Finite Element Analysis and Experiment on a Piezoelectric Harvester with Multiple Cantilevers

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1 doi: /ijep Finite Element Analysis and Experiment on a Piezoelectric Harvester with Multiple Cantilevers Hongbing WANG *1, Chunhua SUN 2, Zhirong LI 3, Yiping ZhANG 4 Department of Mechanical & Electrical Engineering, Suzhou Vocational University, Suzhou, China *1 whb@jssvc.edu.cn; 2 sunch@jssvc.edu.cn; 3 lzr@jssvc.edu.cn; 4 zyp@jssvc.edu.cn Abstract A piezoelectric harvester with multiple cantilevers was proposed for harvesting environment vibration energy from multiple directions and broadening the resonance frequency range. The harvester was composed of a steel base and many different cantilevers directing differently. The single cantilever was analyzed by Finite Element Method (FEM). The effects of the structure parameters of the single cantilever on the nature frequency were gotten by modal analysis. The output voltage value of the single cantilever was maximal at resonance by harmonic analysis. The electricity generating capability of the harvester was tested and the results indicated the harvester could generate the higher output voltage in a special frequency scope comparing with a single cantilever. The effective excitation frequency range of the harvester was 12~20 Hz. The output power of the harvester was about 2.88 mw at vibration acceleration 0.6 g, the outer load 500 Ω and the excitation frequency 16 Hz. The harvester could broaden the work frequency scope and supply electric energy for large distributed wireless sensor systems and subminiature power devices. Key words Multiple Direction; Cantilever Beam Piezoelectric Harvester; Energy Harvesting; Finite Element Method (FEM) Introduction Recently with large distributed wireless sensor systems and subminiature power devices developing quickly, traditional chemical battery could satisfy the need to some extend. But the problems such as huge volume, finite life and periodical substitution were very obvious [1 2]. Many researchers had started to study some new energy harvesting devices which could harvest environmental energy timely [3 4 ]. At present devices of energy harvesting were electromagnetic [5], electrostatic [6] and piezoelectric [7]. It had been proved that piezoelectric harvesting device was more suitable for harvesting environmental energy. In addition to the advantage of small volume and light weight the piezoelectric harvesting device had three times higher energy density as compared to its counterparts electrostatic and electromagnetic [8]. Recently many researchers had paid more attention to the piezoelectric harvesting devices. The piezoelectric harvesting device worked effectively only at the resonance state. However the vibration frequency in ambient changed in a special range, so the piezoelectric harvester could not always work at the resonance and the efficiency was low. It was a difficult problem to advance the efficiency of the piezoelectric harvester. For advancing the efficiency of the piezoelectric harvester, the paper proposed a piezoelectric harvester with multiple cantilevers. Some literature had found that Cantilever piezoelectric harvester had the characteristic of low natural frequency, simple structure and high energy conversion efficiency [9 10]. The piezoelectric harvester with multiple cantilevers was composed of many cantilevers which point to different directions. The proposed harvester could harvest vibration energy from multiple directions and worked at a broad frequency range. So the proposed harvester could work effectively. The vibration characteristic of the proposed harvester was analyzed in the paper by finite element method. The harvester was then fabricated and tested. The test results indicated that the harvester could match the proposed design requirement. Structure and Principle of the Harvester The structure of the harvester was shown in Fig.1. The harvester was composed of many cantilevers which pointed 20

2 International Journal of Energy and Power (IJEP) Volume 4, to different directions. The cantilevers were fixed on a base. The base consisted of two parts. The two parts were connected by a bolt. Between the two parts the cantilevers were fixed on one end. The other end of the cantilever was free. The cantilevers were connected in series in electric circuit. The structure of the single cantilever was shown in Fig.2. The single cantilever consisted of a steel sheet, two piezoelectric ceramics and a steel mass. The piezoelectric ceramics were pasted respectively on the upper and lower surfaces of the steel sheet by glue. The steel mass was set on the end of the surface of one ceramic by paste method. The cantilever The base H1 The two ceramics L 1 The sheet W 1 L 2 FIG.1 STRUCTURE OF THE HARVESTER FIG.2 STRUCTURE OF THE SINGLE CANTILEVER The harvester was set in a vibration environment. The outer load excitation caused the vibration of the cantilever. When the cantilever was bent the upper and lower surface of the ceramic caused shrinkage and extension deformation. Because of the direct piezoelectric effect of the ceramic the internal electrical charge was generated. Piezoelectric Effect of the Harvester The piezoelectric effect was understood as the linear electromechanical interaction between the mechanical and the electrical state in piezoelectric ceramic. The piezoelectric effect was a reversible process exhibiting the direct piezoelectric effect (the internal generation of electrical charge resulting from an applied mechanical force) and the reverse piezoelectric effect (the internal generation of a mechanical strain resulting from an applied electrical field). The piezoelectric equation of the harvester which buried in the asphalt pavement could be described as equation (1) and (2). E i ij j ni n S s T d E (1) T m m j mn n D d T E (2) Where i, j 1,2,3,4,5,6; m, n 1,2,3, D was the electric displacement; E was electric field intensity; d was the T piezoelectric constant matrix; S was the strain tensor; T was the stress tensor; was the dielectric constant tensor E tested at constant stress condition; s was the compliance tensor tested at constant electric field intensity condition. When the harvester was set in a vibration environment, the direct piezoelectric effect could be used to transform the vibration energy into the electric energy. The Vibration Model of the Cantilever [11] H2 The mass The single cantilever consisted of beam and a mass. The mass was set on the end of the beam. The beam was fixed on a base. The vibration model of the cantilever was shown in Fig.3. H3 The base y The cantilever The mass (t) u b x=l x FIG.3 THE VIBRATION MODEL OF THE CANTILEVER Based on Euler Bernoulli hypothesis, the partial differential equation of the free vibration of the cantilever was described as equation (3) uxt (, ) uxt (, ) uxt (, ) YI c 0 4 si m 4 2 x x t t (3) 21

3 Where YI was bending stiffness, m was mass per unit length, ci s was internal strain damp, uxt (, ) was the transverse absolute displacement of the cantilever at time t and location x. The absolute displacement uxt (, ) could be described as the displacement u () t and the transverse displacement ur ( x, t) relative to the base. b uxt (, ) u( t) u( xt, ) (4) b From equation (3) and (4), the forced movement equation of the transverse vibration of the cantilever relative to the base was concluded. r ur x t ur x t ur x t d u 4 s (, ) (, ) (, ) b () t YI c I m m x x t t dt For the cantilever in Fig.3, the natural frequency was given as equation (6). (5) n K 3 YI / L M (33 /140) ml M 3 t (6) Finite Element Analysis of the Single Harvester The harvester consisted of many cantilevers which were connected in series in electric circuit. Each cantilever worked independently. So a single cantilever was selected to analyze the vibration characteristic. Finite element software ANSYS was used to analyze the vibration characteristic of the single cantilever. The initial structure parameters of the single cantilever were showed in Table.1. The materials of the sheet and mass were 45 steel. The material properties of 45 steel were Elastic module 209GPa, Poisson ratio and Density 7860 kg/m3. The material of the piezoelectric ceramic was PZT 8 whose properties were shown in Table.2. TABLE 1 INITIAL STRUCTURE PARAMETERS OF THE CANTILEVER (UNIT:MM) Length Width Height The ceramic L1(70) W1(20) H1(0.2) The sheet L1(70) W1(20) H2(0.4) The mass L2(2) W1(20) H3(0.8) TAB.2 MATERIAL PROPERTIES OF PZT 8 parameter T [ ]( 10 F / m ) d ( 10 C / m ) 10 c ( 10 Pa ) Value The finite element model of the single cantilever was constructed in ANSYS software. In the model the influence of the adjoin part was ignored and the connection of the ceramic and the steel sheet was ideal. The displacement and stress were continual in the adjoin part. The model of the cantilever was analyzed by mode analysis. The first bend mode was shown in Fig.4. The frequency was Hz. The cantilever worked at the bend mode and frequency. The cantilever worked effectively at the resonance frequency. The first bend mode was the work mode of the cantilever. So the first bend frequency should be set to accord with the ambient vibration frequency. The structure parameters of the cantilever were adjusted to change the first bent frequency. 22

4 International Journal of Energy and Power (IJEP) Volume 4, The effect of the parameter W1 on the first bend frequency was shown in Fig.5. In Fig.5 the first bend frequency increased with the parameter W1 increasing. FIG.4 THE FIRST BEND MODE OF THE CANTILEVER FIG.5 THE EFFECT OF THE PARAMETER W1 The effects of the other parameters on the first bend frequency were also acquired. The first bent mode frequency decreases with the parameter L1 increasing. The first bent mode frequency increased with the parameter H2 increasing. The first bent mode frequency increased with the parameter H1 increasing. The first bent mode frequency decreased with the parameter H2 increasing. The first bent mode frequency decreased with the parameter H3 increasing. The sensitivity of the first bent frequency on the structure parameters was analyzed. The results indicated H1 and H2 influenced greatly the first bent mode frequency. The multiple direction cantilever piezoelectric harvester had many cantilevers. If the bend frequency of one cantilever was accord with the vibration frequency, we would think the harvester worked at the resonance frequency. Through selecting the structure parameters of the cantilever the cantilever could have the different bent frequency. If the harvester had six cantilever. The parameters of the six cantilevers were shown in Tab.3. The six cantilevers had the different frequency. Then the resonance frequency range of the harvester was about 13~20Hz which was shown in Fig.6. In Fig.6 the numbers of the six cantilevers were set as 1 6. So the multiple cantilevers harvester could broaden the range of the resonance frequency. 23

5 TAB.3 THE PARAMETERS OF THE SIX CANTILEVERS The cantilever Parameters(W1,L1, L2, H1,H2,H3) The bent frequency(hz) 1 8,120,4,0.2,0.2, ,122,6,0.2,0.2, ,125,6,0.2,0.2, ,130,6,0.2,0.2, ,125,6,0.2,0.2, ,140,6,0.2,0.2, FIG.6 THE RESONANCE FREQUENCY RANGE OF THE HARVESTER Harmonic Analysis of the Cantilever The outer ambient load was set as distribution load which applied on the surface of the cantilever. The finite element model of the cantilever was shown in Fig.7. The cantilever was selected as number 3 shown in Tab.3. The first bend frequency of the cantilever was Hz. The cantilever was analyzed by harmonic analysis. The excitation frequency range was 0~33.434Hz and the step was 20. The outer ambient load was set as 70 Pa. The open circuit voltage response of the ceramic was shown in Fig.8. In fig.8 we could see that the open circuit voltage of the ceramic was maximal at the excitation frequency Hz which was accord with the first bend frequency. The cantilever was in the resonance state. So when the vibration of the outer ambient load was accord with the natural frequency the open circuit voltage was maximal. Distribution load FIG.7 THE FINITE ELEMENT MODEL OF THE CANTILEVER FIG.8 THE OPEN CIRCUIT VOLTAGE RESPONSE OF THE CERAMIC 24

6 International Journal of Energy and Power (IJEP) Volume 4, Experiment of the Harvester According the results of the finite element analysis, the multiple cantilevers harvester was designed and fabricated. The photo of the harvester was shown in Fig.9. The cantilevers were connected in series in electric circuit. For studying the electric generation capacity of the harvester the test device was constructed shown in Fig. 10. The harvester Vibration exciter Oscilloscope Power amplifier Function generator FIG.9 THE PHOTO OF THE HARVESTER FIG.10 THE TEST DEVICE OF THE HARVESTER The test device consisted of GF100 Power amplifier, Vibration exciter, TFG2015G DDS Function generator and Oscilloscope. Function generator exported a sine excitation signal whose frequency was tunable. The signal was magnified by Power amplifier to excite Vibration exciter which provided excitation for the harvester. Oscilloscope was used to test the output voltage for load and the power of the load was calculated. The output power of the harvester with excitation frequency at vibration acceleration 0.6 g, the outer load 500 Ω was shown in Fig.11. The cantilevers were selected according to Tab.3. In Fig.11 the output power of the harvester was higher at the excitation frequency 12~20 Hz. At the excitation frequency 16 Hz the maximal power was 2.88 mw. However the output power of the single cantilever was smaller and the higher power was only at a narrow excitation frequency. The test results were accord with the finite element analysis calculation results. The multiple harvester The single cantilever FIG.11 THE OUTPUT POWER OF THE HARVESTER AND THE SINGLE CANTILEVER WITH THE EXCITATION FREQUENCY Conclusions (1) For harvesting environment vibration energy from multiple directions and broadening the resonance frequency range the piezoelectric harvester with multiple cantilevers was proposed. The harvester was composed of many cantilevers which pointed to different directions. The cantilevers were fixed on a base. (2) Finite element method was used to analyze the vibration characteristic of the single cantilever. The effects of the structure parameters of the harvester on the first bend frequency were studied by mode analysis. The cantilevers of the multiple harvester was selected at the bend frequency range 12~19Hz. By harmonic analysis the open circuit voltage of the single cantilever was maximal at the resonance state. (3) The test device of the harvester was constructed. The effective excitation frequency range of the harvester was 12~20 Hz. The test results were accord with the finite element analysis calculation results. Comparing to the single cantilever the multiple harvester could broaden the resonance frequency range. The output power of the harvester was about 2.88 mw at vibration acceleration 0.6 g, the outer load 500 Ω and the excitation frequency 16 Hz. The harvester could be used to supply electric energy for large distributed wireless sensor systems and subminiature 25

7 power devices. ACKNOWLEDGMENT This work was financially supported by the National Natural Science Foundation of China (No ), The 4th 333 Engineering Research Funding Project of Jiangsu Procince (No.BRA ), Sunzhou vocational university research project (No. 2014SZDCC01 ). REFERENCES [1] Guan M J, Liao W H. On the efficiencies of piezoelectric energy harvesting circuits towards storage device voltages [J]. Smart Materials and Structures, 2007, 16: [2] Guan M J, Liao W H. 0n the efficiencies of piezoelectric energy harvesting circuits towards storage deviee voltages[j]. Smart Materials and Structures, 2007, 16(2): [3] SODANO H A, INMAN D J, PARK G. A review of power harvesting from vibration using piezoelectric materials[j]. Shock and Vibration Digest,2004, 36(3): [4] ERICKA M, VASIC D, COSTA F, et al.. Energy harvesting from vibration using a piezoelectric membrane[j]. J. Phys. IV France, 2005, 128: [5] GlYNNE JONES P, TUDOR M J, BEEBY S P, et al.. An electromagnetic,vibration powered generator for intelligent sensor systems [J]. Sensors and Actuators A, 2004, 110: [6] MITCHESON P D, MIAO P, STARK B H, et al.. MEMS electrostatic micropower generator for low frequency operation [J]. Sensors and Actuators A, 2004, 115: [7] Erturk A, Jamil M R, Daniel J I. Piezoelectric energy harvesting from a L shaped beam mass structure with an application to UAVs [J]. Journal of Intelligent Material Systems and Structures, 2009, 20: [8] Shashank Priya. Advances in energy harvesting using low profile piezoelectric transducers[j]. J Electroceram, 2007, 19: [9] Chew Zhengjun, Li Lijie. Design and characterization of a piezoelectric scavenging device with multiple resonant frequencies [J]. Sensors and Actuators A, 2010, 162: [10] JIANG Shunong, Li Xianfang, Gua Shaohua. Performance of a piezoelectricbimorph for scavenging vibration energy[j]. Smart Mater Struct, 2005, 14: [11] S.Priya, D.J.Inman, ENERGY HARVESTING TECHNOLOGY, Southeast university press, 2010(In chinese). 26

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