This paper presents the modeling and optimization of an electromagnetic-based generator for generating power from ambient vibrations. Basic equations describing such generators are presented and the conditions for maximum power generation are described. Two-centimeter scale prototype generators, which consist of magnets suspended on a beam vibrating relative to a coil, have been built and tested. The measured power and modeled results are compared. It is shown that the experimental results confirm the optimization theory

Beeby, S

Loder, H

O’Donnell, T

Saha, C

Tudor, J

English

Southampton (e-Prints Soton)

IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006 3509Optimization of an ElectromagneticEnergy Harvesting DeviceChitta Ranjan Saha1, Terence O’Donnell1, Heiko Loder2, Steve Beeby3, and John Tudor3Tyndall National Institute, Cork, IrelandDepartment of Electrical Engineering, University of Applied Science, Fachhochschule Gie en-Friedberg 61169, GermanyDepartment of Electrical and Computer Science, University of Southampton, Southampton 30171BJ, U.K.This paper presents the modeling and optimization of an electromagnetic-based generator for generating power from ambient vi-brations. Basic equations describing such generators are presented and the conditions for maximum power generation are described.Two-centimeter scale prototype generators, which consist of magnets suspended on a beam vibrating relative to a coil, have been builtand tested. The measured power and modeled results are compared. It is shown that the experimental results conﬁrm the optimizationtheory.Index Terms—Displacement, energy conversion, generators and resonance.I. INTRODUCTIONENERGY harvesting techniques, where energy is gener-ated from ambient vibrations in the environment haverecently generated interest from the point of view of supplying“everlasting” power for remote sensor nodes. Vibrational powergenerators based on electromagnetic [1]–[4], piezoelectric [5],and electrostatic principles [6] have already been reported.Electromagnetic-based generators have been demonstratedto generate power levels ranging from 0.3 to 800 W fromvibration frequencies of several hundred hertz. For example,El-hami et al. [3] showed that 0.53 mW could be generatedfrom a 25- m amplitude vibration at 322–Hz vibration usinga 510-mg moving mass. Glynne-Jones et al. [4] demonstratedan electromagnetic generator which was capable of generating157 W, when placed in a car engine compartment. Williamset al. [2] described an electromechanical model for electromag-netic generators and derived the optimum damping conditions,however, due to low electromagnetic damping, the optimumcondition could not be veriﬁed in practice. Mitcheson et al.[6] described a general theoretical analysis for vibration drivengenerators, including both electromagnetic and electrostaticapproaches, however, no comparison between the models andmeasurements were presented. In previous work, the authorshave presented the structure, design [7], and fabrication withinitial test results [8] for a micromachined electromagnetic-based vibration generator. However, it proved difﬁcult to verifythe optimization theory on these devices due to their size andstructure.In this paper, the model for an electromagnetic-based,vibrational power generator is presented and the model isused to investigate the optimum conditions for electromag-netic damping and load resistance. Furthermore, the optimumconditions have been veriﬁed using measurements on twomacrogenerators which have been built and tested. The mea-sured and predictedresults for thetwo generatorsare compared.Digital Object Identiﬁer 10.1109/TMAG.2006.879447Fig. 1. Schematic diagram of electromagnetic generator.The eventual aim of this work is to use the veriﬁed modelspresented here to target improvements in the performance ofthe micromachined generators.II. GENERATOR MODELThe basic vibrational energy generator consists of a massmounted on a spring which vibrates relative to housing whensubjected to an external vibrational force. The mechanical en-ergy of the moving mass is transformed to electrical energy byhaving the mass movea magnet relativeto a coil. The mass mayconsistofthemagnetitselforthecoil.Ithasbeensuggestedthatthe motion of such a system can be reasonably well-describedbyasecond-ordermass -spring -damper system,asshown in Fig. 1. The basic equation of motion of the mass rela-tive to the housing when driven by a sinusoidal vibration force,, where is the acceleration), is given by [2](1)where is the relative movement between mass and housing(or between magnet and coil), is the parasitic damping forcedue to air resistance and material loss, and is the electro-magnetic force due to the force between the current in the coiland magnets. This system will have a mechanical resonant fre-quency, , where and, in general, it is desirable0018-9464/$20.00 © 2006 IEEE3510 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006to have the frequency of the driving force equal to the mechan-ical resonant frequency in order to maximize displacement.The electromagnetic damping force is proportional to the ve-locity [6] and can be expressed as(2)where is the electromagnetic damping. The solution of (2)at the resonance condition deﬁnes the displacement,and is given by(3)The average generated electrical power can be obtained from(4)By differentiating with respect to and equating tozero, it can be shown that the maximum electrical power oc-curs when . Therefore, the objective of the gener-ator design should be to achieve this optimum electromagneticdamping, i.e., it should aim to make electromagnetic dampingequaltotheparasiticdamping.Ascanbeseenfrom(2),theelec-tromagnetic damping can be varied by changing the load resis-tance, coil impedance, and magnet ﬂux. For frequencies of lessthan 1 kHz, we assume that the inductive impedance of the coilcanbeneglectedwithrespecttotheresistance.Byassumingthatand using (2) the optimum load resistance given by(5)However, the coil resistance depends on the number of turns. The relationship between the coil resistance and the numberof turns depends on the coil technology. For a ﬁxed size wirewound multilayer coil, the coil resistance can be shown to de-pend on the square of , i.e., [9], where is a pro-portionality constant. Thus, the optimum load resistance wouldbe(6)We can see from (6) that the optimum load resistance can onlybe found (i.e., positive resistance) if is less than the ﬁrst termwithin the brackets in (6). Thus, if parasitic damping is veryhigh or if the ﬂux gradient is low, the situation can arise wherethe optimum load resistance cannot be found. This occurs whenthe electromagnetic damping is low and cannot be increased toequal the parasitic damping.If electromagnetic damping is verylow compared to parasiticdamping , then the displacement given by (3)is determined by the parasitic damping. In this case, the loadpowerissimplyobtainedfromthevoltagedivisionbetweenloadresistance and coil resistance and the maximum power will betransferred to the load when the load and coil impedance areequal.Fig. 2. Image of generator A showing the magnets attached to a copper beamand wire-wound coil.TABLE IGENERATOR PARAMETERSIII. RESULTSTwoelectromagneticgeneratorswerebuiltandvibratedusinga controllable force by an electromagnetic shaker. These con-sisted of four magnets (NdFeB35) as shown in Fig. 2, arrangedto create a high ﬂux gradient and attached to a copper beam. Awire-wound copper coil was placed between the magnets. Thisgeneratorconstructionisbasedonthetypeofgeneratordescribedin[7].TableIgivesthecoilandmagnetparametersforgeneratorsA and B. The generators were vibrated using a sinusoidal accel-eration with the frequency matched to the generator mechanicalresonant frequency. The displacement and voltage were mea-sured for various load resistances. The load power is calculatedfromthevoltageandloadresistance.Thedisplacementatno-load(open circuit) can be used in (3), with to estimate theparasitic damping. The generators were also simulated usinga three-dimensional (3-D) ﬁnite element (FE) transient modelwith the measured displacement as input. The ﬂux gradient canbe obtained from the FE model and used in (2) to calculate theelectromagnetic damping. The parasitic and electromagneticdamping can then be used in (4) to calculate the power.Figs. 3 and 4 show the measured displacement and the mea-sured and modeled load voltage for different load conditions forgenerators A and B, respectively. The measured and modeledvoltages agree quite closely. Figs. 5 and 6 show the measuredand calculated power, and the estimated parasitic and electro-magnetic damping, for generators A and B, respectively.The graph in Fig. 3 shows that there is a signiﬁcant change indisplacement with the change in load, for generator A, however,forgeneratorBthedisplacementdoesnotvarywithload.Thisisconsistent with the fact that for generator A the electromagneticdamping is comparable to the parasitic damping, but for gen-erator B the electromagnetic damping is much lower than theSAHA et al.: OPTIMIZATION OF AN ELECTROMAGNETIC ENERGY HARVESTING DEVICE 3511Fig. 3. Measured displacement and modeled and measured load voltage forgenerator A.Fig. 4. Measured displacement and modeled and measured load voltage forgenerator B.Fig. 5. Measured and calculated load power and estimated parasitic andelectromagnetic damping for generator A.parasitic damping due to the lower coil turns and smaller mag-nets used. This can be seen from Figs. 5 and 6. Furthermore,the graph in Fig. 5 shows that the power is a maximum for thevalue of load resistance at which electromagnetic damping andparasitic damping are equal. For generator B, the electromag-netic damping is always much less than the parasitic dampingand the power is maximized for a load resistance equal to thecoil resistance.IV. CONCLUSIONThe model for an electromagnetic-based vibrational energyharvesting device has been compared to measurements onreal devices in order to verify the modeling approach. TheFig. 6. Measured and calculated load power and estimated parasitic andelectromagnetic damping for generator B.optimum conditions observed from measurements are shownto agree well with the model. However, the experimentalresults suggest that signiﬁcant parasitic damping is alwayspresent. This parasitic damping is likely to be much moreof a problem for generators fabricated on the micro-scale, asthe ability to achieve high electromagnetic damping reducessigniﬁcantly with size [9], thus, making it difﬁcult to achievethe optimum condition of electromagnetic damping equal toparasitic damping.ACKNOWLEDGMENTThis work was supported in part by the European UnionFramework 6 Project VIBES under Project 507911 and bythe Higher Education Authority of Ireland Fund for DigitalResearch.REFERENCES[1] W. J. Li, T. C. H. Ho, G. M. H. Chan, P. H. W. Leong, and H. Y. Wong,“Infrared signal transmission by a laser-micromachined vibration-in-duced power generator,” in 43rd IEEE Symp. Circuits Syst., 2000, pp.236–239.[2] C. B. Williams, C. Shearwood, M. A. Harradine, P. H. Mellor, T. S.Birch, and R. B. Yates, “Development of an electromagnetic micro-gen-erator,” Int. Elect. Eng. Proc. -Circuits Devices Syst., vol. 148, no. 6, pp.337–342, Dec. 2001.[3] M. El-hami, P. Glynne-Jones, N. M. White, M. Hill, S. Beeby, E. James,A.D.Brown,andJ.N.Ross,“Designandfabricationofanewvibration-based electromechanical power generator,” Sens. Actuators A, vol. 92,pp. 335–342, 2001.[4] P.Glynne-Jones,M.J.Tudor,S.P.Beeby,andN.M.White,“Anelectro-magnetic, vibration-powered generator for intelligent sensor systems,”Sens. Actuators, no. 1-3, pp. 344–349, Feb. 2003.[5] S. Roundy and P. K. Wright, “A piezoelectric vibration based gen-erator for wireless electronics,” Smart Mater. Structures, vol. 13, pp.1131–1142, 2004.[6] P. D. Mitcheson, T. C. Green, E. M. Yeatman, and A. S. Holmes, “Ar-chitectures for vibration-driven micropower generators,” J. Microelec-tromech. Syst., vol. 13, no. 3, Jun. 2004.[7] S. P. Beeby, M. J. Tudor, E. Koukharenko, T. O’Donnell, C. Saha, S.Kulkarni, and S. Roy, “Micromachined silicon generator for harvestingpower from vibrations,” in Proc. Power MEMS, 2004, pp. 28–30.[8] S. P. Beeby, M. J. Tudor, E. Koukharenko, N. M. White, T. O’Donnell,C. Saha, S. Kulkarni, and S. Roy, “Design and performance of a micro-electromagnetic vibration powered generator,” Transducers’05, vol. 1,pp. 780–783, Jun. 2005.[9] T. O’Donnell, C. Saha, S. Beeby, and J. Tudor, “Scaling effects for elec-tromagnetic vibrational power generators,” in Proc. DTIP, 2006, pp.25–28.Manuscript received March 13, 2006 (e-mail: chitta@tyndall.ie).

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A.D.Brown,andJ.N.Ross,“Designandfabricationofanewvibrationbased electromechanical power generator,” Sens.

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Design and performance of a microelectromagnetic vibration powered generator,”

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Optimization of an Electromagnetic Energy Harvesting Device

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