Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 56, 3, pp. 687-699, Warsaw 2018 DOI: 10.15632/jtam-pl.56.3.687 EXPERIMENTAL INVESTIGATION ON THE PIEZOELECTRIC ENERGY HARVESTER AS A SELF-POWERED VIBRATION SENSOR Dariusz Grzybek, Piotr Micek AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Cracow, Poland e-mail: dariusz.grzybek@agh.edu.pl; micek pt@agh.edu.pl The article presents an experimental study of a system consisting of a piezoelectric energy harvesting device, Graetz bridge rectifier, capacitor, voltage comparator and radio trans- mitter. In the presented experimental study, the recovered electrical energy is accumulated in the capacitor and is used to send signals by a radio transmitter. In the first part, the application of piezoelectric energy harvesting devices based on the cantilever beam in wire- less monitoring systems is discussed. In the second part, the mathematical model of energy conversion in the piezoelectric energy harvesting devices is presented. In the third part, the characteristics obtained during laboratory research are presented. Keywords:piezoelectric energyharvesting, piezoelectric composite,wireless sensor, vibration 1. Introduction An effective monitoring of some building structures demands measurements of selected para- meters in many places of the monitored structure. Such a problem exists, among other things, in Structural Health Monitoring (SHM) systems, which are used for behaviour monitoring of several objects, e.g. bridges, aircrafts, ships (Lynch and Lohg, 2006). SHM systems can be com- posed of tens or hundreds of sensors, each of which has to be powered. Themonitoring system of three bridges in Hong Kong: Tsing Ma, Ting Kau and Kap Shui Mun contains 300 sensors measuring several variables (deformations, displacements, acceleration, temperature) (Chan et al., 2006). The monitoring system containing 63 sensors measures the stress in the girders of Taylor bridge in Canada (Kim et al., 2007). The monitoring system of the span vibration of Golden Gate bridge in the USA contains 64 sensors (De Roeck et al., 2000). The conventional supply of sensors in such amonitoring system requires the use of either kilometres of wires or a large number of batteries. It should also be noted that in the case of batteries, there is a neces- sity to replace these batteries, which increases operating costs of monitoring systems andmakes the whole system not eco-friendly (Soobum et al., 2009). Hence, nowadays, the development of wireless power of sensors is needed in the monitoring systems. The use of natural properties of piezoelectric materials to conversion of mechanical energy into electric energy in places where sensors are mounted is a promising field of wireless power development. The piezoelectric effects are used to active damping of vibration, see e.g. (Pietrza- kowski, 2000; Przybyłowicz, 1999). The direct piezoelectric effect in piezoelectric materials is the base of building devices converting energy called piezoelectric generators. The generators, in which the main element is a cantilever beam composed of piezoelectric materials and carrying materials, are one of the structureswhich can beused for energy harvesting from themechanical vibration of a building. The subject of recent examinations are piezoelectric beam generators constructed fromabasicmaterial which does not indicate piezoelectric characteristics, e.g. steel, and from a piezoelectric material which can be piezoelectric ceramic, e.g. PZT-4H (Roundy and 688 D. Grzybek, P. Micek Wright, 2004), composite made from piezoelectric ceramics and polymer warp, e.g. MFC (Upa- drashta andYang, 2016), piezoelectric polymer e.g. PVDF (Li et al., 2016) or a structuremade of nanowires (Yu et al., 2012). The use of relatively flexible piezoelectric composite materials allows one to subject the generator beams to loads varying over time which cause large strains of piezoelectric elements (Yang and Tang, 2009). Macro Fiber Composite (MFC) is one of the piezoelectric composites which is used in the piezoelectric generators. MFC contains the piezoceramic phase in the form of square cross-section fibers placed in the polymer matrix. The piezoelectric MFC composite is usually joined with the base material by means of gluing. The latest research indicates that themaximum electrical power harvested by the generator in which the cantilever beam ismade of the MFC and of the steel base material is up to a few mW. For example, the piezoelectric beam generator contains MFC of the following dimensions: 85×28×0.3mm, presented in (Song et al., 2014), produces 1.7mW for a frequency of 30Hz, which was the resonant frequency of that generator. The range of harvested electric power restricts the field of potential applications to supply miniaturized electronic devices with an ultra low power demand. The ideal schema of a typical wireless sensor node powered by the piezoelectric generator is presented in Fig. 1. Fig. 1. Schema of a typical wireless sensor node powered by a piezoelectric generator (Woias et al., 2009) The generated electric energy through a piezoelectric generator is consumed mainly by a sensor and a radio transmitter. The electrical energy, generated by the piezoelectric beam ge- nerators, is enough to supply commercial low-powered micro sensors with commercial ultra low-power radio transmitters in wireless nodes which enable transfer of periodical data, if only the frequency of the vibration source is close to the resonant frequency of the generator. This condition is difficult to fulfil in buildings whose vibrations are excited by natural processes, e.g. wind. One possible solution is broadening of the generator frequency range by e.g. the applica- tion of several beams with various dimensions in the generator structure (Ferrari et al., 2008). The wireless sensor node enabling the periodical data transfer powered by the piezoelectric ge- nerator has to have an electronic system to control and store recovered energy which is needed for the transfer of a proper energy amount. The designing of such a control and store system is the subject of recent scientific research. The abovementioned remarks are the base of a concept of a wireless monitoring system in which several piezoelectric beam generators work as both harvesters and sensors. The piezo- electric beam generator does not supply any sensor, but the electrical energy harvested by this generator is accumulated in the capacitor and is used to send signals by the radio transmitter. Such a defined harvester/sensor consists of the following elements: the piezoelectric beam gene- rator,Graetz bridge rectifier, capacitor, voltage comparator and radio transmitter. In this study, the characteristics of capacitor charging and radio transmission are compared in the frequency domain and evaluated with respect to time between the radio signals for different excitation levels. Experimental investigation on the piezoelectric energy harvester... 689 2. Mathematical model of a piezoelectric energy harvester In this Section, the basicmathematicalmodel of piezoelectric energy conversion by aMFCglued on the top of a steel beam is presented. The basic purpose of this Section is the determination of the dependence between the displacement of the free end of the harvester beam and the course of voltage across the capacitor. The schema of the electrical circuit used to charge the capacitor is presented in Fig. 2. Fig. 2. Schema of the electrical circuit used to the energy harvesting: Vp – generated voltage by the piezoelectric patch, ipREC – rectified current intensity,Cc – capacitance of the capacitor, Vc – voltage across the capacitor The harvester beam is fabricated from stainless steel and a piezoelectric composite which is theMacro Fiber Composite (MFC). The beam structure of the generator is achieved by gluing steel and theMFC (Fig. 3). Fig. 3. Piezoelectric harvester beam structure: lb – length of the beam, lp – length of theMFC patch, wb – width of the beam, tb – thickness of the beam, tp – thickness of theMFC patch TheMacro Fiber Composite (MFC) presented in Fig. 4 has been selected as a piezoelectric material applied in the harvester beam. Fig. 4. Macro Fiber Composite (MFC): tpf – thickness of the piezoelectric fiber, te – thickness of the electrode layer (copper + epoxy), tk – thickness of the kapton layer 690 D. Grzybek, P. Micek The basic equations describing the energy conversion in a piezoelectric material are given by (Nye, 1957) Sp(t)= s (E) pq Tq(t)+d T pkEk(t) for p=1, . . . ,6 q=1, . . . ,6 k=1,2,3 Di(t)= diqTq(t)+ε (T) ik Ek(t) for i=1,2,3 (2.1) where S is strain, T is stress, D is electric induction, E is electric field intensity, s is the compliance constant, d is the electromechanical coupling constant, ε is the permeability tensor. In the case in which electric induction is perpendicular to stress in piezoelectric fibers (along axis 1 in Fig. 4), the basic equations are the following S1(t)= s (E) 11 T1(t)+d31E3(t) D3(t)= d31T1(t)+ε (T) 33 E3(t) (2.2) The dependence among electrical andmechanical variables in the piezoelectric material E(t)=− Vp(t) tpf ip(t)=wplp dD(t) dt (2.3) wherewp is width of the active area of the piezoelectric material. After introduction of (2.3) into (2.2) and their transformation Vp(t)= s (E) 11 tpf d31 T1(t)− tpf d31 S1(t) ip(t)= d31wplp dT1(t) dt − ε (T) 33 wplp tpf dVp(t) dt (2.4) The average stress in the piezoelectric material (Roundy et al., 2003) is T1(t)= 1 lp lp ∫ 0 M(x)td I dx (2.5) where M is the bending moment in the beam, td is the distance from the centre of the steel beam to the centre of the piezoelectric layer, I is the moment of inertia. The bendingmoment in the beam is M(x)=Fz(t)(lb−x) (2.6) whereFz is the theoretical external force acting on the free end of the harvester beam, x is the distance from the beam fixing to the free end of the harvester beam. Fz is calculated on the basis of the displacement of the free end of the harvester beam Fz(t)= 3YMFCI l3 b yout(t) (2.7) where YMFC is Young’s modulus of theMacro Fiber Composite, yout is the displacement of the free end of the harvester beam. The distance from the centre of the steel beam to the centre of the piezoelectric layer is td = 1 2 tb+ tk+ te+ 1 2 tp (2.8) Stress calculated from (Roundy et al., 2003) is T1(t)= 3YMFCtd l3 b ( lb− lp 2 ) yout(t) (2.9) Experimental investigation on the piezoelectric energy harvester... 691 After introduction of (2.9) to (2.4) and its transformation Vp(t)= s (E) 11 tpf d31 3YMFCtd(2lb− lp) 2l3 b yout(t)− tpf d31 S1(t) ip(t)= d31wplp 3YMFCtd(2lb− le) 2l3 b dyout(t) dt − ε (T) 33 wplp tpf dVp(t) dt (2.10) After introduction of the assumption that the electrical circuit is not connected to the load resistance, the rectified current intensity ipREC generated by the piezoelectric generator is equal to the charging intensity ic of the capacitor ipREC(t)= ic(t)=Cc dVc(t) dt (2.11) The dependence between the voltage across the capacitor Vc and the displacement of the free end of the harvester beam yout is dVc(t) dt = 1 Cc d31wplp 3YMFCtd(2lb− le) 2l3 b dyout(t) dt − 1 Cc ε (T) 33 wplp tpf dVp(t) dt (2.12) On the basis of (2.12), the piezoelectric harvesting device and electrical circuit (Fig. 2) can be defined as a multioutput system in which the displacement of the free end of the harve- ster beam yout is the input and voltage across the capacitor Vc, the voltage generated by the piezoelectric patch Vp is the output (Fig. 5). Fig. 5. Energy harvesting circuit as a multioutput system Two research problems appear in such a definition of the piezoelectric harvesting device: • what is the dependence between the courses of the displacement of the free end of the harvester beam yout and voltage across the capacitor Vc, • what is the dependence between the courses of voltage across the capacitor Vc and voltage generated by the piezoelectric Vp. The energy accumulated in the capacitor will be used in the presented concept of wireless monitoring systems to supply the radio transmitter. Hence, the next research problem appears: • what is the dependence between the courses of voltage across the capacitor Vc and the period of time among radio signals which are transmitted by the radio transmitter. These research problems are the subject of experimental experiments presented in Section 3. 3. Experimental study 3.1. Experimental setup In this study, the energy harvesting device based on the cantilever beam andP2-typeMacro Fiber Composite (MFC) material has been designed and fabricated. The MFC patch (from Smart Material Corporation) was glued on the top of a steel cantilever beam. Material and geometric parameters of theMFC patch and the steel beam are listed in Table 1. 692 D. Grzybek, P. Micek Table 1. Material and geometric parameters of the MFC patch (Smart Material Corporation, 2017) Parameter Unit Value Young’s modulus YMFC N/m 2 30.336 ·109 Piezoelectric constant d31 C/N −170 ·10 −12 Permittivity ε33 F/m 13800.13 ·10 −12 Length lp mm 85 Width wp mm 14 Thickness tp mm 0.3 Table 2.Geometric parameters of theMFC patch (Deraemaeker et al., 2009) Parameter Unit Value Thickness of piezoelectric fiber tpf mm 0.18 Thickness of electrode layer te mm 0.018 Thickness of kapton layer tk mm 0.04 The MFC patch consists of piezoceramic fibers, copper electrodes, epoxy and capton. The geometric parameters of these parts of theMFC patch are listed in Table 2. The thickness, length and width of the base stainless steel beam were correspondingly the following 1.24mm, 130mmand 18mm. TheMFCwas connected to a full-bridge rectifier which in turn was connected to an energy harvesting circuit EH301A. EH301A circuit powered the radio transmitter in specific time periods. The steel beam with MFC, the full-bridge rectifier, EH301A circuit and radio transmitter created a system which is called the harvester/sensor in the following Section of this article. The standard full-bridge rectifier (Graetz bridge) converted the generated by the energy harvesting device theACvoltage intoDCvoltage. Figure 6 presents the schema of the whole system of the harvester/sensor. Fig. 6. Schema of the whole system of the harvester/sensor As a voltage comparator, EH301A, developed by Advanced Linear Devices (EH300A data- sheet, 2017) has been applied. When the energy harvesting device starts to supply energy into the inputs of the EH301Amodule in the form of electrical charge impulses, these charge packets are collected and accumulated in a storage capacitor (Yang and Tang, 2009). Figure 7 presents the waveform of the voltage across the capacitor in the EH301A. The start of the voltage, +V, increases from the point 0.0V.When+V reaches 5.2V, the output of EH301A starts to supply the radio transmitter and +V decreases. When +V decreases to 3.1V, the output of EH301A stops to supply the radio transmitter and the charging cycle restarts. The time periods t1 and t2 are limited by the energy from the piezoelectric harvesting devices minus the energy losses by theEH301ASeriesModule. Theperiod time t3 is dependent upon the power consumption of the radio transmitter. In the experiments, theEH301Adevice has beenmodified by the replacement Experimental investigation on the piezoelectric energy harvester... 693 of the capacitor fromAdvancedLinearDevices with a capacitor of 200nF.The reduction of time periods t1 and t2 was the aim of that replacement. Fig. 7. Voltage waveform in the capacitor in the EH301A The radio transmitter applied in the structure of the harvester/sensor is a part of the transmission system consisting of the PT2262 radio transmitter and the PT2272 radio rece- iver (Fig. 8). Fig. 8. Schema of the radio transmission system The operating frequency has been set on 38 Hz both for the radio transmitter and radio receiver. The radio transmitter has 4 digital inputs which allow for sending of 4 different states (0 or 1). The start of the supply of the radio transmitter by the voltage comparator causes sending of the signal to the radio receiver. The voltage comparator starts supply to the radio transmitter when the voltage reaches of 3.1V (Fig. 8). Theexperimental setupconsistingof the energyharvestingdevicewith the radio transmission system as well as the system generating vibrations of the fixed beam end is presented in Fig. 9. 3.2. Results of the laboratory experiments The basic purposes of the laboratory experiments are defined in the last part of Section 2. In the discussion of the results (in the next parts), the following definitions are used: • the displacement of the free end of the harvester beam (yout) is defined by the output frequency ωout and the output amplitudeAout, • the displacement of the fixed end of the harvester beam yin is defined by the input frequ- ency ωin and the input amplitudeAin. In the first step, a dependence between the input frequency ωin and the output amplitudeAout has been experimentally determined. Such a dependence for the input amplitude of 0.2mm is presented in Fig. 10. 694 D. Grzybek, P. Micek Fig. 9. Experimental setup: 1 – system of vibration generation, 2 – steel cantilever beam, 3 – piezoelectric composite (MFC), 4 – laser sensors of displacement, 5 – radio transmitter, 6 – capacitor, 7 – EH301A SeriesModule, 8 – radio receiver Fig. 10. Output amplitude (Aout) versus the input frequency ωin for a constant input amplitude yin: 0.2mm Themaximum output amplitude appears for the resonant frequency of the fabricated beam (17.7Hz). In the next step, the characteristics are experimentally determined: RMS voltage generated by the piezoelectric VpRMS versus the resistive loadRl andRMS current generated by the piezoelectric ipRMS versus the resistive loadRl (Fig. 11). These characteristics are obtained for the input frequency ωin: 17.7Hz. On the basis of Fig. 11a, it can be seen that an increase in the load resistance Rl causes an approximately proportional increase in the rectified voltage generated by the piezoelectric patch VpRMS in the voltage range from 0 to 5V. Such a range of the generated voltage VpRMS has been chosen regarding the range of voltage across the capacitor Vc which was applied in the testing device. The rectified current generated by the piezoelectric patch ipRMS is approximately constant in the rectified voltage range from 0 to 5V (Fig. 11b). Hence, in the following part of this article, the piezoelectric patch is treated as a current source controlled by the displacement of the fixed end of the harvester beam. The comparison between the course of voltage generated by the piezoelectric patch and the voltage across the capacitor obtained in the experiment is presented in Fig. 12. Thecourses shown inFig. 12havebeenobtained in the circuitwithoutany load resistanceRl. It has been found that the voltage across the capacitor is approximately equal to theRootMean Experimental investigation on the piezoelectric energy harvester... 695 Fig. 11. RMS voltage and RMS current generated by theMFC harvester versus resistive load: (a) RMS voltage VpRMS, (b) RMS current ipRMS Fig. 12. Voltage generated by the piezoelectric patch Vp versus voltage across the capacitor Vc for a constant output amplitudeAout =8.20mm and a constant input frequency ωin =17.70Hz Square of the voltage generated by the piezoelectric patch. It can be seen that an increase in voltage across the capacitor Vc caused an increase in voltage generated by the piezoelectric patch Vp. Hence, the charged capacitor can be treated as a load connected to the piezoelectric patch. The charging time of the capacitor strongly depends on the output amplitude Aout. The dependence between the output amplitude Aout and the charging time of the capacitor is presented inFig. 13.Themeasurements of the charging timehave begunwhen the voltage across a capacitor was equal to 3.1V andwere finishedwhen the voltage achieved 5.2V. It can be seen that this dependence can be approximated by an exponential course. The course of voltage generated by the piezoelectric patchVp and the course of voltage across the capacitor Vc, as well as the course of voltage delivered to the radio transmitter Vr and the number of received signals in the radio receiver are presented in Fig. 14. On the basis of the courses presented in Fig. 14, it can be seen that the number of transmitted radio signals is equal to the number of charging cycles of the capacitor, which is a part of the system presented in the previous Section, see Fig. 6. Hence, the charging time of the capacitor (to 5.2V) is equal to 696 D. Grzybek, P. Micek Fig. 13. Dependence between the output amplitude of the free end of the generator beamAout and charging time of the capacitor the period of time among the radio signals which are transmitted by the radio transmitter. This observation allows one to find that the dependence between the output amplitude Aout of the harvester beam and the time among signals transmitted by the radio transmitter is the same as the dependence between the output amplitude of the free end of the generator beam Aout and the charging time of the capacitor, which is presented in Fig. 13. Fig. 14. Characteristics for the constant output amplitudeAout =8.20mm The course of voltage across the capacitor Vc and the course of voltage delivered to the radio transmitter Vr in the same time for several values of output amplitudes are presented in Fig. 15. Experimental investigation on the piezoelectric energy harvester... 697 Fig. 15. Voltage across the capacitor Vc and voltage delivered to the radio transmitter Vr for several values of the output amplitude Fig. 16. Dependence between the input frequencyAout and the period of time among transmitted radio signals for the constant input amplitude of 0.2mm 698 D. Grzybek, P. Micek The output amplitude is strongly dependent upon the input frequency ωin, so the time of radio transmitter supply is also dependent upon this frequency (Fig. 16). The action of piezoelectric harvester/sensor will be changed in the operating time because the problemof electric fatigue appears in piezoelectricmaterials (Goy et al., 2006). This problem should be the subject of next research. 4. Summary On the basis of the conducted experiments whose selected results are shown in the previous Section, the following conclusions have been established: • the piezoelectric patch can be treated as a current source controlled by the displacement of the fixed end of the harvester beam, • an increase in voltage across the capacitor causes an increase in voltage generated by the piezoelectric patch.Hence, the charged capacitor can be treated as a load for the harvester, • periods of time among received radio signals are strongly dependent upon the output amplitude of the free end of the harvester beam. The dependence between the time of radio transmitter supply can be approximated by an exponential course, • the definition of frequency of the free end of the harvester beam is possible on the basis of periods of time among the signals received by the radio receiver for a constant input amplitude. 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