Energy harvesting performance of a dandelion-like multi-directional piezoelectric vibration energy harvester

Sensors and Actuators A 230 (2015) 1–8

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Energy harvesting performance of a dandelion-like multi-directional piezoelectric vibration energy harvester Renwen Chen a,∗ , Long Ren a , Huakang Xia a , Xingwu Yuan a , Xiangjian Liu b a State Key Laboratory of Mechanics & Control of Mechanical Structures, Nanjing University of Aeronautics & Astronautics, 29 Yudao Street, Nanjing 210016, People’s Republic of China b School of Mechanical Electrical Engineering, Jinling Institute of Technology, 99 Hongjing Road, Nanjing 211169, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 26 September 2014 Received in revised form 12 March 2015 Accepted 27 March 2015 Available online 20 April 2015 Keywords: Vibration energy harvesting Multi-directional Piezoelectric Dandelion-like Energy conversion efficiency

a b s t r a c t To achieve effective harvesting of ambient vibration energy in different directions, this paper proposes a dandelion-like multi-directional piezoelectric vibration energy harvester (MD-PVEH). After theoretical design, analysis and optimization of the device, validation experiments were carried out, which shows that the dandelion-like MD-PVEH can harvest relatively more energy in different excitations, although it harvests less energy from excitation in individual directions (for example, the angle between excitation direction and X axis is ␲/2 in XZ plane). Overall, this dandelion-like MD-PVEH with a load resistor of 8 k can reach its maximum output power of about 0.28 mW and maximum energy conversion efficiency of 3% in the harmonic excitation which the frequency and amplitude are 22 Hz and 0.28 mm, respectively. It can meet the needs of many microelectronic devices. © 2015 Elsevier B.V. All rights reserved.

1. Introduction With the increasing development of microelectronics technology, electronic products tend to be miniaturized and integrated. The emergence and development of ultra-low-power communication standards as Bluetooth and Zigbee have urged the electronic products to be wireless and portable. However, the key technical problem that needs to be solved is how to adopt relatively easily applicable methods to supply power. Energy harvesting technology has the potential to liberate these low-power products from their traditional power-supply methods such as electric wire and battery, and makes their applications easier and more flexible. What is more, compared with supplying power by chemistry battery, energy harvesting technology is cleaner and more environmental friendly. Compared with harvesting solar energy and thermal energy, harvesting ambient vibration energy is more widespread [1]. Piezoelectric vibration energy harvesters have advantages of high energy density, non-electromagnetic interference, and easy integration with MEMS. Current researches on piezoelectric energy harvesting structures [2–12] are pretty thorough. Cantilevered beam structure has become mostly considered structure for the energy harvesting device because of its low stiffness, high

∗ Corresponding author. Tel.: +86 25 84893466; fax: +86 25 84892294. E-mail address: [email protected] (R. Chen). http://dx.doi.org/10.1016/j.sna.2015.03.038 0924-4247/© 2015 Elsevier B.V. All rights reserved.

sensitivity, easy calibration, etc. A kind of piezoelectric vibration energy harvester is developed by Shanghai Jiaotong University [13], and its prototype was made in 2007. They made silicon cantilever through MEMS technology, and PZT piezoelectric layers and electrode layers on the surface of cantilevers by Sol-Gel technology. They attached nickel masses to the end of cantilever beams. Under the resonant frequency of 608 Hz, its output power can reach 2.16 ␮W. Lee and other researchers [14] in National Taiwan University developed a kind of inter-digital electrode MEMS piezoelectric energy harvesting device in 2008. The device has a natural frequency of 214 Hz and can export electric power of 0.352 ␮W when driven by a sinusoidal acceleration excitation of 1 g. As can be seen from the above description, most piezoelectric vibration energy harvesters are based on linear single cantilevered beam structure and PZT piezoelectric material. Their structures are simple, and fabrication processes are not complicated. However, sometimes ambient vibration is not only in a single direction and a narrow frequency band. It is noteworthy that Marco Ferrari and Vittorio Ferrari propose a multi-frequency converter array (MFCA), which uses multiple bimorph cantilever beams with different natural frequencies to widen the bandwidth of the vibration energy harvester [15]. Their experiments show that the harvester with MFCA can harvest wideband vibration energy effectively, and supply power for battery-less sensor modules. Marco Ferrari’s team also proposed some different approaches to use nonlinear solutions to scavenge energy from wideband vibrations [16–18]. They

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use a piezoelectric beam converter coupled to permanent magnets to create a bistable system. In the excitation of random vibration, the system bounces between two stable states, which significantly improves the energy harvesting efficiency. In their later study, piezoelectric buckled beams are also used as a bistable scavenger structure for vibration energy harvester. Their research shows that the piezoelectric buckled beams exhibit superior power generation over a large interval of resistive load, with gains up to more than a factor of ten compared to unbuckled beams. Their researches greatly improved the frequency adaptation capability of vibration energy harvesters. However, in some cases, ambient vibrations are also in different directions. Traditional single-cantilevered beam structure is only sensitive to excitation in one direction, and is not able to maximize the harvested energy. This paper aims at designing, characterizing, optimizing and testing a dandelion-like multi-directional piezoelectric vibration energy harvester (MD-PVEH) which can harvest ambient vibration energy in different directions efficiently. This paper is organized as follows. In Section 2, we outline our design concept, theoretical analysis and optimization. In Section 3, we describe the experimental set-up and experiment results of the dandelion-like MD-PVEH, in comparison with the theoretical predictions. Conclusions are finally given in Section 4.

sensitive piezoelectric cantilevered beams can produce forced vibration, and achieve a full harvesting of energy in ambient vibration. This design is simple and easy to manufacture. Moreover, researches on single cantilevered beam piezoelectric energy harvesting structures has accumulated a large number of reliable theoretical and experimental results, which provides a lot of references for the analysis of this structure. For dandelion-like MD-PVEH, we design a multi-source energy harvesting circuit which can harvest output power from more than one source effectively. Because of their different fabrication positions, each single piezoelectric cantilevered beam structure has different vibration sensitive direction. Therefore, their output voltages are different in amplitude and phase. Considering diode and its one-way conductive property, we design a kind of poured-type charging circuit. All outputs of individual single piezoelectric cantilevered beam harvesting structure are connected to full-bridge rectifier circuit, to convert bipolar alternating signal to unipolar signal. After that, we use filter capacitors to convert signal to DC signal with smaller ripple, and charge battery through corresponding diodes and current limiting resistor.

2.2. Theoretical analysis 2. Concept design, analysis and optimization In this section we first propose a concept of MD-PVEH, give its dandelion-like structure design and the corresponding multisource charging circuit design. The theoretical analysis is then used for acquiring its output performance, and then the structural parameters are optimized. 2.1. Concept design Most of the vibration energy harvesters can only harvest energy of vibration in single direction efficiently. However, ambient vibrations are complex and usually change their directions, which is difficult for the application of harvesters. Therefore, to find some kinds of harvesting structures that are sensitive to vibration in different directions are significant. We call this kind of environmental adaptive piezoelectric vibration energy harvesters MD-PVEHs. We propose a dandelion-like MD-PVEH. The structure is shown in Fig. 1. As can be seen, the harvester consists of a number of piezoelectric cantilevered beams, multi-faceted support body, upright column and base. Each cantilevered beam is fixed on the multi-faceted support body in different directions, so they are respectively sensitive to vibration in different directions. When harvester is driven by ambient vibration in different directions, the corresponding

Fig. 1. Dandelion-like multi-directional energy harvesting structure: (a) side view; (b) top view.

Working process of dandelion-like MD-PVEH can be seen as that each single cantilevered beam is fixed on the multi-faceted support body and harvests vibration energy in different direction. The power harvested by the entire device is equal to the sum of which harvested by each single cantilevered beam. Therefore, we can select one of the single cantilevered beams to analyze. Analysis method for other beams is the same. In this way, we select a single cantilevered beam from the device arbitrarily. The single piezoelectric cantilevered beam and its parameters are shown in Fig. 2. Assuming the angle between this cantilevered beam and vibration direction is ˛i (i = 1, 2, . . ., 13), and vibration excitation is usinωt. According to the theory of synthesis and decomposition, excitation component that perpendicular to the cantilevered beam surface is zi = u sin ˛i sin ωt

(1)

Fig. 2. Structure of the single cantilevered beam and its parameters: (a) side view; (b) top view.

R. Chen et al. / Sensors and Actuators A 230 (2015) 1–8

3

When the cantilevered beam vibrates, the position of its neutral layer can be determined by the statics theory where the sum of micro internal forces in the cross section is zero, the equation can be expressed as







1 dAi,1 +

2 dAi,2 +

Ai,1

Ai,2

3 dAi,3 = 0

(7)

Ai,3

On the basis of Eq. (7), we obtain the position of neutral layer is ı= Fig. 3. Equivalent physical model.

In the following, we analyze the open circuit voltage and output power that generated by the cantilevered beam in the forced vibration. For a single piezoelectric cantilevered beam energy harvesting system, it can be modeled as a spring-mass-damper system. Its equivalent model is shown in Fig. 3. Assuming that the mass in the end of the cantilever is m, equivalent stiffness coefficient is k, and equivalent damping coefficient is c. In this equivalent physical model, we assume that zou,i is the displacement of the mass in the direction of vibration. The dynamic model can be expressed as m¨zou,i + c z˙ ou,i + kzou,i = −m¨zi

(2)

By solving Eq. (2), we can obtain the relative steady-state vibrational displacement of the mass, which is zou,i = Bi sin (ωt − ϕ)

(3)

where Bi =



uω2 sin ˛i 2



ϕ = arctan

2ωn ω



ωn2 − ω2

Absolute displacement of the mass is zou,i + zi . According to Newton’s Second Law, when driven by excitation, the inertia force of the mass is Fi = −m(¨zou,i + z¨ i ) = mBi ω2 sin(ωt − ϕ) + muω2 sin ˛i sin ωt

(4)

Assuming



1 zdAi,1 + Ai,1

R=

Ep bp

t3 3 p

−a1,i sin ϕ a1,i cos ϕ + a2,i

3EI (lm + lme )

(12)

3









2 zdAi,2 + Ai,2



3 zdAi,3 =



Ai,3

zdAi,2 + Ai,2

zdAi,1 Ai,1

zdAi,3

(13)

Ai,3

By solving Eq. (14), we achieve equivalent elasticity modulus of cantilevered beam is

Iy =

Driven by the inertia force F that generated by the mass, single cantilevered beam will produce alternating bending vibration. We assume that the strain of cantilevered beam cross section is continuous, the strain in the Z axis of cross section becomes

where R is curvature radius of bending cantilevered beam.

(11)

2 t + 6t t 2 ) + E b t 3 2Ep bp (4tp3 + 3tm p m p m m m 2 t + 6t t 2 ) + b t 3 2bp (4tp3 + 3tm p m p m m

(14)

For inertia moment of cross section to Y axis, following relationship can be achieved according to its definition,



z Sx = R

1 E b t3 12 m m m

−Fi (lm + lme − x) − 12 e31 bp (tp2 + tm tp ) (E3,2 − E3,1 )







2 t + t t2 + + 12 tm p m p

where I is inertia moment of cantilevered beam, and E is equivalent modulus of elasticity. In the following, we analyze the equivalent modulus of elasticity and inertia moment of cantilevered beam. To solve the equivalent elastic modulus of cantilevered beam, we follow the fact that moment of force to Y axis in the same cross section remains the same. We obtain the following equation

E=

= arctan

2

Treated single piezoelectric cantilevered beam vibration system as a spring-mass-damper system, equivalent stiffness coefficient can be approximately calculated by the following equation

(5)

a21,i sin2 ϕ + (a1,i cos ϕ + a2,i )2

(10)

where lm is the length of cantilevered beam, and lme is the length from the centroid of mass to the end of cantilevered beam.with Eqs. (9) and (10), we get curvature radius of single cantilevered beam when it vibrates, which is

The inertia force of mass in the vibration can be expressed as

where

(9)

Ai,3

Mou,i = Fi (lm − x + lme )

+

i)

3 zdAi,3

Ai,2

Ai,1

Fi = −m(¨zou,i + z¨ i ) = a1,i sin(ωt − ϕ) + a2,i sin ωt = ai sin(ωt +



2 zdAi,2 +

Bending moment of the position that away from the fixed end at x is

a2,i = muω2 sin ˛i

i



Min,i =

1 zdAi,1 +

a1,i = mBi ω2

ai =

(8)

For cantilevered beam, the sum of the moment that micro-force to the neutral axis within the cross section is equal to the bending moment on the cross section. We obtain

k=

(ωn2 − ω2 ) + 4 2 ωn2 ω2

1 tm 2

(6)

1 1 2 3 tp + 6tm tp2 ) + bp (4tp3 + 3tm bm tm 6 12

(15)

Internal energy of single piezoelectric cantilevered beam vibration system during electromechanical coupling can be expressed as dup,i,1 = dum =

1 1 1 1 2 S1 1 + E3 D3 = Ep S12 + e31 E3,1 S1 + ε33 E3,1 2 2 2 2

1 1 S1 1 = Em S12 2 2

(16) (17)

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R. Chen et al. / Sensors and Actuators A 230 (2015) 1–8

1 1 1 1 2 S1 1 + E3 D3 = Ep S12 + e31 E3,2 S1 + ε33 E3,2 2 2 2 2

dup,i,2 =

(18)

Gross energy of single piezoelectric cantilevered beam vibration system becomes





Ui =



dup,i,1 dvi,1 +

dum dvi,3 +

vi,1

dup,i,2 dvi,2

vi,3

(19)

vi,2

According to the relationship between electric field intensity and voltage V tp

E3 =

(20)

Substituting dup,i,1 , dum and dup,i,2 in Eqs. (16)–(18) to Eq. (19), we can obtain gross energy of single piezoelectric cantilevered beam vibration system, which is



1

Ui =

621



×

Ep bp Fi2

3 2 3 t tp + tm tp2 4 m 2

tp3 +



1 e31 E3,1 bp −Fi 21

2421 1 621





1

3 Em bm tm Fi2

Fi2



×

2 lad lp



1 e31 E3,3 bp −Fi 21

where 1 = Ep bp

2 3

−

1 + lp2 − lad lp2 3



lad lp −

tp3 +



+ 22 lp + 22 Fi

lad lp −

1 2 l 2 p



2 lp ](tp2







+





22 lp

+ 22 Fi

lad lm −

1 lad lp − lp2 2

1 2 l 2 m



(21)



− 2 lp ](tp2 + tm tp ) +

×



tp3 +



1 2 t tp + tm tp2 2 m



1 3 Em bm tm 12

+

3 2 3 t tp + tm tp2 Fi − 4 m 2

(22)

(tp + tm )Fi

Based on equivalent capacitance principle and electric field formula q = CV, the equivalent capacitance of upper piezoelectric ceramics is Ci,1 =

1 1221



2 e31 Ep b3p lp tp3 +



3 2 3 t tp + tm tp2 (tp + tm )2 + 4 m 2

(23)

1 1 2 e E3,1 b2p lp (tp + tm )2 + ε33 lp bp 21 31 tp

Vi,1 =



1

− e31 Ep b2p (tp 1221

1 e31 bp 21



lad lp − 2

× (tp + tm ) +

1 2 l 2 p

ω2 r(V1,1 C1,1 + V1,2 C1,2 + ... + V13,2 C13,2 )2



ωr(C1,1 + C1,2 + ... + C13,2 ) +

2 2

(28)

ω(V1,1 C1,1 + V1,2 C1,2 + ... + V13,2 C13,2 )2 2 (C1,1 + C1,2 + ... + C13,2 )

(29)

is 2ω(C1,1 + C1,2 + C2,1 + ... + C13,2 )

(30)

+ tm )(2lad lp −



(tp + tm )Fi ]/



lp2 ) 1

1221

tp3

3 2 3 + tm tp + tm tp2 4 2



2 e31 Ep b3p lp

1 1 2 2 2 e b lp (tp + tm ) + ε33 lp bp tp 21 31 p



2 = T

tp3 +



Fi −



3 2 3 t tp + tm tp2 4 m 2

(24)

 0

T 2

1 Mu2 ω2 cos2 ωtdt 2

(31)

where M is the mass of the entire harvester, u is the displacement amplitude of excitation, ω is the angular frequency of excitation, and T is the cycle time of excitation. We can obtain that its maximum energy conversion efficiency is Pmax Pave,in

(32)

In order to analyze the influence of the structural parameters on the energy conversion efficiency, we define the ratio between thickness of metal elastic substrate and that of piezoelectric cantilevered beam as thickness ratio of single piezoelectric cantilevered beam structure. That is, ˛=

tm t

(33)

We define the ratio between length of piezoelectric ceramic and that of metal elastic substrate as length ratio of single piezoelectric cantilevered beam structure. That is, ˇ=

Thus, open circuit voltage generated by upper piezoelectric ceramics is



Pr =

max =



1 e31 bp lad lp − lp 21 2

Assuming vibration frequency of piezoelectric cantilevered beam is f, and outputs of 13 single piezoelectric cantilevered beam energy harvesting structures are connected to charging circuit. Thus, output power can be expressed as

Pave,in

e31 Ep b2p (tp + tm )(2lad lp − lp2 )

1 2

(27)

In the ambient vibration, single piezoelectric cantilevered beam energy harvesting structures in different directions produce forced vibration. The average input power of the entire vibration energy harvester can be expressed as following,

1 2 lp bp tp ε33 E3,3 2

According to Eq. (21), the quantity of electric charge can be obtained as 1

Vi,2 = −Vi,1

2.3. Optimization of structural parameters

lad = lm + lme

1221

(26)

Ropt =

1 2 = e31 bp (tp2 + tm tp )(E3,3 − E3,1 ) 2

Qi,1 = −

Ci,2 = Ci,1

The optimal load corresponding to the maximum output power +

− 1 2 l 2 p

(25)

Pmax =

1 2 + tm tp ) + ε33 E31 lp bp tp + 2

+ 22 lm + 22 Fi

Qi,2 = −Qi,1

where r is the load resistor. Maximum output power of the piezoelectric vibration energy harvester is

+

1 2 2 l − lad lm 3 m

3 2 3 t tp + tm tp2 4 m 2

tp3 +





1 lad lp − lp2 2

2 lad lm +



Ep bp

1 2 l − lad lp2 3 p

2 lad lp +

Similarly, we can obtain that quantity of electric charge, equivalent capacitance and open circuit voltage generated by lower piezoelectric ceramics, respectively, are

lp lm

(34)

Fig. 4 shows the relationship between energy conversion efficiency and thickness ratio. Fig. 5 shows the relationship between energy conversion efficiency and length ratio. As can be seen from Fig. 4, the energy conversion efficiency increases slightly when thickness ratio increases in the range of 0–0.2. When the thickness ratio is about 0.2, the vibration energy harvester can reach its maximum energy conversion efficiency. When the thickness ratio is larger than 0.2, growth of thickness

R. Chen et al. / Sensors and Actuators A 230 (2015) 1–8

Fig. 4. Relationship between energy conversion efficiency and thickness ratio.

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with the increase of ceramic thickness when the thickness ratio under 0.2. When the thickness ratio goes to larger than 0.2, the increase of piezoelectric cantilevered beam stiffness becomes the key factor, the amplitude of forced vibration decreases obviously in the same vibration condition, while the open circuit voltage grows slowly in the beginning and then decreases rapidly with the increase of ceramic thickness, which can be derived from Eq. (24). The phenomenon can be observed is, although the increase of the piezoelectric ceramic thickness leads to better piezoelectric property, its positive effect still cannot counteract its negative effect, i.e. that an optimal thickness ratio 0.2 exists. In Fig. 5, we can see that in the beginning the energy conversion efficiency increases when the length of piezoelectric ceramics increases. In the range of 0.6–0.8, the optimal length ratio is acquired, where the energy conversion efficiency is largest. When length ratio goes to larger than 0.8, the energy conversion efficiency descends. It can be explained as follows: when length ratio is small, i.e. length of piezoelectric ceramics is small, the increase of ceramic length leads to better piezoelectric property. However, when the length ratio is larger than 0.8, the piezoelectric ceramics strengthen the ends of piezoelectric cantilevered beam structures, and it has a negative effect on the start-up of forced vibration. Thus, energy conversion efficiency decreases. 3. Experimental study

Fig. 5. Relationship between energy conversion efficiency and length ratio.

ratio leads to substantially decrease of energy conversion efficiency. It can be explained as following: when the thickness ratio is smaller than 0.2, i.e. the thickness of piezoelectric ceramics is relatively small, the influence of increasing piezoelectric cantilevered beam stiffness which caused by the increase of ceramic thickness is not obvious. However, the increase of ceramic thickness leads to the increase of output power in the same ambient vibration condition, because the open circuit voltage keeps increasing fast

Beryllium bronze and PZT-5H are selected to make the metal elastic substrate and piezoelectric ceramic, respectively. Multi-faceted support body, upright column and masses are manufactured by steel. According to the optimization result, the key parameters are as following: lp = 18 mm, lm = 24.4 mm, lad = 28.2 mm, bp = bm = 6 mm, tp = 0.4 mm, tm = 0.1 mm, and the length of the cubic mass is 7.6 mm. Testing system is shown in Fig. 6. In the experiment, the dandelion-like MD-PVEH is fixed on a multi-directional vibration table, and driven by a HEV-50 vibration exciter. The vibration exciter is driven by Agilent 33120A signal generator and power amplifier. The voltage generated on the electrode surface of piezoelectric ceramic is monitored by a Tektronix TDS210 oscilloscope. Output signal produced by signal generator imports to exciter through power amplifier. In the experiment, this dandelion-like MD-PVEH is driven by the exciter with a harmonic excitation. Its frequency and amplitude are 22 Hz and 0.28 mm, respectively, which is the typical bridge vibration characteristic excited by heavy vehicles. The load resistor is 8 k. The exciter drives fixture and then cantilevered beams. When vibration direction is perpendicular to the base of harvester, open-circuit voltages of the piezoelectric cantilever beams in different directions are shown in Fig. 7.

Fig. 6. Testing system of dandelion-like MD-PVEH: (a) overall system; (b) close top view.

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R. Chen et al. / Sensors and Actuators A 230 (2015) 1–8

Fig. 7. Experimental waveforms of open-circuit voltages of piezoelectric ceramics: (a) angle between piezoelectric beam and vibration direction is 90◦ ; (b) angle between piezoelectric beam and vibration direction is 45◦ ; (c) angle between piezoelectric beam and vibration direction is 0◦ .

Fig. 9. Relationship between load power and load resistor/excitation frequency. Fig. 8. Experimental waveforms of charging circuit.

Terminal voltage of piezoelectric ceramic Vpiezo and rectified DC voltage VDC are shown in Fig. 8. Fig. 9 gives the relationship between load power, load resistor and excitation frequency. These values are acquired by experiment. Excitation direction is perpendicular to the base of harvester, and its amplitude keeps in 0.28 mm. Fig. 9 shows that the optimal load resistor is 8 k, which is consistent with the theoretical calculation value. In order to discuss the relationships between load power and direction of excitation, a Cartesian coordinate system is built for the dandelion-like vibration energy harvester. It is shown in Fig. 10. When external excitation changes its direction in the XY plane, the relationship between load power and excitation direction is shown in Fig. 11. We can see that when the angle between excitation direction and X axis is 90◦ , the device can reach its maximum output power of about 0.28 mW, and the energy conversion efficiency can reach 3%. When that angle is 0◦ or 180◦ , minimum

output power can be acquired. The experimental results are consistent with the theoretical derivation above. Fig. 11 also may be explained simply as that most of the cantilevered beams are sensitive for excitation when excitation direction is parallel to Y-axis, while least of them are sensitive when excitation direction is parallel to X-axis. When external excitation changes its direction in the XZ plane, the relationship between load power and excitation direction is shown in Fig. 12. We can see that when the angle between excitation direction and X axis is 45◦ or 135◦ , the device reaches its maximum output power of about 0.07 mW. When the angle is 90◦ , it reaches its minimum output power. The experimental results also verify the theoretical calculations. However, it should be noted that the output power decreases a lot when excitation direction is around 90◦ . The phenomenon reveals that this dandelion-like structure still cannot absorb vibration energy in several particular directions, because its vibration sensitivity is not perfectly isotropic. Overall,

R. Chen et al. / Sensors and Actuators A 230 (2015) 1–8

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it can harvest energy from vibration in many directions effectively and meet the needs of many microelectronic devices. 4. Conclusion

Fig. 10. Dandelion-like MD-PVEH and its Cartesian coordinate system.

In this paper, we propose a type of dandelion-like multidirectional piezoelectric vibration energy harvester. It can achieve an effective harvesting of ambient vibration energy in different directions, instead of considering much about environment and installation. By theoretical calculation, structural parameters of the transducer elements are optimized. Its optimal thickness ratio and length ratio corresponding to the maximum energy conversion efficiency are obtained. In experimental study, the prototype of dandelion-like MD-PVEH is manufactured, and its energy harvesting performance is obtained by measuring its output voltage. When the frequency and amplitude of the harmonic excitation are 22 Hz and 0.28 mm, respectively, and the load resistance is 8 k, the load power can reach as much as 0.28 mW, and the energy conversion efficiency can reach 3%. In majority of excitation directions, the load power can be maintained at a relatively high level. However, it should be noted that the load power decrease a lot in some particular excitation directions. It reveals that the energy harvesting capability of this dandelion-like MD-PVEH is still not perfectly isotropic. Further research is underway to improve the energy harvesting structure and its capability to harvest vibration energy in all directions. Acknowledgement This work is supported by a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), National Natural Science Foundation of China (10972102), Research Fund for the Doctoral Program of Higher Education of China (200802870007), Technology Research and Development Program of Jiangsu Province (BE2009163). The authors gratefully acknowledge these supports. References

Fig. 11. Relationship between load power and excitation direction in the XY plane.

Fig. 12. Relationship between load power and excitation direction in the XZ plane.

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Biographies Renwen Chen graduated from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China in 1991 and received his Ph.D. degree from NUAA in 1999, both in Measurement and Testing Technology and Instruments. He also spent half a year as a visiting scholar in University of California, Berkeley, USA. His current research interests are in the field of energy harvesting, active vibration control, wireless sensors network and intelligent monitoring and control.

Long Ren graduated from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China in 2011, and received his M.E. degree from NUAA in 2014, and is currently working toward the Ph.D. degree in Intelligent Monitoring and Control at State Key Laboratory of Mechanics and Control of Mechanical Structures, NUAA, Nanjing, China. His current field of interest focuses on energy harvesting and active vibration control.

Huakang Xia graduated from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China in 2012, and is currently working toward the Ph.D. degree in Measurement and Testing Technology and Instruments at State Key Laboratory of Mechanics and Control of Mechanical Structures, NUAA, Nanjing, China. His current field of interest focuses on energy harvesting, wireless sensor networks, as well as embedded technology.

Xingwu Yuan graduated from Hunan University of Science and Technology (HNUST), Xiangtan, China and received his B.E. degree from HNUST in 2013, and is currently working toward the M.E. degree in Aeronautical engineering at State Key Laboratory of Mechanics and Control of Mechanical Structures, NUAA, Nanjing, China. His current field of interest focuses on signal transmission and control and vibration energy harvesting technology.

Xiangjian Liu is a lecturer with Ph.D. degree of Jinling Institute of Technology. His main research interest is vibration energy harvesting technology.