A Sustainable Energy Harvesting Machine

Transcription

1 Proeedings of te World Congress on Engineering 13 Vol III, WCE 13, July 3-5, 13, London, U.K. A Sustainable Energy Harvesting Maine Geoff Angel, George Haritos, Ian Campbell Abstrat tis paper introdues a new type of maine tat is intended to transform sustainable solar energy into eletrial power via te attament of an additional generator, for spae appliations. Te energy transformation meanism is via a set of radial pre- urved bimetalli blades arranged in a similar way to a gas turbine layout. Te blades are ylially eated and ooled tus produing a linear fore tat is translated into rotary output motion in te maine. Index Terms design, energy, oneptual, spae, sustainable I. INTRODUCTION Tere are many patents for termal motors, Low [1]or O'Hare[], to mention just a few, tat work on te priniple of utilizing te work done by eating and ooling a bimetalli strip in some manner, but most are quite omplex ontraptions tat are neiter simple or pratial, or proven. Te termal maine onept tat tis paper puts forward, is bot extremely simple and elegant, and as been proven to operate and maintain a ontinuity of rotary output motion wen exposed to a eating and ooling yle. A series of pre-urved bimetalli blades are radially deployed witin te motor to produe an axial trust, te trust and reation witin te motor reates rotational movement of te output saft of te motor. In tis so paper, te major steps of te matematial model of te motor are provided. Te basi Timosenko[3] bi-metalli urvature equation is applied wit minor adjustments, to enable te evaluation of te straigtening out from an initially smaller radius of urvature, to a larger radius of urvature, as opposed to bending from flat. Figure 1, sows te basi pre-urved bimetalli blade geometry and its ord displaement axis. At ambient or old temperatures, te pre-urved blade possesses a smaller radius of urvature. If mounted so tat one end is freely pivoted, and te oter end is free to move wit a rotational degree of freedom, ten te bending of te blade due to a uniform temperature ange, is transformed into an axial extension of te free end, along te ord displaement axis. Manusript reeived Feb, 13; revised July 3, 13. Tis work was suppoed in pa by te University of Hefordsire, Geoff. Angel is wit te University of Hefordsire, Sool of Engineering and Tenology, University of Hefordsire, College Lane, Campus Hatfield, Hes. AL1 9AB,UK ( g.d.angel@es.a.uk), Tel: Dr George Haritos is wit te University of Hefordsire, Sool of Engineering and Tenology,( g.aritos@es.a.uk) Tel Ian Campbell is wit te te University of Hefordsire, Sool of Engineering and Tenology, ( ianampbell1@gmail.om) Tel Fig. 1 Cord axial displaement, straigtening up of a bi-metalli blade. For te ondition tat te blade straigtens up as in Figure 1, te material sides of te bimetal need to be as sown in Figure. A pre-urved bi-metalli blade beaves in te same way as a straigt bi-metalli strip, tat is, wen uniformly eated it will tend to bend due to te differential expansion rates of te intimately bonded metals. Te different expansion rates produe internal stresses, fores and ouples tat ultimately bend te strip. In a pre-urved bi-metalli blade, te material side wit te iger oeffiient of linear expansion must be on te inside fae of te blade, for it to straigten out, see Figure. and 1 denote te separate oeffiients of linear expansion for te two metals making up te bimetalli blade. Fig.. Bimetalli strip and te oeffiients of linear expansions 1,. II. THERMAL MACHINE CONCEPT DESCRIPTION Te maine onept tat tis paper proposes, onsists of a series of radially orientated pre-urved bimetalli blades tat are assembled between a rotating outer rotor, and a fixed entral ratet, see Figure 3. Te maine put forward in tis paper is entirely novel, and altoug tere are many bimetalli powered engines patented, none of tem are in te onfiguration proposed ere. ISBN: ISSN: (Print); ISSN: (Online) WCE 13

2 Proeedings of te World Congress on Engineering 13 Vol III, WCE 13, July 3-5, 13, London, U.K. III. MODE OF OPERATION Wen an external eat soure is applied loally to a urved bimetalli blade witin te motor, te differential expansion rates of te two metals of te blade auses te blade to bend, wen mounted as previously stated, te bending of te blade translates into a straigtening ation along te ord displaement axis, te extension of te straigtening ation, produes a reationary trust between te movable outer rotor and te fixed inner ratet, tat results in outer rotor movement. If te motor onsists of many radial blades as sown in Figure 3, and providing tat a eating and ooling yle for ea blade an be ontrived, ten ontinuous motion of te output rotor is possible, wilst te eating soure is applied. onfigurations of tis type of termal maine. If te main omponents tat make up te maine as proposed are: a rotor, a series of radial blades, and a stator, ten te possible layout permutations and onfigurations are as follows: A) Inner stator fixed, outer ratet moving, ere te blades are stationary. B) Outer stator fixed, inner ratet moving, ere te blades are stationary C) Inner ratet fixed, outer rotor moving, ere te blades move wit te outer rotor D) Inner rotor moving, outer ratet fixed, ere te blades are moving wit inner rotor. Te osen layout onept as sown in Figure 3, was C), tat is inner ratet fixed, outer rotor moving. Fig.3 Termal maine design onept. IV. DESIRED DESIGN FEATURES Te following essential requirements or features govern and drive te ideology of te proposed termal maine: Te maine ad to be inerently simple & elegant in operation, i.e. only one rotating pa. Te maine ad to be modular in onept, i.e. failitate multi-stage expansion. Te maine ad to utilize existing proven tenology. Te maine ad to failitate te ability to sale up or down, for different appliations. Te maine ad to be flexible as to its eating and ooling soures. Te maine ad to be quiet and vibration less in operation. Te maine ad to be designed for zero maintenane requirements. Te manufature of te maine must be possible in low tenology regions around te world. Te maine must not pollute or produe outgasses or exausts fumes of any kind. All te above riteria were met in te onept design put fo in tis paper, te maine as sown in Fig. 3. Fig. 4 Termal maine layout oies. For Prototype 1, as designed in Figure 3, and as realized in Figure 5, onept layout C was osen, tat is, te inner stationary ratet was fixed, and te outer rim on wi te blades were all pivoted, was te output moving rim. Te rationale for piking onfiguration C or D is tat it is easier to ave a fixed eating and ooling zone, tan to ave a rotating eating and ooling meanism, wi itself means more omponents and ontradits te design ideal of a simple, single moving element design. V. THERMAL MACHINE LAYOUT Figure 3, sows just one of te possible layout ISBN: ISSN: (Print); ISSN: (Online) WCE 13

3 Proeedings of te World Congress on Engineering 13 Vol III, WCE 13, July 3-5, 13, London, U.K. Fig.5 Prototype 1 wit radial pus blades In layout onfigurations A & B of Figure 4, te position of te blades are fixed, for tese two onepts to work, te eating and ooling meanism would need to travel around te maine. In onepts C&D, te blades are pivoted on te moving output saft, tus te eating and ooling areas an be fixed, su tat te blades automatially self - drive into and out of te fixed eating and ooling zones, as te rotor moves around. To evaluate te number of blades, and tus overlap yles required to maintain te ontinuity of motion in a bimetalli powered maine, is a omplex and involved alulation, beause it is a funtion of many variables tat are desribed later in tis paper. Figure 7 depits a simple 5-blade overlap yle wit blades number 1 to 5. Aording to te overlap yle, as blade 1 eats up, it moves te rotor, tat in turn brings blade into te eating zone. As blade eats up, it too adds displament to te rotor bringing blade 3 into te eating zone, and so fo. At point 1, blade 1 as reaed maximum temperature and displaement and now beomes an inative blade, tat is being driven by te rest of te ative blades, into te ooling zone, for it s yle to repeat. Figure 5, sows a single layer maine and Figure 8 depits te reent development termal maine, a 6-stak, multilayer 54 blade prototype. Te 6-stak prototype is a resear projet tat is urrently being developed at te University of Hefordsire Sustainable Energy Tenologies Centre.[4] Fig.6 Ideal termal yle of blade An ideal eating and ooling yle of a single blade is sown in Fig.6. Te yle sown is redued to te basi events of eating up te bimetalli and ooling it down again. Te eat transfer meanism assumes uniform eating and ooling along te entire lengt of blade, and te rate of eat transfer gain is te same for eating up, as it for eat transfer loss in ooling down. To aieve a repeatable yle time, te eat up and ool down time must also be te same. Te meanism to obtain ontinous rotational motion in te maine is aieved by te overlap yle. Te overlap yle ensures ontinuity of motion by overlapping te individual termal yles of all te blades in te maine, see Fig. 7. Fig.8 6-stak termal maine VI. THEORETICAL PRINCIPLES Te evaluation of te fore tat an be derived by te appliation of uniform eat to an individual pre-urved bimetalli blade, an be alulated wit te aid of two separate impoant formulae. Te first formula is by Timosenko[3], wo provides te radius of urvature of a bimetalli strip as a funtion of temperature. Te seond step in evaluating te trust generated by tis ange of urvature, wen mounted as previously stated, is by te appliation of te Castigliano s[4] minimum energy teorem to find te axial fore and displaement in beams. Due to te nature of tis paper only te major steps of te matematial model of te termal motor are inluded. Te full derivation of te Castigliano[4]formula ontains fuer work on te geometry of ars, and tat setion of te derivation as been omitted for te sake of brevity. Fig.7 Teoretial overlap yle of 4 blades ISBN: ISSN: (Print); ISSN: (Online) WCE 13

4 Proeedings of te World Congress on Engineering 13 Vol III, WCE 13, July 3-5, 13, London, U.K. VII. APPLICATION OF TIMOSHENKO S CURVATURE EQUATION L : is te ord lengt R : is te radius of urvature A : is te ar lengt (in radians) pa of a true irle Ar A After eating Before eating R Ar A L R Fig.9 & 1 for a strip of a material wit is on te inside. L Assumptions Pre-urved bimetalli strip is simply suppoed at ea end wit a rotational degree of freedom. Strip is uniformly eated along te entire lengt of strip, and te strip remains truly irular. is te n No external loads are applied during eating Te material wit te iger oeffiient of linear termal expansion is on te inside radius R. is te All equations and formulae are in S.I. units, i.e. N, mm, C Tus by Timosenko [3] 1 t 3(1 m) (1 m n) ( m ) m n 6 ( 1) ( TH TC ) (1 m) (1) Were ρ is te radius of urvature as a funtion of temperature from an ambient flat strip. t t 1 t : total tikness of te strip, t,t being te 1 material tiknesses t1 m : ratio of tiknesses t Fou E1 n : ratio of Young s Modulus E T & : ot and old temperatures states of te strip H T C E 1, E : are te linear Modulus of te two separate materials & 1: are te oeffiients of linear termal expansion for te two metals wereby is assumed to be numerially larger tan 1. Te R orretion equation evaluates te radius of urvature of a eated bimetalli strip from an initially preurved radius of urvature R by adding te reiproals of bot radii 1 1. R Wit te R establised by te appliation of te Timosenko formula, te orresponding ot ord lengt L an now be found. Te general ord lengt of any ar is generally known to be given by: A L Rsin( ) () R Fig.1 Ambient and eated bimetalli blade radii. Tus A LH R sin( ) (3) R and Ab L R sin( ) (4) R Wereby A b is te urved ar lengt of te bimetalli strip Hene, using Timosenko s radius of urvature formula wit te ord formulae, it is possible to evaluate te ot lengt of bimetalli strip, L. Given tat L an be easily evaluated if te pre-urved radius of urvature R is known, ten te unloaded displaement x, from L to L an be evaluated by simple subtration. Tus; x L L (5) Given A & R, and from Timosenko tat gives R. b VIII. DISPLACEMENT AND FORCE Appliation of te Castigliano [4],formula, for evaluating bot te fore and ord displaement of te pre-urved blade wen onsidered to be a beam, after integration is given by : 3 4FR 3sin( ) os( ) (6). EI 4 4 Te total axial defletion of te urved bimetalli strip wen subjeted to an axial fore F By re-arranging (6) in terms of F, te fore developed by a urved bimetalli strip subjeted to eating is obtained as a funtion of te extension x provided previously in (5). Tus: EIx F R ( os( ) sin( ) 4 (7) Fore developed by te bimetalli strip by eating alone. Were: x L L was evaluated by Timosenko previously, and values previously. H, E, I and R ave all been stated ISBN: ISSN: (Print); ISSN: (Online) WCE 13

5 Proeedings of te World Congress on Engineering 13 Vol III, WCE 13, July 3-5, 13, London, U.K. : is te total defletion due to load F, te diretion of F E: is te averaged modulus of metals in te bimetalli strip F: an externally applied axial load /or Fore by te strip I: is te Moment of Ineia of setion of strip R : is te radius of urvature of te bimetalli strip at ambient temperature. A : is te total ar lengt of te bimetalli strip Ab : total angle of te entire ar A b of L R Te full derivation of te formulae is outside te sope of tis so paper, but an be aessed by ontating te autor. Tus for any externally applied stati load F, te net loaded displaement x for any temperature differential t, experiened by te strip is given by: x L L (8) For any appliation of te above formulae, it is normal to know initial values of R, Ab, Ea, I, & 1, T, T, from wi all oter values an be alulated. IX. MACHINE GEOMETRY For a termal maine layout type C of Figure 4, te general blade geometry witin te termal motor is sown in Figure 11. urvature R, itself, a funtion of te Timosenko formula (1). Te fore F developed by a single bimetalli blade is now translated into a tangential fore vetor by (13), see te fore vetor geometry in Figure 1. From te geometry in Figure 1, angle is equal to: ri L R ri L R Ro (1) x (11) R L x (1) F t F os() (13) Tus from te geometry formulae just sown, it is possible to evaluate te tangential fore omponent as a result of te trust generated by a single bimetalli blade, onto te moving output saft. Figure 1, sows te geometry of a single bimetalli blade witin te motor. It an be seen tat as te angle of μ dereases, te greater te tangential fore vetor F t beomes. It sould be noted tat angle is dependent on te relative sizes of te radii R and r i, and R, r i ontrol te blade geometry, tat is, te lengt of te bimetalli blade A b and its ambient radius of urvature R. Te optimum onfiguration for performane is tus dependent on many geometri variables, and tese variables are dependent upon te overall size of maine itself, wi is a funtion of te required appliation. Fig.11 sowing a single bimetalli blade in two states of eating For an ideal maine wit no external load, upon eating a single blade wi is pivoted on te outer moving rim at one end, and is engaged into a ratet toot of te fixed stator, will ange its ord lengt and displae as (). Tis linear displaement, or straigtening up of te blade, auses an angular displaement of te outer moving rim as a reation troug te blade ours. It an be sown tat te outer rim displaes troug an angle given by te following formula using te Cosine rule: R Ro L aos aos (9) Ro Ro Na Tus te angle of rotation due to one blade expanding during its eating yle is alulated by (9). Angle N is a funtion of L wi is driven by te ot radius of ISBN: ISSN: (Print); ISSN: (Online) a Fig.1 Fore F geometry as a funtion of angle Te fore vetor F t of a single blade times te distane R, provides te output torque of te maine. Tus Tout Ft R (14) Output torque of a single blade as a funtion of a temperature differene. X. DISCUSSIONS Te formulae presented ere are te major stages of te matematial model of te termal maine, owever to evaluate te maine performane in dept, more WCE 13

6 Proeedings of te World Congress on Engineering 13 Vol III, WCE 13, July 3-5, 13, London, U.K. information is required wi is beyond te sope of tis so paper. Te formulae presented ere are for te evaluation of a single bimetalli blade in ideal onditions, assuming perfet eat transfer to and from te blade during te eating and ooling yle. For a full matematial model, te following detailed information is required: mass, size, geometry of te termal maine omponents, available potential temperature differenes, and required external driving loads. Wit tis information, a eating and ooling yle an be alulated wi inludes te number, size, geometry of te blades, and te required overlap yle. Te overall effiieny of te maine is defined by te lassial definition; energy in, divided by energy out, minus internal fritional losses. In a maine of tis type, te overall effiieny is aknowledged to be very low; tis is due to te very low frequeny of te eating and ooling yle. However, wilst evaluating te effiieny, it sould be noted tat tis devie does not onsume valuable, diminising fossil fuel based produts, and tus for eain appliations, te waste of te input energy, or effiieny, is not a problem, te question is, an te devie provide suffiient, reliable non-polluting power to satisfy te requirements of te appliation?, wereby te input energy to te maine, omes from a renewable energy soure su as solar power. Te answer to tis question, is igly dependent on te size and detail design of te maine and te materials used. From te early test data of te first Prototype1 Fig.(5), te rotational speed of te outside moving rim was approximately 1 degree per se, tis was for blades in a single stak or layer maine, wit only one or two blades ative any time. Te size of Prototype 1 was ϕ3mm and te blades were 8mm long wit a radius of urvature R = 4mm. Anoter impoant aspet of te maine, is tat ould be designed to apture waste energy su as ot exaust gases tat would oterwise be lost to te surroundings. Te overall effiieny of te maine is igly dependent on te eat transfer meanism, wi is a funtion of te design of te maine, inluding materials osen and te geometry of te blades. Te size of te maine also as a diret bearing on te effiieny of te devie, in tat, te larger te maine an be, te greater te energy arvesting sale fator. XI. CONCLUSION Te termal maine onept proposed, is terefore a very simple, elegant maine tat provides many advantages for tose speial appliations, tat require te attributes tat tis type of sustainable devie offers. Altoug spae appliations are te ideal environment for tis devie beause of its inerent simpliity, reliability and lak of maintenane, it ould equally be used in remote terrestrial dese region appliations wereby a set and forget power soure is required. Te onept an also be used to reapture fossil fuel based waste exaust energies tat would oterwise be lost to te surroundings. Moreover, beause te devie is versatile, in tat it only requires a temperature differential to work, it ould be designed to be powered by solar radiation, ot and old gases, liquids, or geotermal energy. A typial terrestrial appliation would be to power a water pump in te remote ot dese. ACKNOWLEDGMENT G.D.Angel would like to tank te University of Hefordsire for affording bot te finanial suppo and exellent resear failities to ondut tis ongoing projet. REFERENCES [1] Low GMea. Termal Motor. In: USPO, editor. USA: NASA; 197. p. 6. [] O'Hare LR. Bimetalli Solar Engine. In: USPO, editor [3] Timosenko S. Analysis of Bi-metal Termostats. JOSA. 195;11: [4] Egeloff CJea. Appliation of modern engineering tools in te analysis of te stepped saft: Teaing a strutured problem-solving approa using energy teniques1. ADDITIONAL USEFUL REFERENCES ASTM STANDARD B "Standard Test Metods for Flexivity of Termostat Metals" ASTM International: West Consooken, PA, 8, DOI: 1.15/B16-8, ASTM STANDARD B "Standard Speifiation for Termostat Metal Seet and Strip". ASTM International, West Consooken, PA, 1, DOI: 1.15/B388-6R1, BOISSEAU.S. 1. A bimetal and eletret-based onveer for termal energy arvesting Classial Pysis, 3. CHURCHILL, W. H. E. A Heat Motor. USA patent appliation. CLARK, R. O Termal Motor and Generator. USA patent appliation. DAYTON, C. S Termal Motor. DIN "Termostat metals: tenial delivery onditions". DIN Deutses Institut für Normung e. V. Am DIN-Plazt, Burggrafenstabe 6, 1787 Berlin,Germany,ttp:// DIN "Testing te speifi termal urvature". DIN Deutses Institut für Normung e. V. Am DIN-Plazt, Burggrafenstabe 6, 1787 Berlin,Germany,ttp:// KANTHAL 8. Kantal Termostati Bimetal Handbook, Box 5, SE Hallstaammar, Sweden, Kantal. SANDOVAL, D. J Termal Motor. USA patent appliation. SHIVALIK, 13. Bimetalli strip supplier [Online]. Available: ttp:// UHLIG, W. ET AL 7. Termostati Metal, Manufature and Appliation, Hammerplatz 1, D- 88,Aue/Sasen, Auerammer Metallwerk GMBH. ISBN: ISSN: (Print); ISSN: (Online) WCE 13