Design of an electromagnetic-transducer energy harvester

Transcription

1 Journa of Physcs: Conference Seres PAPE OPEN ACCESS Desgn of an eecromagnec-ransducer energy harveser To ce hs arce: L Smeone e a 06 J. Phys.: Conf. Ser eaed conen - A non-near 3D prned eecromagnec vbraon energy harveser P Consannou and S oy - An mpanabe fudc vbraona energy harveser S Inoue, T Takahash, M Kumemura e a. - Eecrosac Vbraon Energy Harveser Pre-charged Wreessy a.45 GHz Z. Sadd, H. Takhedm, A. Karam e a. Vew he arce onne for updaes and enhancemens. Ths conen was downoaded from IP address on /04/09 a :06

2 Desgn of an eecromagnec-ransducer energy harveser L Smeone *, M Ghandch Tehran and S J Eo Insue of Sound and Vbraon esearch, Unversy of Souhampon, SO7 BJ, Uned Kngdom * Auhor o whom any correspondence shoud be addressed sn@soon.ac.uk Absrac. Ths paper presens he desgn and he manufacurng of an eecromagnecransducer energy harveser. The desgn consders he coupng beween he mechanca vbrang behavour, generaed by a base excaon, and he eecromagnec converson of energy, whch s amed o produce he voage across a oad ressance. The desgn s based on some consrans, whch are reaed o he characerscs of he shaker and amed o oban he bes performance of he devce. Curren ess show he presence frcon a ow npu eves, whch s assocaed wh he gearbox. The oupu voage and he harvesed power of he devce are suded expermenay for dfferen vaues of oad. By ncreasng he vaue of he oad from zero (shor crcu) o hgh vaues (open crcu) he swng ange ncreases, whe he harvesed power presens a peak assocaed wh he eecrca dampng. Aso, harmonc ess are run a resonance for dfferen eves of excaon o demonsrae he effec of he nonneary on he voage and he harvesed power. A nonnear oad ressance, s hen nroduced as par of fuure work. The am s o ry o ncrease he harvesed power wh respec o he near oad, a ow eve of excaon.. Inroducon In severa appcaons such as he moon of he sea waves [] and he roaon of he roor n hecopers [], he source of excaon s characersed by a narrow frequency bandwdh and, as a consequence, he excaon can be approxmaed as harmonc. Moreover, a harmonc anayss s aways he sarng pon o desgn a new mechanca sysem [, 3-9]. In order o ncrease he performance, over whch he vbraon energy harveser operaes, varous nonnear arrangemens were suggesed, parcuary usng nonnear sprngs [4, 0]. In conras, was receny shown ha he dynamc range of a vbraon energy harveser can be ncreased usng a nonnear damper. For exampe, Ghandch Tehran and Eo [5] nroduced he use of he cubc dampng for enargng he dynamc range of performance of an energy-harvesng devce. I was shown ha a shuned cubc ressance generaes cubc dampng no he sysem, whch s a fourh power funcon of he orque consan. The auhors demonsraed ha he harvesed power obaned by usng a cubc damper can be sgnfcany arger han ha of a near harvesng devce when exced a resonance, a ampudes beow s maxmum operaona m Y max. An mporan sudy was conduced n []. The auhors suded an energy harveser wh an nerna ressance n seres wh a cubc oad. I was found ha he nerna ressance provdes an upper m for he eecrca dampng when usng a nonnear oad. In addon, a hgh eves of excaon, he harveser behaves neary, whe, he behavour becomes Conen from hs work may be used under he erms of he Creave Commons Arbuon 3.0 cence. Any furher dsrbuon of hs work mus manan arbuon o he auhor(s) and he e of he work, journa caon and DOI. Pubshed under cence by Ld

3 more smar o a harveser wh purey nonnear dampng as ong as he npu eve decreases. However, no expermena resus were repored n hs sudy. Ths paper presens he desgn of a consraned eecromagnec ransducer energy harveser. The work s amed o show ha he use of a gearbox o ncrease he oupu voage aso ncreases he amoun of mechanca dampng no he sysem. Aso, he effec of a near oad on he oupu voage and he harvesed power s esmaed expermenay. The as secon s dedcaed o he nroducon of a nonnear oad, whch s amed o ncrease he harvesed power over he dynamc range of he harveser.. Desgn of roaona energy harveser The harveser s desgned o behave ke a snge-degree-of-freedom penduum, as shown n Fgure. The sysem can roae by means of a hnge on he ef sde, whe on he rgh sde, a umped mass M s aached o he beam of mass m. The momen of nera assocaed wh he roaon of he masses s ndcaed wh J. The sysem s conneced o he ground by a sprng k and s subjeced o a base excaon y hrough a shaker. The hnge s conneced o a gear box and a generaor, whch coupes he mechanca and he eecrca crcu. DC moor and gear box aso provde a arge amoun of mechanca dampng, ha can be sp n boh vscous c m and frcon τ s. The roaona moon s used o produce voage across a oad and, herefore, harvesed power. The devce s desgned o be harmoncay exced, even hough oher ypes of excaon w aso be consdered n he fuure. Assumng ha an eecrca generaor wh emf-consan K and an nerna resance s couped o he mechanca sysem, hen a curren s nduced n he eecrca crcu, when a swng roaon θ s produced by he base moon. The harvesng process can sar when a oad s aached o he ermnas of he moor. Fgure : Eecromagnec energy harveser The genera behavour of he couped sysem can be descrbed as J c sgn( ) k K m M d m s m y, K () Where m s he poson of he sprng wh respec o he hnge, s he engh of he beam and d s he engh of he cubod umped mass. The frs equaon s referred o he mechanca crcu, whe he second equaon, descrbes he dynamcs of he eecrca crcu, n whch ony he effec of he nerna ressance and he oad ressance was consdered, and he capacy, as we as he nducance, were negeced snce hey do no affec he sysem a he frequency of neres. For harmonc base excaon y Y sn, he ampude of he anguar dspacemen Θ can be obaned by usng he harmonc baance mehod as ()

4 Θ Y m M d ω k Jω c c c m m 4τ ω s πθ (3) The erm 4 s represen he descrbng funcon of he couomb frcon. The coeffcens c s he conrbuon of he eecrca ressance o he vscous dampng and s K (4) c whe c s he eecrca vscous dampng produced by he oad ressance c K However, even hough hey boh generae dampng, c s responsbe for he harvesed power produced by he voage across he oad ressance, whe c conrbues o he dsspaons. For he energy harvesng, s we-known [] ha he power can be ncreased by seecng a arger mass, because, a resonance, he oupu ncreases as confrmed n equaon (3). However, n pracca appcaons, due o he maons on he hrow, he mass canno be as bg as one wans. Therefore, he desgn s usuay carred ou n he worse condons scenaro, where he sysem, exced a resonance f res a he maxmum npu ampude Y max, responses wh he maxmum hrow ϴ max... Consraned desgn As aforemenoned, he hrow s he man, bu no he ony, consran ha has o be respeced. The desgn of an energy harveser shoud ake no accoun he envronmen and he ype of excaon. In hs case, he envronmen represens he shaker, and he excaon s harmonc. Accordng o he characersc of he shaker, s chosen o have a harveser ha resonaes a 0 Hz. Ths vaue represens a compromse beween he performance of he shaker, whch canno provde he desred base dspacemen Y max beow 7 Hz, and he negry of he devce, whch s sressed a oo hgh frequency due o he presence of oher modes. The mposed consrans are he foowng: f res=0hz; ϴ max=5.5deg; ζ=0.07< /; m=/; d=/6; a/b=.5; The frs consran pons ou ha he resonance shoud no be hgh so ha he gearbox, moor or he oher componens of he assemby do no nerac wh he dynamcs of he harveser. A he same me, he desgn s consraned by he shaker, snce does no perform we a ow frequences. The consran mposed on he swng ange s o make sure ha he sprng behaves neary. If he swng ange s arge, he sprng s subjeced o an anguar dspacemen and can behave n a nonnear manner. The mporance of he dampng rao s hghghed n he hrd consran. I s known [] ha he mechanca dampng shoud be as sma as possbe o maxmze he harvesed power, because he power depends on he square of he swng dspacemen. Therefore, he sysem s forced o be underdamped. The vaue of 0.07 s chosen arbrary beow /, whch s he vaue over whch he second-order sysem does no resonae. The fourh consran s he poson of he sprng m, whch s (5) 3

5 paced aong he axa engh of he beam, n parcuar a haf of he beam engh. If m=, he sffness s very ow and hen sprng can show nonnear behavour. On he oher hand, f m<</, he sffness becomes very hgh o manan he resonance a 0Hz, and hs may affec he negry of he srucure, snce energy woud be ransmed o he connecon beween he beam and he gearbox. The dmenson d of he umped mass shoud no be oo arge o avod fexura modes a ow frequency, bu, a he same me, can ncrease he swng ange, and, herefore, he oupu voage. The as consran ensures smar modes (verca and horzona bendng modes) are no cose o each oher n frequency. The frs agebrac equaon s referred o he resonance frequency f res as f res m 3 k m d M The maxmum hrow ϴ max akes pace a he naura frequency, when he maxmum npu s Y max. consdered Therefore, m MLω Y (7) n max Θmax 4τ c c c ω s m n πθmax For he dampng rao s hen mposed (6) c m c The poson m of he sprng s m The edge d of he added mass and he rao beween he cross secon dmensons a and b s J c n (8) (9) d 6, a. b 5 (0) There are 8 parameers o compue, whch are m, M, k,, m, d, a, b. However, he number of equaons s sx. Therefore, wo equaons are added, reang he mass of he beam and he umped mass wh her voumes. For he beam, s m ab () and for he umped mass s M d 3 () The npu parameers, whch ncude aso he characerscs of he DC moor (Maxon moor 70W), are presened n Tabe : 4

6 Tabe. Inpu desgn parameers Parameer Vaue Coupng coeffcen (K ) Nm/A Inerna ressance ( ) 0.68 Ω Load ressance ( ) 0.68 Ω mechanca dampng (c m) 0. Nsm Sac frcon (τ s) Nm Gear rao (G) 8 Inpu dspacemen (Y) m Densy (ρ) 7700 kg/m^3 In Tabe, he mechanca vscous dampng c m s known and prevousy esmaed by aachng a penduum o he gearbox and measurng he me decay. The ogarhmc decremen mehod s hen apped o he frs perods of oscaon (avodng he frcon) and he dampng s compued. The vaue of he esmaed dampng ncudes he dampng of he gearbox, he moor and penduum, whch s no par of he devce. However, hs approxmae vaue s used for smuaons. The vaue of he sac frcon s esmaed separaey wh a sac es. An L-shaped nner hexagona spanner s fxed o he gear box, and weghs are added o he edge un he wegh of he mass s hgher han he sac frcon. I s we-known ha here exss an opmum oad ressance such ha he harvesed power s maxmzed. For consraned energy harveser, was demonsraed ha he opmum condon s acheved when he oad equas he nerna ressance [7, ]. Therefore, he harveser s desgned accordng o hs resu, herefore s mposed =, as shown n Tabe. By sovng he prevous agebrac sysem, a he desgn parameers were compued and a CAD mode can be bu n Sodwork (Fgure (a)). However, durng he manufacurng process some of he parameers were vared and he desgn parameers were updaed accordng o hese modfcaons. The updaed se of parameers s he repored n Tabe. Tabe. Desgn parameers Parameer Beam mass (m) Lumped mass (M) Beam engh () Lumped mass engh (d) Sprng poson ( m) Sffness (k) Cross secon, (a) Cross secon, (b) Vaue 0.45 kg 0. kg 0.8 m 0.03 m 0.09 m 6700 N/m 0.08 m 0.0 m 5

7 (a) (b) Fgure : Cad mode (a) and es rg (b) of he energy harveser 3. Expermena characerscs of he energy harveser In hs secon, he frs ess conduced on he energy harveser are shown. They are amed o evauae he resonance of he sysem and he presence of nonneary. To do ha, a random whe nose npu sgna was sen o he ampfer by he sgna generaor. The power ampfer suppes power o he shaker, whch exces he harveser from he base. Two acceeromeers were fxed on he srucure, as shown n Fgure (b). One s paced on he umped mass, whch provdes he acceeraon of x, and one on he base, whch reads he acceeraon of y. The equpmen used s sed n Tabe 3: Tabe 3: Equpmen for he conduced ess Equpmen Type Ampfer 3.. Deecon of nonneary DaaPhyscs 30W Shaker Derrnron Vbraors VP4 Acceeromeer B&K charge ype 4375 Acquson sysem LMS Scadas 8 channes The frs se of es s carred ou o characerse he dynamcs of he harveser. A hs sage no eecrca oad s aached, and he devce s n open crcu condon ( ). In parcuar, a random excaon was mposed by he sgna generaor n he range 5-00Hz and 5 averages were aken. The number of specra was se a 048, whch mpes a frequency resouon of Hz and an acquson me of 0.48 s. Ths acquson parameers w be used aso for he random es dscussed n he nex subsecon. The es was conduced a dfferen npu voage eves o verfy wheher nonneary was presen. The absoue rasmssby, n Fgure 3(a), and he coeherence funcon, n Fgure 3(b), are used o check he precence of he nonneary a dfferen npu voages. The absoue ransmssby T a s obaned expermenay as he rao beween he acceeraons measured from he acceeromeer x and he acceeromeer y. x (3) T a y 6

8 (a) Absoue ransmssby 0 0 =0.0055V =0.03V =0.04V =0.08V Coherence xy (b) =0.0055V =0.03V =0.04V =0.08V Frequency [Hz] Fgure 3: Absoue ransmssby (a) and coherence funcon (b) for dfferen npu eves n he range 5-5 Hz From he absoue ransmssby n Fgure 3(a), can be seen ha he resonance s around 0,3Hz. Ths vaue s n agreemen wh he desgn esmaon and he sma varaon (0.3Hz) may be due o he varaon of some desgn parameers durng he manufacurng process. A a frs gance, he sysem s nonnear a ow npus due o frcon. The absoue ransmssby moves upwards when he voage s ncreased from (sod back ne) o 0.03 (dash back ne), and remans consan up o 0.04, whch means ha he sysem s near n hs range. A 0.08V, he ransmssby sars droppng agan due o a rang effec, whch generaes vbraon nsde he gearbox. In hs condon, a bgger ncrease of npu voage does no produce a arger roaon of he moor shaf, bu ony arger mpacs beween he gears. A confrmaon of he presence of he rang effec s gven aso by he coherence funcon. Indeed, by ookng a he back doed ne n Fgure 3(b), s evden how he coherence drops as a ceran amoun of he energy nroduced no he sysem s wased by he mpacs beween he eeh of he gearbox. 3.. Infuence of he eecrca crcu Frequency [Hz] The prevous anayses were made n open crcu condon, whch means ha, even hough a voage can be deeced from he moor, here s no curren and herefore he power s zero. On he oppose, n shor crcu, he oad ressance equas zero, and he curren s presen, bu he voage equas zero, herefore harvesed power s s zero. These wo condons are here anaysed ogeher wh a oad condon ( =Ω) by measurng he me response acceeraon x of he beam. Assumng, ha he eecrca crcu s near, expeced o see ha n open crcu he response s arger snce he eecrca dampng goes o zero n fac K (4) c cm cm On he oher hand, when he crcu s shored, he oad ressance s zero, and K K (5) c cm cm As shown by he equaon (3) and equaon (4), he eecrca dampng s nversey proporona o and herefore, by ncreasng he oad he dampng ends o reduce. The effec of he oad on he acceeraon x s shown n Fgure 4. 7

9 50 Open crcu = Shor crcu Acceeraon x [m/s ] 0 Fgure 4: Effec of he oad ressance he x-acceeraon for a base acceeraon Inpu =.9V From Fgure 4, can be noced how he oad ressor affecs he beam acceeraon. To oban hs resu, a harmonc es was performed a resonance, n open crcu (back sod ne), oad crcu (back dash ne) and shor crcu (back do ne). I s seen ha open and shor crcus represen exreme condons and, when a oad s aached, he response s paced n beween. I can be summarsed ha he response s expeced o have a monoone rend wh respec o he oad, as aso demonsraed n eraure [, 8, 9]. 4. Dynamc range of he harveser As aforemenoned, he advanage of mpemenng a cubc dampng s o ncrease he dynamc range. In oher words, when a harmoncay base exced harveser s exced a ow npu eves, he force (or he voage) acng on he damper (or he eecrc oad ressance) s ower wh respec o a near damper (or he eecrc oad ressance). Therefore, he response s arger and more harvesed power s provded. Indeed, recang he ampude of he swng ange n frequency doman, n equaon (7), s m 4 MLY s (6) n c c c m For underdamped srucures, he maxmum power s obaned a he naura frequency, and can be reaed o he swng ampude as: Pharv Ec (7) G c The harvesed power can be compued as he mean vaue of he dampng force, assocaed wh he oad ressance, and he veocy. When he oad s defned, he power ony depends on he square of he ampude of he swng ange mes he frequency of excaon and, s maxmum a resonance. 4.. Oupu voage and harvesed power Tme [s] The eecrc oad conrbues o he harvesed power. Therefore, he voage across he oad s reaed o he harvesed power. For a near oad ressance, he voage depends on he swng veocy and s gven as n 8

10 V GK (8) So, he nsananeous power depends on he square of voage as V (9) Pharv E In Fgure 5(a), he voage across he oad s measured a resonance for dfferen oad ressances, such as 0.3Ω, Ω, 0Ω and 00Ω. (a) (b) Fgure 5: Oupu voage (a) and nsananeous power (b) as a funcon of me for hree dfferen oad ressors - Inpu =.9V I can be seen ha, by ncreasng he oad, he voage across ends o go hgher. When he oad s zero (shor crcu), he voage across he oad s zero, even hough curren passes hrough he crcu. When he crcu s open, hus, an asympoc condon s acheved, whch corresponds o have no curren hrough he crcu, bu a non-zero voage. From Fgure 5(b), he nsananeous harvesed power s suded as a funcon of he oad. I can be seen ha from 0.3Ω o 0Ω, he power ncreases sharpy, and hen drops a 00Ω. As demonsraed [, 7-9,, ], he harvesed power usuay shows a peak of power n correspondence of an opmum vaue of oad. The reason s ha he eecrca dampng, shown n equaon (5), presens a peak vaue as a funcon of he oad, as shown n Fgure 6. However, snce K s sma, here s no a huge varaon of c and, herefore, he peak of power s hard o be deeced expermenay. 9

11 x 0-4 c [Nms] [] Fgure 6: Effec of he oad ressance on he vscous dampng 4.. Leve curves The response of he devce shoud be near n erms of boh swng ange and voage, when he oad s mposed, and he devce s harmoncay exced a dfferen npu eves. (a) -0-5 = (b) -0-0 = / max [db] V /V,max [db] Y/Y max [db] Y/Y max [db] Fgure 7: Leve curves of swng ange and voage across he oad for dfferen npu eves - Θ max=5.5deg and V max=v From Fgure 7, he sysem responds neary boh n swng ange and voage from -0dB onwards. Beow -0dB, nsead, he sysem shows nonnear behavour, whch s assocaed o he frcon. In parcuar, can be noced ha he harveser does no provde voage beow -db, because he excaon s sma and he amoun of dspacemen produced s wased by frcon. ecang equaon (8), he eve curves for he harvesed power are provded n Fgure 8. 0

12 0 = -0 P harv /P harv,max [db] Fgure 8: Leve curves of he harvesed power for dfferen npu eves - P max=w The presence of he frcon, deeced n he swng ange and n he voage, has a srong consequence on he harvesed power. The behavour s smar o wha shown n Fgure 7. The power s subjeced o a huge reducon as he npu eve s decreased. As a consequence, he eve of he npu shoud be kep as arge as possbe so ha a arge swng ange woud no be affeced by frcon. Obvousy he npu eve depends on how hgh he sauraon m of he ampfer s, and how arge s he dspacemen he shaker can provde Fuure work: mahemaca mode of a nonnear energy harveser The goa of mpemenng a nonnear oad s o ncrease he dynamc range of he harveser. By deberaey nroducng nonneary no he eecrca crcu, s expeced a varaon of he performance, especay a ow npu eves. The agebrac equaon descrbng he dynamcs of he eecrca crcu assumes now he foowng form K 3 (0) Ths equaon s a hrd-degree agebrac poynoma n wh hree souons, n whch ony one s rea, and s 6K z K z K z () Y/Y max [db] K z 3 4 7K z Anayses are beng curreny run on hs mode and w be presened n fuure pubcaons. 5. Concusons and fuure work The presen paper shows he desgn and he ess of an eecromagnec ransducer energy harveser, whch s amed o ransform he energy provded by he base moon no harvesed power. The desgn process was conduced by mposng consrans amed o guaranee he correc operave condons. Frs ess were conduced o anayse he dynamcs of he sysem n open crcu. andom whe nose npu was used o exce he sysem a dfferen npu eves. esus show nonnear behavour a ow npu eves, whch s assocaed wh he frcon nsde he gearbox and a hgh npu eves, reaed o rang phenomena. The effec of he oad s hen consdered. The devce was

13 subjeced o a harmonc base excaon a resonance, and he response of he sysem, n erms of swng acceeraon x and voage was suded a dfferen oads. The nroducon of an eecrca ressance acs on he vscous dampng of sysem, and resus n an nermedae condon beween open crcu ( ) and shor crcu ( =0). For harmonc excaon wh a consan npu eve of excaon, he voage across he oad and he swng ange end o ge arger as ong as he ressance ncreases, because he vscous dampng s nversey proporsona o. The deecon of he nonneary was aso nvesgaed wh varabe npu eves. Assumng a consan oad, he sysem was harmoncay esed a dfferen npus Y max. I was shown ha he presence of frcon many affecs he sysem a ow npu eves and he sysem behaves neary as ong as he npu ncreases. The nonneary was evden n he swng ange as we as he voage and he harvesed power. In parcuar, he harvesed power drops dramacay for ow npu eve, herefore he npu shoud be kep as hgh as possbe (accordng o he performance of he shaker and of he ampfer) o produce a hgher swng ange and o ncrease he effec of he coupng on he harvesed power. Fuure works w be focused on mprovng he desgn o oban a beer coupng beween he eecrca and he mechanca crcus and on he updang of he mahemaca mode, especay of he dampng force, and on a comparson wh he expermena resus. Aso, he expermena mpemenaon of a cubc oad represens a cruca sep o demonsrae he effecveness of he approach proposed n he as subsecon. 6. Aknowedgmen The work here presened was funded by he EPSC hrough he Engneerng Nonneary program (EP/K003836/). 7. eferences [] M Hendjanzadeh, Desgn and opmsaon of consraned eecromagnec energy harvesng devces, PhD dsseraon, Unversy of Souhampon, 04; [] T J Suon, S J Eo, M J Brennan, K H Heron, D A Jessop, Acve soaon of mupe srucura waves on a hecoper gearbox suppor sru, Journa of Sound and Vbraon, vo. 05, 8 0, 997; [3] C B Wams, B Yaes, Anayss of a mcro-eecrc generaor for mcrosysems, Sensors and Acuaors, 8, 996; [4] B P Mann, N D Sms, Energy harvesng from he nonnear oscaons of magnec evaon, Journa of Sound and Vbraon, vo. 39, , 009; [5] M Ghandch Tehran, S J Eo, Exendng he dynamc range of an energy harveser usng nonnear dampng, Journa of Sound and Vbraon, vo. 333, 63 69, 04; [6] L Smeone, M G Tehran, S J Eo, M. Hendjanzadeh, Nonnear dampng n an energy harvesng devce, ISMA 6h Inernaona Conference, 04; [7] N G Sephen, On energy harvesng from amben vbraon, Journa of Sound and Vbraon, , 006; [8] M Hendjanzadeh, S M Sharkh, S J Eo, M Moshref-Torba, Oupu power and effcency of eecromagnec energy harvesng sysems wh consraned range of moon, Journa of Smar Maeras and Srucures, vo., 5009 (0pp), 03; [9] M Hendjanzadeh, M Moshref-Torba, S M Sharkh, Consraned Desgn Opmzaon of Vbraon Energy Harvesng Devces, Journa of Vbraon and Acouscs, vo. 36, 6, 04; [0] O L Green, K Worden, K Aaah, N D Sms, The benefs of Duffng-ype nonneares and eecrca opmsaon of a mono-sabe energy harveser under whe Gaussan excaons, Journa of Sound and Vbraon, vo. 33, , 0; [] M Hendjanzadeh, S J Eo, M Ghandch Tehran, The effec of he nerna ressance on an energy harveser wh cubc ressance oad, ICSV The nd Inernaona Congress on Sound and Vbraon, -6 Juy, 05; [] M Hendjanzadeh, Consraned desgn opmsaon of vbraon energy harvesng devces, Journa of Vbraon and Acouscs, vo. 36/000--6, 04;