Figure 2.2, anequivalent circuit is introduced to represent the linear generator and is formularized as
LdI (t )
+ rI (t ) + RI (t ) = E (t )
dt

(2.1)

where L is the inductance [H], 𝑟𝑟 is the internal resistance [Ω], R is the resistance of thecircuit [Ω], I is the current [A] and E is the electromotive force [V]. Based on Faraday’slaw, the electromotive force E(t) has been defined as
E (t ) = k emf

dx(t )dt(2.2)

in which kemf is an electromotive force coefficient [Vs/m], and dx(t)/dt is the velocityof the moving part of the electromagnetic power generator. The damping force byelectromagnetic power generator F e (t) is formularized as
Fe (t ) = k emf I (t )(2.3)

Harvested electric power and electrical loss from electromagnetic power generators is
expressed as
W (t ) = RI 2 (t ),Wloss (t )= rI 2 (t )(2.4)

The total electric power generation [VA or Nm/s] from combining the above, andconsidering the electromagnetic power generator to include equivalent damping is
Wtotal (t ) = (ceh + cel )x12 (t )

15

(2.5)

where 𝑥𝑥̇ is the velocity, and ceh and cel are damping coefficients due to harvested

electric power and electrical loss respectively. These equivalent electrical damping
coefficients can be defined as
2
k emf

Rr
ceh =
,
r (1 + Rr )2

2
k emf

cel =

r

1
(1 + Rr )2(2.6)

where Rr = R / r is the resistance ratio. Equation (2.6) demonstrates that the equivalent
electrical damping coefficients increase when the resistance ratio Rr decreases. The
ratio of harvested electric power to total electric power generation, which theelectromagnetic power generator absorbs, is hereafter called converting ratio and isformularized ash=ceh
ceh + cel

(2.7)

Next, the power factor of the electric circuit is introduced as follows
Pf =1 + Rr(2.8)

L + (1 + Rr )22rwhere Lr = ωL / r is the impedance ratio. Thus, the resistance ratio Rr and Lr can be
expressed, using the converting ratio h and power factor Pf , as
Rr =

h
,
1− h

Lr =

Pf−2 − 1

(2.9)

1− h

When subjected to forced excitation F(t) = F0 sin(ωt) as shown in Figure 2.1, thegoverning equation for the vibration energy harvester is expressed asm1 x1 (t ) + k1 (x1 (t ) − X (t )) = − Fe (t )MX (t ) − k1 (x1 (t ) − X (t )) + KX (t ) + C M X (t ) = Fe (t ) + F (t )(2.10)

The following non-dimensional quantities are introduced.
ζM =CM
2 M ⋅K, ζ e1 =ce
2 m1 ⋅ k1, µ1 =

m1, γ1 =
M

K /M
k1 / m1

, λ=

ω
K /M

where ζM is the damping ratio of the bridge, ζe1 is the equivalent damping ratio due tothe electric load, μ1 is the mass ratio, γ1 is the frequency ratio, and λ is the normalized
excitation frequency. The equivalent damping coefficient due to the electric load ce isformularized as follows

16

ce =

2
k emf

r

1 + RrL2r + (1 + Rr )2

(2.11)

Dimensionless displacement X is defined as the ratio of displacement to static
displacement X0 as follows
X (t ) =X (t )X (t )=X0
F0 / K(2.12)

The following dimensionless harvesting power can also be introduced as
W (t ) =RI 2 (t )(2.13)

F02 M ⋅ K

When the excitation force F(t) in equation (2.10) is harmonic, the correspondingtransfer function of the current GI1 and the displacement GX1 can be formularized byusing the Laplace transform as follows
GI 1 (s ) = −GX 1 (s ) =M ⋅ k emf ⋅ µ1 ⋅ s 3

2⋅ s{d 2 (s ) + d 3 (s )} + d 1 (s ) ⋅ d 2 (s ) ⋅ d 3 (s ) − d 4 (s )
k emf
2
k emf
⋅ s + d1 (s ) ⋅ d 2 (s )2k emf
⋅ s{d 2 (s ) + d 3 (s )} + d1 (s ) ⋅ d 2 (s ) ⋅ d 3 (s ) − d 4 (s )(2.14)(2.15)

Where

(

)

d1 (s ) = r s ⋅ M / K ⋅ Lr / λ + Rr + 1

d 2 (s ) = M ⋅ µ1 ⋅ s + K ⋅ µ1 / γ
22
1d 3 (s ) = K + C M ⋅ s + M ⋅ s 2 + K ⋅ µ1 / γ 122
⋅ µ1 / γ 12
d 4 (s ) = d1 (s ) ⋅ K 2 ⋅ µ12 / γ 14 + 2 ⋅ s ⋅ K ⋅ k emf

In order to consider the characteristics of single-mass vibration energy harvesters forenergy harvesting and vibration control, steady-state harvesting power and vibration
amplitude responses with various electric damping ratios ζe are obtained as shown in
Figure 2.3 and Figure 2.4. If the bridge damping ratio ζM is 0.02, and the mass ratio
μ1 is 0.0011 (1.1 ‰), the value of mass ratio is equal to the total mass ratio of dualmass systems mentioned in the next chapter. If the bridge damping is low or the mass
ratio μ1 is high, the efficiency of energy harvesting and vibration control increases.
The dashed line in Figure 2.3 shows the electric damping ratio, where the maximum
harvesting power response is indicated by the red point. The dashed line in Figure 2.4
shows the electric damping ratio where the minimum value of local maximum vibration
amplitude response is indicated by the blue point. These two electric damping ratios

17are not equal, as the appropriate design of parameters is for energy harvesting or
vibration control. Figure 2.5 and Figure 2.6 show the response of harvesting power
and vibration amplitude, respectively. The responses are sensitive to the tuning ofelectric damping ratio ζe hence the efficiency of energy harvesting drops with theslightest change in ζe .

2.2.2. Dual-Mass Vibration Energy Harvesters
Figure 2.7 indicates a dual-mass vibration energy harvester, where two masses m1
and m2 are connected in series with springs k1 and k2 . An electromagnetic power
generator is installed between the two masses. F(t) is the excitation force, F e (t) is thedamping force by the electromagnetic power generator. Bridge mass M is connected tothe base with an equivalent spring K and a damping coefficient C M . x 1 (t), x 2 (t) and X(t)express the displacement of the mass m1 , mass m2 and the bridge mass M. Whensubjected to forced excitation, the governing equations for the vibration energy
harvester can be expressed as− m2 x2 (t ) + k 2 (x2 (t ) − x1 (t )) = − Fe (t )m1 x1 (t ) + k1 (x1 (t ) − X (t )) + k 2 (x2 (t ) − x1 (t )) = + Fe (t )MX (t ) − k (x (t ) − X (t )) + KX (t ) + C X (t ) = F (t )1

1

(2.16)M

In addition, the following non-dimensional quantities are defined as follows
µ2 =

m2
,
m1

γ2 =

k 2 / m2,

k1 / m1

ζ e2 =ce
2 m2 ⋅ k 2

where μ2 is the mass ratio, γ2 is the frequency ratio, and ζe2 is the electric damping
ratio of the dual-mass system. When the forced excitation F(t) in equation (2.16) isharmonic, the corresponding transfer function of the current GI2 and the displacement
GX2 can be formulated by using the Laplace transform as follows
GI 2 ( s ) =− s 3 K ⋅ M ⋅ k emf ⋅ µ12 ⋅ µ 2 / γ 122d 3 (s ) ⋅ d 6 (s ) − K 2 ⋅ µ12 / γ 14 ⋅ d1 (s ) ⋅ d 2 (s ) + k emf⋅ s − d 3 (s ) ⋅ d 4 (s )GX 2 ( s ) =d 6 (s ) − d 4 (s )2d 3 (s ) ⋅ d 6 (s ) − K 2 ⋅ µ12 / γ 14 ⋅ d1 (s ) ⋅ d 2 (s ) + k emf⋅ s − d 3 (s ) ⋅ d 4 (s )

Where

18

(2.17)(2.18)

)(d1 (s ) = r ⋅ s ⋅ M / K ⋅ Lr / λ + Rr + 1

d 2 (s ) = M ⋅ µ1 ⋅ µ 2 ⋅ s + K ⋅ µ1 ⋅ µ 2 ⋅ γ 22 / γ 122d 3 (s ) = K + C M ⋅ s + M ⋅ s 2 + K ⋅ µ1 / γ 122
⋅ µ1 ⋅ µ 22 ⋅ γ 22 / γ 12
d 4 (s ) = d1 (s ) ⋅ K 2 ⋅ µ12 ⋅ µ 22 ⋅ γ 24 / γ 14 + 2 ⋅ s ⋅ K ⋅ k emf(

d 5 (s ) = M ⋅ µ1 ⋅ s 2 + K ⋅ µ1 / γ 12 + µ1 ⋅ µ 2 ⋅ γ 22 / γ 12

d 6 (s ) = k

2
emf

)

⋅ s ⋅ (d 2 (s ) + d 5 (s )) + d1 (s ) ⋅ d 2 (s ) ⋅ d 5 (s )To consider the characteristics of dual-mass vibration energy harvesters for energy
harvesting and vibration control, steady-state harvesting power and vibration
amplitude responses with various electric damping ratios ζe2 have been demonstrated
as shown in Figure 2.8 and Figure 2.9. If bridge damping ratio ζM is 0.02, and mass
ratio μ1 and μ2 are set to be 0.001 and 0.1, the total mass ratio of dual-mass systems isequal to the mass ratio of single-mass systems 0.0011 (1.1 ‰). If bridge damping is
low or the mass ratio μ1 is high, the efficiency of energy harvesting and vibration
control increases. The dashed line in Figure 2.8 indicates the electric damping ratio,
where the maximum harvesting power response is indicated by the red point. The
dashed line in Figure 2.9 shows the electric damping ratio, where the minimum valueof local maximum vibration amplitude response is indicated by the blue point. These
two electric damping ratios are not equal; in other words, the appropriate design ofparameters for energy harvesting or vibration control is similar to single-mass systems.
Figure 2.10 and Figure 2.11 show the response of harvesting power and vibration
amplitude, respectively. The responses are less sensitive against the tuning of electric
damping ratio ζe2 compared to single-mass systems namely the efficiency of energy
harvesting does not drop with a slight change in electric damping ratio.

2.3. Comparison between Single-Mass and Dual-Mass Systems
To consider the unstable bridge vibration, the electric power response spectrumsof dual-mass systems and single-mass systems are shown in Figure 2.12 and Figure
2.13. The displacement response spectrums are shown in Figure 2.14 and Figure 2.15.
The response spectrums in 2% and 4% reduce of γ1 are shown in these figures. As
shown in Figure 2.12 and Figure 2.13, the peak value of electric power response19reduces when γ1 reduces. To adapt this phenomena, the tuning of the mass or springs
can be considered. However, it is difficult to tune these parameters on the field. The
tunable parameter of single mass systems is only the electric damping ratio of theelectromagnetic power generator ζe . Meanwhile, only the peak value can be changedby tuning electric damping ratio ζe , the frequency cannot be tuned. Therefore, thismethod is not effective to adapt TMG to the unstable bridge vibration. On the other
hand, the parameters of second mass in dual-mass systems, such as mass ratio μ2 andfrequency ratio γ2 are available to tune on the field. The frequency which gives thepeak value can be shifted by tuning the mass ratio μ2 and the peak value can be tunedby the frequency ratio γ2 or electric damping ratio ζe . Figure 2.16 and Figure 2.17
show the tuned frequency response spectrum of the power generation and thedisplacement by changing the combination of γ2 and μ2 . Generally, it is hard to tune
parameters exactly same as the designed values. Therefore, the robustness against
tuning errors is important. As a consequent, the dual-mass systems have an advantage
over single-mass systems for the applicability of tuning parameters.
From the results obtained in this chapter, a vibration energy harvester using a dualmass system, named Tuned Mass Generator (TMG) has been deemed most appropriate
for this study.

2.4. Summary
Based on the aforementioned researches and issues encountered in this chapter, anenergy harvester, using a tuned dual-mass system and electromagnetic power generator(or transducer), named hereafter Tuned Mass Generator (TMG), has subsequently been
proposed. In addition, the characteristics of TMG have been theoretically explainedfor energy harvesting to achieve greater power generation from bridge vibrations. The
findings from this chapter are summarized below.
(a) The electromagnetic power generator is represented by an equivalent electric
circuit for modeling TMG. The corresponding transfer function of the power
generation and the displacement can be formulated by using Laplace transform.
(b) In dual-mass systems, the efficiency of energy harvesting does not drop with a20

slight change in electric damping ratio as in the case of single-mass systems.
Consequently, dual-mass systems have an advantage over single-mass systems
for effectively using harvested energy for charging.
(c) The appropriate design of parameters for energy harvesting or vibration control
is different for single-mass and dual-mass systems. The balance between the two
designs can be controlled by changing the electric damping ratios of theelectromagnetic power generator.
(d) Robustness of TMG against tuning errors is important. Accordingly, dual-masssystems have an advantage over single-mass systems for the applicability oftuning parameters.
Dual-mass systems have several advantages over single-mass systems for power
generation, such as efficiency of harvesting energy in charging and robustness oftuning. Based on this finding, a bridge vibration energy harvester using a dual-masssystem, named Tuned Mass Generator (TMG), has been proposed and will be further
enhanced to enable TMG to harvest energy.

21Single-mass
harvester

𝑘𝑘1

Bridge𝐾𝐾
Figure 2.1

𝑚𝑚1
𝑀𝑀𝐹𝐹𝑒𝑒 (𝑡𝑡)
C𝑀𝑀

𝑥𝑥1

𝐹𝐹(𝑡𝑡) = 𝐹𝐹0 sin(𝜔𝜔𝜔𝜔)𝑋𝑋

Analysis model of single mass systems

𝐸𝐸(𝑡𝑡)𝑟𝑟

𝐿𝐿

𝑅𝑅

𝐼𝐼(𝑡𝑡)

Electromagnetictransducer
Figure 2.2

Electric circuit

22

𝑉𝑉(𝑡𝑡)

2

0.1
1

2

1

Single-Mass
γ1 = 1µ1 = 0.0011
ζM = 0.02
2

2

1

3
3

2

1

3

4

2

4

3

1

0.05

1

3

0
0.95

Figure 2.3

4
21

1

1.05

Harvesting power Wmax response of single mass systems withvarious electric damping ratios (0 ≤ ζe ≤ 5)

10

14

10

Single-Mass
γ1 = 1

18

14

0.1

10

10

14

0.05

18

14

18

µ1 = 0.0011
ζM = 0.02

14

18
14

10

1

22

14

2

18

Figure 2.4

22

10 6

14
18

0
0.95

1.05

Bridge vibration displacement Xmax response of single mass
systems with various electric damping ratios (0 ≤ ζe ≤ 5)23

5

← ζe = 0.01

Single-Mass
γ1 = 14 µ = 0.0011
1← ζe = 0.03

3
← ζ = 0.05
e

2
1
0
0.9

Figure 2.5

0.95

1
1.05
ized excitation frequency 𝜆1.1Harvesting power Wmax response of single mass systems withdifferent electric damping ratios (ζe = 0.01, 0.03, 0.05)30Single-Mass
25 γ1 = 1
µ1 = 0.0011

Without Energy Harvester↓← ζ = 0.0520e← ζ = 0.01e

15

← ζe = 0.03

10
5
0
0.9

Figure 2.6

0.95

1

1.05

1.1

Bridge vibration displacement Xmax response of single mass
systems with different electric damping ratios (ζe = 0.01, 0.03,
0.05)

24

𝑚𝑚2

𝑘𝑘2

Dual-mass
harvester

𝑘𝑘1
Bridge𝐾𝐾
Figure 2.7

𝑥𝑥2𝐹𝐹𝑒𝑒 (𝑡𝑡)𝑚𝑚1

𝑥𝑥1
𝐹𝐹(𝑡𝑡) = 𝐹𝐹0 sin(𝜔𝜔𝜔𝜔)

𝑀𝑀

C𝑀𝑀

𝑋𝑋

Analysis model of dual-mass systems

25

4

Dual-Massγ2 = 1

3

1
2

Electric damping ratio ζe

3
4

5
4
1

γ1 = 0.95

2µ2 = 0.14µ1 = 0.001

3
4

3
3

2

1

ζM = 0.02

2

1

2
4

1

3

2

1

0
0.95

2

1

3

4

1

1.05

1

Normalized excitation frequency λFigure 2.8

Harvesting power Wmax responses of dual-mass systems with

18
14

18

10

18

5
14

10

µ1 = 0.001
14

14

10

18

18

14

µ2 = 0.1

314ζM = 0.02

18

2

Dual-Massγ2 = 1γ1 = 0.95

10

18

4

14

various electric damping ratios (0 ≤ ζe ≤ 5)

10

14
14

1
22

1

18

Figure 2.9

14

10

0
0.95

18

1.05

Bridge vibration amplitude Xmax responses of dual-masssystems with various electric damping ratios (0 ≤ ζe ≤ 5)

26

5
4
3

← ζe = 2.00

Dual-Massγ2 = 1γ1 = 0.95µ2 = 0.1µ1 = 0.001← ζe = 1.00

2
← ζ = 3.00

1
0
0.9

Figure 2.10

e

0.95

1

λ

1.05

1.1

Harvesting power Wmax responses of dual-mass systems withdifferent electric damping ratios (ζe = 0.01, 0.03, 0.05)30

Dual-Mass
γ =1
25 2
γ1 = 0.95µ2 = 0.1
20 µ = 0.001
1Without energy harvester↓← ζe = 3.00
← ζ = 2.00e
← ζe = 1.00

15
10
5
0
0.9

Figure 2.11

0.95

1

1.05

1.1

Bridge vibration amplitude Xmax responses of dual-masssystems with different electric damping ratios (ζe = 0.01, 0.03,
0.05)

27

5

← 1.00 γ1Single-Mass43

γ1 = 1← 0.98 γ1µ1 = 0.0011
ζe = 0.014← 0.96 γ1

2
1
0
0.9
Figure 2.12

0.95

1.1

1.05
1
d excitation frequency 𝜆Harvesting power Wmax responses of single-mass systems withdifferent frequency ratio

5
4
3← 1.00 γ

Dual-Mass1

γ2 = 1.3
γ1 = 0.948← 0.98 γ

1µ2 = 0.1µ1 = 0.001
ζe = 1← 0.96 γ

1

2
1
0
0.9

Figure 2.13

0.95

1

1.05

1.1

Harvesting power Wmax responses of dual-mass systems withdifferent frequency ratio

28

Displacement Xmax

Figure 2.14

Normalized excitation frequency 𝜆Vibration amplitude Xmax responses of single-mass systems

Displacement Xmax

with different frequency ratio

Figure 2.15

Normalized excitation frequency 𝜆Vibration amplitude Xmax responses of dual-mass systems withdifferent frequency ratio

29

Harvesting power Wmax
Figure 2.16

Normalized excitation frequency 𝜆Tuning of harvesting power responses of dual-mass systems

Displacement Xmax

with second mass ratio and frequency ratio

Figure 2.17

Normalized excitation frequency 𝜆Vibration amplitude Xmax responses of dual-mass systems withsecond mass ratio and frequency ratio

30

Chapter 3
Proposal of Tuning Design Method

Abstract .
In the previous chapter, advantages of dual-mass systems over single-masssystems for power generation from vibrations of bridge structures wereexplained. Based on the results, a bridge vibration based energy harvester
using a tuned dual-mass system and electromagnetic power generator, named
Tuned Mass Generator (TMG), has been proposed. In addition, characteristics
required to design TMG have been formulated using an equivalent electric
circuit of an electromagnetic power generator. In this chapter, a multi-physics
parameter design method has been developed to tune TMG. Results fromparametric studies show that for effective energy harvesting, first, it isessential to determine the relationship between the required characteristics forthe electromagnetic power generator, and second, that TMG requires a robust
parameter design for uncertain bridge vibrations, accuracy of assembling
TMG and tuning errors.

31

3.1. Overview
In the previous chapter, characteristics of energy harvesters using tuned mass
systems have been formulated using an equivalent electric circuit of a linear
electromagnetic power generator. In addition, advantages of dual-mass systems oversingle-mass systems for power generation from vibrations of bridge structures were
investigated. Based on the findings, a bridge vibration energy harvester using dualmass systems and an electromagnetic power generator, named Tuned Mass Generator(TMG), has been proposed. However, an appropriate tuning design is necessary toenable the most effective performance of TMG for power generation from thevibrations of bridge structures.
In this chapter, effects of parameters on energy harvesting were investigated for
efficient energy harvesting from bridge structural vibrations. In addition, a multiphysics parameter design method has been developed to tune TMG.

3.2. Effects of Parameters on Energy Harvesting in Dual-Mass
Systems
In order to evaluate the effect of parameters on the efficiency of energy harvesting,first, the energy flow of the bridge-TMG vibration system was considered. Figure
3.1(a) and Figure 3.1(b) show the energy flow in a bridge-TMG model for every
vibration cycle. A part of the bridge vibration energy flows into the main mass of
TMG (A) in mechanical form, although the damping from bridge structures (O)dissipates the main part of bridge vibration energy. In the mechanical domain, thevibration energy of the main mass flows into the second mass (E), where some of theenergy continues to cycle as the vibration of the main mass (M), while somemechanically dissipates (C). The electromagnetic power generator converts some of
the mechanical energy into electrical energy (D and F). In the electrical domain, someelectrical energy is harvested (J), while the remaining electrical energy is converted
into thermal energy from the internal resistance of the electromagnetic power
generator (H), or continues to cycle as reactive energy (I).

32

The sole target of this study is energy harvesting. In order to maximize theefficiency of energy harvesting, there are three possible options. First, increase theenergy flow into TMG (A), second, increase the transducing energy from themechanical domain to the electrical domain (D and F), and thirdly, increase the power
factor or converting ratio of electrical energy to energy harvesting (H, I and J). Theenergy flow into TMG increases with an increase in the mass ratio 𝜇𝜇1 . When using thesame mass ratio, an appropriate frequency ratio exists to maximize the energy flow.
In order to increase the transducing energy from the mechanical domain to theelectrical domain, an appropriate electrical damping for the electromagnetic power
generator should be designed.
The electric circuit and characteristics of the electromagnetic power generator
design the converting ratio of electrical energy. For the aforementioned reasons,frequency ratios and electrical damping ratio are considered as the key parametersthat need tuning, whereas the mass ratio μ1 is fixed as 0.001 (1 ‰). The mass ratio
was designed by considering watt-order power generation from bridge structural
vibrations. The damping ratio of a bridge ζM is fixed as a generally used value of 0.02.
The power factor and converting ratio predominantly depend on the specifications of
the electromagnetic power generator; if the power factor and converting ratio take amaximum value, all electrical energy is harvested. The power factor can become themaximum using the power factor correction (PFC) circuit. The PFC circuit uses aphase advanced capacitor and its capacitance C * is designed as follows
C* =

1

ω2L

(3.1)

where ω is the angular frequency [rad] and L is the inductance of the coil in theelectromagnetic power generator [H]. As previously shown in equation (3.1), theconverting ratio cannot become 1 except for in extreme cases where the internal
resistance r = 0 or resistance R = ∞. Considering general cases, the power factor andconverting ratio are fixed as 1 and 0.8, respectively.
To analyze the influence of parameters on the efficiency of energy harvesting,parametric study was conducted. First, a frequency response of power ratio based on
the response function in equation 2.13 and equation 2.17 in Chapter 2 was
calculated where parameters were designed as follows: μ2 = 0.1, γ1 = 0.948, γ2 = 1.4,33ζe = 1 . These parameters were designed using the parameter design method as
mentioned next. Next, parameters were varied from this combination of parameters.
The normalized cross-correlation coefficient of harvesting power response with a lagof zero was introduced as follows{}

∑λlh W (λ ) ⋅ W0 (λ )R xy (0 ) =2
λ∑λh W0 (λ )
λ

l

{

}

(3.2)

where normalized excitation frequencies λl , λh are in the range of −∞ < λl ≤ λ ≤ λh < +∞,W is the harvesting power response in dimensionless form, and W0 is the harvesting
power response with μ2 = 0.1, γ1 = 0.948, γ2 = 1.4, ζe = 1.0, named A1. The closer thenormalized harvesting power response W gets to W0 , the closer the normalized crosscoefficient of harvesting power response with a lag of zero gets to the value of 1.
Figure 3.2 shows the normalized cross-correlation coefficient of harvesting
power response with a lag of zero, for various electric damping ratios ζe and frequency
ratios γ2 . The normalized cross-correlation coefficient with a lag of zero has one
maximum value at A1. In Figure 3.2, B1 shows the value with γ2 = 1.4 and ζe = 0.5,

C1 shows the value with γ2 = 0.95 and ζe = 1.0, and D1 shows the value with γ2 = 0.95
and ζe = 1.6. Other parameters, μ2 = 0.1 and γ1 = 0.948, are fixed. Figure 3.3 shows thefrequency responses of power ratio of the four cases, A1, B1, C1 and D1. As shownin Figure 3.2, the normalized cross-correlation coefficient with a lag of zero is
obtained almost the same as the maximum value when the combination of parameters
corresponds to the dashed line (D1 is an example case), whereas the harvesting power
value decreases when the combination of parameters moves away from the dashedline (such as B1 and C1). Consequently, the appropriate combination of parameters ζeand γ2 gives almost the same harvesting power response as the maximum response,
although only one combination of parameters exists to maximize the efficiency ofenergy harvesting. Fundamentally, it is practically impossible to tune parameters tobe identical to the designed values, yet this characteristic can be used to minimize thetuning error through an appropriate combination of parameters.
Figure 3.4 shows the normalized cross-correlation coefficient with a lag of zerofor various combinations of mass ratio μ2 and frequency ratio γ1 parameters. A2 is thecase when the harvesting power response in dimensionless form with μ2 = 0.10 ,34

γ1 = 0.948, γ2 = 1.3, ζe = 1.0. The normalized cross-correlation coefficient with a lag ofzero has one maximum value at A2. B2 shows the value with μ2 = 0.12 and γ1 = 0.948,
C2 shows the value with μ2 = 0.10 and γ1 = 0.938 , and D2 shows the value with
μ2 = 0.12 and γ1 = 0.938. Other parameters, γ2 = 1.3 and ζe = 1.0, are fixed. Figure 3.5
shows the frequency responses of power ratio of the four cases, A2, B2, C2 and D2.
As shown in Figure 3.4, the normalized cross-correlation coefficient at a lag of zerotakes almost the same maximum value when the combination of parameters
corresponds to the dashed line, whereas the harvesting power value decreases when
the combination of parameters moves away from the dashed line. Therefore, if theappropriate combination of parameters μ2 and γ1 are used a harvesting power response
almost the same as the maximum response can be obtained. However only one
combination of parameters can maximize the efficiency of energy harvesting. Precise
tuning of μ2 is comparatively less difficult than tuning of γ1 since there is a limitationin the variety of springs or the size of the main mass m1 . From these parametric studies,
the parameters γ1 , γ2 and ζe were determined as the parameters to be designed, while
μ2 is fixed as 0.1.

3.3. Multi-Physics Parameter Design Method for Power
Generation

Since the natural frequency of bridges is uncertain due to many factors, including
traffic conditions and temperature [4,44-51], the purpose of multi-physics parameter
design is to maximize power generation and ensure robustness against changes invibration frequency. Figure 2.7 showed the analysis model. All input and output
parameters have been transformed into dimensionless form, and thus any reference toparameters or outputs henceforth are dimensionless. Harvesting power response insteady-state vibration is obtained by changing the frequency ratios γ1 , γ2 and theequivalent electrical damping ratio ζe . In this study, it has been proposed that to ensure
robustness against changes in vibration frequency, the amplitude of harvesting power
response W in equation (2.13) must satisfy the minimum amplitude of harvesting35

power Wc in the range between the normalized excitation frequencies λl and λh , using
the constraint function. Similarly, the harvesting power response must maximize
electric power generation when λ = 1, using the objective function. The constraintfunction and objective function are defined as follows(

Q1 = min W (γ 1 , γ 1 , ζ e , λ ) λ =λl ,λhG1 = W (γ 1 , γ 1 , ζ e , λ ) λ =1

)

(3.3)

(3.4)

The balance between robustness and peak power generation can be adjusted throughthe constraint function Q1 . Figure 3.6 shows some harvesting power responses using
the constraint function equation (3.3) and objective function equation (3.4), withdifferent parameters. Normalized excitation frequencies λl , λh and minimum power
generation Wc can be modified depending on the purpose of energy harvesting. Figure
3.7 shows the sequence of the proposed design method. For various combinations of
the aforementioned parameters, γ1 , γ2 and ζe , the harvesting power spectrum is
calculated by reiterating the sequence of the presented analysis procedure. Thissequence of iterations is continued until the maximum objective function G1 isobtained. The parameters are designed to maximize the objective function G1 by usinga Sequential Quadratic Programming (SQP) method. SQP method can be considered asa generalized version of Newton’s method, and it is one of the most effective methods
for nonlinear constrained optimization problems. However, various local maximum
power generation were found for various combination of parameters by only applying
the SQP method. In this study, not only by using SQP method, but also by using the
proposed objective function G1 by considering the upper and lower limits of electric
damping, a local maximum value equal to a global maximum value can be found. The
distribution of G1 using variations of the three tuning parameters γ1 , γ2 and ζe is shownin Figure 3.8(a) to demonstrate the local maximum value. Figure 3.8(b) shows theupper view of the three-dimensional Figure 3.8(a). As shown in Figure 3.8(b), thelocal maximum values of G1 have a wide distribution range when the electric damping
ratio ζe is modified. However, when the electric damping ratio is low, the density of
G1 which satisfies the constraint function Q1 is also low. In other words, if the electric
damping ζe is low, the efficiency of energy harvesting is highly sensitive to tuning36

errors, and can drop with the slightest change of tuning parameters (Figure 3.8(b)). It
is therefore essential to consider robustness not only against changes in vibration
frequency, but also against tuning errors, hence, the electric damping ratio should behigh. Nonetheless, the converting ratio decreases if the electrical damping ratio
increases when a fixed value of electromotive force coefficient kemf is used. Thus,
robustness against tuning errors (or changes of tuning parameters) and efficiency ofenergy harvesting have a trade-off relationship. Upper and lower limits of electric
damping and converting ratio can be used to design the balance of this trade-off
relationship.

3.4. Multi-Physics Parameter Design Method for Energy Storage

The purpose of multi-physics parameter design regarding energy storage is tomaximize energy storage and ensure robustness against changes in vibration frequency.
Figure 3.9 shows the electric circuit for storing energy into a battery (capacitor).
Equations for this electric circuit are derived as follows.
 'dI (t )
 E (t ) = rI (t ) + LdtdI (t )'
− E (t ) = rI (t ) + L
dt E ' (t ) = 0 E ' (t ) > 0
 E (t ) ≥ 0 
 E ' (t ) > 0
 E (t ) < 0 [ else ]

(3.5)

Where
E ' (t ) = E (t ) − Vb (t ) − Vd

Vb (t ) =t

1
I (t ) dt + Vb (0 )C ∫0Where E(t) is the electromotive force, E ’ (t) is induced voltage to the battery, V b (t)is the battery voltage, V d is the voltage dropped by diodes in a rectifier circuit, I(t) isthe current, r is the internal resistance of a coil of the power generator, L is the selfinductance of the coil and C is the capacitance of the battery. If the capacitance C isenough large, a change in battery (capacitor) voltage is negligible; the battery voltage

37

can be treated as a fixed value. The electric circuit experiences energy loss caused by
the internal resistance r, and the diode’s voltage drop Vd . The reactive energy generated
from coils of the electromagnetic power generator does not charge any energy to thebattery; it keeps cycling the energy in the electric circuit. The critical vibration
frequency of bridges usually has low natural frequency, hence, the diode’s voltage
drop Vd can be simplified as a fixed value in low-frequency circuits. The dimensionlessparameters are defined as follows.
Br =Vb ⋅ k emf
F0 ⋅ r,Dr =Vd ⋅ k emf
F0 ⋅ r

,

ζe =

2
k emf

2 r k 2 ⋅ m2

Where B r is the battery voltage ratio, and D r is the diode’s voltage drop ratio. The
following non-dimensional quantities were also introduced.
W2 =Wrms =

Vb ⋅ A
2
0

F

(3.6)

K ⋅M

ω 2π
∫ A(t )dt
K ⋅ M 2π 0

Vb
F02

(3.7)

where W2 is the harvesting power response when battery circuits are used, Wrms is theroute mean square value of harvesting power response, and the current to the capacitor
is corrected to A(t) = |I(t)| by the rectifier. All input and output parameters have once

again been made into dimensionless form, and thus any reference to parameters or
outputs henceforth are dimensionless. In the case of energy storage, the route meansquare value of harvesting power is more important than amplitude, unlike power
generation. The route mean square value of harvesting power response in steady-statevibration is obtained by changing the frequency ratios γ1 , γ2 , and the battery voltage
ratio Br . In this study, it has been shown that to ensure robustness against changes invibration frequency, the root mean square value of harvesting power response insteady-state vibration Wrms must satisfy the minimum power Wc in the range between
the normalized excitation frequencies, λl and λh , using the constraint function.
Concurrently, the spectrum for power generation must maximize electric power
generation when λ = 1, using the objective function. The constraint function andobjective function for energy storage are defined as(

Q2 = min Wrms (γ 1 , γ 1 , Br , λ ) λ = λl , λ h

38

)

(3.8)

G 2 = Wrms (γ 1 , γ 1 , B r , λ ) λ =1

(3.9)

The balance between robustness and route mean square values of harvesting power
can be adjusted through the constraint function Q2 . Normalized excitation frequencies
λl , λh and minimum power Wc can be modified depending on the purpose of energy
harvesting. Figure 3.10 shows the sequence of the proposed design method. For
various combinations of the aforementioned parameters, γ1 , γ2 and Br , the harvesting
power response is calculated by reiterating the presented sequence of analysis. Thissequence of iterations is continued until the maximum objective function G2 isobtained using the SQP method. In general, by this method a local maximum value ofG2 , equal to a global maximum, could be found. Therefore, as shown in Figure 3.11(a),varying the three design parameters γ1 , γ2 and Br , influences the distribution of G2 .
Figure 3.11(b) shows the side view of the three-dimensional Figure 3.11(a). Thesefigure enables a better comprehension of the local maximum. As shown in Figure
3.11(b) the local maximum values of G2 have a distribution range between thefrequency ratios γ1 and γ2 . However, if the battery voltage ratio Br is high, the densityof G2 which satisfies the constraint function Q2 is low. In other words, the efficiencyof energy harvesting is highly sensitive to tuning errors. Conversely, as shown in
Figure 3.11(a), if the battery voltage ratio is low, the robustness against tuning errorsof γ1 or γ2 increases, while the harvesting power response becomes highly sensitive tochanges in Br . Fundamentally, the battery voltage ratio Br is variable as it depends on
the amplitude of forced excitation F0 . It is vital to consider robustness against not
only changes in vibration frequency, but also against tuning errors, and againstchanges in Br . Therefore, robustness against tuning errors of γ1 or γ2 and changes in
Br are a trade-off relationship. Upper and lower limits of the battery voltage ratio canbe designed to balance this trade-off relationship.

3.5. Summary

Effects of parameters on energy harvesting have been investigated for efficientenergy harvesting from bridge structural vibrations. To achieve the efficient energy

39harvesting, three important factors were revealed. First, increase the energy flow into
TMG, second, increase the transducing energy from the mechanical domain to theelectrical domain, and thirdly, increase the power factor or converting ratio ofelectrical energy to energy harvesting. In addition, a multi-physics parameter design
method has been developed to tune TMG. Results from parametric studies have shownthat for effective energy harvesting, first, it is essential to determine the relationshipbetween the required characteristics for the electromagnetic power generator, andsecond, that TMG requires a robust parameter design for random bridge vibrations,accuracy of assembling TMG and tuning errors.
It should be noted that there is also the potential for the proposed TMG to befurther developed so that nonlinear characteristics of the energy harvester during
charging can be controlled under variable bridge vibrations due to heavy traffic.

40Mechanical energy of second mass
Electrical energy

TMG

𝑚𝑚1

Mechanical energy of main mass
Mechanical dissipation by
structural damping of TMG

𝑀𝑀Bridge vibration energy
Mechanical dissipation bybridge structural damping

Figure 3.1(a)𝑚𝑚2BridgeEnergy flow model of bridge-TMG system

Energy storage
EnergyharvestingJ

Thermal energy

H

F

I

MechanicalElectricalenergyElectricaldissipation

E energy of

G

𝒎𝟐

D

K

C

Mechanicaldissipation

B
A

Mechanicalenergy of
𝒎𝟏

M

L

N

Bridge vibration energyO
Mechanicaldissipation

Figure 3.1(b)Energy flow of TMG with a dual-mass system on the bridge

41

3.0
0.9

γ1 = 0.948µ2 = 0.1µ1 = 0.001
ζM = 0.02

2.5

4
0.9

0.9

0.9

ζe

4

2.0

0.9

D1

1.5
0.9

0.9

1.0
0.5
0.6

Figure 3.2

0.98

0.9

4

8

0.9

1.0

0.9

0.9

A1

C1

0.8

4

γ2

0.94

1.2

8

0.98

B1

1.4

09

1.6

Distribution of harvesting power responses of the dual-masssystem for various combinations of γ2 and ζe

5

A1 →

← D1

B1 →

← C1

Wmax

4

γ1 = 0.948µ2 = 0.1µ1 = 0.001

ζM = 0.02

3
2
1
0
0.9

Figure 3.3

0.95

1

λ

1.05

1.1

Harvesting power responses of the dual-mass system fordifferent combinations of γ2 and ζe42γ2 = 1.3

0.9

0.16

4

0.9

0.9

8

0.14

µ1 = 0.001
ζe = 1.00

8

0.9

A2

8

0.9

0.9

µ2

4

D2

0.10

ζM = 0.02

B2

0.9

4
0.90.9

0.12

8

C2

0.9

4

4

0.08

0.9

0.9

0.9

0.9

0.06
0.92

F igure 3.4

0.93

0.94

γ1

0.95

8

0.96

0.97

Distribution of harvesting power responses of the dual-masssystem for various combinations of γ1 and μ2

5

Wmax

4

A2 →

← D2

γ2 = 1.3

← C2

B2 →

µ1 = 0.001
ζe = 1.00
ζM = 0.02

3
2
1
0
0.9

Figure 3.5

0.95

1

λ

1.05

1.1

Harvesting power responses of the dual-mass system fordifferent combinations of γ1 and μ2

43Amplitude of harvesting power W

5
Objectivefunction
4
Constraintfunction

3

2

Wc
1

0

0.9

0.95

1.0

1.05

1.1

Tuning ratio

Figure 3.6

Objective and constraint functions of the proposed parameter
design method and frequency responses of power generation indimensionless form

44

Optimal 𝐺1

START
𝑖 = 1, 2
Given parameters𝜇𝜇𝑎𝑎 , 𝛾𝛾𝑎𝑎 , 𝜁𝜁𝑒𝑒 , 𝑃𝑓 , ℎCalculate𝑄1 and 𝐺1

Optimal 𝐺1

𝐺1 > 𝑊𝑊𝑐𝑐

Decrease 𝑑𝛾𝛾𝑎𝑎 , 𝑑𝜁𝜁𝑒𝑒

Was 𝐺1peak value?

Optimal 𝐺2
Was 𝑊𝑊
increased ?

Yes

Was 𝑊𝑊maximized ?

No

No

Vary
𝛾𝛾𝑎𝑎 , 𝜁𝜁𝑒𝑒

No

No

Vary
𝛾𝛾𝑎𝑎 , 𝜁𝜁𝑒𝑒

Yes

Vary
𝛾𝛾𝑎𝑎 , 𝜁𝜁𝑒𝑒

Yes

Determine the values 𝛾𝛾𝑎𝑎∗ , 𝜁𝜁𝑒𝑒∗
END

Figure 3.7

Flow of the multi-physics parameters design method

45

γ2

ζe

γ1

2

3D view of distribution of amplitude of 𝑊𝑊 with variations of

Figure 3.8(a)three design parameters γ1 , γ2 and ζe

2

ζe

γ1
Figure 3.8(b)2D view of distribution of amplitude of 𝑊𝑊 with variations of
three design parameters γ1 , γ2 and ζe

46

𝐸𝐸(𝑡𝑡)𝑟𝑟

𝐴𝐴(𝑡𝑡)𝐿𝐿

𝑉𝑉𝑑𝑑

𝐼𝐼(𝑡𝑡)

Power generator

Figure 3.9

𝑉𝑉𝑏𝑏

RectifierElectric circuit for charging

Optimal 𝐺2

START
𝑖 = 1, 2
Given parameters𝜇𝜇𝑎𝑎 , 𝛾𝛾𝑎𝑎 , 𝜁𝜁𝑒𝑒 , 𝐵𝐵𝑎𝑎 , 𝐷𝑎𝑎 , 𝑃𝑓 , ℎCalculate𝑄2 and 𝐺2

Optimal 𝐺2

𝑄2 > 𝑊𝑊𝑐𝑐

Decrease 𝑑𝛾𝛾𝑎𝑎 , 𝑑𝐵𝐵𝑎𝑎

Was 𝐺2peak value?

Optimal 𝐺2
Was 𝐺2increased ?

Yes

Was 𝐺2maximized ?

No

No

𝐶𝐶

Vary
𝛾𝛾𝑎𝑎 , 𝐵𝐵𝑎𝑎

No

No

Vary
𝛾𝛾𝑎𝑎 , 𝐵𝐵𝑎𝑎

Yes

Vary
𝛾𝛾𝑎𝑎 , 𝐵𝐵𝑎𝑎

Yes

Determine the values 𝛾𝛾𝑎𝑎∗ , 𝐵𝐵𝑎𝑎∗
END

Figure 3.10

Flow of the multi-physics parameters tuning method for energy
storage47

Figure 3.11(a) 3D view of distribution of amplitude of Wrms under variations of
three design parameters γ1 , γ2 and Br

2
1.8

γ2

1.6
1.4
1.2
1
0.96

0.94

0.92

γ1

0.9

0.88

0.86

Figure 3.11(b) 2D view of distribution of amplitude of Wrms under variations of
three design parameters γ1 , γ2 and Br

48

Chapter 4
Trial Applications of TMG to an Actual Bridge

Abstract .
In this chapter, a prototype TMG was developed. To investigate theconfiguration of TMG considering the performance of energy harvesting, first,
an application procedure and installation location of TMG were considered,and next, a tuned mass generator was applied to an actual expressway bridge.
According to the experiments on the existing bridge, it has been demonstrated
that TMG can generate electric power on a watt scale, which is required forthe structural health monitoring of bridges. This indicates that TMG cancompensate for the energy consumed by monitoring systems or other lowpower devices. In addition, the relationship between electric power generationand the traffic of large vehicles has been investigated.

49

4.1. Overview

In the previous chapters, parametric studies demonstrated that for effective energy
harvesting, TMG requires a robust parameter design for uncertain bridge vibrations,accuracy when assembling the TMG, and tuning errors. To enable the most effective
performance of TMG, a multi-physics parameter design method has been developed.
Consequently, a prototype TMG using a dual-mass system and electromagnetic power
generator has been developed.
In this chapter, to investigate the configuration of TMG considering theperformance of energy harvesting, first, an application procedure and installation
location of TMG were considered, and next, a prototype TMG was applied to an actual
expressway bridge. In addition, it was tested to see whether batteries could be charged
to make use of the energy harvested from the unused reserve of bridge vibrations. Ifbatteries could be successfully charged, TMG could be used for monitoring systems ofbridge structures. It would therefore be possible to establish sustainable healthmonitoring systems which do not require physical access for periodic battery
replacement or power supply construction.

4.2. Target Power Generation and Application Procedure

For health monitoring, bridge structural vibrations are generally measured todetect conditions of bridge structures. To date, energy harvesting devices fromvibration energy have been developed [9, 13, 14, 28, 39], however, the power
generation level obtained from bridge vibrations has generally been around micro-wattto milli-watt and is not still satisfied.

In this study, to achieve a required power

generation for the monitoring system of bridge structures with the smallest mass ratio,
the aim has been to obtain watt order power generation to supply energy to monitoring
devices. Therefore, TMG was developed as a prototype energy harvester using bridge
vibrations, and the mass ratio of TMG over bridge mass was set as 0.05 %, which isone order smaller than mass ratios of conventional tuned mass dampers used for50

vibration control of bridge structures. To achieve the target power generation, it isessential to bring out the ability of TMG by considering an application method of TMG
and vibration characteristics of bridge structures. To evaluate the ability of power
generation from actual bridge vibrations, the efficiency of converting absorbed energy
by TMG to power generation has been investigated.
The proposed application procedure of TMG is shown in Figure 4.1. First, a target
vibration mode of bridge structures and installation locations of TMG were considered.
Characteristics of bridge structures, such as modal masses and modal damping ratios
were then investigated. Next, parameters of TMG were determined through anexperimental evaluation procedure. The parameters of TMG were then tuned using the
proposed parameter design method. Finally, TMG was designed and developed. This
TMG was then applied on an existing bridge to investigate the characteristics of power
generation from vibrations of bridge structures.

4.3. Target Vibration Frequency and Installation location

First, target vibration modes and installation locations of the TMG were examined
to obtain the best performance of the developed TMG. TMG was designed to obtainelectricity for health monitoring systems from vibrations of bridge structures due totraffic loads of large vehicles. Higher the traffic volume, higher the induced energy.
To discuss the generality of TMG, the traffic volume should therefore be considered.
Dominant vibration frequencies of typical bridges are generally within 1 to 15 Hz on
vertical stringers or main girders. As an example of application to actual bridges, a
trial bridge, which is a 216 meters three span continuous steel truss bridge located on
an expressway in Gifu prefecture, was selected as shown in Figure 4.2. The target
bridge was selected by considering the traffic volume and dominant natural vibration
frequencies of the bridge. The traffic volume of large vehicles is around five to eight
thousands per day, and dominant natural vibration frequencies on the vertical girder ofthe bridge occur within 1 to 15 Hz.

51

4.3.1. Detection of Natural Vibration Frequency of the Trial Bridge
To detect the natural vibration frequencies of the trial bridge, acceleration
measurements were conducted. A strain gauge based accelerometer (sensitivity:
1 με.s2/m) was installed one quarter of the way along the first span of the target bridge(18 m from the start of the bridge) and a 500 Hz logging sampling rate was selected.
The frequency power spectrum density of the bridge vibration acceleration was
obtained as shown in Figure 4.3.
4.3.2. Decision of the TMG Installation Location
To determine an effective TMG installation location for energy harvesting fromvibrations of the bridge, acceleration measurements on the trial bridge were conductedusing two piezoelectric-based accelerometers (sensitivity: 6.42 pC.s 2 /m). One
accelerometer (named hereafter accelerometer A) was installed 18 m from the bridge
start as a fixed measuring point, and another accelerometer (named hereafter
accelerometer B) was installed onto various measuring locations as shown by the redpoints in Figure 4.2, for taking multiple measurements. Accelerometer A is expressedby the blue point. Target vibrations of TMG are the vertical vibrations of bridge
structures, therefore, acceleration measurements were taken from the central verticalgirders of the bridge. Since vibrations on the first span of the bridge are highest, agreater number of measuring points were located on the first span compared to otherspans. Acceleration measurements were then taken during two minutes in eachmeasurement step, with a sampling rate of 256 Hz.
To determine bridge vibration mode shapes, a modal analysis method of structures
vibrating under variable external loadings proposed by Kaito et al. [86] was applied.
First, the first five vertical vibration modes were focused on as they normally havelarge vibration energy. The detected five vertical vibration modes are shown in Figure
4.4(a) to Figure 4.4(e). Oscillation amplitudes of the detected vibration mode shapes
were then normalized. From the modal analysis, the vibration mode at 14.2 Hz had thelargest vibration acceleration among the natural frequencies of the target bridge, andso has been considered as the local structural vibration. To investigate the applicabilityof TMG, two vibration frequencies of the bridge were focused on; (a) large vibration
accelerations, (b) a low bridge vibration mode. By considering the tunable range of
TMG (higher than 5 Hz or more), the target vibration frequencies were determined as52

(a) 14.2 Hz and (b) 6.1 Hz. TMG can therefore generate maximum power where themode has the highest amplitude. From these results, the TMG installation location has
been decided to be one quarter of the way along the first span of the bridge (18 m fromthe bridge start).
In this research, to accurately identify the vertical vibration modes due to trafficloads, acceleration measurements were taken at multiple locations. However, it should
be noted that for practical use, the number of vibration measurement locations can befurther reduced.

4.4. Modal Mass and Damping
Characteristics of the bridge such as modal equivalent masses and modal damping
ratios were determined to design TMG.

4.4.1. Modal Equivalent Masses
The modal mass of the bridge was calculated using an eigenvector method [87]which is generally used for modal analysis. Normalized eigenvectors of vibration
modes and a mass matrix are used to calculate the modal mass at a particular location.
In the case of a N degree-of-freedom system as shown in Figure 4.5, the modal massof the i-order mode at j point-mass is formulated as follows.

{ } [M ]{X }M ij = X ij

T

(4.1)

ij

Where, [M] is mass matrix, {X ij } is the eigenvector of the i-order mode which isnormalized by the j point-mass as follows{X } = x {x , x ,..., x ,...x }
T

ij

−1
ij

i1

i2

ij

iN

(4.2)

In this study, a 21 degree-of-freedom point-mass model was considered. The mass
matrix [M] of the analysis model was created by assuming a uniform distribution of
the total mass of the bridge. The determined vertical vibration modes were used foreigenvector {X ij }. Using equation (4.1) and equation (4.2), the modal masses at 18m
from the start of the bridge were determined as shown in Table 4.1.

53

4.4.2. Modal Damping Ratio
The modal damping ratio was determined using the free vibration in each vibrationmode, using band-pass filters. The modal damping influences the efficiency of energy
harvesting since the bridge damping consumes vibration energy. To evaluate theharvested energy of TMG, the normal distribution of damping ratios was considered
and the modal damping ratio ζi (90 %) was determined as the upper limit value. Thisratio was selected for practical analysis of harvesting energy, since the variation below
the average modal damping ratio is advantageous for power generation and is not a
problem. The proportion above the upper limit value is therefore set to be 10 % of thetotal. The determined modal damping ratios of the bridge are shown in Table 4.1.

4.5. Determination of Characteristics of TMG

Figure 4.6 shows images of the developed prototype TMG and the power
generator. Figure 4.7 shows the analysis model which consists of a bridge and TMG.
The bridge is expressed by a modal mass M, modal stiffness K and modal damping
coefficient C M . The TMG model consists of two masses, m 1 and m 2 , and the two masses
and the bridge are connected in series with springs k 1 and k 2 . When the external
excitation force F(t) is induced to the bridge mass M, displacement of the bridge mass
M is expressed by X(t). x 1 (t) and x 2 (t) indicate the displacement of each mass of TMG.
A power generator is introduced between the two masses m 1 and m 2 , and the electric
damping force of the power generator is expressed by F e (t). For effective design of
TMG using the proposed tuning design method in Chapter 3, characteristics of TMG
should be evaluated first. Mechanical and electric experiments for evaluating TMG
characteristics have thus been conducted by using an excitation vibration machine andan electric circuit.

4.5.1. Mechanical Damping Characteristics of TMG
To evaluate the mechanical damping effect of TMG, the half power method [88]has been applied. The half power method is a classical method using the experimental

54

responses under random excitation forces. The applicable range of the damping ratiois 10 % or less. The evaluation formula of the damping ratio ζ is shown as follows.
ζ =1 fb − fa
2 fp

(4.3)

Where fa and fb are the frequencies at -3dB from the peak value of frequency response
spectrum (f a < f b ) [Hz], and f p is the resonant frequency [Hz].
A sweep excitation force from 1 Hz to 20 Hz was induced to TMG using theexcitation machine shown in Figure 4.8. The accelerations of the two masses and theactuator of the excitation machine were then measured. The frequency acceleration
response spectrums were obtained and the mechanical damping were experimentally
evaluated as follows.
c1 = 82.5 Ns/m, c 2 = 118.0 Ns/m

Where, the frequency spectrums used are expressed as follows.
H 1 ( jω ) =x1 ( jω )x ( jω ), H 2 ( jω ) = 2
X ( jω )x1 ( jω )(4.4)

4.5.2. Mechanical Coil Spring Characteristics of TMG
Regarding the long-term serviceability of TMG systems, it is essential that the coilspring is used within the allowable deflection range. Therefore, stoppers above andbelow each mass were designed to prevent the allowable deflection from being
exceeded. Also, the fatigue life of the coil springs was evaluated using a fatigue
strength diagram for helical compression springs according to JIS B 2704-1 (2009)[89]. If springs are operated at 80 % of the full stroke, the fatigue life is in the orderof 10 6 to 10 7 . In actual bridge vibrations, this level of vibration amplitude occurs
several times per hour. Therefore, if vibration of this level occurs 100 times per hour,
the fatigue life is in the order of ten years or more.

4.5.3. Electric Characteristics of Power Generator
In Chapter 2, the characteristics of power generators were theoreticallyexplained using an equivalent circuit of a power generator. The equivalent circuit of
the power generator and an external electric load R is shown in Figure 4.9. The power55

generator is expressed by the DC resistance r and the self-inductance L in theequivalent circuit. The DC resistance r is related to the conversion efficiency whenelectric power is generated from voltage induction. The smaller the DC resistance, thehigher the conversion efficiency. AC impedance �(2π∙ f∙ L)2 + r2 is related to the power

ratio, where f is frequency [Hz]. The smaller the AC impedance, the higher the power
ratio. Hence evaluation of the electric characteristics of the power generator is highly
important to achieve the best performance of the power generator.

4.5.4. Electromotive Force Coefficient: k emf
To evaluate the electromotive force coefficient k emf , experiments using an
excitation machine were conducted. The sine wave vibration was induced to themoving part of the power generator from the actuator of the excitation machine. The
induced voltage at the coil of the power generator were measured, and theelectromotive force coefficient was determined using the formula shown as follows.
k emf =

Vrms
v rms

(4.7)

Where, V rms is the root mean square value of induced voltage at the coil [V], and v rms
is the root mean square value of velocity of the moving part [m/s]. The velocity of themoving part was obtained from the displacement signal of the actuator. The
electromotive force coefficient k emf has been experimentally obtained as follows.
k emf = 250 V.s/m

4.5.5. DC Resistance of the Internal Coil: r
To evaluate the DC resistance of the internal coil of the power generator, aclassical method named I-V method was applied. I-V method evaluates the impedanceof the electric circuit by measuring the current and the voltage. The electric circuit
used in the experiment is shown in Figure 4.10. A voltage source and a shunt resistance(r s = 40 mΩ) were connected in series, where the voltage differential at the internalcoil V 1 [V] and the induced voltage at the shunt resistance V 2 [V] were measured. The
DC resistance of the internal coil was obtained using the formula below.
r=

V1
R
V2

56

(4.8)

From the experimental evaluation, the DC resistance of the internal coil has beenobtained as follows.
r = 5 .7 Ω

4.5.6. Inductance of the Internal Coil: L
The self-inductance of the internal coil was experimentally determined by using
the I-V method. The electric circuit used in the experiment is shown in Figure 4.11.
The AC voltage source and shunt resistance (r s = 40 mΩ) were connected in series tothe power generator. The root mean square value of the induced voltage at the power
generator V 1rms [V] and the detected voltage at the shunt resistance V 2rms [V] were
measured. The self-inductance of the internal coil L is obtained using the formula
below
L=

1

V12rmsω V22rms

R2 − r 2(4.9)

Where, ω is the radial frequency of the AC voltage source [rad/s]. The determined selfinductance of the internal coil L [H] is a function of radial frequency and can beapproximately expressed by the following equation.
L = −0.099 log(ω ) + 0.742 H(4.10)

4.6. Parameter Design
To determine the effective parameters of TMG to maximize the power generationfrom vibrations of bridge structures, a numerical analysis of power generation was
conducted using the equivalent forced excitations estimated from the acceleration
measurements of the target bridge. The analysis model is shown in Figure 4.7. The
equivalent force was calculated using the proposed method by Taguchi et al. [90].
In this study, the mass ratio of the first mass of TMG to the bridge mode mass isaround 0.05 % with the aim to obtain watt order power generation from bridge
vibration. The weight of the first mass of TMG was therefore determined as 104 kg.

57

The damping ratio of the bridge vibration mode was obtained using the measured freevibration acceleration data of the bridge using a band-pass filter. The mechanicaldamping coefficients of TMG were obtained using the half power method. The target
tuning parameters were the frequencies of two masses f1 , f2 and the electric damping
coefficient of the power generator c e . The parameters aiming to maximize the energy
harvested were determined using the proposed analysis iteration flow shown in Figure
3.7 in Chapter 3. A target frequency range of harvesting energy was 5.7 Hz to 6.1 Hz,
considering the frequency response of the target bridge, and the determined parameters
f*1 ， f*2 ， c*e for two target vibration modes are shown in Table 4.2 and Table 4.3
respectively. According to researches on the bridge vibration monitoring [4,50,51],
seasonal changes of natural frequency of bridges are less than 0.1 % (or less than 0.2
Hz). The target frequency range of harvesting energy includes therefore generalseasonal changes of natural frequency of bridges. According to another research on thebridge vibration monitoring [46], it is considered that the damages on local bridge
structural members, such as fatigue clacks and corrosion, has little influence on
vibration characteristics of whole bridges. Therefore, when TMG is designed tocorrespond to a whole vibration mode of bridge structures, the long-term influence bydamages of bridge structures on the harvesting energy can be comparatively smaller
than the influence by seasonal changes of natural frequency of bridges.

4.7. Application of TMG to the Trial Bridge
4.7.1. Experiment for Power Generation
The designed TMG for the two different vibration modes, namely 6.1 Hz and 14.2
Hz, was installed onto the selected location of 18 m from the start of the bridge asshown in Figure 4.12. To evaluate the characteristics of power generation on the actual
bridge, a one-day experiment was conducted. Regarding the long-term serviceabilityof the TMG system, the TMG was covered with an aluminum case to protect it fromweather influences, and the electric circuit was covered with a waterproof anddustproof housing. The electric circuit for the power generation shown in Figure 4.12

58

was used in this experiment. To improve the efficiency of electric circuit, a power
factor correlation capacitor C was introduced in this electric circuit. As shown in
Figure 4.13 and Figure 4.14, the hourly harvested energy was obtained from themeasured voltage generation of TMG. The hourly traffic of large vehicles was alsomeasured and plotted. The blue line shows the hourly harvested energy, and the bar
chart shows the hourly traffic of large vehicles measured by a traffic counter device
located 1.2 km away from the trial bridge. The results of each target frequency are
explained below.
4.7.1.1. Target Frequency of 14.2 Hz
As shown in Figure 4.13, the average hourly energy harvested in the one-day
measuring period was 2.9 mWh. The maximum power generation was around 0.5 to 2
W when large vehicles passed. This power obtained is several orders higher thanprevious vibration energy harvesting in low frequency vibrations [8,9,12-14]. Powergeneration is analyzed in further detail in section 4.8.3. The hourly energy harvested
is strongly related to the traffic of large vehicles. As can be seen the peak value of theenergy harvested and traffic of large vehicles occurred at midnight, and the hourly
energy harvested changed with traffic.
4.7.1.2. Target Frequency of 6.1 Hz
As shown in Figure 4.14, The average hourly energy harvested in the one-day
measuring period was 2.9 mWh. The maximum power generation was around 0.5 to 3
W when large vehicles passed. Table 4.4 shows the basic power consumption ofsensing devices and data loggers. The power supply ratio expresses the average power
generation of TMG to the power consumption of sensing devices. TMG can compensate
all electric energy when the power supply ratio is over 100 %. On the other hand, TMG
can only compensate a part of electric energy and extend the service life of sensing
devices when the power supply ratio is less than 100 %. The energy harvested isplanned to mainly charge batteries, and be periodically used to monitor the bridge’s
structural condition. Therefore, the experimentally harvested energy of TMG fromvibrations of bridge structures can satisfy the general use of monitoring systems.

4.7.2. Experiment for Charging Batteries using Harvested Energy59For effective charging of batteries using harvested energy, it is important to reduce
the two negative effects as follows; (i) charging power loss and (ii) natural dischargeof batteries. (i) Charging power loss is mainly caused by a voltage drop in the rectifier
circuit and internal resistance of batteries. The natural discharge of batteries can be
reduced if the battery voltage is small. Therefore, to increase the charging efficiency
of batteries using the energy harvested, Schottky Barrier Diodes (SBD) were applied
to reduce the voltage drop in the rectifier circuit. In addition, electric double-layer
capacitors (named hereafter super capacitors) were selected as the batteries for thisstudy since their internal resistance is generally smaller than other batteries. Moreover,the super capacitors have the advantage of long-term reliability, longer life from charge
and discharge, and larger temperature ranges over a normal capacitor. SBD also havean advantage in efficiency of rectification over a general-purpose rectification diodeas the voltage drop is lower. The charged energy to the super capacitors was obtained
as follows.
J (t ) =(1
Cb V 2 (t ) − V 2 (0)2)(4.11)

Where, C b is the capacitance [F], J(t) is the charged energy [J], V(t) is the capacitor
voltage [V] and V(0) is the initial capacitor voltage. The charging electric circuit usedin the experiment is shown in Figure 4.15. A super capacitor array, witch thecapacitance C b = 80 F, 7.5 V withstand voltage and 38 mΩ of DC resistance, was used.
To consider the effect of the natural discharge of the super capacitor array, a naturaldischarging experiment was conducted in laboratory. Figure 4.16(a) shows the
charging circuit used in the experiment, and Figure 4.16(b) shows the experimental
results. The voltage drop V d was larger when the capacitor voltage was higher. On theother hand, the voltage drop rate was constant when the capacitor voltage was less thanaround 3 V. The current supplied to the charging electric circuit was in the order ofaround 1 to 10 mA, and the voltage drop of the rectifier circuit using SBD was around
0.4 to 0.6 V. The charging experiments to the supper capacitor array were conducted
for each target bridge vibration mode.
4.7.2.1. Target Frequency of 14.2Hz
Figure 4.17 shows the charged electric energy to the super capacitor array with ablue line. The initial voltage was around 1 V because charging energy loss is higher

60when the capacitor voltage V(t) is near 0 V. As shown in Figure 4.17, the increase inrate of charged energy was smaller on November 9 th , 15 th , 16 th and 22 th , 2014, because
the traffic of large vehicles was lower. Furthermore, the increase in rate of the charged
energy was higher when the capacitor voltage was lower. On the other hand, theincrease in rate of the charged energy was lower when the capacitor voltage was higher.
One reason is that harvested electric energy is dependent on the capacitor voltage,
hence the efficiency of charging electric energy changes. Moreover, the naturalelectrical discharge of the capacitor increases when the capacitor voltage is high. Basedon the natural electrical discharge characteristics of the super capacitor array (Figure
4.16(b)), the natural discharged energy in a charging experiment can be obtained. Theenergy harvested by TMG can be expressed as the summation of the charged energy
and the natural discharged energy, as shown by the red dashed line in Figure 4.17. The
increase in rate of energy harvested by TMG was higher when the capacitor voltage
was higher. However, the natural electrical discharged energy increased with anincrease in the capacitor voltage. Therefore, the increase in the charged energy ratio
reduced with an increase in the capacitor voltage. Based on these results obtained in
the charging experiment, the natural electrical discharge effect should be consideredto improve the charging efficiency.
4.7.2.2. Target Frequency of 6.1 Hz
Figure 4.18 shows that the charged energy in the super capacitor array is shownwith a blue line. The initial voltage V(0) was 1.7 V. The total charged energy in theexperiment lasting two weeks was 280 J. The increase in rate of charged energy was
smaller on November 30 th , December 1 st , 6 th and 7 th , 2014, because the traffic of large
vehicles was low. The discharged energy from the super capacitor array was obtained,
and the energy harvested by TMG was expressed as the summation of the measured
charged energy and discharged energy, as shown by the red line in Figure 4.18.
According to these results from the charging experiment, the increase in rate ofharvested energy of TMG was higher when the capacitor voltage was around 2 V. The
natural discharged energy increased with an increase in the capacitor voltage.
Therefore, the increase of charged energy ratio reduced with an increase in thecapacitor voltage. Based on the charging experiment results, the capacitor voltage

61

could be determined as the parameter to improve energy harvesting and energy
charging.

4.7.3. Efficiency of Power Generation
Figure 4.19 to Figure 4.21 indicate an example of traffic-induced bridge
acceleration, generated voltage and power generation data in time domain, during 30
seconds of the one-day measuring period. The accelerations of the two masses of TMG
were also measured. From these measured data, the energy flow of the bridge-TMG
system was obtained and is shown in Figure 4.22. The maximum generated power was
3.2 W. This power is several orders higher than previous vibration energy harvesting
methods, namely micro-watt to milli-watt orders in low frequency vibrations [10-17].
It is therefore a significant result. The equivalent masses depend on bridge vibration
modes, therefore, band-pass filters were used to separate the first to fifth vibration
modes. The vibration energy in each bridge vibration mode were separately obtained
and summated. As shown in Figure 4.22, the total induced energy from the externaltraffic load was 143 J. Most of the energy was dissipated by the bridge’s structural
damping as shown in Table 4.1. 3.3 J or 2.3 % of the total energy was harvested andconverted to electric energy using TMG. This efficiency is two orders higher than themass ratio of around 0.05 %, which is another significant result. The energy flow ofeach vibration mode are shown in Figure 4.23(a) to Figure 4.23(e), respectively.
Figure 4.24 shows the combined band-pass filters used to separate the vibration modes.
As shown in Figure 4.23, over 99 % of the total electric energy was generated in the
6.1 Hz bridge vibration mode. The absorbed energy using TMG is expressed as thesummation of the consumed energy in mechanical damping (3.0 J) and energy
harvested (3.3 J). The converting efficiency of TMG is around 52 %, which is obtainedby dividing the energy harvested by the total absorbed energy. Hence, TMG could
generate electric energy from more than half of the absorbed energy.

4.7.4. Vibration Energy
To consider the vibration energy of bridge structures, the modal vibration energy
distributions were examined. First, the vibration modes of the bridge were identified,and second, the vibration energy of each vibration mode was obtained. To identify the62modal vibration energy distributions, a method using vibration measurements ofbridges was considered. The modal vibration energy distribution has been obtainedusing the excitation force due to traffic loads. This method was proposed by Taguchi
et al. [90] and to evaluate the modal vibration energy from traffic loads, bridge
characteristics such as modal mass and damping were used (Table 4.1).
The modal vibration energy distribution was evaluated from acceleration
measurements of the target bridge. Figure 4.25(a) shows the hourly traffic of large
vehicles, Figure 4.25(b) shows the hourly modal vibration energy distribution, andFigure 4.25(c) shows the total modal vibration energy distribution between the 8 th and9 th November 2014. Figure 4.26 show the results between the 25 th and 26 th November
2014, and Figure 4.27 show the results between 17 th and 18 th November 2015. As
shown in these figures, the second vertical vibration mode at 3.1 Hz had the highest
energy, around half of the total bridge vibration energy, and the third vertical vibration
mode at 6.1 Hz had the second highest energy. The efficiency of energy harvesting by
TMG could be further improved if TMG could be tuned for the lower vibration
frequency. Although the total vibration energy depended highly on the traffic of large
vehicles and had peaks at midnight, the modal vibration at 6.1 Hz was induced not onlyat midnight, but also during daytime. Since the total traffic including normal vehicles
is large during daytime, it is considered that the third vertical mode at 6.1 Hz is induced
by not only the traffic of large vehicles, but also small vibrations. This finding can beadvantageous for harvesting energy from bridge vibration. Namely, harvesting energy
from the third vertical mode at 6.1 Hz of this bridge is effective if electric energy canbe harvested from not only large vibrations by traffic of large vehicles, but also small
vibrations. The characteristics of power generators can be further designed to improvethe efficiency of power generation.

4.8. Summary
To harvest and make use of the unused reserve of vibration energy from bridge
structures, a prototype of TMG was developed. To investigate the configuration of63

TMG considering the performance of energy harvesting, TMG has been applied to an
actual expressway bridge. The findings are summarized below.
A) Installation and tuning procedures of TMG were proposed and demonstrated fromacceleration measurements on the trial bridge. The target vibration modes andinstallation locations of TMG were provisionally determined by using the
proposed method of vibration modal analysis.
B) By using the proposed tuning design method, TMG was tuned to adapt to two
different bridge vibration modes. The ability of the two tuning designs were
demonstrated through an experiment on the trial bridge.
C) TMG was found to achieve watt order power generation, which was the aim of thetuning design. The energy harvested by TMG from experiment was found to satisfy
the energy required for the general use of monitoring systems.
D) TMG could generate electric energy greater than 2 % of the traffic-induced
vibration energy of the bridge. This efficiency is two orders higher than the mass
ratio of the bridge and TMG, which is around 0.05 %, and so is satisfactory. It wasalso demonstrated that TMG could generate electric energy from more than half of
the unused reserve of energy which conventional tuned mass dampers absorb.
In addition, the applicability of TMG could be further improved if TMG could beapplied to lower bridge vibration modes (less than 5 Hz) since large energy is expected
in low bridge vibration modes. The tunable range of TMG was mechanically limitedby the nominal stroke of coil springs. Moreover, the characteristics of the power
generator could be designed to improve the efficiency of power generation or to reducethe magnetic force.

64

Investigation of the Target Vibration Mode and Installation Location
・Power Spectrum
・Cross-Spectrum

Investigation of Modal Characteristic (Mass and Damping)・Free vibration method

Investigation of electro-mechanical characteristic of TMG
・Half power method
・I-V method

Parameter Design of TMG
・Numerical analysis

Experimental Evaluation of Efficiency of Power Generation
・Energy harvesting with power generation circuit
・Electricity charging with battery circuit

Figure 4.1

Flow of the proposed application method of TMG

Installation
Location of TMG
(18m)

A2

P3

P4

1 st Span

2 n d SpanA2

3 r d Span
P3

P4

14.800286.000
72.000

P1

P2
72.00034.000

unit: [m]Start45.00045.00021.00019.00072.000

P1

P2

Accelerometer A

Traffic Direction

Accelerometer B

x [m]
0m

Figure 4.2

Trial bridge and installation location of TMG and accelerometers65

5Acceleration [gal]

4

3

2

1

0

Figure 4.3

0m

0

5

10
15
Frequency [Hz]20

Frequency spectrum of acceleration of bridge

72m

144m

216m

Figure 4.4(a) Bridge vibration mode at 1.5Hz

0m

72m

144m

216m

Figure 4.4(b) Bridge vibration mode at 3Hz

66

0m

72m

144m

216m

Figure 4.4(c) Bridge vibration mode at 6Hz

0m

72m

144m

216m

Figure 4.4(d) Bridge vibration mode at 9Hz

0m

72m

144m

216m

Figure 4.4(e) Bridge vibration mode at 12Hz

67

𝑥𝑥𝑎𝑎1𝑚𝑚1Figure 4.5

Table 4.1

𝑥𝑥𝑎𝑎2

…

𝑚𝑚2

𝑥𝑥𝑎𝑎𝑗
𝑚𝑚𝑗

…

𝑥𝑥𝑎𝑎𝑁
𝑚𝑚𝑁

N-degree of freedom model in i-order modal vibration

Natural frequency in each vibration mode of bridge and equivalent mass at
installation location of TMG

Vibration Frequency
Equivalent Mass M(Mass Ratio
over Total Bridge
Mass)
Damping Ratio of
Bridge1 st mode
1.6Hz

2 nd mode
3.1Hz

3 rd mode
6.1Hz

4 th mode
9.1Hz

5 th mode
12.5Hz245ton(34.8%)

470ton(66.8%)

233ton(33.2%)

129ton(18.4%)

361ton(51.4%)

0.035

0.019

0.017

0.031

0.012

68

2 nd mass: m2

Shaft(Moving part)

Power generator

Coil yoke(Fixed part)

250

360

620
Main mass: m1116

Unit: [mm](a) TMG

Unit: [mm](b) Power generator

Stopper

66

Power generator

75

2nd mass

70

65

Coil spring

83

Main mass

Coil spring
Stopper620

Unit: [mm](C) Drawing of TMG (front view)

Figure 4.6 Image of TMG and the electromagnetic power generator

69

𝑘𝑘2
𝑘𝑘1
𝐾𝐾

𝑚𝑚2

𝑐2

𝑚𝑚1
𝑀𝑀

𝑥𝑥2 (𝑡𝑡)

𝐹𝐹𝑒𝑒 (𝑡𝑡)𝑐1
𝐶𝐶𝑀𝑀

𝑥𝑥1 (𝑡𝑡)

TMG

𝐹𝐹 (𝑡𝑡)𝑋𝑋(𝑡𝑡)

BridgeFigure 4.7

Analysis model of TMG and bridge system

Figure 4.8

Setup of TMG on an excitation machine70𝐸𝐸(𝑡𝑡)

𝑟𝑟

𝐿𝐿

𝑅𝑅

𝐼𝐼(𝑡𝑡)𝑉𝑉(𝑡𝑡)

Electromagnetictransducer
Figure 4.9

Electric circuit for power generation

Electromagnetictransducer

V

𝐿𝐿

𝑅𝑅
𝑟𝑟𝑠

V 𝑉𝑉1

𝑟𝑟

Figure 4.10

𝑉𝑉2

𝐸𝐸

Electric circuit for evaluation of DC resistance of the internalcoil of the power generator

Electromagnetictransducer

V

𝐿𝐿

𝑟𝑟𝑅𝑅𝑠

𝑟𝑟

Figure 4.11

𝑉𝑉2𝑎𝑎𝑚𝑚𝑠

V 𝑉𝑉1𝑎𝑎𝑚𝑚𝑠

𝐸𝐸(𝑡𝑡)

Electric circuit for evaluation of self-inductance of the internalcoil of the power generator

71

Table 4.2

Tuning parameters for 14.2Hz vibration mode

Second mass
Main mass
Natural frequency of second mass

m2 = 12 kg
m1 = 104 kg

Natural frequency of main mass

f*2 = 18.50 Hz

Damping of second mass
Damping of main mass
Electric damping
Capacitance for power factor correlation

f1* = 16.98 Hz

c2 = 118.0 Ns/m
c1 = 82.5 Ns/mc*𝑒𝑒 = 1615 Ns/m
C = 220 μF

Table 4.3

Tuning parameters for 6.1Hz vibration mode

Second mass
Main mass
Natural frequency of second mass

m2 = 31 kg
m1 = 104 kg

Natural frequency of main mass

f*2 = 10.2 Hz

Damping of second mass
Damping of main mass
Electric damping
Capacitance for power factor correlation

f1* = 6.92 Hz

c2 = 118.0 Ns/m
c1 = 82.5 Ns/mc*𝑒𝑒 = 1972 Ns/m
C = 1200 μF

𝐸𝐸(𝑡𝑡)𝑟𝑟

𝐶𝐶

𝐿𝐿
𝐼𝐼(𝑡𝑡)𝑅𝑅

𝑉𝑉(𝑡𝑡)

Electromagnetictransducer

Figure 4.12 Electric circuit model used in the experiment72

Figure 4.13

Generated electric energy and traffic per hour

6

600

4

400

2

200

0
12:00

Figure 4.14

18:00

00:00
Time

06:00

0
12:00

Generated electric energy and traffic per hour(target frequency: 6.1 Hz)

73

Traffic volume (large vehicle)

Amount of electric power [mWh](target frequency: 14.2 Hz)

Table 4.4Power consumption of general monitoring devices of bridge
structures and power supply ratio by TMG

Monitoring Device
MEMS accelerometers
MEMS Temperature
sensors
Low-power
consumption datalogger𝐸𝐸(𝑡𝑡)

𝑟𝑟

Power
Consumption
0.1~1mW
0.01~0.3mW

Power Supply
Ratio by TMG
300% or more
1000% or more

1mW~

300% or less

𝐿𝐿

Electromagnetictransducer

𝑉𝑉𝑑𝑑

RectifierFigure 4.15 Charging circuit

74

𝐶𝐶𝑏𝑏 𝑉𝑉(𝑡𝑡)Super capacitor array
To avoltageloggerRectifier

To TMG

Figure 4.16(a) Setup of the charging circuit with a super capacitor array usedin the experiment

Capacitor voltage [V]

4

3.5

3

2.5

Figure 4.16(b)

0

500

1000
1500
Time [hour]

2000

Discharge characteristic curve of the super capacitor array75

×1000
8

600

6

400

4

200

2

0
Nov.09Figure 4.17

Nov.13

Nov.17

Traffic volume (large vehicle)

Energy [J]8000Nov.21

Storage electric energy and hourly traffic

800

×1000
8

600

6

400

4

200

2

0
Nov.28Figure 4.18

Dec.02

Dec.06

Dec.10Storage electric energy and hourly traffic(target frequency: 6.1 Hz)

76

0

Traffic volume (large vehicle)

Energy [J](target frequency: 14 Hz)

10Voltage [V]

5

0

−5

−10

0

10

20

30

Time [sec]Figure 4.19 Generated voltage by TMG

300

Accelerations [gal]

200
100
0
−100
−200
−300

0

10

20

30

Time [sec]Figure 4.20

Bridge acceleration measured at 18m from the bridge start at
the installation location of TMG

77

4

Power [VA]

3

2

1

0

0

10

20

30

Time [sec]Figure 4.21 Generated power by TMG

150

Energy [J]

100

50

0

0

10

20

30

Time [sec]Figure 4.22 Energy flow in the bridge-TMG vibration system

78

100

Energy [J]

80

60

40

20

0

0

10

20

30

Time [sec]Figure 4.23(a) Energy flow of 1.5Hz vibration mode in the bridge-TMG
vibration system

100

Energy [J]

80

60

40

20

0

0

20

10

30

Time [sec]Figure 4.23(b) Energy flow of 3Hz vibration mode in the bridge-TMG
vibration system

79

100

Energy [J]

80

60

40

20

0

0

20

10

30

Time [sec]Figure 4.23(c) Energy flow of 6Hz vibration mode in the bridge-TMG
vibration system

100

Energy [J]

80

60

40

20

0

0

10

20

30

Time [sec]Figure 4.23(d) Energy flow of 9Hz vibration mode in the bridge-TMG
vibration system

80

100

Energy [J]

80

60

40

20

0

0

10

20

30

Time [sec]Figure 4.23(e) Energy flow of 12Hz vibration mode in the bridge-TMG
vibration system

20
0

dB

−20
−40
−60
−80
−100

Figure 4.240510Frequency [Hz]15

Summation of band-pass filters that was used in the modal
analysis of energy flows

81

600
500

Large Vehicles

400
300
200
100
0
18:00

0:00

6:00

12:00

Figure 4.25(a) Hourly traffic of large vehicles between 8 th and 9 thNovember 2014
800

Energy [mWh]

600

400

200

0
18:00

0:00

6:00

12:00

Figure 4.25(b) Hourly distribution of bridge vibration energy between
8 th and 9 th November 20148

12.5Hz (11.2%)
Total Energy [Wh]6

9.1Hz (13.9%)
4

6.05Hz (18.2%)
3.1Hz (51.1%)

2

1.6Hz (5.6%)

0

Figure 4.25(c) Distribution of total bridge vibration energy between
8 th and 9 th November 2014

82

600
500

Large Vehicles

400
300
200
100
0
12:00

18:00

0:00

6:00

Figure 4.26(a) Hourly traffic of large vehicles between 25 th to 26 th
November 2014
800

Energy [mWh]

600

400

200

0
12:00

18:00

0:00

6:00

Figure 4.26(b) Hourly distribution of bridge vibration energy between
25 th to 26 th November 20148

12.5Hz (12.1%)

Total Energy [Wh]6

9.1Hz (12.6%)
6.05Hz (16.2%)

4

3.1Hz (52.9%)

2

1.6Hz (6.3%)
0

Figure 4.26(c) Distribution of total bridge vibration energy between
25 th to 26 th November 2014

83

600
500

Large Vehicles

400
300
200
100
0
18:00

0:00

6:00

Figure 4.27(a) Hourly traffic of large vehicle between 17 th to 18 th
November 2015
800

Energy [mWh]

600

400

200

0
18:00

0:00

6:00

Figure 4.27(b) Hourly distribution of bridge vibration energy between
17 th to 18 th November 20158

12.5Hz (20.7%)
Total Energy [Wh]6

9.1Hz (16.5%)
4

6.05Hz (15.1%)

2

3.1Hz (40.9%)
1.6Hz (6.8%)

0

Figure 4.27(c) Distribution of total bridge vibration energy between
17 th to 18 th November 201584

Chapter 5
Efficiency Enhancement of Power Generators forEnergy Harvesting

Abstract .
Based on the findings in the field experiments, a potential of the efficiency
enhancement of power generators was revealed. In this chapter, a structuraldesign of power generators has been considered for the purpose of applying
TMG to constructively use vibrations of bridge structures. Yoke shapes andpermanent magnet shapes were considered as design parameters. Based on thefindings in parametric studies, the nonlinearity of the damping force of power
generation can be controlled and the magnetic spring force can also be
considered. Finally, a power generator for the TMG system has been designed
and developed, and its performance has been experimentally demonstrated.

85

5.1. Overview

In the previous chapters, TMG was applied to an actual expressway bridge andwatt order power was generated from vibrations of the bridge structure. In addition, tomake use of the energy harvested from bridge vibrations, batteries were successfully
charged. There is potential for these charged batteries to be used for monitoring
systems of bridge structures. However, the structural design of power generators for
effective power generation from vibrations of bridge structures has not yet been
established. A high performance power generator was used in Chapter 4 to achieve
high electric damping forces under low vibration frequencies of bridges. Although wattorder power was obtained from actual vibrations of the bridge structure, the fabrication
cost of the power generator was the greatest in the TMG system. Hence for practicaluse of TMG, the specifications of power generators should be controlled for improving
its use.
To investigate the structural design of power generators, Zhu et al. [83] proposeda power generator with vertical magnetic flux. The characteristics of electric power
generation and damping force of the power generator were analytically andexperimentally demonstrated. A power generator with radial magnetic flux has also
been proposed and it has been found to generate higher voltage with a smaller magnet
volume than the power generator with vertical magnetic flux [41,43]. However, it
should be noted that the structural design for a radial magnetic flux is generally more
complicated than power generators with vertical magnetic flux.
In this study, for the harvesting of energy generated from vibrations of bridge
structures, power generators have been enhanced considering their structural design.
In addition, the nonlinear characteristics of power generation and magnetic springs
were investigated. If the characteristics of power generators can be controlled anddesigned, factors such as the cost effectiveness of TMG can be further improved.

865.2. Design Concept

Figure 5.1 shows a model electromagnetic power generator. The electromagnetic
power generator consists of a moving part and fixed part. The moving part consists ofexternal magnets and a magnet yoke, while the fixed part consists of an electric coiland a coil yoke. By inducing velocity to the magnetic field generated by the permanent
magnet, an induced electromotive force is generated at the coil. To simplify the
analysis, the power generator has been expressed by an axis-symmetric model (Figure
5.2).

5.2.1. Analysis Model
The structural design of a power generator has been conducted using Finite
Element Analysis (FEA). In this study, COMSOL® ver.5.2 has been used as the FEA
software for electromagnetic analysis. The material properties and conditions of FEA
are shown in Table 5.1 and Figure 5.3. As shown in Figure 5.3, the nonlinear
characteristic of the yoke material (steel: SS400) has been considered in this analysis
model. Figure 5.4(a) shows an entire view of the analysis model, and Figure 5.4(b)shows one part of the model in closer detail. As shown in Figure 5.4(c), the moving
part of the analysis model slides up and down within a range of ±20 mm. BDF(Backward Differentiation Formula) method is applied as a time stepping method. To
enhance electromagnetic power generators, not only should the accuracy of analysis
be considered, but also the analysis time, since iterative FEA is carried out to design
dimensional parameters of electromagnetic power generators.
5.2.1.1. Analysis Accuracy and Analysis Time
In order to obtain high computational accuracy of FEA results, it is important toconsider the following factors(a) The aspect ratio of elements(b) Mesh size(c) Absolute and relative tolerance87Since the aspect ratio of elements can be considered when creating a mesh, theinfluence of (b) mesh size and (c) absolute and relative tolerances, on analysis accuracy
and analysis time was investigated. The most accurate FE model is shown in Figure5.5, which is a closer view of Figure 5.4(b). A triangular second-order Lagrangianelement is applied. The number of degrees of freedom are 569.6 k, the absolute
tolerance is 10 -5 and the relative tolerance is 10 -6 . Although this is a highly accurate
result, it is not practical as the mesh size and tolerances were greatly reduced in themodel, which greatly increases the computational time accordingly.
As shown in Figure 5.6(a) to Figure 5.6(d), four finite element models withdifferent mesh sizes (number of degrees of freedom = 113.7×103 , 73.8×103 , 32.4×103 ,16.7×103 ) were considered. First, the influence of the various relative tolerances on theanalysis error and the analysis time were investigated as shown in Figure 5.7 andFigure 5.8 (the absolute tolerance is fixed at 0.001). The analysis error is evaluatedby the electromotive force value that is expressed by the following equation.

∑ (V (x ) − V (x ))analysis error =∑V ( x )

2

0

x

2

(5.1)

0

x

Where, V(x) is the induced electromotive force [V] of the analysis model, V 0 (x) is
the induced electromotive force [V] of the model shown in Figure 5.5 (degrees of
freedom: 569.6 k, absolute tolerance: 10 -5 , relative tolerance: 10 -6 ). As Figure 5.7
indicates, when the relative tolerance decreases, the analysis error decreases also,
hence the analysis accuracy increases. However, a decrease in analysis error, namely
the improvement of the analysis accuracy, does not occur when the relative tolerance
is 0.001 or less. As shown in Figure 5.8, the smaller the relative tolerance, the longer
the analysis time, which is unfavorable. However, the analysis time does not increase
when the relative tolerance is 0.001 or less. Moreover, the larger the number of
elements, the longer the analysis time, which again is unfavorable, and there is also no
considerable difference in the analysis accuracy.
Next, the influence of the various relative tolerances on the analysis accuracy andthe analysis time are indicated in Figure 5.9 and Figure 5.10 (the absolute tolerance
is fixed at 0.00001). As shown in Figure 5.9, if the absolute tolerance reduces from0.001 to 0.00001, the analysis accuracy increases, namely the analysis error decreases

88

by approximately 50% or more. However, the analysis accuracy does not increase when
the accuracy of the relative tolerance is around 0.001 or less. As Figure 5.10 indicates,
the smaller the relative tolerance, the longer the analysis time. In particular, theanalysis time increases sharply, as the analysis time increases if the relative tolerance
is less than 0.001.
Based on these findings, the balance between analysis accuracy and analysis time
has been considered, and it has been concluded that the appropriate analysis toleranceof about 1% will be used in this study. The analysis degree of freedom will be between
30000 to 40000 (30 to 40 k, similar to model C shown in Figure 5.6(c)), with anabsolute tolerance of 0.001, and relative tolerance of 0.001.

5.2.2. Target Design Parameters
5.2.2.1. Electromotive Force Coefficient
Based on Faraday's law of electromagnetic induction, when the moving part isshifted, the non-load induced voltage E(t) is applied to both ends of the coil inproportion to the amount of change in the magnetic flux φ(t) in the coil, as shown in
the following formula.
E (t ) =δφ (t )
δt

(5.2)

In Chapter 2, the magnetic flux was treated as a constant, irrespective of the positionof the moving part x(t) [mm]. The electromotive force coefficient was expressed as aconstant by using the relationship where the change in the magnetic flux was
proportional to the velocity of the moving part as shown in the formula.
δφ (t ) δx(t )
∝
δt
δt

(5.3)

However, it is expected that this linear relationship is not applicable when the positionof the moving part moves greatly. Therefore, the electromotive force E has been
considered as a function of not only time t, but also of the position of the moving partx.
kemf (x ) =E ( x, t )v ( x, t )

89

(5.4)

in which kemf is the electromotive force coefficient [Vs/m], and v(x,t) is the velocity ofthe moving part of the electromagnetic power generator. As shown in equation (5.4)
the electromotive force coefficient k emf (x) [V.s/m] is considered as a function of theposition of the moving part.
5.2.2.2. Maximum Electric Damping CoefficientElectric power is generated when the moving part is forced to move by externalloads. The relationship between the electric power and the power of the external forces
is expressed as follows.
 Rr
F (x, t )v(x, t ) = E 2 ( x, t ) +22 (R + r ) (R + r ) (5.5)

Where, the first right term of the equation expresses the induced electric power to theelectric resistance R, and the second right term of the equation expresses the induced
electric power in the internal coil of the power generator. F(x,t) [N] is proportional tothe velocity of the moving part. Therefore, F(x,t) can be expressed with the electric
damping coefficient c(x) [N.s/m] as follows.
F ( x, t ) = c ( x ) ⋅ v ( x, t )c(x ) =

2
(x )
kemf

r

(5.6)

1
Rr + 1(5.7)

Where, Rr = R / r is the resistance ratio. The resistance ratio is a dimensionless2
parameter, therefore, it is clear that k emf(x ) / r has the same dimension with thedamping coefficient [N.s/m]. Equation (5.7) demonstrates that the equivalent
electrical damping coefficient increases when the resistance ratio Rr decreases.
The total electric power generation [VA or N.m/s] by combining the above
equations, and considering the electromagnetic power generator to include equivalent
damping becomes
Wtotal (t ) = (ceh (x ) + cel (x ))x 2 (t )(5.8)

Where ẋ (t) is the velocity, and ceh (x) and cel (x) are damping coefficients due toharvested electric power and electrical loss respectively. These equivalent electrical
damping coefficients can be defined as
ceh (x ) =

2
kemf
( x)

r

Rr
,
(1 + Rr )2cel (x ) =

90

2
kemf
( x)

r

1
(1 + Rr )2(5.9)

5.2.2.3. Magnetic Spring Force Effect
The moving part is influenced by the magnetic force which occurs between thepermanent magnet and the coil yoke. This force is generally called cogging force. In
general, the higher the cogging force, the higher the moving resistance. This causes a
decrease in power generation efficiency. However, in this study, the cogging force has
been treated as the restoring and repelling forces towards the neutral position of themoving part (x = 0mm), similar to the spring force of a tuned mass system. This effect,
namely the magnetic spring effect, is considered in the use of the power generator.

5.3. Design of Power Generator

The ability of power generation is highly influenced by the yoke shapes of power
generators, since the magnetic path through the coil, from the north-pole to the southpole, is controlled by the yoke shapes. The magnetic path is generally called magnetic
circuit. The magnet shape of power generators is also important, since themagnetomotive force in the magnetic circuit is induced by the magnet shape. Therefore,
the yoke and magnet shapes should be designed to increase the magnetic flux passing
through the coil.
In this study, the yoke and magnet shapes were designed to control thecharacteristics of power generators. Design parameters with seven dimensions, namely
magnet yoke tooth height, My_th, magnet yoke width, My_w, coil yoke tooth height,
Cy_th, coil yoke tooth width, Cy_tw, magnet height, M_h, magnet yoke height, My_h,and coil yoke height, Cy_h, were introduced as shown in Figure 5.2. The
corresponding dimensional values are indicated in Table 5.2. In addition, the air gap
between the moving part and the fixed part should be as small as possible, since themagnetic resistance in the magnetic circuit is higher in the air than in the steel yoke.
An air gap of 0.5mm has been selected for this study and this value is realistic,
considering the balance between the accuracy of assembly and fabrication cost.

91Based on the findings obtained from the experiments of harvesting energy on thetrial bridge in Chapter 4, two important requirements for power generators werediscovered;(a) high efficiency for small vibrations(b) wide stroke range for large vibrations
In addition, a reduction of the friction force and a reduction of the fabrication cost
are also important. To reduce the friction force, the shaft part was made non-magnetic
to eliminate the horizontal absorption force with the bearing part, and to reduce thefrictional resistance. The air gap between the moving part and the fixed part was
designed as 0.5mm, and this design can be achieved with basic fabrication accuracy.
For this reason, fabrication costs can be reduced by one order from the conventional
power generator used in Chapter 4.

5.3.1. Parameter Design Method of Power Generator
In this study, dimensional parameters of power generators have been considered
to obtain the required power generation and the required damping effect of power
generators. Table 5.2 shows the design parameters of the power generator, the initial
power generator values, and parameter value limitations. The objective function F opt
is shown in Table 5.3. To take into consideration the two aforementioned important
requirements for power generators, (a) high efficiency for small vibration and (b) wide
stroke range for large vibration, were separately studied. As indicated by the blue
rectangle in the left hand figure or the red rectangle in the right hand figure of Table
5.3, the objective function F opt is the minimum of the electromotive force coefficientk emf [V.s/m] in the stroke range X min ≤ X ≤ X max [mm]. Combinations of design
parameters that maximize the objective function F opt were identified by iterative
calculations of the FEA analysis for (a) and (b), respectively. The parameters identified
are shown in Table 5.3.
As indicated in Table 5.3, the electromotive force coefficient k emf [V.s/m] and thestroke range (X max - X min ) [mm] are in a trade-off relationship. Therefore, multiobjective functions (a) high efficiency for small vibration, and (b) wide stroke range

92

for large vibration were introduced to the power generator for harvesting energy fromvibrations of bridge structures. By controlling the balance between the electromotive
force coefficient and stroke range, appropriate dimensional parameters for power
generators has been proposed. Designed power generators satisfy the required power
generation performance by using multi-objective functions.

5.3.2. Iteration Procedure
Since the computational complexity increases in iterative computations of FE
models, efficient FEA with an appropriate balance between analysis accuracy andanalysis time has been acquired by using the analysis conditions discussed in Section
5.2.1.1. The dimensional parameters were designed to maximize the multi-objectivefunctions by using a dynamic search method. The dynamic search method can beconsidered as a generalized version of Newton’s method. Through a trial and error
procedure, it was concluded that this method is effective to obtain an enhanced power
generator.

5.3.3. Design of Power Generator
To attain the best performance of TMG, multi-objective functions were decided
based on the two requirements of the power generator as follows.
(a) High efficiency for small vibrations
To maximize the minimum electromotive force coefficient k emf within a ±2 mm
stroke range.
(b) Wide stroke range for large vibrations
To satisfy the minimum required electromotive force coefficient of k emf = 100[V.s/m] within a ±10 mm stroke range.
These objective functions are indicated in Figure 5.11. The red area shows theobjective function for high efficiency for small vibrations, the blue area shows theobjective function for wide stroke range for large vibrations. Figure 5.11 shows also
the examples of characteristics of the electromotive force coefficient versus
displacement of the moving part by gray dotted lines. The target parameters are93

indicated in Figure 5.2. First, FEA results are checked if the electromotive force
coefficient satisfies the objective function for wide stroke range (blue area in Figure5.11), and next, parameters are changed to maximize the objective function for highefficiency (red area in Figure 5.11) which satisfy the two objective functions
simultaneously. Finally, the design parameters were determined through iterative FEA
using the direct search method as shown in Table 5.4. Determined characteristics ofthe electromotive force coefficient versus displacement of the moving part is shown in
Figure 5.11 by a red line.

5.4. Experimental Evaluation

Based on the designed dimensional parameters, an electromagnetic power
generator has been developed (Figure 5.12). The three key characteristics of theelectromagnetic power generator, namely the electromotive force coefficient k emf , thedynamic friction force and the magnetic spring force, were experimentally evaluated.

5.4.1. Electromotive Force Coefficient k emf
The newly developed electromagnetic power generator was set on an excitation
machine as shown in Figure 5.12. The moving part of the power generator was forced
to slide up and down by the actuator. The electromotive force coefficient k emf was
obtained from the experimentally measured induced voltage. The electromotive force
coefficient was designed to satisfy the required efficiency within the wide stroke range
and obtain high efficiency within the short stroke range. To evaluate the nonlinear
characteristics of the voltage induction, the triangular wave excitation was carried out(5 mm/s, ±20 mm). The sampling rate was 1000 Hz.
Figure 5.13 shows the induced voltage and the velocity of the moving part, which
was obtained by division of the displacement of the actuator. Figure 5.14 shows therelationship between the electromotive force coefficient and the position of the moving
part. The blue line shows the electromotive force when the moving part slides upwards,
while the red line shows the electromotive force when the moving part slides

94

downwards. As shown in Figure 5.14, the electromotive coefficient is a function of
the position of the moving part, and this characteristic is the same as the designed
values in FEA. The errors in the designed values from FEA were 10 % or less. The
cause of the difference between the two lines is considered to be due to the hysteresis
effect.

5.4.2. Dynamic Friction ForceFriction force is one of the largest losses when harvesting vibration energy, and it
occurs mainly on the shaft holders of the power generator. In addition, the larger thefriction force, the shorter the rating life of the shaft holders. Therefore, the friction
force should be evaluated clearly. The experiment system is shown in Figure 5.12. The
induced force to the moving part was measured by the strain load cell (capacity: 5kN,
output: 2 mV/V) .
Figure 5.15 shows the relationship between the induced force and the position of
the moving part. The upper line shows the induced force when the moving part slides
upwards. The lower line shows the induced force when the moving part slides
downwards. Therefore, the dynamic friction force can be obtained by
Dynamic friction force = (upper line – lower line) / 2(5.10)The relationship between the dynamic friction force and the position of the moving
part is shown in Figure 5.16. Based on the results, the rating life of the shaft holdersof the power generator were evaluated. The rating life of shaft holders is normally
expressed as a distance as follows.
2 f ⋅ f ⋅ f C
L =  H T C  ⋅ 50 [km]fWP(5.11)

where, L is rating life [km]，f H is hardness factor, f T is temperature factor, f C is contact
factor, f W is weighted factor, C is basic load [N] and P is working load [N]. To estimate
the rating life time, a converting formula was introduced.
Ly =L[year]
2 ⋅ ls ⋅ n1 ⋅ 526(5.12)

Where, L y is rating life [year], l s is stroke [m] and n 1 is number of cycles per minute[cpm]. Based on the specification of the applied shaft holders, the basic load and95

factors are shown C = 412 N, f H = 0.8, f T = 1.0, f C = 0.81 and f W = 2.0. From theexperimental results, the working load to the shaft holders was selected as P = 100 N,
since the variation below the working load is advantageous for the rating life and is
not a problem. From the experimental result on the bridge, the average stroke andnumber of cycles per minute were selected as l s = ±5 mm, n 1 = 100 cpm. According tothese formula, the rating life of the two linear bushes used in the power generator are
120 km or 13.5 years or more.

5.4.3. Magnetic Spring
The magnetic spring force is obtained as the average of the upper and lower linesof the force-displacement graph (Figure 5.15) namely
Magnetic spring force = (upper line + lower line) / 2(5.13)

Figure 5.17 shows the relationship between the magnetic spring force and theposition of the moving part. The aforementioned characteristics can be used fordesigning TMG.

5.4.4. Design of TMG
To enable the best performance of TMG, a nonlinear characteristic of theelectromagnetic power generator, namely the electromagnetic damping force F e (x,𝑥𝑥̇ )that is induced by an electromotive force and a magnetic spring force F m (x), wasconsidered. The analysis model is indicated in Figure 5.18. In this analysis model,
nonlinear characteristics of the developed power generator and friction forces σ1 andσ2 are considered. The electromagnetic damping force is expressed as follows.
Fe (x, x ) ={k (x )}

2

emf

R+r

⋅ x 2(5.14)

Where, k emf (x) is the electromotive force coefficient [V.s/m], R is external electric load[Ω], r is DC resistance of the coil [Ω], x is the position of the moving part of the power
generator from its neutral position. The nonlinear characteristics of electromotive force
coefficient k emf (x) and magnetic spring force F m (x) were experimentally evaluated96(Figure 5.14 and Figure 5.17). By using this analysis model, TMG can be tuned tobring out the best performance of the efficiency enhanced power generator.

5.5. Summary

In this chapter, an effective structural design of a power generator has been
proposed to control the specifications of power generators to adapt with TMG for
effective energy harvesting from vibrations of bridge structures. In addition, thenonlinear characteristics of power generation and magnetic springs were investigatedwith FEA to obtain the best performance of TMG. The following results were obtained.
A) The yoke and magnet shapes in the power generator have been designed to control
the characteristics of power generators. Considering the magnetic circuit, sevendimensional parameters of power generators have been selected as design
parameters.
B) A design method has been proposed using multi-objective functions to satisfy thetwo important requirements for the power generator, namely high efficiency forsmall vibrations, and a wide stroke range for large vibrations.
C) With the proposed design method, the power generator has been designed anddeveloped. The characteristics of the power generator have been verified throughexperiment.
In addition, if the dynamic friction loss can be reduced to 1 N or less, TMG systems
could harvest energy even from vibrations induced by small vehicles. Efficiency of
power generation could be further improved if the air gap between the moving part andfixed part could be reduced, or if the volume of neodymium magnet and/or the coil
could be increased.

97

ShaftCoil yoke
Coil

Fixed part
MagnetMagnet yoke

Figure 5.1[mm]

Moving partA model of electromagnetic power generators

Axial symmetric
Magnet yoke

Shaft

M_h

My_h

Magnet

Coil

Cy_th

Cy_th

Yoke teeth

Cy_tw

My_w

My_tw

Coil yoke[mm]Figure 5.2

Analysis model of electromagnetic power generators by 2D
axial symmetric model

98

Table 5.1

Relative permeability of each material of the power generator,
magnetic flux density of the neodymium magnet, and coil turns
for Finite Element Analysis
𝝁𝝁𝒚𝒚𝒚𝒚𝒚𝒚𝒚𝒚

Yoke (steel: SS400)
Air
Coil (cooper)

𝜇𝜇𝑎𝑎𝑎𝑎𝑎𝑎
𝜇𝜇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝜇𝜇𝑚𝑚𝑚𝑚𝑚𝑚
𝐵𝐵𝑟𝑟

Neodymium magnet

1.00
1.00
1.05
1.2 [T]

1300
𝑁𝑁
Note: Nonlinear relative permeability of the yoke material μyoke is shown in Figure 5.3 .
Coil turns

yoke

1500

Relative permiability:

1000

500

0
10

3

10

Magnetic field:

Figure 5.3

4

10

5

H [A/m]Nonlinear characteristic of relative permeability of yokes(steel: SS400)

99

Zoom
Fig.
5.5 and Fig. 5.6

Air

Coil

Coil Yoke

Axial Symmetry

Axial Symmetry(b)MagnetFig. 5.4(b)Magnet Yoke

Air

[mm]

[mm]

Figure 5.4(a) Entire view of theanalysis model

Figure 5.4(b) A closer view of theanalysis model
Fixed Part

Axial Symmetry

Moving Part[mm]

Figure 5.4(c)Entire view of the moving part and the fixed part of
the analysis model100

Magnet Yoke
Coil Yoke

Coil

MagnetNumber of degrees of freedom = 569.6k

Figure 5.5

Element division of the most accurate Finite Element model

Magnet Yoke

Magnet Yoke
Coil Yoke

MagnetCoil Yoke

Coil

MagnetNumber of degrees of freedom = 113.7k

Figure 5.6(a)FE model A

Number of degrees of freedom = 73.8k

Figure 5.6(b)Magnet Yoke

Coil Yoke

Coil

MagnetNumber of degrees of freedom = 32.4k

Figure 5.6(c)FE model B

Magnet Yoke
Coil Yoke

MagnetCoil

Coil

Number of degrees of freedom = 16.7k

FE model C

Figure 5.6(d)101

FE model D

Figure 5.7

Relationship between analysis accuracy for voltage generation
and relative tolerance of various FE models

Figure 5.8

Relationship between analysis time and relative tolerance of

3

0

7

3

7

3

various FE models

102Figure 5.9

Relationship between analysis accuracy and relative tolerance
in the case of two different absolute tolerances

Figure 5.10

Relationship between analysis time and relative tolerance in

3

0

3

)

3

3

)

)

3

)

the case of two different absolute tolerances103

Table 5.2

Initial value of dimensional parameters of the power
generator and limitations
Parameters

Initial Value

Lower Bound

Upper Bound

My_h

Magnet yoke height

82[mm]

70[mm]

110[mm]Cy_h

Coil yoke height

73[mm]

65[mm]

95[mm]

Cy_th

Coil yoke tooth height

17[mm]

3[mm]Cy_h/2

My_th

Magnet yoke tooth

8[mm]

3[mm]

(My_h-

heightMy_w

56[mm])/2

Magnet yoke width

Table 5.3

10[mm]

5[mm]Two different design objective functions F opt and theidentified dimensional parameters of the power generator
(b)

200

200

150

150

EMF Coefficient [Vs/m]

EMF Coefficient [Vs/m]

(a)

100

50

0
-15

17[mm]

Fobj [V.s]
-10

-5

0

5

Fobj
50

0
-15

15

10

100

[V.s]

-5

-10

0

5

10

15

Displacement [mm]Displacement [mm]Electromotive force coefficient anddisplacement

Electromotive force coefficient anddisplacement-10 mm ≤ X ≤ 10 mm-2.5 mm ≤ X ≤ 2.5 mm

Objective of design parameters: maximizing F obj[]

Fobj = min k emf ( X ) ⋅ ( X max − X min )

[ ]

[ ]

max Fobj = 1.796 V.smax Fobj = 0.807 V.s

My_h = 105.1 mm

My_h = 94.5 mm

Cy_h = 76.3 mm

Cy_h = 82.1 mm

Cy_th = 21.1 mm

Cy_th = 17.8 mm

My_th = 7.1 mm

My_th = 10.0 mm

My_w = 14.9 mm

My_w = 14.9 mm

104Figure 5.11

Electromotive force coefficients verses displacement for various
combination of parameters for multi-objective functions

Table 5.4

Designed dimensional parameters of the power generator

Magnet yoke tooth height
Magnet yoke width

My_th
My_w

13.0 mm18.0 mm

Coil yoke tooth height

Cy_th

20.0 mm

Coil yoke tooth width
Magnet height

Cy_tw

2.5 mmM_h54.0 mm

Magnet yoke height

My_h95.0 mm

Coil yoke height

Cy_h74.0 mm105

Powergenerator

Fixed partMoving part
Load cell

Actuator

Figure 5.12

Power generator and equipment of experimental evaluation test
using an excitation machine

[mm]

20

0

-20
0

5

10

15

20

25

30

0

5

10

15

20

25

30

0

5

10

15

20

25

30

[mm/s]

10

0

-10

[V]

2

0

-2

Time [sec.]

Figure 5.13

Displacement applied to the moving part, velocity of themoving part, and induced voltage signal of the power generator
in the experimental evaluation test

106

300
250

EMF Coefficient [Vs/m]

200
150
100
50
0
-50
-20

-10

0

10

20

Displacement [mm]Figure 5.14

Electromotive force coefficients of displacement in theexperimental evaluation test

30
20

Force [N]

10
0
-10
-20
-30
-20

-10

0

10

20

Displacement [mm]Figure 5.15

Relationship between force and position of the moving part ofthe power generator

107

60
50

Friction Force [N]

40
30
20
10
0
-20

-10

0

10

20

Displacement [mm]Figure 5.16

Relationship between friction force and position of the moving
part of the power generator in the experimental evaluation test

30

Magnetic Spring Force [N]

20
10
0
-10
-20
-30
-20

-10

0

10

20

Displacement [mm]Figure 5.17

Relationship between magnetic spring force and position of themoving part of the power generator in the experimental
evaluation test

108

m2
k2

σ2

x2(t)
Fe(x, ẋ )
x1(t)

m1
k1

σ1

c1

X(t)

M
𝐾𝐾

Figure 5.18

F(t)

𝐶𝐶𝑀𝑀

Analysis model of bridge-TMG system using nonlinear
characteristics of the developed power generator and friction
forces109

Chapter 6
Proposal of Uses of the Developed Energy
Harvesting System

Abstract .
In this chapter, an application and operation method of a prototype TMG forvibrations of bridge structures has been investigated. From experiments using
the developed device on the existing bridge, the performance of harvestingenergy was demonstrated. In addition, it was attempted to supply the harvested
electric energy to a monitoring system of a bridge structure.

1106.1. Overview

To apply TMG for health monitoring of bridge structures, reliability and efficiency
should be considered, and it is also necessary to establish an application procedure toharvest energy. In Chapter 4, an application procedure of TMG was proposed. In
Chapter 5, for effective energy harvesting from vibrations of bridge structures, theefficiency enhanced power generator was then actually developed.
In this chapter, to consider the reliability of TMG systems, attempts were made tostore the harvested energy in batteries and use them in a health monitoring system ofbridge structures. In addition, long-term harvesting energy was evaluated based on the
numerical analysis result. The nonlinear characteristics of power generation andmagnetic springs were considered, and so these characteristics were actively
incorporated into the TMG design. It is considered that these characteristics improve
the ability of power generation of entire TMG systems.

6.2. Application of TMG Systems

According to the application procedure defined in Chapter 4, it has been
attempted to charge lithium ion secondary batteries using the harvested energy andmoreover, the harvested energy has been used to operate a monitoring system.

6.2.1. Target Power for Monitoring Systems of Bridge Structures
To consider supplying electricity to health monitoring systems of bridge structures,the target harvesting energy must be determined. However, monitoring plans dependon each bridge structure and target to be monitored, and the required power varies
depending on sensing devices used for monitoring. To detect the bridge structural
conditions, bridge structural vibrations are generally used in many researches. For
example, bridge structural vibrations are measured by accelerometers for five minutes
every four hours, during two to four weeks for each season in reference [50]. In otherresearches, the bridge vibration acceleration data for several minutes are acquired per

111

day, or bridge vibration acceleration during disasters, such as earthquakes or typhoons,are measured using trigger functions. Considering these existing health monitoring
using accelerometers of bridge structures, the required harvesting energy for eachmonitoring plan was calculated. As examples, four monitoring plans were proposed inthis study to evaluate the required harvesting energy for health monitoring systems ofbridge structures.
Plan A: 5 minutes measurement per day is carried out everydayPlan B: 5 minutes measurement per hour is carried out two days per monthPlan C: 5 minutes measurement per hour is carried out one week per quarterPlan D: 24 hours continuous measurement per quarterIn these health monitoring plans, bridge structural accelerations were

continuously measured during the measuring periods. In plan A and plan B, the bridge
vibration modal analysis is mainly focused. In plan C, the bridge vibration modal
analysis under traffic induced vibration is focused. To measure the bridge vibrationmode, a plural number of sensing devices is generally used. In plan A to plan C, fivesensing devices are considered to be supplied electricity from one TMG as an example.
On the other hand, in plan D, continuous traffic induced vibrations is focused for the
purpose of such as weigh-in-motion. Since MEMS sensors and wireless data transfer
systems have rapidly been developed in recent years, a monitoring device using awireless communication system equipped with a MEMS accelerometer was selected(Figure 6.1). The specifications of the monitoring device used in this study are shownin Table 6.1. The sampling rate of the acceleration measurement of bridge structural
vibration is generally within the range between 100 Hz and 500 Hz. Each monitoringplan and its power consumption was then evaluated in Table 6.1.

112

6.3. Experimental Application of TMG Systems for Healthmonitoring systems of Bridge Structures

6.3.1. Experiment for Power Generation
The designed TMG for the third vertical vibration mode (6.1 Hz) was installed
onto the decided location, namely 18 m from the start of the bridge. To evaluatecharacteristics of power generation on the existing bridge, a one-day experimental
measurement was carried out. To consider the long-term usage of TMG, TMG wascovered with an aluminum case to protect it from weather influences. The designed
external electric load for the power generation was 40 Ω. Tuning frequencies of themain mass f 1 and second mass f 2 were 6.73 Hz and 10.2 Hz, respectively. These
parameters were designed using the proposed analysis iteration flow shown in Figure
3.7 in Chapter 3. As indicated in Figure 6.2, the hourly harvested energy was
obtained. As shown in Figure 6.2, the average hourly harvested energy in the one-day
measuring period was 2.3 mWh. Hence, the average harvested power generation was
2.3 mW in one day. This power is of the same level as the experiment in Chapter 4,
yet the fabrication cost of the power generator is one order smaller. The instantaneous
maximum power generation was around 1 to 3 W. This power is also of the same level
as the experiment in Chapter 4.
Based on the findings obtained in the experiments, first, the average harvested
energy and instantaneous maximum power generation were of the same level as theexperiment in Chapter 4. Second, TMG was adapted not only for smaller bridge
vibrations, but also for dominant excitation by traffic loads.

6.3.2. Application TMG to A Monitoring System of Bridge Structure
In the experimental application of TMG to the trial bridge in Chapter 4, thecharging circuit, which consists of the super capacitor array and the rectifier circuitwith shottky barrier diodes, was developed so that harvested energy can charge
batteries (Figure 6.3). The super capacitor array had low internal resistance and highelectricity storage efficiency. However, a large spontaneous discharge occurred at 3 Vor more in the experiment. Another problem was that the cost per energy density was113higher than that of a common used secondary battery, such as a lithium ion battery, by
an order of one or more. To solve these problems, lithium ion secondary batteries wereused. Although the internal resistance of the lithium-ion secondary battery is double
or more than that of the super capacitor (Figure 6.4), the spontaneous discharge
amount is smaller by one order or less. In addition, the charged energy in the lithium
ion secondary battery can be easily used for the monitoring device since only a smallchange in voltage occurs. The battery device consists of two AA-size lithium ion
batteries connected in series.
The charged electric energy in the battery was supplied to the monitoring device
and it was attempted to continuously operate the monitoring system of the bridge
structure (Figure 6.5). The monitoring plan was that five minutes of acceleration wasmeasured, and next, wireless data was transmitted to the base station once an hour.
This plan simulates the proposed monitoring plan A, B and C (Table 6.1).
The time series measured charged electric energy in the lithium ion batteries isshown by a red line in Figure 6.6. The battery device consists of two AA-size lithium
ion batteries connected in series, and the combined battery voltage is between 2.2 and
2.7 V. As shown in Figure6.6, the charging and consuming of batteries were repeatedin one-hour cycles. The battery energy was mainly consumed when the monitoring
device was communicating with the base station and transferring the sensing data once
an hour. At first, the voltage gradually decreased with repeating charging andconsuming energy. However, the battery voltage started to increase during a period of
daytime. The smaller the battery voltage, the smaller the rate at which the battery
voltage decreases. Therefore, it is possible that the energy supply and consumption canbe balanced when battery voltage is low.
To consider the effect of the energy harvested, the energy consumed by themonitoring device was estimated and is indicated with the black line in Figure 6.6.
The lower limitation of the operating voltage of the monitoring device is around 2.3 V.
As shown in Figure 6.6, the operating life-time of the monitoring device was extended
by suppling the electric energy from bridge vibration. In this experiment, themonitoring plan with high frequency measurements of five minutes monitoring period
once an hour was selected, namely simulating the proposed monitoring plan A, B andC (Table 6.1). Based on the results, it is estimated that the consumed energy by the114

monitoring device during the three days measuring period can be compensated witharound three days of charging batteries by TMG.

There are three solutions to improve the charging efficiency.
(i) increasing the induced voltage(ii) reducing the necessary voltage of the monitoring device
To increase the induced voltage, the number of turns of the coil should be increased.
This change is not difficult and can be attained with slight change in fabrication cost.
It is also considered to reduce the necessary voltage of monitoring devices. TMG canbe further developed if these problems are solved.

6.3.3. Evaluation of Energy Harvesting in Long-Term Uses

For practical application of TMG systems, it is important to comprehend how
much power generation can be expected in long-term use. In addition, it is also
important to verify if the designed TMG can satisfy the required power generation andif the stroke of the power generator is not over the limit. The numerical simulation ofenergy harvesting in a bridge-TMG system was therefore carried out. The analysis
model was shown in Chapter 5 (Figure 5.18), and Table 6.2 shows parameters usedin the numerical simulation. In this research, in order to comprehend the power
generation characteristics of TMG in detail, bridge acceleration data from one-day(between 25 th to 26 th November 2014) was used. The acceleration data length can befurther reduced to simplify this verification procedure. The analysis results are shownin Figure 6.7. The average harvested energy was 3.86 mWh/h in one day.
A method to estimate the amount of long-term energy harvested is proposed byusing the relationship between short-term energy harvested and traffic of large vehicles,
as demonstrated in the application experiment on the bridge in Chapter 4. The
proposed procedure for evaluating long-term energy harvested is indicated in Figure
6.8. First, the average energy harvested per large vehicle, named hereafter unit

115

harvesting energy, is obtained by dividing the energy harvested by the traffic of large
vehicles. Next, the long-term harvested energy is estimated by multiplying the longterm traffic of large vehicles by the unit harvesting energy.
The phenomena of harvesting energy from vibrations of bridge structures can beconsidered as scattered induced random vibration due to traffic loads that reach the
TMG through multiple paths. Rayleigh distribution is used to evaluate the expectedvalue of unit harvesting energy [91-93]. Rayleigh distribution is as follows.
P(x ) =bˆ =

 x2 
xexp
− 2 
b2
 2b 

(6.2)

1 n
X i2
∑
2n i =1(6.3)

π
Xˆ = bˆ2(6.4)

� is the expected value. By using the results
Where, b� is the Rayleigh parameter and X

� and 95 %obtained in Figure 6.7, the expected value of unit harvesting energy X

�95 have been evaluated as indicated in Table 6.3. Next, based on theconfidence level X
long-term traffic data (in this study, data from 7 th November 2014 to 12 th December
2014 were used), the long-term harvesting energy was evaluated (Figure 6.9 and Table
6.3). The expected value of harvesting energy per a day 𝐸𝐸� is 68.6 mWh/day, which isthe average calculated from five weeks’ worth of data. Table 6.9 indicates the balance
between the energy supply from TMG and energy consumption by monitoring systems
in each monitoring plan (shown in Table 6.1). The expected value of harvesting energy
𝐸𝐸� can sufficiently supply required energy for the monitoring plans A, B and C. In caseof plan D, the expected value of harvesting energy 𝐸𝐸� can enable long battery life. As

results, long-term applicability of the TMG system was evaluated based on the
numerical analysis.

116

6.4. Summary

For the practical use of TMG, a TMG system design procedure has been proposedconsidering the demand electric power, the cost effectiveness and the long-term
applicability. In addition, it has been attempted to charge batteries using the harvested
energy. The key factors of this chapter are summarized below.
A) In the experiments, energy harvested by TMG from vibrations of bridge structures
were found to satisfy the general use of monitoring systems, which was the aim of
the tuning design.
B) The harvested energy could be stored in secondary lithium-ion battery devices andused for health monitoring systems of bridges. TMG can therefore improve theservice life of monitoring systems.
C) Moreover, long-term applicability of the TMG system was evaluated based on the
numerical analysis. The nonlinear characteristics of power generation andmagnetic springs were considered into the evaluation procedure.
In addition, the applicability of TMG could be further improved if the energy loss
during battery charging is decreased by increasing the voltage induced by power
generators, by reducing the necessary voltage of monitoring devices.

117

Figure 6.1

Example of health monitoring device (wireless datatransmission, 3-axis MEMS accelerometers, voltage sensor,
temperature and humidity sensors)

Table 6.1

Configuration of a monitoring system and required energy formonitoring plans
Wireless Structural Sensing & Logging Device for Bridges(3-Axis MEMS Accelerometers, Voltage sensor, Temperature & Humidity Sensors)

6mA (Sensing), 33mA (Communication) @ 2.5V
Sampling rate: 128 Hz (Accelerometers)

Plan A
Plan B
Plan C
Plan D

Measurement
5 mins / day
5 mins / hour
5 mins /hour
24 hours

Period of Timeeveryday
2 days / month
1 week /quarter1 day / quarter

118

Number55
51Required Energy
23mWh/day
36mWh/day
42mWh/day
101mWh/day

Table 6.2

Parameters of the analysis model of Bridge-TMG systemm2

Second mass

k2

Coil spring of second mass

σ2

R
r

Friction force(second mass & power generator)
Electromagnetic damping force
Magnetic spring force
External electric load
DC resistanceF e (x,ẋ )F m (x)
40 Ω
10 Ω

m1

Main mass

104 kgk1

Coil spring of main mass

c1

Viscous damping

σ1

Friction force of the first mass

M

Bridge modal mass

K

Bridge modal stiffness

CM

Bridge modal viscous damping

F e (x,ẋ )32 kg
131.4 kN/m
(10.2 Hz)
6.0 N

186.0 kN/m
(6.73 Hz)44.0 N.s/m(0.5 %)
1.0 N
320000 kg
470.1 MN/m
(6.1 Hz)417.0 kN.s/m(1.7 %)

4

Energy [mWh]

3

2

1

0
18:00

Figure 6.2

0:00

6:00

Experimental result of the hourly harvested energy from bridge
vibrations of the trial bridge

119

Rectifier(SBD)

Batteries(Lithium-ion)Figure 6.3

Charging circuit using lithium-ion batteries and schottky
barrier diodes (SBD)

0.25

Voltage drop VF [V]Lithium-ion battery A

0.2

Lithium-ion battery B

0.15
Super capacitor
20F 2.5V

0.1

0.05
0
0

0.2

0.4

0.6

0.8

1

Ampere [A]Figure 6.4

Comparison of voltage drop of lithium-ion batteries and asuper capacitor (Experiment)120

Figure 6.5

Proposed continuous health monitoring system suppling
harvested energy

2.6

Battery Voltage [V]

2.5

2.4

2.3

2.2
12/02

12/03

12/04

12/05

Time

Figure 6.6

Battery voltage – time with supplying electricity to themonitoring system

121

8

Energy [mWh]

6

4

2

0
12:00

Figure 6.7

18:00

0:00

6:00

Evaluation of harvested energy (numerical analysis)

Wh/Traffic

40

Electric Energy per
Electric Energy [μWh]＝
Number of Large Vehicle
1 Large Vehicle

20

0
12:00

Parameter Estimation ofRayleigh distribution
1 n
∑
b� =
X2
2n i=1 i

18:00

0:00

6:00

Long-term traffic data

0.1

0
10

0

20

30

40

Wh/Traffic
800

Traffic / hour� = b� π/2 [μWh/Number]
Expected value X

Probability density

0.2

400

0
11/10

11/17

11/24

12/1

12/8

12/01

12/8

Date

Long-term electric energy harvesting

Energy [mWh]

2000

1000

0
11/10

11/17

11/24

Date

Figure 6.8

Evaluation procedure of long-term electric energy harvesting

122

50

4

Energy [Wh]

3

2

1

0
11/07

11/17

11/27

12/07

Date

Figure 6.9

Evaluation of long-term electric energy harvesting based on
the numerical analysis

Table 6.3

Unit energy harvesting per large vehicle and evaluated longterm harvested energy (average in 5 weeks)
Unit energy harvesting per large vehicle(Used traffic data: 2014/11/25 12:00 ~ 2014/11/26 11:00)

Expected value
95% confidence level

�
X

�95
X

13.2 μWh/Truck
11.0~16.6 μWh/Truck

Evaluated long-term harvested energy (average in 5 weeks)(Used traffic data: 2014/11/07 0:00 ~ 2014/12/12 24:00)
Expected value
95% confidence level

Table 6.4

�
E

�95
E

68.6 mWh/day
60.0~91.4 mWh/day

Evaluation of power supply in each monitoring plan

Plan A

Sufficiently supply: 261%~397%

Plan B

Sufficiently supply: 167%~254%

Plan C

Sufficiently supply: 143%~218%

Plan D

Long-life battery: 2.5~10.5 times

123Chapter 7
Conclusions

124

The results of these investigations support the following conclusions related to theobjectives of this study.
I.

Investigation of the structural characteristics of an energy harvester
Characteristics of an energy harvester, named Tuned Mass Generator (TMG), havebeen theoretically explained for harvesting energy to achieve greater power generationfrom bridge vibrations using an equivalent electric circuit of a power generator. It wasalso found that dual-mass systems have several advantages over single-mass systems
for robustness and efficiency of power generation. Based on these findings, TMG using
a tuned dual-mass system and electromagnetic power generator has been proposed.

II. Proposal of a parameter design method for effective energy harvesting
A multi-physics parameter design method has been proposed to tune TMG.
Results from the parametric studies shown that for effective energy harvesting, first,
it is essential to determine the relationship between the required characteristics forelectromagnetic power generators, and second, TMG requires a robust parameter
design for uncertain bridge vibration, accuracy of assembling TMG and tuning errors.

III. Evaluation of the applicability of TMG to an existing bridge
To investigate the configuration of TMG considering the performance of energy
harvesting, a prototype TMG has been applied to an existing expressway bridge.
Subsequently, performances of the tuning design of TMG were demonstrated throughan experiment on the trial bridge. In addition, the energy harvested from vibrations ofbridge structures was found to satisfy the energy required for the general use ofmonitoring systems.

IV. Enhancement of a power generators efficiency
An effective structural design of a power generator has been proposed to control
the specifications of power generators to adapt with TMG systems for effective energy
harvesting from vibrations of bridge structures. In addition, the nonlinear
characteristics of power generation and magnetic springs were investigated with FE
analysis to obtain the most effective performance of TMG. A design method was

125

proposed using multi-objective functions to satisfy the two important requirements for
power generator, namely high efficiency for small vibrations and wide stroke range forlarge vibrations. Enhanced performances of the power generator were verified throughexperiment.

V. Development of a TMG system that includes a health monitoring system ofbridge structures
To achieve practical use of TMG and to consider the reliability and long-term
applicability of the TMG system, attempts were made to store the harvested energy inbatteries and use them in a health monitoring system of bridge structures. Nonlinear
characteristics of power generation and magnetic spring effect, and othercharacteristics were actively incorporated into the design procedure to improve theability of power generation of the entire TMG system. In addition, it was demonstrated
that the energy harvested could be stored in the secondary lithium-ion batteries andconsequently used for a health monitoring system of bridges.

Finally, a method to harvest bridge vibration energy has been successfully
achieved using a developed TMG system. A health monitoring of bridge structuresusing a TMG system has been proposed and the ability for continuous healthmonitoring has been demonstrated.
Vibration-based energy harvesting using TMG has several advantages over otherpower sources, such as solar power generation. First, a stable electric energy can begenerated from bridge structures where a common traffic volume of large vehicles is
expected, such as expressway. Second, energy harvesting using TMG does not affectedby weather conditions and even a power failure, due to such as lightning and strongwind. Third, TMG system can reduce a long-term maintenance cost and an
environmental load since the TMG system can reduce power line installation work, andthe electricity rate is not required. In addition, TMG has a potential to monitor the
structural behavior using generated voltage signals, since TMG generate electricity
according to vibrations of bridge structures.

126

The proposed method in this research can be applied to various bridges, of which
the dominant natural frequency is higher than 5 Hz such as middle span bridges. To
obtain greater energy, it is essential to correspond to a lower natural frequency ofbridges. However, at present, it is difficult to achieve the greater harvesting energy
from bridge vibrations, because of the mechanical systems such as the stroke of coilsprings and the friction loss. The efficiency and applicability of TMG could be further
improved if TMG could be applied to lower bridge vibration modes.

127

Recommendations
The practical power generation according to the required energy level formonitoring systems is demanded. Since monitoring plans for bridge structures havebeen discussed in various studies, several required energy levels were examined byconsidering monitoring plans (plan A to D) in this study. It is possible to harvest energy
from bridge vibrations for regular monitoring, which obtains dynamic behaviors ofbridge structures using accelerometers. However, in order to measure dynamic
behavior continuously, a larger generated electric power is required. By improving theefficiency and enabling power generation at lower frequencies, TMG can achieve therequired energy level for such as continuous dynamic monitoring of bridge structures.
From the conclusions of this study, the following are proposed as further potential
enhancements of harvesting energy from vibrations of bridge structures.
(a) If the dynamic friction force can be reduced to the 1N or less, TMG could harvest
energy even from vibrations induced by small vehicles or from wind induced
vibrations. The friction force could also be improved considering the mechanicaldevices used in the power generator.
(b) TMG applicability could be further improved if the charging energy loss wasdecreased by improving the induced voltage of the power generator, by reducing
the necessary voltage of the monitoring device, or by boosting the battery voltage
to the required voltage of the health monitoring device.

128

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