Advances in Theoretical and Applied Mechanics, Vol. 9, 2016, no. 1, 43-54 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/atam.2016.634 Piezoelectric Vibration Energy Harvesting Characteristics of Barium Titanate Laminates Fumio Narita *, Xiaolong Zhu and Yasuhide Shindo Department of Materials Processing, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-02, Sendai 980-8579, Japan * Corresponding author Copyright 2016 Fumio Narita, Xiaolong Zhu and Yasuhide Shindo. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper studies the vibration energy harvesting characteristics of poled barium titanate (BT) unimorph cantilevers both analytically and experimentally. The unimorph cantilever consists of the BT layer and Cu shim, and the BT layer has sensing, grounding and driving electrodes. The output voltage of the cantilever excited by bending vibration was predicted by three dimensional finite element analysis (FEA). The output voltage was also measured, and a comparison was made between prediction and experiment. The effects of sensing electrode geometry and load resistance on the dynamic electromechanical fields and output power were then discussed in detail. Keywords: Piezomechanics, Finite element method, Material testing, Barium titanate laminates, Electromechanical field concentrations, Energy harvesting 1. Introduction Piezoelectric ceramics and composites have been used in a wide range of sensor and actuator applications, and many studies have been conducted on the performance of piezoelectric devices [2, 3, 8]. On the other hand, the direction of research has changed slightly from just sensors and actuators to an interest in extracting and storing energy from the environment [5, 9], and Shindo and Narita [7] have recently investigated the output voltage and power of S-shaped piezoelectric energy harvester excited by bending/torsion vibration. Some investigations have also focused on the design of self-powering, self-sensing and
44 Fumio Narita et al. self-controlling devices. Wang and Inman [11] examined the concept and design of a multifunctional composite sandwich structure for simultaneous energy harvesting and vibration control. They proposed the glass fiber reinforced composites with lead zirconate titanate (PZT) harvester, sensor and actuator, and studied the configurations, locations and operating modes of PZT materials for optimal power generation. Lead oxide-based ferroelectrics, especially PZTs, have high piezoelectric properties. Due to lead toxicity, however, the introduction of legislation in Europe to limit the usage of lead in automotive and electronic products has led to a worldwide search for lead-free compounds [6]. BT (BaTiO3) is a well known lead-free material. Although many investigators are developing the multifunctional composites using PZT materials, few of the BT-based multifunctional composites have been studied. In this paper, we discuss the vibration energy harvesting characteristics of poled BT unimorph cantilevers with sensing, grounding and driving electrodes. A three-dimensional FEA was carried out to predict the output voltage in the BT unimorph cantilevers subjected to bending vibration. The output voltage was also measured, and numerical results were compared with measured values. The dynamic electromechanical fields and output power were then examined for various sensing electrode geometries and load resistances. 2. Analysis 2.1 Basic equations Equations of motion and Gauss law are given by u (1) ji, j i, tt D 0 (2) ii where ij is the component of stress tensor, u i is the component of displacement vector, is the mass density, D i is the component of electric displacement vector, and a comma denotes partial differentiation with respect to the coordinates xi ( i1 2 3) or the time t. We have employed Cartesian tensor notation and the summation convention for repeated tensor indices. Constitutive relations can be written as s d E (3) ij ijkl kl kij k where D d є T E (4) i ikl kl ik k ij is the component of strain tensor, E i is the component of electric T field intensity vector, and sijkl dkij and є ik are the elastic compliance, direct piezoelectric coefficient and permittivity at constant stress, which satisfy the following symmetry relations:
Piezoelectric vibration energy harvesting characteristics 45 s s s s d d є є (5) T T ijkl jikl ijlk klij kij kji ij ji The relation between the strain tensor and the displacement vector is given by 1 ij ( uji uij ) (6) 2 and the electric field intensity vector is E i (7) where is the electric potential. The constitutive relations (3) and (4) for piezoelectric ceramics poled in the x3 -direction are given in Appendix A. 2.2 Finite element method Fig. 1(a) shows a unimorph cantilever constructed of BT layer and Cu shim. Let the coordinate axes x = x1 and y = x2 be chosen such that they coincide with the interface and the z = x3 axis is perpendicular to this plane. The origin of the coordinate system is located at the center of the bottom left side of BT layer, and the edge at x = 0 is clamped. Fig. 1(b) shows a geometry and dimensions of the unimorph cantilever. BT layer of length l = 50 mm, width w = 25 mm and thickness 1 mm is added to the upper surface of Cu shim of length 50 mm, width 25 mm and thickness 0.5 mm. The total thickness is 1.5 mm. BT layer has sensing, grounding and driving electrodes. The sensing and driving electrodes are located at the center and outer parts of the top surface of BT layer, respectively. In order to suppress coupling, there is a grounding electrode between these two electrodes [10]. On the other hand, only a whole grounding electrode is located on the opposite side. The dimensions of the electrodes are shown in Fig. 1(b). The length and width of the sensing electrode is ls and ws, respectively. We used a commercial finite element package ANSYS with three-dimensional (3D) eight-node elements to perform the analysis. For simplicity, the electrode layers were not incorporated into the model. This is because the thickness of the electrode layer is much smaller than the thickness of the BT layer. The imposed base excitation was given by the displacement uz0exp(it) of the clamped end (x = 0 plane), where uz0 is amplitude of applied displacement and is angular frequency. The top and bottom grounding electrode surfaces are connected to the ground, so that = 0. The output voltage of sensing electrode was then solved. The dynamic electromechanical fields for the cantilever were also predicted. Here, damping parameters were not included in the model for simplicity [4]. 3. Experimental procedure The unimorph cantilever was fabricated using BT layer (NEC/Tokin Co. Ltd., Japan) and Cu substrate. Electrodes were coated on both sides of BT layer, i
46 Fumio Narita et al. and the BT layer was bonded to the upper surface of Cu shim by conductive bonding as shown in Fig. 1. Fig. 2 shows the unimorph sample. The material properties of BT layer are listed in Table 1. Elastic T compliances s11 s33, direct piezoelectric coefficients d31 d33, permittivity є 33 and mass density can be found in the published data, while the remaining properties are assumed to be the same as those of BT ceramics reported by Jaffe and Berlincourt [1]. The elastic compliance, Poisson s ratio and mass density of Cu shim are 7.69 10-12 m 2 /N, 0.34 and 8920 kg/m 3, respectively. The fabricated cantilever was mounted on the vibration shaker (ET-132, Labworks Inc., USA). The imposed displacement vibration was applied with the shaker, and the acceleration of the imposed displacement uz0 2 was measured with a laser displacement sensor (LK-G10, KEYENCE, Co. Ltd., Japan). Output voltage Vout of the sensing electrode was also measured for the cantilever using an oscilloscope (GDS-1062A, Good Will Instrument Co., Ltd., Japan). Then, a resistive load was connected to the cantilever, and the output voltage Vout of the sensing electrode was measured. Moreover, the output power Pout from the cantilever can be calculated using the output voltage Vout and load resistance R. 4. Results and discussion Here, the numerical and experimental results under the applied displacement amplitude uz0 = 0.1 mm are presented. Fig. 3 shows the measured output peak voltage Vout of the BT layer as a function of frequency f = ω/2π for the unimorph cantilever (ls/l = 0.8 and ws/w = 0.16) at open circuit condition (R ). The solid line represents the value of the output peak voltage predicted by the FEA, and the solid circle denotes the average of two measured data. For comparison, the predicted output peak voltage by the FEA for PZT C-203 unimorph cantilever (Fuji Ceramics Co. Ltd., Japan) is also shown as dashed line. The material properties of C-203 are listed in Table 2. Although the damping parameters are not included in the model, the results of the FEA are in agreement with measured data. It can be seen that the output peak voltage of the BT layer is smaller than that of C-203 layer. Fig.4 shows the predicted output peak voltage Vout versus the ratio of sensing electrode width to cantilever width ws/w for the cantilever (ls/l = 0.8) under f = 50 Hz at R. It is noted that as the sensing electrode width decreases, the output peak voltage increases. Fig.5 shows the predicted output peak voltage Vout versus the ratio of sensing electrode length to cantilever length ls/l for the cantilever (ws/w = 0.16) under f = 50 Hz at R. As the sensing electrode length decreases, the output peak voltage increases. It is interesting to note that the effect of sensing electrode length on the output voltage is remarkably larger than that of sensing electrode width. The output peak voltage of the BT unimorph cantilevers under f = 50 Hz at R for three types of sensing electrode geometry, obtained from the FEA, is shown in Fig.6. Although the areas of sensing electrode are the same, the output voltage for ls = 2 mm, ws = 8 mm is larger than that for ls = 8 mm, ws = 2 mm.
Piezoelectric vibration energy harvesting characteristics 47 The variation of normal stress σxx along the length direction is calculated for the BT unimorph cantilever (ls/l = 0.8, ws/w = 0.16) at a chosen point (y = 0 mm and z = 0 mm here) under f = 50 Hz at R and the result is shown in Fig.7. The normal stress near the clamped end in the cantilever is larger than that near the free end. Fig.8 shows the output power for BT unimorph cantilever (ls/l = 0.8, ws/w = 0.16) under f = 50 Hz. The output power tends to increase with load resistance reaching a peak and then to decrease in magnitude. It is found that the optimal resistance for BT unimorph cantilever is about 0.6 MΩ. Moreover, it is expected that smaller sensing electrode length or width leads to larger output power, since the output peak voltage increases as the sensing electrode length or width decreases (see Figs. 4 and 5). 5. Conclusion BT unimorph cantilevers with sensing, grounding and driving electrodes were proposed, and a numerical and experimental study was conducted to discuss the effect of sensing electrode geometry on the piezoelectric vibration energy harvesting behavior. The output voltage of BT unimorph cantilever increases as the area of sensing electrode decreases, and the output power of BT unimorph cantilever under an applied displacement amplitude of 0.1 mm can achieve about 5.2 nw at a frequency of 50 Hz. Our present study is useful in designing new piezoelectric energy harvesters, and provides a basis for refining the real device design in order to increase output power. Appendix A For piezoelectric ceramics which exhibit symmetry of a hexagonal crystal of class 6 mm with respect to principal x1 x2 and x 3 (poling) axes, the constitutive relations can be written in the following form: 11 s11 s12 s13 0 0 0 11 0 0 d31 22 s12 s11 s13 0 0 0 22 0 0 d 31 E1 33 s13 s13 s33 0 0 0 33 0 0 d 33 E2 223 0 0 0 s44 0 0 23 0 d15 0 E 3 2 31 0 0 0 0 s44 0 31 d15 0 0 212 0 0 0 0 0 s66 12 0 0 0 (A.1) 11 22 T D1 0 0 0 0 d15 0 є11 0 0 E1 33 T D 2 0 0 0 d15 0 0 0 є11 0 E2 23 T D 3 d31 d31 d33 0 0 0 0 0 є 33 E 3 31 12 (A.2)
48 Fumio Narita et al. where, (A.3) 23 32 31 13, 12 21, (A.4) 23 32 31 13, 12 21 s s 11 44 s 1111 4s 2323 s 2222 4s, 3131, s 12 s s 66 1122, 4s 1212 s 13 s 2 s 1133 11 s s 12 2233, s 33 s 3333, (A.5) d 2d 2 d, d d d, d d (A.6) 15 131 223 31 311 322 33 333 References [1] H. Jaffe and D. A. Berlincourt, Piezoelectric transducer material, Proceedings IEEE, 53 (1965), 1372-1386. http://dx.doi.org/10.1109/proc.1965.4253 [2] F. Narita, R. Hasegawa and Y. Shindo, Electromechanical response of multilayer piezoelectric actuators for fuel injectors at high temperatures, Journal of Applied Physics, 115 (2014), no. 18. http://dx.doi.org/10.1063/1.4875487 [3] F. Narita, Y. Shindo and K. Sato, Evaluation of electromechanical properties and field concentrations near electrodes in piezoelectric thick films for MEMS mirrors by simulations and tests, Computers and Structures, 89 (2011), 1077-1085. http://dx.doi.org/10.1016/j.compstruc.2010.12.008 [4] F. Narita, Y. Shindo and T. Watanabe, Dynamic characteristics and electromechanical fields of 1-3 piezoelectric/polymer composites under AC electric fields, Smart Mater. Struct., 19 (2010), no. 7. http://dx.doi.org/10.1088/0964-1726/19/7/075004 [5] M. Okayasu, D. Sato, Y. Sato, M. Konno and T. Shiraishi, A study of the effects of vibration on the electric power generation properties of lead zirconate titanate piezoelectric ceramic, Ceramics International, 38 (2012), 4445-4451. http://dx.doi.org/10.1016/j.ceramint.2012.02.018 [6] Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nagaya and M. Nakamura, Lead-free piezoceramics, Nature, 432 (2004), 84-87. http://dx.doi.org/10.1038/nature03028 [7] Y. Shindo and F. Narita, Dynamic bending/torsion and output power of s-shaped piezoelectric energy harvesters, International Journal of Mechanics and Materials in Design, 10 (2014), 305-311. http://dx.doi.org/10.1007/s10999-014-9247-0
Piezoelectric vibration energy harvesting characteristics 49 [8] Y. Shindo, T. Sasakura and F. Narita, Dynamic electromechanical response of multilayered piezoelectric composites from room to cryogenic temperatures for fuel injector applications, ASME Journal of Engineering Materials and Technology, 134 (2012), 1-7. http://dx.doi.org/10.1115/1.4006504 [9] D. Vatansever, R. L. Hadimani, T. Shah and E. Siores, An investigation of energy harvesting from renewable sources with PVDF and PZT, Smart Materials and Structures, 20 (2011), no. 5. http://dx.doi.org/10.1088/0964-1726/20/5/055019 [10] N. Wakatsuki, H. Yokoyama and S. Kudo, Piezoelectric actuator of LiNbO3 with an integrated displacement sensor, Jpn. J. Appl. Phys., 37 (1998), 2970-2973. http://dx.doi.org/10.1143/jjap.37.2970 [11] Y. Wang and D. J. Inman, Simultaneous energy harvesting and gust alleviation for a multifunctional composite wing spar using reduced energy control via piezoceramics, Journal of Composite Materials, 47 (2013), 125-146. http://dx.doi.org/10.1177/0021998312448677 Table 1. Material properties of BT Elastic compliance Direct piezoelectric coefficient Permittivity Mass density ( 10-12 m 2 /N) ( 10-12 m/v) ( 10-10 C/Vm) (kg/m 3 ) s 11 s 33 s 44 s 12 s 13 d 31 d 33 d 15 є T 11 є T 33 8.85 a 8.95 a 22.8-2.7-2.9-60 a 140 a 260 128 102 a 5400 a a NEC/Tokin s product data sheets Table 2. Material properties of C-203 Elastic compliance Direct piezoelectric coefficient Permittivity Mass density ( 10-12 m 2 /N) ( 10-12 m/v) ( 10-10 C/Vm) (kg/m 3 ) s 11 s 33 s 44 s 12 s 13 d 31 d 33 d 15 є T 11 є T 33 13.9 16.7 42.7-4.1-6.4-144 325 522 131 129 7700
50 Fumio Narita et al. z y Grounding electrode Driving electrode Sensing electrode O x Barium Titanate layer Copper shim (a) 4 ls 1 l = 50 1 1 1 ws w = 25 1 (b) 0.5 unit: mm Fig.1 Schematic drawing of (a) BT unimorph cantilever and (b) dimensions
Piezoelectric vibration energy harvesting characteristics 51 Fig.2 BT unimorph sample V out (V) 3 2 1 BT PZT C-203 u z0 = 0.1 mm l s / l = 0.8 w s / w = 0.16 R FEA Test 0 50 100 f (Hz) Fig.3 Output peak voltage versus frequency for unimorph cantilevers
52 Fumio Narita et al. 0.24 u z0 = 0.1 mm f = 50 Hz V out (V) 0.23 l s / l = 0.8 R 0.22 FEA BT 0.2 0.4 0.6 w s / w Fig.4 Output peak voltage versus ratio of sensing electrode width to cantilever width V out (V) 0.8 0.6 0.4 u z0 = 0.1 mm f = 50 Hz w s / w = 0.16 R 0.2 FEA BT 0.2 0.4 0.6 0.8 l s / l Fig.5 Output peak voltage versus ratio of sensing electrode length to cantilever length
Piezoelectric vibration energy harvesting characteristics 53 Fig.6 Output peak voltage for unimorph BT cantilevers with three types of sensing electrode geometry 3 u z0 = 0.1 mm f = 50 Hz xx (MPa) 2 1 FEA BT y = 0 mm, z = 0 mm l s / l = 0.8 w s / w = 0.16 R 0 10 20 30 40 50 x (mm) Fig.7 Normal stress distribution along the length direction for the BT unimorph cantilever
54 Fumio Narita et al. Fig.8 Output power versus load resistance Received: March 24, 2016; Published: September 19, 2016