Research Article Capacitance-Based Frequency Adjustment of Micro Piezoelectric Vibration Generator

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1 e cientific World Journal Article ID 31 pages Research Article apacitance-based Frequency Adjustment of Micro Viration Generator Xinhua Mao 1 Qing He 1 Hong Li 1 and Dongliang hu 1 1 chool of Energy Power and Mechanical Engineering North hina Electric Power University Beijing 1 hina Henan Institute of cience and Technology Xinxiang 33 hina orrespondence should e addressed to Qing He; hqng@13.com Received April 1; Accepted June 1; Pulished 1 July 1 Academic Editor: Wenming Zhang opyright 1 Xinhua Mao et al. This is an open access article distriuted under the reative ommons Attriution License which permits unrestricted use distriution and reproduction in any medium provided the original work is properly cited. Micro piezoelectric viration generator has a wide application in the field of microelectronics. Its natural frequency is unchanged after eing manufactured. However resonance cannot occur when the natural frequencies of a piezoelectric generator and the source of viration frequency are not consistent. Output voltage of the piezoelectric generator will sharply decline. It cannot normally supply power for electronic devices. In order to make the natural frequency of the generator approach the frequency of viration source the capacitance FM technology is adopted in this paper. Different capacitance FM schemes are designed y different locations of the adjustment. The corresponding capacitance FM models have een estalished. haracteristic and effect of the capacitance FM have een simulated y the FM model. Experimental results show that the natural frequency of the generator could vary from. Hz to. Hz when the ypass capacitance value increases from nf to 3 nf. The natural frequency of a piezoelectric viration generator could e continuously adjusted y this method. 1. Introduction With the development of monitoring technology wireless sensor networks are widely applied in medical monitoring structural health monitoring and industrial equipment condition monitoring and other fields. At present it has many prolems in supplying power for wireless sensor network nodes. For example atteries have limited lifetime and serious pollutions. Power lines have high costs. In order to fundamentally solve the power supply prolem of wireless sensornetworknodesmanyscholarshaveeentryingto extract viration energy from the environment and convert it into electricity. Because a cantilever piezoelectric viration generator has a simple structure small volume low cost and high output voltage it ecomes a research hotspot for converting viration energy into electric energy [1 1]. A cantilever piezoelectric viration generator is sensitive to frequency changes of environmental viration sources. If environmental frequency deviates 3Hz from the natural frequency of piezoelectric generator it will lead to output power sharply dropping [13 19]. In order to improve its adaptation environmental aility a cantilever piezoelectric viration generator is designed usually to add external mechanical device for changing the structure or stiffness of the eam. The purpose is to adjust its natural frequency. However it would increase the piezoelectric generator volume and production difficulty and also raise the cost of production y this method. The semiactive synchronous switch circuit was adopted to adjust the generator stiffness []. It could achieve to regulate the natural frequency. But the control circuit itself would consume energy which wouldreducetheoutputpowerofthevirationgenerator.a multicantilever and single-mass piezoelectric generator was designed [1]. The piezoelectric generator has a lot of natural frequencies ut rings out new manufacturing difficulties. It would cause high production costs. For solving the aove prolems on the asis of the relationship of the piezoelectric capacitance Young s modulis capacitance FM technology is adopted to turn the ending stiffness of the piezoelectric eam in this paper. The purpose is to adjust the natural frequency. Different frequency regulation schemes are designed. FM effects of different schemes are simulated. The authors have analyzed structure parameters of piezoelectric generator influence on the frequency adjusting range. Experiments have een carried out to verify FM effects.

2 The cientific World Journal K K P K T Figure 1: The equivalent stiffness of piezoelectric eam.. apacitance FM Principle and Theory Model of a Micro Generator.1. apacitance FM Principle. The relationship of natural frequencyωstiffness Kandmass M is descried as follows:.. apacitance FM cheme and Theory Model. By various position relations among the adjusting the piezoelectric and the sustrate FM schemes of a piezoelectric generator have the following four cases ased on capacitance FM technique. It is shown in Figure. The ending stiffness of a piezoelectric generator is [ 7] YI = Y s I s +Y p I p +Y t I t (3) where Y s I s is the ending stiffness of the sustrate Y p I p is the ending stiffness of the piezoelectric s and Y t I t is the ending stiffness of the piezoelectric adjusting. The young modulus of the adjustment is as follows: Y t = (s E 11 d 31 l 1 h t z ) () ω= K M. (1) The mass of a piezoelectric generator is unchanged after eing manufactured. If you want to change its natural frequency you need to change the stiffness of a piezoelectric generator. According to the literature [ ] we found the following relations: K=K +K P +K T =K +K P +θ T 1 θ () where K is the stiffness of the elastic sustrate K P is the mechanical stiffness of the piezoelectric K T is the electromechanical coupling stiffness is the piezoelectric capacitance and θ is electromechanical coupling coefficient. The equivalent connection type is shown in Figure 1. According to () we found that the system stiffness canchangewhenelectromechanicalcouplingorcapacitance value of the piezoelectric is adjusted. Because of its characteristics eing decided y the piezoelectric material characteristic and geometrical feature of the piezoelectric eam the electromechanical coupling term is not easy to change. Therefore the natural frequency is adjusted only y changing the piezoelectric capacitance values. We can design an adjustment for adjusting the stiffness y the aove situation. A ypass capacitor is lain aside the adjustment ; it is showed in Figure. The natural frequency of the system can e adjusted with the ypass capacitance changes. Frequency regulation method with shunt capacity is showed in Figure 3. The total capacitance of the system equals the sum of the ypass capacitance and the piezoelectric capacitance. When = K T =. Equivalent stiffness of the piezoelectric eam is the smallest and the natural frequency is the lowest. When = K T =. The natural frequency would e maximized. Equivalent stiffness of the piezoelectric eam is the iggest and the natural frequency is the highest. From the aove analysis we know that the adjusting range of the natural frequency is decided y short circuit and open circuit states of the ypass capacitor. where z equals to the sum of the piezoelectric capacitor t and the parallel capacitor. According to ()and(3) (1)can e written as ω=λ Y si s +Y p I p +I t (s E 11 d 31 l/h t ( t + s )) 1 r. M In scheme A elasticity modulus of the piezoelectric eam in neutral axis position is descried as follows [ 3]: Y= n ph p y p +n t h t y t +h s y s n p h p +n t h t +h s = n ph p (h s +h t +h p /) + n t h t (h s +h t /) + h s / n p h p +nh t +h s where h t h p andh s respectively are the thicknesses of the piezoelectric the adjustment and elastic sustrate; n t n p andn s respectivelyaretheelasticmodulusratiosofthe piezoelectric the adjustment and elastic sustrate; Y is the neutral axis position of the piezoelectric eam; y t y p andy s respectively are the neutral axis positions of the piezoelectric the adjustment and elastic sustrate;inertia moment is descried as follows: I p =I p +A pd p = 1 1 n ph 3 p +n ph p (h s +h t + h p Y) I t =I t +A td t = 1 1 n th 3 t +n th t (h s + h t Y) I s =I s +A sd s = 1 1 h3 s +h s( h s Y) where A t A s respectivelyarecross-sectionalareasofthe piezoelectric and elastic sustrate; d t d p d s respectively are the distances among the neutral axis. () () (7)

3 The cientific World Journal 3 Adjustment sustrate h p h t h s Y p Y t Y s Figure : apacitance FM principle. I p =I p +A pd p = 1 1 n ph 3 p +n ph p (h t +h s + h p Y) s I s =I s +A sd s = 1 1 h3 s +h s(h t + h s Y) I t =I t +A pd p = 1 1 n th 3 t +n th t ( h t Y). (1) Open circuit The capacitor ypass hort circuit The aove-mentioned () (1) aretheory models of different schemes ased on capacitance FM technology. Figure 3: Frequency regulation method with shunt capacity. In scheme B the elasticity modulus and inertia moment of the piezoelectric eam are descried as follows: Y= n th t y t +n p h p y p +h s y s n t h t +n p h p +h s = n th t (h s +h p +h t /) + n p h p (h s +h p /) + h s / nh t +n p h p +h s I t =I t +A pd p = 1 1 n th 3 t +n th t (h s +h p + h t Y) I p =I p +A pd p = 1 1 n ph 3 p +n ph p (h s + h p Y) I s =I s +A sd s = 1 1 h3 s +h s( h s Y). This has the same elasticity modulus and inertia moment of the piezoelectric eam in scheme and scheme D; it is descried as follows: Y= n ph p y p +h s y s +n t h t y t n p h p +h s +n t h t = n ph p (h t +h s +h p /) + h s (h t +h s /) + n t (h t /) n p h p +h s +nh t () (9) 3. imulation and Analysis Based on FM Technology 3.1. The Adjusting Range Analysis of Different chemes. According to the aove equations from () to (1) we could otain rules of the natural frequency with the ypass capacitance changes. It is shown in Figure. The figure shows that the natural frequency of the piezoelectric eam would gradually reduce with the increase of the ypass capacitor value. When the ypass capacitor is continuously adjusted we could otain aritrary frequency etween the opencircuit frequency and the closed-circuit frequency. Frequency adjusting ranges are close and the largest in schemes and D. When < s / p < the natural frequency has ovious adjustment effects y adjusting ypass capacitors. And when s / p < it hardly has any effects. According to the aove analysis if making frequency adjustment range the largest there is not only a suitale capacitor FM scheme ut also a reasonale ratio of the ypass capacitance to the piezoelectric capacitance. 3.. tructure Parameters of a Beam Effect on the FM Range. In order to study the effect of piezoelectric generator geometry on the capacitor FM technology material properties of the cantilever remain the same. Keep the cantilever thickness unchanged and analyze the influence of length change and width change on the frequency tuning range.itisshowninfigure.thefiguresshowthatchanges ofthelengthandwidthofthepiezoelectriceamhavenoany effects on the natural frequency adjusting range. Keep the piezoelectric adjustment thickness unchanged and adjust the thicknesses of the sustrate and the piezoelectric. We could otain the rules of the

4 The cientific World Journal Adjustment sustrate sustrate Adjustment (a) Regulation locates at top and sustrate locates at ottom () Regulation locates in the middle and sustrate locates at ottom Adjustment sustrate sustrate Adjustment (c) Regulation locates at top and sustrate locates in the middle (d) Regulation locates at ottom and sustrate locates in the middle Figure : chemes of the piezoelectric generator ased on capacitor FM. ω /ω d cheme A cheme B s / p cheme cheme D Figure : Natural frequency ratio versus capacity ratio. natural frequency with the piezoelectric eam thickness ratio changes. It is shown in Figure 7. The figures show that the smaller thickness ratio the larger the natural frequency adjustale range. This is ecause the fact that the piezoelectric adjustment is relatively thicker when the thickness ratio is smaller and stiffness adjustale range is relatively larger. tiffness adjustment characteristics are affected y viration. tiffness ratio would fall sharply. When anyone of two thickness ratios is greater than adjustale ranges of the natural frequency would fast ecome small in schemes A and B. When anyone of two thickness ratios is greater than adjustale ranges of the natural frequency would fast ecome small in schemes and D.. Experiments and Result Analysis Experimental schemes are shown in Figure.Thecantilever of micro piezoelectric virating generators used in the experiment is mm long mm wide and. mm thick. The mass size is mm long mm wide and mm thick. And its density is 113 kg/m 3.Theloadresistanceis1Ω. The acceleration of the viration exciter is m/s. An experimental platform of the piezoelectric generator is shown in Figure 9.Adjustment ranges of the ypass capacitor are from to 3 nf. When the ypass capacitor is opened or closed adjust the signal frequency and oserve the oscilloscope. Initial natural frequencies of different schemes would e otained. When the switch is disconnected adjusting the ypass capacitor the ypasscapacitancevaluewouldincreasegraduallyfromsmall toig.apacitancefmrangesandoutvoltagesofdifferent generators are shown in Figure 1. The experimental results show that the natural frequency is.9 Hz in short circuit and 7.1 Hz in open circuit in scheme A. The adjustale frequency range is aout 1. Hz. The natural frequency is.1 Hz in short circuit and. Hz in opencircuitinschemeb.theadjustalefrequencyrangeis aout 1.7 Hz. The natural frequency is.3 Hz in short circuit and.hzinopencircuitinscheme.theadjustale frequency range is aout 3.9 Hz. The natural frequency is. Hz in short circuit and. Hz in open circuit in

5 The cientific World Journal 1.1 antilever of scheme D 1.1 antilever of scheme D ω /ω d antilever of scheme B antilever of scheme ω /ω d antilever of scheme B antilever of scheme 1. antilever of scheme A 1. antilever of scheme A Length (m) (a) Width (m) () Figure : apacity frequency regulation range versus length and width. The frequency ratio of the open circuit and the short circuit piezoelectric and the adjusting 1 sustrate and the adjusting The frequency ratio of the open circuit and the short circuit piezoelectric and the adjusting 1 sustrate and the adjusting (a) A scheme () B scheme The frequency ratio of the open circuit and the short circuit piezoelectric and the adjusting 1 sustrate and the adjusting The frequency ratio of the open circuit and the short circuit piezoelectric and the adjusting 1 sustrate and the adjusting (c) scheme (d) D scheme Figure 7: Natural frequency ratio versus thickness ratio.

6 The cientific World Journal Load resistance Load resistance Oscilloscope Oscilloscope Viration exciter Power amplifier Viration exciter Power amplifier ignal generator A ignal generator A (a) cheme A () cheme B Load resistance Load resistance Oscilloscope Oscilloscope Viration exciter Power amplifier Viration exciter Power amplifier ignal generator A ignal generator A (c) cheme (d) cheme D Figure : Experiment scheme ased on capacitance FM.. onclusions In order to make the natural frequency of a piezoelectric generator approaching the environment frequency the capacitance FM technology is adopted to adjust the natural frequency of piezoelectric generator in this paper. Different FM schemes are designed and the FM theory model has een uilt. This has carried out the theoretical analysis and numerical simulation. The main research conclusions are as follows. Figure 9: Experimental platform of piezoelectric generator. scheme D. The adjustale frequency range is aout.1 Hz. o schemes D and are close and etter than schemes A and B. These results are consistent with the previous theoretical analysis. When ypass capacitance is less than nf the natural frequency could continuously change y adjusting the ypass capacitance. When the ypass capacitance is more than nf the natural frequency of the piezoelectric generatorisessentiallythesame.thismayeduetothefact that the ratio of the ypass capacitance to the piezoelectric capacitance exceeds. It is an unreasonale ratio. (1) The natural frequency of piezoelectric generator could e continuously adjusted y capacitance FM technology. However the adjusting range is not larger. Itneedstoeusedinconcertwithotheradjustment frequency methods. () In order to get maximum FM range it needs not only suitale capacitance FM scheme ut also the reasonale ratio of ypass capacitance to piezoelectric capacitance. (3) Adjusting range of the natural frequency has nothing to do with piezoelectric eam length and width. It is closely related to thicknesses among the adjustment the piezoelectric and the sustrate.

7 The cientific World Journal 7 The natural frequency (Hz) The ypass capacitance (nf) Voltage (V) Frequency (Hz) cheme A cheme B cheme cheme D cheme A cheme B cheme cheme D (a) Natural frequency versus ypass capacitor () Output voltage versus frequency Figure 1: Experimental results of capacitance FM technology. onflict of Interests The authors declare that there is no conflict of interests regarding the pulication of this paper. Acknowledgment The work was supported y the Fundamental Research Funds for the entral Universities of hina Grant no. 13X13. References [1] N. Gokhale M. Parmar K. Rajanna and M. M. Nayak zinc oxide thin film for MEM application: a comparative study in Proceedings of the 3rd International onference on ensing Technology (IT ) pp. 3 Tainan Taiwan Novemer. [] R. L. Harne Modeling and analysis of distriuted electromagnetic oscillators for roadand viration attenuation and concurrent energy harvesting Applied Mathematical Modelling vol.37no.pp [3]. H. Kim J. H. Ahn H. M. hung and H. Kang Analysis of piezoelectric effects on various loading conditions for energy harvesting in a ridge system ensors and Actuators A: Physicalvol.17no.pp [] Z. Hou R. hen and X. Liu Optimization design of multidirection piezoelectric viration energy harvester Viration and hockvol.31no.1pp [] Y. Zou X. Huang and L. Tan First-order resonance frequency and power output of a cantilever piezoelectric generator outheast University (Natural cience Edition)vol.1 no. pp [] J.L.KauffmanandG.A.Lesieutre Alow-ordermodelforthe design of piezoelectric energy harvesting devices Intelligent Material ystems and tructures vol.no.pp [7] Y. B. Jeon R. ood J.-H. Jeong and.-g. Kim MEM power generator with transverse mode thin film PZT ensors and Actuators A: Physicalvol.1no.1pp.1. [] Y. Zhen Research on Theory and Key Technologies of Viration Generator for Improving Generating apacity North hina Electric Power University Beijing hina 1. [9] X.WuH.FangJ.LinT.RenandL.Liu MEMpiezocantilever for viration energy harvesting Functional Materials and Devicesvol.1no.pp [1] F. hen K. un L. Li et al. Research status and development trend of miniature piezoelectric energy harvesting devices Huei University of Technologyvol.7pp.1 1. [11] X. Liu and R. hen urrent situation and developing trend of piezoelectric viration energy harvesters Viration and hockvol.31no.1pp [1].RoundyE..LelandJ.Bakeretal. Improvingpower output for viration-ased energy scavengers IEEE Pervasive omputingvol.no.1pp. 3. [13] W.J.hoiY.JeonJ.-H.JeongR.oodand.G.Kim Energy harvesting MEM device ased on thin film piezoelectric cantilevers Electroceramicsvol.17no. pp.3. [1]J.Q.LiuH.B.FangZ.Y.Xuetal. AMEM-asedpiezoelectric power generator array for viration energy harvesting Microelectronics Journalvol.39no.pp.. [1] J. Lin Z. Luo and L. Tong A new multi-ojective programming scheme for topology optimization of compliant mechanisms tructural and Multidisciplinary Optimization vol. pp [1] H. Liu. Lee T. Koayashi. J. Tay and. Quan MEM-ased wideand energy harvesting systems using a frequency-up-conversion cantilever stopper ensors and Actuatorsvol.1pp. 1. [17] D.-A. Wang.-Y. hiu and H.-T. Pham Electromagnetic energy harvesting from virations induced y Kármán vortex street Mechatronicsvol.no.pp [1] L.ZhuR.henX.LiuandZ.Long Improveddesignofselftuning roadand piezoelectric viration generator Nanjing University of Aeronautics and Astronauticsvol.no. 3 pp

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