Modeling on energy harvesting from a railway system using

Smart Materials and Structures Smart Mater. Struct. 24 (2015) 105017 (13pp)

doi:10.1088/0964-1726/24/10/105017

Modeling on energy harvesting from a railway system using piezoelectric transducers Jianjun Wang1, Zhifei Shi1, Hongjun Xiang1 and Gangbing Song2 1 2

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, People’s Republic of China Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA

E-mail: [email protected] and [email protected] Received 9 February 2015, revised 20 May 2015 Accepted for publication 13 July 2015 Published 9 September 2015 Abstract

Theoretical models of piezoelectric energy harvesting from railway systems using patch-type and stack-type piezoelectric transducers are studied. An infinite Euler–Bernoulli beam on a Winkler foundation subjected to moving multi-loads is adopted to describe the dynamic behavior of railway track. The voltage and electric power of piezoelectric transducers installed at the bottom of a steel rail are derived analytically. Comparisons with earlier works and experimental results are given, indicating that the present solutions are reliable. Additionally, a parametric study is conducted to discuss the effects of axle loads, running velocity and load resistors on the solutions. The numerical results show that patch-type and stack-type piezoelectric transducers can harvest the available energy from track vibration to supply power for a wireless sensor network node and can also serve as sensors to monitor basic train information, such as the running velocity, the location and the axle load. The present investigations provide a theoretical guide in the design of piezoelectric patch and stack energy harvesters used in railway systems, which can serve as power sources for distributed wireless sensor networks in remote areas. The research results also demonstrate the potential of piezoelectric patches and stack harvesters in designing self-powered wireless sensor networks used in railway systems to ensure train operation safety. Keywords: piezoelectric transducer, energy harvesting, railway system (Some figures may appear in colour only in the online journal) robust [4]. Therefore, searching for an alternative energy source to provide electricity to these remote areas is still a key challenge. The vibrational mechanical energy of track structures induced by passing trains is huge [5]. This energy is a potential alternative energy source, however, it is still not being used effectively. Converting vibrational mechanical energy as the assistant power source for wireless sensor networks is a technological barrier. Two main kinds of energy harvesters have been developed to harvest energy from track vibrations. One is an electromagnetic energy harvester. Wang et al [5] and Pourghodrat et al [6] have both designed a kind of electromagnetic energy harvester to harvest track vibration energy. The two devices have similar design concepts that convert the linear vertical displacement of the track into the

1. Introduction Over the past few decades, traffic has developed rapidly in China, especially in rail transit. In 2014, China had more than 110 000 kilometers of railway. Ensuring vehicle running safety has become a critical issue. An effective measure is to install a huge amount of wireless sensor networks along railway lines to monitor the basic information of the train (such as running velocity, location and axle load) and the health status of tracks, bridges and sleepers [1–3]. When the wireless sensor networks are installed in remote areas, power supply is a difficult issue. Traditional power cables or battery replacement are excessively expensive or infeasible in this type of application, and the use of other alternative sources of electricity such as solar and wind energy is not reliable or 0964-1726/15/105017+13$33.00

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rotational motion of a generator by using a gear and rack mechanism, and maintaining the rotational motion of the generator with roller clutches and a flywheel. Installed on two adjacent sleepers, these electromagnetic energy harvesters can generate a much larger power output in the level of W. The other is a piezoelectric energy harvester. This is a promising kind of device [7, 8], which has been utilized widely to harvest various vibrational energy sources, such as human motion [9, 10], wind [11, 12], water flow energy [13], traffic-induced pavement vibrations [14–18] and trafficinduced bridge vibrations [19, 20], etc. Several piezoelectric generators have been explored to harvest energy from track vibration. Nelson et al [21] mounted a piezoelectric film at the bottom of a rail to scavenge power from the deformation of the rail. The average power harvested was about 1 mW. However, a detailed model was not established. Innowattech, an Israeli company, developed an energy harvesting pad composed of piezoelectric stacks installed under the rail fastener for a larger power application [22]. However, the detailed techniques were not reported publicly. Li et al [23] designed a cantilever-type harvester with a tip mass to harvest the vibrational mechanical energy of railway track induced by passing trains. A key technique is to match the resonant frequency of the cantilever-type harvester and the dominant frequency range of the rail vibration. Subsequently Li et al [24] designed a wide band piezoelectric array assembled from six different piezoelectric beams, and mounted it on the side of a rail track to evaluate its energy harvesting performance in a field test. The field test results do not reach the expected design goal. The related work still needs further exploration and improvement [24]. Yuan et al [4] designed a type of drum transducer installed under the sleeper for harvesting energy from track vibration and established a corresponding theoretical model. The model was also verified reliably by developing an experiment rig. The simulation and experiment results show that the drum transducer can generate about 100 mW in a real track situation and about a 50–70 V peak open-circuit voltage at the full load of the train. The results show that the power harvested from track vibrations is sufficient to supply power for the wireless sensors. In [4, 21, 23, 24], the power output of the designed piezoelectric energy harvesters is smaller than that of the electromagnetic harvesters [5, 6]. However, the energy harvested is capable of supplying the wireless sensor network node. Compared with electromagnetic harvesters, piezoelectric energy harvesters have some advantages in that they are simple structures with small volumes. Moreover, a larger power application has been reported by the Israeli company [22]. These results show that piezoelectric energy harvesters have a bright future in harvesting the energy from track vibration. However, reports about the modeling of energy harvesting from railway systems using piezoelectric transducers are very rare. This paper aims to give a theoretical analysis of energy harvesting using patch-type and stack-type piezoelectric transducers from the track deformation caused by passing trains. In section 2, an infinite Euler–Bernoulli beam on a Winkler foundation subjected to moving multi-loads is

Figure 1. Schematic of railway track structure with piezoelectric

energy harvesters.

adopted to describe the dynamic behavior of railway track structure. In section 3, the voltage and electric power of piezoelectric transducers installed at the bottom of a steel rail are derived analytically. In section 4, comparisons with earlier works and experiment results are presented to validate the reliability of the theoretical solutions. In section 5, a parametric study is conducted to discuss the effects of axle loads, running velocity and load resistors on the solutions. Then, the performance of stack sensors in monitoring the basic information of the train is explored.

2. The modeling of a beam on a Winkler elastic foundation subjected to moving loads As shown in figure 1, a schematic of railway track structure with piezoelectric patch-type and stack-type energy harvesters is illustrated. In the figure, a piezoelectric patch-type energy harvester is mounted at the bottom of a rail. A piezoelectric stack-type energy harvester is also installed at the bottom of the steel rail by a connecting device. Because the piezoelectric transducers are much smaller than the track structure as a whole, we neglect their effects on the whole track structure. The differential equation of motion for a beam on a Winkler elastic foundation subjected to moving loads describing the dynamic behavior of railway track structure is given by [25, 26] EI

¶ 4w ¶ 2w r + + kw = ¶x 4 ¶t 2

N

åPi d ( x - xi - vt )

(1 )

i=1

where w = w (x, t ) is the transverse deflection of the rail, E is the Young modulus of the rail, I is the moment of inertia of the rail, EI is the flexural rigidity of the rail, r is the mass per unit length of the track structure, k is the equivalent stiffness of the track structure, Pi is the load of the ith pair of wheels, xi is the space coordinate of the ith pair of wheels, d is the Dirac delta function and t is the time. As shown in figure 1, the load Pi is applied on the coordinate xi at the initial time (i.e. t = 0 ), and x1 = 0, xi = -li - 1, where li - 1 denotes the distance between the first and the ith pair of wheels. 2

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exhibited in figure 2. Considering that the piezoelectric transducer is polarized along the z-axis, the d31-type constitutive equations can be expressed as [29–32] ex = S11E sx + d31Ez

(5 )

ks33 Ez

(6 )

Dz = d31sx +

where sx and ex are the axial stress and the axial strain of the patch transducer respectively. Dz and Ez are the electric s and displacement and the electric field respectively. S11E , k 33 d31 are the elastic compliance at constant electric field, the dielectric permittivity at constant stress and the piezoelectric strain constant respectively. The axial strain ex can be expressed approximately as Figure 2. I-I cross-section of the rail.

Define as b 2 =

k , EI

a=

r 2EI

¶ 4w ¶ 2w + 2a 2 + b2 w = 4 ¶x ¶t

ex = -h pc

in equation (1), to get N

P

å EIi d ( x - xi - vt )

(2 )

Dz = e31ex + ke33 Ez

b a

Here, the critical velocity = is defined. Its physical meaning is the lowest phase velocity of a bending wave in the beam [27, 28]. When the load velocity reaches the critical velocity, beam resonance occurs. In fact, the resonance phenomenon must be avoided to ensure train operation safety. Subsequently, equation (2) is solved by using the Fourier transform and the Residue Theorem [26] under v < vcr . Thus, the steady-state solution of the transverse deflection of the rail can be derived as w=

e k 33

d⎛ ⎜ dt ⎝

i=1

where

Cp

xi  0

where Cp =

(4 ) xi < 0

s S11E k 33 )

p

⎞ V (t ) Dz dA p ⎟ = ⎠ R

(9 )

d V (t ) d V (t ) + = Q (t ) dt R dt

k e33 bp l p hp

(10)

, Q (t ) = -e31 h pc bp [ ¶¶wx ∣x = L + lp - ¶¶wx ∣x = L ].

bp , h p and l p are the width, thickness and length of the piezoelectric patch. Solving equation (10) with the initial condition Q ( 0) V (0) = C = 0, yields

in which, xi = x - xi - vt, a = b -2av , b = b +2av . The above dynamic solution is solved without consideration of the damping influence. The reason for this is that damping has a great effect on dynamic response near the resonance [15, 27], i.e. the critical velocity. When the load velocity is far from the critical velocity, the influence of damping is very small, or even negligible. 2

òA

2 d 31

where V (t ) is the voltage across the resistive load and Ap is the area of the piezoelectric patch. Substituting equations (7) and (8) into equation (9) yields

(3 )

⎧ Pi e-axi b cos bxi + a sin bxi ] , ⎪ ⎪ 4EIbab [ wi = ⎨ ⎪ Pi eaxi [ b cos bxi - a sin bxi], ⎪ ⎩ 4EIbab

(8 )

s k 33 (1

where e31 = d31 S11E and are the = effective piezoelectric stress constant and the dielectric permittivity at constant strain respectively. As the electrodes are connected by an electric circuit with a load resistor R and the electric field is taken as Ez = -V (t ) hp , the electrical equation can be formulated as

N

åwi

(7 )

where h pc is the distance from the neutral axis of the steel rail to the center of the patch transducer in the z-direction. Substituting equation (5) into equation (6) yields [33, 34]

i=1

vcr2

¶ 2w ¶x 2

2

p

V (t ) =

Q (t ) 1 - RCt p e Cp RCp2

ò0

t

t

Q (t ) e RC p dt .

(11)

Solving equation (11), the voltage can be derived analytically. V (t ) =

3. Energy harvesting using piezoelectric transducers

Q (t ) 1 - RCt p e Cp RCp2

{ ⎡⎣ Y

total

( L + lp, t )

-Ytotal ( L + lp, 0)⎤⎦ - [ Ytotal (L, t ) - Ytotal (L, 0)] }

3.1. Patch-type piezoelectric transducer

As shown in figure 1, a patch-type piezoelectric transducer is placed at the bottom of a steel rail to harvest the mechanical energy induced by the moving train. A detailed I-I crosssection of the 60 kg m−1 rail with the piezoelectric patch is

(12)

where Ytotal (x , t ) =

N

åYi (x , t ) + C i=1

3

(13)

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in which C is the integral constant. t ⎧ ⎪ Pi e RC p e-axi ⎡⎣ A˜ cos bxi + B˜ sin bxi ⎤⎦ , ⎪ e31h pc bp ⎪ xi  0 t ⎨ Yi (x , t ) = 4EIab ⎪ Pi e RC p eaxi ⎡⎣ C˜ cos bxi - D˜ sin bxi ⎤⎦ ⎪ x- x i ⎪ + P e vRC p A˜ - C˜ , x < 0 i i ⎩

(

)

(14)

in which A˜ =

B˜ =

( bv ) , ⎞2 ⎛ 1 ⎟ (bv)2 + a2 ⎜ v + aRCp ⎠ ⎝ ⎛ 1 ⎞ ⎟ a ⎜v + aRCp ⎠ ⎝

Figure 3. Installation schematic of piezoelectric stack.

stack and rail is finished through a piezoelectric stack device and a magnetic base. The piezoelectric stack device includes a displacement transmission rod, a compression spring, a force transmission unit, a piezoelectric stack, a whole metal shell, screw bolts and a wire hole. The transverse track displacement of the rail is converted into a force through the compression spring, and is then transferred to the piezoelectric stack. A schematic of this device and its photo are exhibited in figure 4. Furthermore, the piezoelectric stack under the excitation of dynamic pressure q (t ) in the z-direction (3-direction) shown in figure 5 can be used to match this case. All piezoelectric layers are polarized along the z-axis. The d33-type constitutive equation of piezoelectric material can be expressed as [9, 35, 36]

2 ⎛ 1 ⎞ ⎟ (bv)2 + a2 ⎜ v + aRCp ⎠ ⎝ ( bv ) C˜ = , 2 ⎛ 1 ⎞ 2 2 ⎟ ( bv ) + a ⎜ v aRCp ⎠ ⎝ ⎛ 1 ⎞ ⎟ a ⎜v aRCp ⎠ ⎝ ˜ D= . 2 ⎛ 1 ⎞ 2 2 ⎟ ( bv ) + a ⎜ v aRCp ⎠ ⎝

Dz = d33 sz + ks33 Ez

where sz is the stress of piezoelectric material along the zdirection, which is induced by the deformation of the rail. Dz and Ez are the electric displacement and the electric field respectively. k s33 and d33 are the dielectric constant and the piezoelectric coefficient respectively. However, it is very difficult to obtain the exact stress along the z-axis in the stack transducer. For simplicity, the inertial force in the transducer itself is ignored. Previous works show that this method is feasible and reasonable [36, 37]. Thus, the stress sz in the transducer can be expressed approximately as

When R  ¥ , the second term will disappear in equation (12) and then the open circuit voltage can be obtained. VOC (t ) =

Q (t ) . Cp

(15)

The electric power can further be expressed as V 2 (t ) . R

P (t ) =

(16)

sz = q (t ) =

The total energy Wtotal is defined as Wtotal =

òT

T2

P (t ) d t

(18)

ks w As

(19)

where k s is the stiffness of compression spring. Stack-type constitutive equations can be formulated approximately as [9, 37]

(17)

1

⋅eq Dz = d33 sz + ks33⋅ eq Ez

where T1 and T2 are the start and stop time of the effective electric power signal respectively.

⋅eq d 33

(20)

k s33⋅ eq

where = nd33 and = nk s33 are the effective piezoelectric and dielectric constants respectively. As the electrodes are connected by an electric circuit with a load resistor R and the electric field is taken as Ez = -V (t ) hs, the electrical equation can be formulated as

3.2. Stack-type piezoelectric transducer

As shown in figure 1, a stack-type piezoelectric transducer is placed at the bottom of a steel rail to harvest the mechanical energy induced by the moving train. A detailed installation schematic of the piezoelectric stack is exhibited in figure 3. In figure 3, the coupling connection between the piezoelectric

d⎛ ⎜ dt ⎝ 4

òA

s

⎞ V (t ) Dz dAs ⎟ = ⎠ R

(21)

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Figure 4. Schematic of a piezoelectric stack device and its photo.

Yi (x , t ) =

⋅eq d33 ks 4EIbab

t ⎧ ⋅eq ⎪ Pi e RC p e-axi ⎡⎣ A˜ 0 a + B˜0 b cos bxi ⎪ ⎪ + B˜0 a - A˜ 0 b sin bxi ⎤⎦ , xi  0 ⎪ t ⎪ ⋅eq ⎪ Pi e RC p eaxi ⎡⎣ -C˜ 0 a - D˜ 0 b cos bxi ´⎨ ⎪ + D˜ 0 a - C˜ 0 b sin bx ⎤ i⎦ ⎪ x- x i ⎪ ⋅eq ⎪ + Pi e vRC p ⎡⎣ A˜ 0 a + B˜0 b ⎪ ⎤ ˜ ˜ ⎪ ⎩ + C0 a + D 0 b ⎦ , xi < 0

(

)

(

)

(

)

(

)

(

)

(

Figure 5. Simplified schematic of a piezoelectric stack under the excitation of dynamic pressure.

in which A˜ 0 =

where V (t ) is the voltage across the resistive load. hs and As are the thickness and area of every piezoelectric patch. Substituting equations (19) and (20) into equation (21) yields Cp⋅eq

Cp⋅eq

d V (t ) d V (t ) + = Q (t ) dt R dt

eq ks⋅ 33 As

(22)

B˜0 =

2

p

- t ⋅eq 1 Q (t ) e RC p ⋅eq ⋅eq2 Cp RCp

´ ⎡⎣ Ytotal ( L 0, t ) - Ytotal ( L 0, 0) ⎤⎦

{

}

(23)

where Ytotal (x , t ) =

N

åYi (x , t ) + C

( bv ) , 2 ⎛ ⎞ 1 ⎟ (bv)2 + a2 ⎜⎜ v + ⋅eq ⎟ RC a ⎝ p ⎠ ⎛ 1 ⎞ ⎟⎟ a ⎜⎜ v + aRCp⋅eq ⎠ ⎝

2 ⎛ 1 ⎞ ⎜ ⎟ ( bv ) + a ⎜ v + ⎟ aRCp⋅eq ⎠ ⎝ ( bv ) C˜ 0 = , ⎛ ⎞2 1 ⎟⎟ (bv)2 + a2 ⎜⎜ v aRCp⋅eq ⎠ ⎝ ⎛ 1 ⎞ ⎟⎟ a ⎜⎜ v aRCp⋅eq ⎠ ⎝ D˜ 0 = 2 ⎛ 1 ⎞ 2 2 ⎜ ⎟ ( bv ) + a ⎜ v ⎟ aRCp⋅eq ⎠ ⎝

⋅eq d 33 k s w ∣x = L 0 .

where = h , Q (t ) = s Solving equation (22) with the initial condition Q ( 0) V (0) = C ⋅eq = 0, the voltage can be derived analytically. V (t ) =

)

(24)

i=1

5

2

(25)

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4. Validation 4.1. Patch-type piezoelectric transducer

In the earlier work [15], a theoretical analysis of piezoelectric energy harvesting from the traffic induced deformation of pavements was conducted. Pavement behavior was described by an infinite Bernoulli-Euler beam resting on a Winkler foundation, and a theoretical formula of output voltage was derived when the wheel load was characterized as a distributed load model. Using equation (12), the analytical voltage without damping could be obtained when the wheel load was characterized as a concentrated load model. Furthermore, the analytical electric power can also be solved by equation (16). The results for different load models can be plotted in figure 6. Related parameters are taken from the earlier work [15]. Comparative results show that the present analytical solution is correct. 4.2. Stack-type piezoelectric transducer

In the previous work [35], an analytical model is proposed to study the dynamic properties of a piezoelectric stack generator. It is very valuable as a guide to the detailed design of a piezoelectric stack. However, the analytical model is complicated and inconvenient in the actual application. A common simplified model [36, 37] is appropriate in the present case, as shown in equation (22). However, the simplified model must meet an assumption that the highest frequency content of the dynamic pressure is much lower than the fundamental resonance of the stack [37]. In this section, comparisons between the simplified model and the earlier analytical model [35] are presented to prove the reasonability of the simplified model in the application of a railway system. When the dynamic pressure is considered as a harmonic form q (t ) = q0 e jwt (where q0 is the load amplitude, j = -1 is the unit imaginary number, w = 2pf is the circular frequency, and t is the time), then the steady-state voltage can be expressed as V (t ) = V0 e jwt , where the complex voltage V0 can be derived as [37] V0 =

⋅eq jwd33 As q0 ⋅eq jwCp + (1 R)

Figure 6. Comparisons of time history for a distributed load and a

concentrated load. (a) Voltage–time history. (b) Power–time history.

and two protective ceramic layers, whose material properties are taken from the earlier work [35], as shown in table 2. This stack is a basic component in designing the piezoelectric stack devices used in railway systems in the following discussion. Subsequently, a piezoelectric stack device was fabricated based on the above stack, as shown in figure 4. Its main design sizes are 50 mm×50 mm×165 mm. In the actual situation, the compression spring is designed as a replaceable component to meet the needs of multi-stiffness, and its stiffness must be negligible compared to that of the rail to ensure vehicle operation safety. In addition, the spring should have a large deflection to cover the main range of track displacement [5, 39]. Two kinds of springs are appropriate, as shown in table 3. An experiment has been done to explore the energy harvesting performance of the piezoelectric stack device and validate the reasonability of the simplified model. Figure 8 shows a photograph of the experiment setup. The test system consists of a low-frequency fatigue testing machine, a resistor control box and a digital oscilloscope. A displacement load signal is first applied to the device by the fatigue testing

(26)

Taking F = 400 N and R = 1 MW (where F = q0 As is the axial force amplitude), figure 7(a) shows the voltage amplitude change with the load frequency. It can be seen that when the load frequency increases to a specific value, the difference between the two models observed is obvious. An error analysis is listed in table 1. The results show that the simplified model has good accuracy when the load frequency is below 3000 Hz. This frequency range is broad enough for the application of a railway system [38]. Furthermore, the voltage amplitude change with the load resistor under F = 400 N and f = 88.4 Hz is plotted in figure 7(b). The comparative results ensure further reliability of the simplified model. The target stack exhibits an area of 20 mm ´ 20 mm, and consists of 20 layers of PZT-5H, 21 brass electrode layers 6

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arranged in figure 10 under a displacement amplitude of 4 mm with a frequency of 4 Hz. The comparative results present good consistency. Furthermore, an error analysis of open circuit voltage amplitude between the experiment and the theory is listed in table 4. About 10% of the errors might have been caused by the following: (1) the specific material properties were not very precisely measured since the material parameters are provided by the manufacturer rather than being measured individually; (2) the friction forces between the displacement transmission rod, the compression spring, the force transmission unit and the external metal shell, which exist in the experiment, have not been considered.

5. Discussion 5.1. Energy harvesting for moving multi-loads

In the work [25], a sleeper distance of d = 0.57 m and a 60 kg m−1 rail was adopted. For the 60 kg m−1 rail shown in figure 2, the distance he between the neutral axis and the bottom of the rail is 81.2 mm. Other parameters of railway track structure are adopted, as shown in table 5. In the work [39], an X2 train with five cars—one of which is the engine— is considered. The geometrical properties and the axle-loads of the train are listed in figure 11. In the following calculation, P1 = F1 and x1 = 0 m, P2 = F1 and x2 = -2.9 m, and so on. Firstly, energy harvesting using a piezoelectric patch will be discussed. The size of the piezoelectric patch is 20 mm ´ 20 mm ´ 0.2 mm, and the PZT-5H listed in table 2 is adopted. In the following analysis, the piezoelectric patch is installed at the location L = 300d + (d - l p ) 2. Here, the total energy Wtotal is defined for describing the energy harvesting property. Figure 12 presents the effects of velocity and load resistor on the total energy Wtotal. It indicates that there is a matching load resistor to obtain the maximum total energy, and that the matching load resistor will decrease with an increase in running velocity. This phenomenon is similar to the typical characteristics of piezoelectric energy harvesters under the harmonic load [8]. For a given load frequency, a certain value of load resistor exists that obtains the maximum level of electric power. In the present case, the velocity is related to the load frequency, and the total energy Wtotal is related to the electric power. Under the guidance of this conclusion, we can design different external loads in different limited speed zones to harvest more energy. For v = 30 m s-1, the matching load resistor and the maximum total energy are approximately Rmatch = 211 kW and Wtotal = 0.214 mJ respectively. In fact, the axle loads of every coach are different. Figure 13 shows the effects of axle loads on the total energy of coaches 2, 3 and 4. It can be seen that the total energy increases with the increase in axle loads. For the X2 train examined with five coaches, the same change in the axle loads of coach 2, coach 3 and coach 4 has almost no effect on the total energy. Figure 14 plots the voltage-time history and power-time history at v = 30 m s-1 and Rmatch = 211 k W. To estimate the output voltage and power conveniently, the root mean square (RMS) of the output

Figure 7. Comparisons between the simplified model and the

analytical model (a) voltage amplitude versus the load frequency and (b) voltage amplitude versus the resistor load.

Table 1. Error analysis between the simplified model and the analytical model.

Load frequency f (Hz) Method Simplified model Analytical model Error (%)

100

1000

2000

3000

31.68 31.68 0.00

31.68 31.69 0.03

31.68 31.72 0.13

31.68 31.77 0.28

Error=(analytical model-simplified model)/analytical model.

machine. This displacement load signal includes a preloaded displacement load and a cyclic displacement load, as shown in figure 9. Then, an expected resistor is adjusted by using the resistor control box, and the generated electrical signals can be observed by the oscilloscope. Finally, when the vibration is stable, oscilloscope data is saved on a U-disk. The experiment data and the simplified theoretical results are 7

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Table 2. Properties of PZT-5H, elastic electrode (brass) and normal ceramic [35].

Material type Piezoelectric coefficient d33 (10−12 C N−1) Piezoelectric constant d31 (10−12 C N−1) Elastic compliance constant S11E (10−12 m2/N) Elastic coefficient C33 (GPa) Permittivity coefficient ks33 (nF m−1) Density r (103 kg m−3) Layer thickness (mm) Layer number

PZT-5H 700 −186 13 62.22 34.03 7.45 1.54 20

H62-Brass ∼ ∼ ∼ 100 ∼ 8.43 0.1 21

Ceramic ∼ ∼ ∼ 60.6 ∼ 7.50 1.48 2

Table 3. Spring parameters.

Number

Model

Outside diameter (mm)

Inside diameter (mm)

Free length (mm)

Maximum deflection (mm)

Spring stiffness (kgf mm−1)

1

SM20×10×60

20

10

60

19.2

4.16

2

SH20×10×60

20

10

60

14.4

8.33

1 N=0.102 kgf.

Figure 8. Experiment setup. Figure 10. Output voltage amplitude change with the load resistor. Table 4. Comparisons of open circuit voltage amplitude between

experiment and theory. Open circuit voltage amplitude (V) Method Experiment Theory Error (%)

Spring 1

Spring 2

11.60 12.92 10.21

23.36 25.87 9.70

Error=(theory-experiment)/theory. Table 5. Parameters and critical velocity of railway track

structure [25].

k (MN m-2)

56.15 Figure 9. An applied displacement load signal.

8

EI (MN ⋅ m2)

r (kg m-1)

vcr (m s-1)

13.25

2735

141

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Figure 11. The geometrical properties and the axle-loads of the X2 train [39].

Figure 12. Total energy versus the load resistor (patch).

signal is defined as RMS (f (t )) =

1 T

Figure 13. Total energy change with the axle loads of different

coaches (patch).

T

2 2 òT1 f (t ) . Here, T

(T = T2 - T1 ) is an effective time period, and T1 and T2 are the start and stop time of the effective signal respectively. The details can be observed in figure 14. In this case, an output power (RMS) of about 0.19 mW and an output voltage (RMS) of about 4.82 V can be generated. Subsequently, the optimal resistor and its corresponding output voltage and power change with increasing velocity are plotted in figure 15. It can be seen that with the increase of the running velocity, the optimal resistor decreases, but the corresponding output voltage and power increase. Secondly, energy harvesting using a piezoelectric stack will be discussed. The stack includes 20 piezoelectric patches, which are connected mechanically in series but electrically in parallel. Its material properties are listed in table 2. In the following analysis, the location L 0 = 400d + d 2, and the stiffness of the compression spring k s = 81.67 ´ 103 N m-1 are adopted, unless otherwise stated. Similarly to the above investigation, figure 16 presents the effects of velocity and load resistor on the total energy Wtotal. It shows a similar change rule as in figure 12. The difference is, that the matching load resistor and the maximum total energy are approximately Rmatch = 180 k W and Wtotal = 0.0547 mJ at v = 30 m s-1 respectively. In addition, figure 17 also presents the same effects of axle loads on the total energy of coaches 2,

Figure 14. Time history of voltage and electric power (patch).

3 and 4 as shown in figure 13. The stiffness of the compression spring of the piezoelectric stack device is an important factor in the design process, and the corresponding results are plotted in figure 18. It shows that the total energy increases with the increase of the stiffness of the compression spring. In the actual situation, two effective methods are appropriate for increasing the stiffness of the compression spring. One is to exchange it for a spring with a higher 9

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Figure 15. The optimal resistor and its corresponding output voltage

and power change with the velocity (patch).

Figure 18. Total energy change with the stiffness of the compression spring of a piezoelectric stack device.

Figure 16. Total energy versus the load resistor (stack).

Figure 19. Time history of voltage and electric power (stack).

Figure 17. Total energy change with the axle loads of different coaches (stack).

Figure 20. The optimal resistor and its corresponding output voltage

stiffness; the other is to combine multi-springs mechanically in parallel. Figure 19 plots the voltage-time history and power-time history at v = 30 m s-1 and Rmatch = 180 kW. Similarly, the root mean square (RMS) of the output signal is

used to estimate the output voltage and power. For the above case, an output power (RMS) of about 0.027 mW and an output voltage (RMS) of about 1.59 V can be generated. Subsequently, figure 20 presents the effects of the running

and power change with the velocity (stack).

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transducer respectively. The harvested energy can be used to activate the wireless sensor 6 times and once respectively. The results show that the harvested energy from the stack transducer is smaller. That is because the stiffness of the compression spring is smaller. When the stiffness of the compression spring is increased to a larger value of 1 MN m-1, the maximum total energy can reach up to 3276 mJ, which can be used to activate the wireless sensor network sensor 254 times. In the above discussions, an external resistor is used to simplify a power-conditioning circuit, and the energy dissipated is analyzed in an optimized resistor. In practice, use of power-conditioning circuits will decrease the conversion efficiency. In the earlier work [20], a relative efficiency h of an ALD EH300 circuit compared to the reference resistor is estimated as 0.6. If the efficiency h can be used to estimate the present conversion efficiency approximately, the generated energy can still supply enough power to the wireless sensor network node.

Figure 21. Installation schematic of stack sensors.

5.2. Sensor performance in monitoring the basic information of the train

Generally, an optimal resistor is designed for the harvester. However, a large resistor is designed for the sensor, i.e. the open-circuit case. The patch and stack sensors have similar characteristics. In the following analysis, the performance of the stack sensor will be stated. In order to monitor basic information, such as the train running velocity, axle load and location, a basic sensor element includes at least two stack sensors, as shown in figure 21. Two sensors are installed at location A and location B respectively. The distances between the location and the coordinate origin are defined as LA and LB respectively. Here, LA = L 0 = 400d + d 2, and DLAB = LB - LA = 1000d . Figure 22 presents the sensor performance. From figure 22(a), the running velocity can be calculated through the formulation v = DLAB Dt. In addition, the location of the train can be determined by judging the voltage signal source (location A or location B). In figure 22(b), it can be seen that the voltage signal better reflects the change in the axle load. Furthermore, there is a corresponding relationship between the peak voltage and the axle load, so the magnitude of the axle load can be determined by analyzing the corresponding peak voltage.

Figure 22. Performance of the stack sensors (a) running velocity and location and (b) axle load.

velocity on the optimal resistor and its corresponding output voltage and power. It can also be seen that with the increase of the running velocity, the optimal resistor decreases, but the corresponding output voltage and power increase. The above sections have discussed the basic energy harvesting performance of piezoelectric patch and stack transducers. The aim of the harvested energy will be to supply power to the wireless sensor network node. In [40], the necessary minimum energy of the wireless sensor network node in a working cycle is 12.85 mJ. When a whole train consists of four X2 coaches, and about 100 trains run each day at v = 30 m s-1, the maximum total energy produced is 85.6 mJ for the patch transducer and 21.88 mJ for the stack

6. Conclusion Energy harvesting from railway systems using patch-type and stack-type piezoelectric transducers has been studied. An infinite Euler–Bernoulli beam on a Winkler foundation subjected to moving multi-loads was adopted to describe the dynamic behavior of railway track structure. The voltage and electric power of piezoelectric transducers installed at the bottom of a steel rail has been derived analytically. Comparisons with earlier works and experimental results validate the reasonability of the present solutions. Numerical analysis is presented to investigate the energy harvesting performance 11

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[2] Jang S, Jo H, Cho S, Mechitov K, Rice J A, Sim S H, Jung H J, Yun C B, Spencer B F Jr and Agha G 2010 Structural health monitoring of a cable-stayed bridge using smart sensor technology: deployment and evaluation Smart Struct. Syst. 6 439–59 [3] Li P, Gu H, Song G, Zheng R and Mo Y L 2010 Concrete structural health monitoring using piezoceramic-based wireless sensor networks Smart Struct. Syst. 6 731–48 [4] Yuan T, Yang J, Song R and Liu X 2014 Vibration energy harvesting system for railroad safety based on running vehicles Smart Mater. Struct. 23 125046 [5] Wang J J, Penamalli G and Zuo L 2012 Electromagnetic energy harvesting from train induced railway track vibrations 2012 IEEE/ASME Int. Conf. on Mechatronics and Embedded Systems and Applications (MESA) pp 29–34 [6] Pourghodrat A, Nelson C A, Phillips K J and Fateh M 2011 Improving an energy harvesting device for railroad safety applications Proc. SPIE 7977 79770U [7] Anton S R and Sodano H A 2007 A review of power harvesting using piezoelectric materials (2003–2006) Smart Mater. Struct. 16 R1–21 [8] Erturk A and Inman D J 2011 Piezoelectric Energy Harvesting (Chichester: Wiley) [9] Feenstra J, Granstrom J and Sodano H A 2008 Energy harvesting through a backpack employing a mechanically amplified piezoelectric stack Mech. Syst. Signal Pr. 22 721–34 [10] Platt S R, Farritor S and Haider H 2005 On low-frequency electric power generation with PZT ceramics IEEE/ASME T. Mech. 10 240–52 [11] Priya S 2005 Modeling of electric energy harvesting using piezoelectric windmill Appl. Phys. Lett. 87 184101 [12] Tang L, Zhao L, Yang Y and Lefeuvre E 2014 Equivalent circuit representation and analysis of galloping-based wind energy harvesting IEEE/ASME T. Mech. 20 834–44 [13] Taylor G W, Burns J, Kammann S, Powers W B and Welsh T R 2001 The energy harvesting eel: a small subsurface ocean/river power generator IEEE J. Oceanic Eng. 26 539–47 [14] Jiang X, Li Y, Li J, Wang J and Yao J 2014 Piezoelectric energy harvesting from traffic-induced pavement vibrations J Renew. Sustain. Ener. 6 043110 [15] Xiang H J, Wang J J, Shi Z F and Zhang Z W 2013 Theoretical analysis of piezoelectric energy harvesting from traffic induced deformation of pavements Smart Mater. Struct. 22 095024 [16] Zhang Z W, Xiang H J and Shi Z F 2015 Modeling on piezoelectric energy harvesting from pavements under traffic loads J. Intell. Mater. Syst. Struct. doi:10.1177/ 1045389X15575081 [17] Zhao H D, Ling J M and Yu J 2012 A comparative analysis of piezoelectric transducers for harvesting energy from asphalt pavement J. Ceram. Soc. Jpn. 120 317–23 [18] Zhao H D, Yu J and Ling J M 2010 Finite element analysis of Cymbal piezoelectric transducers for harvesting energy from asphalt pavement J. Ceram. Soc. Jpn. 118 909–15 [19] Cahill P, Nuallain N A N, Jackson N, Mathewson A, Karoumi R and Pakrashi V 2014 Energy harvesting from train-induced response in bridges J Bridge Eng. 19 04014034 [20] Peigney M and Siegert D 2013 Piezoelectric energy harvesting from traffic-induced bridge vibrations Smart Mater. Struct. 22 095019 [21] Nelson C A, Platt S R, Albrecht D, Kamarajugadda V and Fateh M 2008 Power harvesting for railroad track health monitoring using piezoelectric and inductive devices Proc. SPIE 6928 69280R

of piezoelectric transducers. The results can be described as follows: (1) Patch-type and stack-type piezoelectric transducers can both harvest more energy at high velocity and under heavy axle loads. However, these two harvesters have a different energy harvesting mechanism. Patch-type transducers harvest energy from the longitudinal strain of the bending rail using a d31 mode, but stack-type transducers harvest energy from the vertical displacement of the bending rail using a d33 mode. In addition, patch-type transducers are bonded to the bottom of the rail using epoxy, but stack-type transducers are installed at the bottom of the rail with a piezoelectric stack device and a magnetic base. (2) For stack-type harvesters, the stiffness of the compression spring must be negligible compared to that of the rail to ensure train operation safety. In these conditions, the total energy increases with the increase of the stiffness of the compression spring. In the actual situation, two effective methods are appropriate for increasing the stiffness of the compression spring. One is to exchange it for a spring with a higher stiffness, another is to combine multi-springs mechanically in parallel. (3) A single piezoelectric patch or piezoelectric stack device can harvest energy in mJ from track vibrations, which is the same as the energy necessary for the wireless sensor network node. In particular, when the stiffness of the compression spring of the piezoelectric stack device is increased to a larger value of 1 MN m-1, the harvested energy can reach levels of up to 1000 mJ. These results have proved that these harvesters can serve as a power source for the wireless sensor network node. Numerical results also show that these harvesters can serve as sensors to monitor the basic information of the train, such as the running velocity, the location and the axle load. The research results demonstrate the potential of piezoelectric patch and stack harvesters in designing the self-powered wireless sensor networks used in railway systems to ensure train operation safety.

Acknowledgments This work is supported by the National Natural Science Foundation of China (51472022, 51178040), and the Fundamental Research Funds for the Central Universities (2014YJS107). The authors greatly appreciate the reviewer’s comments, which have helped to improve the quality of the paper.

References [1] Hada A, Soga K, Liu R and Wassell I J 2012 Lagrangian heuristic method for the wireless sensor network design problem in railway structural health monitoring Mech. Syst. Signal Pr. 28 20–35 12

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J Wang et al

[32] Yan W, Lim C W, Cai J B and Chen W Q 2007 An electromechanical impedance approach for quantitative damage detection in Timoshenko beams with piezoelectric patches Smart Mater. Struct. 16 1390–400 [33] Erturk A 2011 Piezoelectric energy harvesting for civil infrastructure system applications: Moving loads and surface strain fluctuations J. Intell. Mater. Syst. Struct. 22 1959–73 [34] Zhao S and Erturk A 2013 Electroelastic modeling and experimental validations of piezoelectric energy harvesting from broadband random vibrations of cantilevered bimorphs Smart Mater. Struct. 22 015002 [35] Wang J J, Shi Z F and Han Z J 2013 Analytical solution of piezoelectric composite stack transducers J. Intell. Mater. Syst. Struct. 24 1626–36 [36] Zhao S and Erturk A 2013 Energy harvesting from harmonic and noise excitation of multilayer piezoelectric stacks: modeling and experiment Proc. SPIE 8688 86881Q [37] Zhao S and Erturk A 2014 Deterministic and band-limited stochastic energy harvesting from uniaxial excitation of a multilayer piezoelectric stack Sensors Actuators A 214 58–65 [38] Tan Y, He Z and Li Z 2009 Mitigation analysis of WIB for low-frequency vibration induced by subway Int. Conf. on Transportation Engineering 2009 pp 741–6 [39] Karlström A and Boström A 2006 An analytical model for train-induced ground vibrations from railways J. Sound Vib. 292 221–41 [40] Li P, Wen Y, Yin W and Wu H 2014 An Upconversion management circuit for low-frequency vibrating energy harvesting IEEE T. Ind. Electron. 61 3349–58

[22] Innowattech—energy harvesting systems www.innowattech. co.il/index.aspx [23] Li J, Jang S and Tang J 2012 Design of a bimorph piezoelectric energy harvester for railway monitoring J. Korean Soc. Nondestruct. Test. 32 661–8 [24] Li J, Jang S and Tang J 2014 Implementation of a piezoelectric energy harvester in railway health monitoring Proc. SPIE 9061 90612Q [25] Lei X Y 2007 Dynamic analyses of track structure with fourier transform technique J. China Railw. Soc. 29 67–71 (in Chinese) [26] Mallik A K, Chandra S and Singh A B 2006 Steady-state response of an elastically supported infinite beam to a moving load J. Sound Vib. 291 1148–69 [27] Kenney J T 1954 Steady-state vibrations of beam on elastic foundation for moving load J. Appl. Mech. ASME 21 359–64 [28] Wang R-T 1997 Vibration of multi-span Timoshenko beams to a moving force J. Sound Vib. 207 731–42 [29] Wang J J, Shi Z F and Xiang H J 2013 Electromechanical analysis of piezoelectric beam-type transducers with interlayer slip IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60 1768–76 [30] Yan W, Cai J B and Chen W Q 2011 An electro-mechanical impedance model of a cracked composite beam with adhesively bonded piezoelectric patches J. Sound Vib. 330 287–307 [31] Yan W, Chen W Q, Lim C W and Cai J B 2008 Application of EMI technique for crack detection in continuous beams adhesively bonded with multiple piezoelectric patches Mech. Adv. Mater. Struct. 15 1–11

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