Study on tangentially polarized composite cylindrical piezoelectric transducer with high electro-mechanical coupling coefficient

Ultrasonics 74 (2017) 204–210

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Study on tangentially polarized composite cylindrical piezoelectric transducer with high electro-mechanical coupling coefficient Longyang Jia, Guangbing Zhang ⇑, Xiaofeng Zhang, Yu Yao, Shuyu Lin College of Physics and Information Technology, Shanxi Normal University, State Key Laboratory of Shaanxi Province, Xi’an 710119, China

a r t i c l e

i n f o

Article history: Received 9 March 2016 Received in revised form 27 September 2016 Accepted 28 October 2016 Available online 31 October 2016 Keywords: Tangential polarized Equivalent circuits FEM Resonance frequencies EMCC

a b s t r a c t In this work, we proposed an effective way to fabricate a tangentially polarized composite cylindrical transducer with high electro-mechanical coupling coefficient (EMCC) by radially connecting an inner tangential polarized piezoelectric tube with an outer metal ring. The resonance frequency and EMCC of the proposed transducer are calculated according to frequency equations, which are obtained from the equivalent circuit of the transducer, and the results indicate that EMCC of the tangentially polarized cylindrical transducer is much higher than that of the cylindrical transducer polarized in radial direction. Furthermore, the Finite Element Method (FEM) model of the transducer is established and used for numerical simulation of the vibration models and the optimum configuration parameters. On the basis of those theoretical results, serials of prototype transducers are manufactured with an inner tangential polarized piezoelectric tube connecting with different outer metal cylindrical shells. The admittance characteristics of the fabricated transducers measured by Impedance Analyzer clearly demonstrate that the resonance frequencies of the transducers are in good agreement with those of simulation results, and the effective EMCC of transducers varies with the material of metal cylindrical shell, in which aluminum metal shell possesses the highest EMCC. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction With the rapid development of electronic, computer and materials science, high power piezoelectric ultrasonic transducer is more and more widely used in the fields of aviation, navigation, national defense, biotechnology, optical fiber communications and electronics [1–8]. Lots of high power piezoelectric ultrasonic transducers with composite structure have been successfully designed and used, such as longitudinal composite transducer, longitudinal sandwich transducer, radial composite cylindrical piezoelectric transducer, and radial sandwich cylindrical transducer [9–20]. Piezoelectric cylindrical tube has received increasing attentions due to its stable performance, no directivity in horizontal direction and higher receiving sensitivity. In order to improve sound radiation area, composite cylindrical piezoelectric transducer is proposed, many theories and experimental works have been developed to improve the energy conversion efficiency of the transducer [21–23]. For example, Lu obtained a formula to estimate the transverse frequencies of the piezoelectric cylindrical shells [24]. Lin designed a kind of radial sandwiched piezoelectric

⇑ Corresponding author. E-mail address: [email protected] (G. Zhang). http://dx.doi.org/10.1016/j.ultras.2016.10.013 0041-624X/Ó 2016 Elsevier B.V. All rights reserved.

transducer using analytical and numerical method [25]. He also proved that the transducer polarized in axially direction has larger sound radiating area [26–28]. Ebenezer and Kim studied the radial vibration of a radial polarized piezoelectric transducer under some assumptions [29,30]. Liu got the electromechanical model for a thin-walled cylindrical radial composite piezoelectric ceramic transducer [31]. Aronov et al. studied the effects of coupled vibrations in piezoelectric circular tubes with energy method [32,33]. According to polarization direction acted on piezoelectric tube, the composite piezoelectric ultrasonic transducer can be classified into radial polarization, axial polarization, and tangentially polarization transducer. To the best of our knowledge, the existed studies mainly focus on fabrications of cylindrical composite piezoelectric transducers with the manner of radial polarization and axial polarization, tangentially polarized composite cylindrical piezoelectric transducer has never been designed and studied. However, recent studies indicated tangentially polarized stripeelectroded piezoelectric tube possesses a higher effective electromechanical coupling coefficient (EMCC) compared with those of radial polarized and axial polarized piezoelectric tubes [34–36]. On the basis of those works, the present study aims to design a novel tangentially polarized composite cylindrical transducer with high EMCC by radially connecting an inner tangential polarized piezoelectric tube with an outer metal ring. The performance of

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the designed transducer is studied by equivalent circuit and finite element methods. In the following sections, the equivalent circuit and the frequency equation of the transducer is deduced and then the vibration characteristics of the transducer are analyzed by finite element simulation. Finally, prototype transducers are made and the performances of the transducers are measured experimentally. 2. The equivalent circuit of the tangentially polarized hybrid piezoelectric cylindrical transducer Fig. 1 shows the structure of the tangential polarized cylindrical transducer. The inner part of the transducer is a tangentially polarized piezoelectric ring, which has outer radius b; inner radius c and height l. The piezoelectric ring consists of 12 rectangular silver electrodes which cover the inner and outer walls of the tube. There are six positive electrodes and six negative electrodes. The positive electrodes and negative electrodes are alternately arranged at equal intervals and the polarization direction denoted by arrows in Fig. 2(a) is approximately parallel to the tangential direction of the tube. The polarization direction of each segment coincides with the polarity of the excitation electric field. The electrical connection of the transducer is shown in Fig. 2(b), where six positive electrodes are connected in parallel to serve as the positive pole and six negative electrodes are connected in parallel to serve as the negative pole of the transducer. The outer part of the transducer is metal tube, which has outer radius a and inner radius b. When the height of the cylindrical transducer is less than its diameter,

the radial vibration can be regarded as an ideal plane radial vibration. Based on the structure of the transducer shown in Fig. 1, the piezoelectric equations can be written as:

nr =r 0 ¼ SE33 T h þ d33 Eh

ð1Þ

D2 ¼ d33 T h þ eT33 Eh

ð2Þ

where subscript 3 represents the circumferential direction, r0 ¼ ðb þ cÞ=2 is mean radius of the cylinder ring, SE33 is elastic compliance constant, d33 is piezoelectric strain constant, eT33 is dielectric constant, Eh is tangential electric field, T h is shear stress, and nr is radial displacement. The mass of the piezoelectric tube can be expressed as 2qpwr0 l, in which w is the thickness of the piezoelectric tube. Let radial displacement and the radial vibration velocity be nr and dnr =dt, respectively, then the wave equation in radial direction can be written as:

q

a

o

2

Th ¼

¼

Th Fr  r 0 Aw

ð3Þ

nr d33  Eh r0 sE33 sE33

ð4Þ

Based on Eqs. (3) and (4), we can obtain the radial wave equation, that is:

q

2

d nr dt

2

þ

nr d33 Fr ¼ Eh  Aw r 20 sE33 r 20 sE33

ð5Þ

€r ¼ jxn_ r . If each Let nr ¼ nr0 expðjxtÞ, then we have n_ r ¼ jxnr , n patch connects in parallel, the tangential electric field intensity Eh can be expressed as Eh ¼ V=LC ¼ nV=2pr0 , where LC ¼ 2pr0 =n is the thickness of each piezoelectric patch and n is the number of ceramic patches. Then the radial equation can be written as:

c RZT Ring Metal Ring

l

dt

where A ¼ 2pr0 l denotes the lateral area and F r is the external force exerted to the outer surface of the piezoelectric tube in radial direction. From Eq. (1), we have:

Z

b

2

d nr

o

y

r x Fig. 1. The structure of the tangentially polarized cylindrical transducer.

ðjxm þ 1=ðjxC m ÞÞn_ r2 þ F r ¼ uV

ð6Þ

Here, C m ¼ r 0 sE33 =2pwl; u ¼ and ¼ 1=sE33 are elastic compliance constant, electromechanical conversion coefficient and phase modulus of the piezoelectric tube, respectively. According to Eqs. (2) and (4), we can deduce the electric displacement Dh ; that is E d33 nlwY 0 =r 0 ;

Fig. 2. The structure of the piezoelectric ring. (a) Polarization direction and (b) electrical connection.

Y E0

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Dh ¼

d33 Y E0 nr þ eT33 ð1  K 233 ÞEh r0

ð7Þ

2

x 10

-3

2

In Eq. (7), K 233 ¼ d33 Y E0 =sT33 is the EMCC, which is much larger than K 31 in general. The total area of the electrodes is Nlw, in which N is the number

Admittance (s)

1

2 Nlw, then: of the electrodes. The current through the tube is I ¼ dD dt

I ¼ jxC 0 V þ un_ r

ð8Þ

Here, C 0 ¼ N 2 lweT33 ð1  K 233 Þ=2pr is the clamped capacitance when radial vibration is considered. According to Eqs. (6) and (8), the equivalent circuit of the tangential polarized piezoelectric tube vibrated in radial direction is obtained, which is shown in Fig. 3. From Fig. 3 and the equivalent circuit of the metal shell [31], the hybrid equivalent circuit of a tangential polarity transducer can be obtained, which is shown in Fig. 4. The load impedance of the transducer is ignored in the theory deduction. In Fig. 4, M ¼ 2pR0 qlt denotes the mass and C M ¼ R0 =ð2pltEÞ is the elastic compliance constant of the metal shell. The height, wall thickness, density, Young’s modulus and mean radius of the metal shell are denoted as l, t, q, E and R0 ; respectively. From Fig. 4, the input electric admittance Y e of the tangentially polarized tube can be obtained:

Ye ¼

I u2 þ jxðzm þ zM Þ ¼ V zm þ zM

I3 V

1: ϕ

C0

ð9Þ

m

Cm

δr2 F2

V

1: ϕ

C0

m Cm

M CM

-3

10

20

30

40

Fig. 5. The admittance curves computed by equivalent circuit for the transducers with different metal cylinder shells.

Here, Z m ¼ jxm þ 1=ðjxC m Þ is the mechanical impedance of the metal ring and Z M ¼ jxM þ 1=ðjxC M Þ is the mechanical impedance of the piezoelectric tube. The resonance frequency f r of the transducer is computed when Y e ! 1, while the anti-resonance frequency f a is computed when Y e ¼ 0. Three different metal shells are used in the numeral calculations and the geometrical dimensions and parameters of the metal material are listed in Tables 1 and 2, respectively. The piezoelectric tube for theoretically calculation is PZT-5j and the material parameters are as followings:

q0 ¼ 7400 kg=m3 ; sE33 ¼ 23:5  1012 m2 =N; eT33 ¼ 2800; d33 ¼ 550  1012 C=N; e0 e0 ¼ 8:85  1012 C2 =ðN m2 Þ: From Fig. 5 we can see that f r ¼ 27:647 kHz and f a ¼ 31:782 kHz for the transducer with aluminum shell, f r ¼ 23:499 kHz and f a ¼ 25:894 kHz for the transducer with copper shell, and f r ¼ 31:387 kHz and f a ¼ 33:406 kHz for the transducer with steel shell, respectively. The effective EMCC keff is computed using equation

"

Table 1 The geometrical dimensions of the transducer. Transducer part

Inner diameter (mm)

External diameter (mm)

Height (mm)

Piezoelectric tube Metal ring

37 42

42 52

35 35

Table 2 The parameters of the metal materials.

q (kg/m3)

0

Freqency (KHz)

keff

v

aluminum copper steel

-2

Z1

Fig. 4. Hybrid equivalent circuit of the transducer.

Metal material

-1

N ¼ 12;

Fig. 3. The equivalent circuit of the tangential polarity piezoelectric tube.

I3

0

E (N/m2)

Aluminum

0.34

2700

7:15  1010

Copper

0.34

8960

12:00  1010

Steel

0.28

7800

2:09  1011


2 #1=2 f ¼ 1 r fa

ð10Þ

In order to study the effective EMCC of the tangential polarized piezoelectric transducer, the effective EMCC are computed for the transducer with different metal shells and the results are compared to that of the radial polarized transducer. The geometrical dimensions and material parameters used in the calculation are same as those in Ref. [31] for the radial polarized transducer and the comparative results are shown in Fig. 6. From Fig. 6 we found that keff of the tangential polarized transducer is much higher than that of the radial polarized transducer. The effective EMCC decreases when the thickness of the outer metal shell increased. The transducer with aluminum metal shell has higher EMCC than those with steel metal shells for both tangential and radial polarized transducers. 3. FEM simulation Commercial finite element software COMSOL Multiphysic4.4 is used to simulate the vibration modes and the optimal structure parameters of the transducers. The FEM model of the cylindrical

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Effective electro-mechanical coupling coefficient

L. Jia et al. / Ultrasonics 74 (2017) 204–210

0.8 0.7 tangential polarized transducer with aluminum tube

0.6 0.5 tangential polarized transducer with steel tube

0.4 radial polarized transducer with aluminum tube

0.3 0.2 radial polarized transducer with steel tube

0.1

2

4

6

8

10

12

14

t (mm) Fig. 6. The relationship between EMCC and the thickness of metal shells for radial and tangential polarized transducers.

Fig. 7. The FEM model of the tangential polarity transducer: (a) physical model and (b) meshing model.

transducer with tangentially polarized piezoelectric tube is shown in Fig. 7, where Fig. 7(a) is the physical model and Fig. 7(b) is the meshing model which is created by the free meshing tool. The geometry and material parameters of the transducer are the same as those in the previous section. When free boundary condition is considered, the vibration modes of the transducer are obtained using the Modal Analysis of the FEM simulation, which are shown in Fig. 8. When dielectric loss and mass damping are ignored, the relationship between admittance and frequency for different metal cylinder shells are firstly obtained using FEM and the results are shown in Fig. 9. From Fig. 9 we can see that f r ¼ 27:771 kHz, f a ¼ 30:584 kHz for aluminum shell, f r ¼ 24:307 kHz, f a ¼ 25:913 kHz for copper shell, and f r ¼ 31:773 kHz, f a ¼ 33:233 kHz for steel shell. Compared the FEM simulation results with those shown in Fig. 5, we can find that the FEM results are in good agreement with the equivalent circuit calculation results. In practice applications, the dielectric loss, mass damping and pre-stress usually have effects on the performance of the trans-

ducer. By setting dielectric loss as 1%, mass damping parameter as 1500 s1 [37], and pre-stress as 200 MPa [38], we computed the admittance and phase curves of transducer using FEM and the results are shown in Fig. 10. From Fig. 10 we can see when the losses and pre-stress are considered, the resonant frequency is a different with the transducer without them. The resonance and anti-resonance frequencies are f r ¼ 26:988 kHz; f a ¼ 28:844 kHz for aluminum shell, f r ¼ 23:160 kHz, f a ¼ 24:204 kHz for copper shell, and f r ¼ 30:932 kHz, f a ¼ 31:806 kHz for steel shell. The influence of pre-stress on the transducer resonant frequency is analyzed by COMSOL and the results are shown in Fig. 11. From simulation results it can be seen that the resonance frequency is decreased as the pre-stress is increased.

4. Prototype tangential polarity cylindrical transducer The prototype tangential polarity cylindrical transducers are designed and made. The material of the inner piezoelectric tube

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Fig. 8. The radial vibration mode for the transducers with different metal cylinder shells. (a) aluminum, (b) copper, and (c) steel.

x 10

-3

35

aluminum copper steel

2

Freqency (KHz)

Admittance (s)

0

-2

-4

aluminum copper steel

-6

30

25

20

50

100

-8 0

10

20

30

40

Freqency (KHz) Fig. 9. The admittance curves for the transducer without considering the losses and damping computed by FEM.

is PZT-5, and the outer metal shell materials are aluminum, cooper and steel, respectively. Two transducers are made for each metal shell and a photograph of the prototype transducers is shown in Fig. 12(a). An insulation layer is added between the metal tube and piezoelectric ceramic ring to prevent short circuit. The two half-pipe metal tubes are connected together by screws to control the radial pre-stress conveniently. The admittance characteristics

100

aluminum copper steel

0.01 0.008 0.006

50

0

0.004

-50 0.002 0 22

24

26

28

30

250

300

were measured by IM3570 Impedance Analyzer. The positive pole of the transducer is connected with the positive terminal and the negative pole of the transducer is connected with the negative terminal of the impedance analyzer. The experiment setup is shown in Fig. 12(b). The measured admittance curves are given in Fig. 13. From Fig. 13 we can see that f r and f a for the transducer with steel shell are the biggest, for the transducer with aluminum shell are the second ones, and for the transducer with copper shell are the smallest.

Phase (deg)

Admittance (s)

200

Fig. 11. The frequency vs stress for the transducers with difference metal cylinder shells.

aluminum copper steel

0.012

150

Stress (MPa)

32

-100 22

24

26

28

30

Freqency (KHz)

Freqency (KHz)

(a)

(b)

32

Fig. 10. The admittance and phase curves of the transducers computed by FEM. (a) Admittance and (b) phase.

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Fig. 12. The measurement of prototype tangentially polarized piezoelectric transducers (a) prototype transducers. (b) experiment setup.

x 10

-4

-50

aluminum copper steel

4

Phase (deg)

Admittance (s)

5

3 2 1 22

24

26

28

30

-70 -80 -90 22

32

aluminum copper steel

-60

24

26

28

30

Freqency (KHz)

Freqency (KHz)

(a)

(b)

32

Fig. 13. The measured admittance and phase curves of the transducers (a) admittance and (b) phase.

Table 3 The comparative results of the theoretic, and FEM without considering the losses, mass damping and pre-stress. Metal material

Aluminum Copper Steel

Theoretic results

FEM results

f r (kHz)

f a (kHz)

keff

f r (kHz)

f a (kHz)

keff

27.647 23.499 31.387

31.782 25.894 33.406

0.493 0.420 0.342

27.771 24.307 31.773

30.584 25.913 33.233

0.418 0347 0.293

Table 4 The comparative results of experimental measurement and FEM simulation by considering the dielectric loss, damping and pre-stress. Metal material

Aluminum Copper Steel

FEM results

Measured results

f r (kHz)

f a (kHz)

keff

f r (kHz)

f a (kHz)

keff

26.988 23.160 30.932

28.844 24.204 31.806

0.353 0.291 0.233

28.182 23.030 30.909

30.303 24.545 32.121

0368 0.346 0.272

5. Discussions The comparative results of the theoretic and FEM simulation for the transducer without considering the losses, mass damping and pre-stress are given in Table 3. It can be found that the frequencies computed by theoretic and FEM are in good agreement. Then, we compare the experimental results with FEM simulation results when the dielectric loss, mass damping and prestress are considered. The comparative results are shown in Table 4. It can be found that the measurement results are agreement with the FEM simulation results. But a few differences also appeared in the comparative data. The differences may result from the following reasons. Firstly, the parameters of the piezoelectric tube

and the metal shell used in FEM simulation are not exactly same as those of the prototype transducers. Secondly, the presence of the radial clamping force between the inner and outer part of the transducer resulted from the tightness of the screw has effect on the resonance frequency [39–45]. Thirdly, the dielectric losses and mass damping of the transducer have effects on the vibration performance of the transducer, especially for effective EMCC of the transducer. 6. Conclusions In this work, a tangential polarity cylindrical transducer is presented and analyzed. The equivalent circuit method is used to

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analyze the performance of the transducer theoretically and the resonance frequency and the effective EMCC are computed. The vibration model and the optimum configuration parameters of the transducer are obtained by FEM simulation and then the prototype transducers are made and the performances of the transducers are measured experimentally. The following conclusions can be drawn: (1) The effective EMCC of the tangential polarized cylindrical transducer is much higher than that of radial polarized transducer. (2) The effective EMCC varies with the material of metal cylindrical shells and the thickness of the metal tube. The transducer with aluminum outer shell has higher effective EMCC than those with steel shell or copper shell. (3) Resonance frequencies calculated from frequency equations and FEM simulation are good agreement with the real experimental results. Acknowledgment A part of this study was supported by the National Natural Science Foundation of China (Grant Nos. 11574191 and 11674208) and Fundamental Research Funds for the Central University (GK201401003). References [1] A. Amir, S. Mohsen, P. Abbas, An approach to design a high power piezoelectric ultrasonic transducer, J. Electroceram. 22 (2009) 369–382. [2] F. Oohira, M. Iwase, T. Matsui, M. Hosogi, I. Ishiraaru, G. Hashiguchi, Y. Mihara, A. Lino, Self-hold and precisely controllable optical crossconnect switches using ultrasonic micro motors, IEEE J. Sel. Top. Quantum Electron. 10 (2004) 551–557. [3] S.P. Schenker, Y. Bar-Cohen, D.K. Brown, R.A. Lindemann, M.S. Garrett, E.T. Baumgartner, S. Lee, S. Lih, B. Joffe, Composite manipulator utilizing rotary piezoelectric motors: new robotic technologies for mars in-situ planetary science, in: M.E. Regelbrugge (Ed.), Smart Structures and Integrated Systems, Proceedings of SPIE, San Diego, 1997, pp. 918–926. [4] Z.J. Chen, X.T. Li, G. Liu, S.X. Dong, A two degrees of-freedom piezoelectric single-crystal micromotor, J. Appl. Phys. 116 (2014) 224101. [5] K. Yamashita, L. Chansomphou, H. Murakami, M. Okuyama, Ultrasonic micro array sensors using piezoelectric thin films and resonant frequency tuning, Sens. Actuators, A 114 (2004) 147–153. [6] N. Takayuki, F. Takamichi, E. Masayoshi, T. Shuji, A large-scan-angle piezoelectric MEMS optical scanner actuated by a Nb-doped PZT thin film, J. Micromech. Microeng. 24 (2014) 10–15. [7] D. Liua, B. Zhoua, S.H. Yoona, H.C. Wikle IIIa, Y. Wangb, M. Parkb, B.C. Proroka, D.J. Kim, Effects of the structural layer in MEMS substrates on mechanical and electrical properties of Pb(Zr0.52Ti0.48)O3 films, Ceram. Int. 37 (2011) 2821–2828. [8] Q. Zhang, S. Shi, W. Chen, An electromechanical coupling model of a longitudinal vibration type piezoelectric ultrasonic transducer, Ceram. Int. 41 (2015) 638–644. [9] C. Irinela, Underwater flextensional piezoceramic sandwich transducer, Sens. Actuators, A 100 (2002) 287–292. [10] D. Chacón, G. Rodríguez-Corral, L. Gaete-Garretón, E. Riera-Franco de arabia, J. A. Gallego-Juárez, A procedure for the efficient selection of piezoelectric ceramics constituting high-power ultrasonic transducers, Ultrasonics 44 (2006) 517–521. [11] F.J. Arnold, S.S. Muhlen, The mechanical pre-stressing in ultrasonic piezotransducers, Ultrasonics 39 (2001) 7–11. [12] J.A. Gallego-Juárez, G. Rodriguez, V. Acosta, E. Riera, Power ultrasonic transducers with extensive radiators for industrial processing, Ultrason. Sonochem. 17 (2010) 953–964. [13] G.P. Zhou, The performance and design of ultrasonic vibration system for flexural mode, Ultrasonics 38 (2000) 979–984. [14] J.D. Zhang, W.J. Hughes, P. Bouchilloux, R.J. Meyer, K. Uchino, R.E. Newnham, A class V flextensional transducer: the cymbal, Ultrasonics 37 (1999) 387–393.

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