ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
perphasefor20minutes.Themeasuredchangeinheliumboil-offrateasafunctionoftimeisshownin Figure4.(TheheatisalsoestimatedinmW,using2.6J/mlfortheheatofvaporization ofhelium.)Ascan beseen,thereappearstobelittledifference.However,hadthemodulerunlongeruntilequilibrium was achieved,amoresignificantdifferencemighthavebeenapparent.Fortheapplication athand,though, witharelativelylowdutycycleundernormaloperation,theDicronite®DL-5lubricantwillnotbeofgreat benefit. O.35 25O 0.3 0.25 E ._ ¢... •"g-0.2 # "5 (D 0.15 ,o o 0.1 t- #O 0.05power off i I t i _ )_(T_T(( )T_ Xnolubricant;_ Otungsten disulfide , I t--200 E 150._c &{,- ¢..- ¥100N E w --50 0:00 0:15 0:30 0:45 1:00 1:15 1:30 1:45 2:00 Time (hh:mm) Figure4.EffectofDicronite 8DL-5lubricant onwormgear' DutyCycleVariations Withthelubricant applied tothewormgearing, another seriesofheatloadtestswereperformed to determine theexpected heatloadfromcontinuous rotation oftheHWP,fromstepped rotation ofthe HWP,andfromthemagnetoresistive sensor alone.Foreachscenario, theboil-off rateofliquidhelium wasallowed tocometoequilibrium. Figure5showstheextraheatonthe4Ksurface foreachscenario in termsofboil-off rateandestimated milliwatts. InTable2,themeasured equilibrium values are summarized. Ascanbeseen,thecryogenic motorwhenruncontinuously produces moreheatthanwouldbepredicted frominputelectrical power(recallthe108mWtotalpreviously computed). Obviously, fromFigure5,the measured heatloadfromthemotorisnearlytwicethatexpected. Sinceinputpowershouldtheoretically equalthemotor's outputpluslosses, thissurplus heating isnotclearly identifiable. Creating amore efficient mechanism couldcertainly reduce thisheating some.However, utilizing areduced dutycycle seemstobethemosteffective meansoflimiting heatloadsfromthecryogenic motorandrotation ofthe HWP.Fortunately, fortheintended polarimeter, thisispossible. NASA/CPm2002-211506 33
0.35 0.3-- 0.25 0.2 0.15 0.1 0.05/k/x/k A /k /xpower off(cont.) A Xsensor only O5secevery 55sec []5secevery 25sec /xmotor continuous ............. :25O 200 •150 /k X X AX [] XOOOI-qO O O 01_ .... 0:00 0:15 0:30 0:45XX power off(25sec) [] E]O •fq F3[] 1:00 1:15poweroff(sensor) X X power off(55sec) O O O ]........................ 1:30 1:45 2:00 2:15 2:30 Time (hh:mm)-100 -5O X ..... 0 2:45 3:00 Figure 5.Effect ofvariations indutycycleandsensor heatload Table2.Equilibrium heatloads LHeboil-off Estimated heat %increase (l/hr) (mW) abovebaseline Noelectronics baseline 0.37 267 Magnetoresistive sensoralone 0.14 101 38% Continuous motorw/osensor 0.32 231 86% Motor5secevery55secw/osensor 0.03 22 8% Motor5secevery25secw/osensor 0.05 36 14% Sensor HeatLoad InFigure 5,itcanalsobeseenthatthemagnet•resistive sensor addsalargeamount ofheattothe4K surface relative tonormal operation ofthecryogenic motor. Themagnet•resistive sensor consists oftwo 100_resistors inseries at5Vpotential. Itshould therefore dissipate about125mWofpower atroom temperature; usingameasured resistance of0.34£2atLHetemperature, itshould dissipate 73mWof power. Thiscorrelates reasonably wellwiththeresults shown inthegraphandtable,givingasense of theaccuracy ofthemeasurements made. Because oftherelatively highheatdissipation bythesensor, future module design andsensor implementation mayrequire either adifferent sensing device or necessitate adutycycleconsistent withthemotor. NASA/CP--2002-211506 34
Conclusion Someconclusions thatcanbedrawnfromthisworkare: •Testing oftheprototype HWPmodule wassuccessful, exhibiting confidence inanewapproach to measure polarization atmultiple FIRpassbands. •Selection ofabearing forcryogenic application isacriticalstep.Aprecision X-bearing apparently overconstrained andboundthemechanism whensignificant cooling occurred, necessitating looserdiametral clearance between theballsandraces. •Centering theHWPbearing withanelastomeric o-ringallowed bothroomtemperature and cryogenic operation whendissimilar materials werepresent andtolerances factored intoaccount forshrinkage. •Fortheapplication athand,witharelatively lowdutycycleundernormal operation, the Dicronite® DL-5lubricant applied tothewormgearing willnotbeofgreatbenefit. •Thecontinuously energized Infineon magnetoresistive sensor heatloadwashigherthandesired, indicating aneedtoinvestigate othersensing meansoremploy alowdutycycleonthesensor, similartothemotor,toreducethisheatload. •Futureworkwillbefocused uponreducing themodule massandlowering theheatloadfurther. Thesuccess ofthissmallprojectnowlayssomeofthegroundwork foranext-generation polarimeter for far-infrared astronomy. Acknowledgements WewouldliketothankG.Kelderhouse andH.KrebsofTheUniversity ofChicago, A.Kepley ofCase Western Reserve University, W.Lahmadi andJ.Lagdam ofPhytron, Inc.,W.Tenbrink ofKaydon Corporation, andE.Shankland ofInfineon Technologies. Thisworkhasbeensupported byNSFgrant 9987441. J.Vaillancourt wassupported byNASAGraduate Student Research Program grantNGT5-63. A.Kepley wassupported byNSFfunding through theCenter forAstrophysical Research inAntarctica (CARA) Research Experience forUndergraduates (REU)program. References 1.Becklin, E.E."Stratospheric Observatory forInfrared Astronomy (SOFIA)." Proceedings oftheESA Symposium TheFarInfrared AndSubmillimetre Universe 15-17April1997,Grenoble, France, ESA SP-401 (August 1997),201-206. 2.Differential Magnetoresistive Sensor FP212L100,DataSheet1999-04-01, Infineon Technologies. 3.Platt,S.R.,R.H.Hildebrand, R.J.Pernic, J.A.Davidson andG.Novak. "100--IJm ArrayPolarimeter fromtheKuiperAirborne Observatory: Instrumentation, Techniques, andFirstResults." Publications oftheAstronomical Society ofthePacific, 103(November 1991),1193-1210. NASA/C Pm2002-211506 35
Tape-Spring Rolling Hinges AlanM.Watt*andSergioPellegrino* Abstract Thispaperpresents anewdesignofalowcost,unlubricated, self-deploying, self-locking hingewhose properties canbeeasilymodified tomeetdifferent requirements. Aparticular implementation is considered, providing ahingethatis135-mm long,30-mm highand45-mm wide,withadeployment moment varying between 0.1and0.3Nmandalocking moment of13Nm.Stiffness testshavebeen carried outonthehingeinthedeployed configuration, anditisshownthatthesixstiffness coefficients canbeestimated usingsimple analytical models. Themoment versus rotation profileofthehingeis shownalongwiththeresultsfoundfromafinite-element simulation. Theresultsofdeployment testing, including shockimparted uponlatching ofthehinge,arepresented forhingeswithavarietyofdamping mechanisms. Introduction Anumber ofspace-based deployable structures thatarebeingdeveloped atpresent, suchasmembrane synthetic aperture radarsandultra-high powersolararrays,involve theuseofstiffmembers connected by self-locking hinges. Thedesignofsuchframes canbesimplified andtheircostgreatlyreduced bytheuse ofcontinuous, elasticconnections instead ofstandard mechanical hinges. Thispaperpresents anewdesign foraTape-Spring Rolling (TSR)hinge(Figure 1),whichisa combination ofsteeltapesprings, mainlyproviding thedeployment andlocking moments, andarolling hingeconsisting oftwosetsof"wheels" heldtogether bywireswrapped around them.Thesewiresare heldwithingrooves cutintothebodyofthewheels andarefreetopassfromonewheeltotheotherwhen thewheels arerotated. Thisverylowfriction arrangement issometimes knownasa"rolamite hinge" (Chironis andSclater, 1996),andhaswell-defined kinematic properties. Notethatthereisnosliding, only rollingcontact, andthatthekinematic behavior ofthehingeisdetermined onlybythosepartsofthe rolamite wheels whichcomeintocontact; therestofthewheelcanhaveanarbitrary' shape. Rolamite wheels Tapesprings \ /\/ \ L/\ (a)d_. I / / / (b) Figure1.TSRHinge Theproposed design canbereadily tailored tomeetdifferent applications and,inparticular, ismore compact andlighterthanearlier designs. Thestiffness, moment-rotation properties, anddamping behavior havebeencharacterized andarepresented inthispaper. *Department ofEngineering, University ofCambridge. Cambridge, UK Proceedings ofthe36mAerospace Mechanisms Symposium, GlennResearch CenterMay15-17,2002 NASA/C P--2002-211506 37
ii__i:i,i' ] (a) (b) Figure2.Configurations oftape-spring hinges Review ofRelated HingeDesigns Simple, self-actuating, self-locking hinges havebeendeveloped foranumber ofyearsforuseas deployment mechanisms forsolararraypanels, synthetic aperture radars(SARs), booms, radiators and thelike. Several successful designs havemadeuseofcurvedelasticelements (tapesprings). Tape-spring hinges offeranumber ofbenefits overstandard hingesinvolving relative motionbetween rigidmechanical parts thatmakethemparticularly suitable foruseindeployable spacestructures: •Zerofrictionandbacklash. •Elasticlatching intolockedposition, givinghighlyrepeatable andaccurate positioning. •Nomoving partstojamorbindduetolong-term storage oradverse environmental conditions. •Simple manufacture andlowcost. Vyvyan (1968), Figure2(a),patented amethod ofincreasing thelocking moment produced byatapespring hingebyplacing thetape-springs inaparallel configuration, henceputting theminoverall compression andtension ratherthanbending. Analternate arrangement isshown inFigure 2(b) (Chiappetta etal.,1993)where,unlikeFigure2(a),thetape-springs comeintocontact uponfolding. Amajordisadvantage inherent intheuseoftape-spring hingesisthattheyhaveverylowstiffness inthe foldedconfiguration. Thiscancauseuncertainties indeployment andmakesgravitycompensation during groundtestingproblematic. Aerospatiale (Auternaud etal.,1992)proposed asolution tothisdrawback byattaching arollinghingeto thetape-spring, asshown inFigure3.Afunctionally similar design hasbeenmanufactured byTRW Astro.Bothdesigns provide betterdeployment controlthantheprevious hinges, however bothofthese hinges weredeveloped primarily forsolararraypanels, andhencearetoowideformanyother applications. Also,theAerospatiale hingeisheavy(1.17kg)andcomplex, whereas thelocking stiffness oftheTRWAstrohingeisexpected tobequitelimited. NASA/CP--2002-211506 38
Figure3.Aerospatiale hinge Arollinghingewasdeveloped byHilberry etal.(1976), Figure4,andfunctions byholding tworolling surfaces incontact bymeansoftensioned bands.Asthehingerotates, thebandspassfromonerolling surface totheotherandtheircurvatures change signs.Thereistherefore noslidingcontact withinthis hinge,thusmaking frictionverylowandremoving theneedforlubrication. Figure4.Rolling hinge Hilberry etal.(1976)alsodescribe howtheperformance ofarollinghingecanbeimproved bychanging theprofileoftherollingsurfaces orofthesurfaces supporting thetension bands.Forinstance, theforce pullingthetwohalvesofthehingetogether isincreased ifthebandsrunonasurface withasmaller radiusthantherollingsurface, Figure5(a).Alternatively bymaking someofthetension bandsurfaces smaller thantheothers, asinFigure5(b),arestoring moment iscreated uponrollingthehingeinthe direction shown. NewHingeDesign Thenewhingedesign, firstpresented inPellegrino etal.(2000), introduces twofundamental design changes: Adouble tape-spring isused.Thisproduces ahigherdeployed bending stiffness andamuch higherlocking moment, bothofwhichcanbetailored toanyparticular application byvarying the spacing ofthetapes.Thusthecomplex lockingmechanism oftheAerospatiale hingeisnolonger required. NASA/CP--2002-211506 39
(a)Resultant forcefrom contact Resultant forcefromwires (b) Figure5.Alternative formsofrollinghinge Steelbandsintherollinghingearereplaced bywires.Thisreduces theoverall widthofthe mechanism andhenceitsweight, andallowsamuchsimpler andmoreefficient wiretightening mechanism tobeutilised. Themaingeometric characteristics ofthehingearedefined inFigure1andareasfollows: •Thelength,L,ofthetape-springs, measured between theendsoftheclamps. •Theseparation distance, s,between thetapes,i.e.thedistance between theneutralaxesofthe twosprings. •Theoffsetdistance, d,between thecenter-line through thetape-springs andthecenter-line through therolamite wheels. •Theradius,r,oftherolamite wheels. Theparticular TSRhingethatisinvestigated inthispaperhasL=88mm, s=12.5mm, d=11mm and r=28.1mmgivingoveralldimensions of135mmby45mmby30mm.Itweighs 0.11kgincluding all connections. Thedimensions ofthehingeareconstrained bytherequirement thatthetapesprings should notbedamaged duringfolding/unfolding. Thesmallest hingethathasbeenconstructed withthesame tapesprings hasdimensions of106mmby44mmby21mm. ThenewTSRhingecanbeseeninFigure6.Themainpartsoftherollinghingearemanufactured from8mmthickDelrin(aspace-qualified AcetylResin)plate.Aluminium-alloy blocksconnect therollingpartsto thetapesprings. Nyloncoated, 1-mmdiameter stainless steelwireterminated bycrimped aluminium tubesisusedtoholdtogether therollingparts;tension adjustment isprovided atoneendbythewire passing through ascrewwithalock-nut ontheend.Thepre-stress inthewiresissufficiently largethat compressive contact between therolamite wheels isalways maintained. Thetapesprings arecutfrom 25.4-mm wide,0.1-mm thick,transverse radius15mm,"Contractor Grade" steeltapemeasure, supplied bySearsRoebuck andCo. TSRhingeswithtwooreventhreestacked tapesprings alsoworkwell,andboththedeployment and locking moments increase roughly proportionally, butnotethatthehingedescribed inthispaperismade fromasinglepairoftapesprings. Deployed Stiffness Inordertoestimate thenatural frequency andstiffness ofastructure utilizing TSRhinges, thelinear stiffnesses (Kxx,KxxandKzz)andtherotational stiffnesses (Txx,TxzandTzz)ofthehingearerequired; the directions ofx,y,andzaredefined inFigure6.Thestiffnesses ofthecomponent partsofahingewere bothmeasured andpredicted withvarious linearelasticanalytical andfiniteelement models. Asummary ofallthetestresultsandanalytical predictions isgiveninTable1.Thetestresultsfortheoverallstiffness ofthehingeineachcomponent direction canbeseeninFigure7. NASA/C P--2002-211506 40
Figure6.TSRhinge Table1.Summary ofStiffness Results Experiments Direction Rolamite Kxx 1768 Kyy Kz_31.9 115 T_ 40 myy T_ 36OTape Total 5400 7223 236 221 10134 29 75 228 480a 48O 782Predictions Rolamite Tape Total Units 1272 12172 13442 N/mm 47 702 749 N/mm 72 33 106 N/mm 45 54 99 Nm/rad 0 475 614 Nm/rad 779 453 1232 Nm/rad aThisparticular valuewasmeasured onahingewithd=4.5mm. Analytical predictions forthestiffnesses wereobtained usingtheexpressions givenbelow.Notethateach equation contains twoseparate terms, whichcorrespond totherolamite andtape-spring stiffness contributions, respectively. Thedefinition andnumerical valuegiventoeachtermintheseexpressions arelistedinTable2.Thefiniteelement predictions wereslightly moreaccurate, butarenotpresented herebecause theyaremuchhardertoobtainandcannotbereadilytransferred tootherhingedesigns. Theaxialstiffness, Kxx,waspredicted bymodelling therolamite (subscript r)partofthehingewithtwo equivalent beamswhoseaxialstiffness takesintoaccount thecompliance ofthehertzian contact between thepairsofwheels (Johnson, 1987);thetape-springs (subscript t)werealsomodelled astwobeams:  xx;-- + In 1+-- 2brdrEr_wEr Or L HereQristhecontact force,whosevaluedoesnotsignificantly affecttheresultsintherangeconsidered. NASA/CP--2002-211506 41
4OO 300 200 _100v _o0 LLKxxstiffnessJs s s s F i ss ss I ss -100i/-200: -300 i -400tJ ! i J 4 -0.25-0.2-0.15-0.1-0.05 00.050.10.15 Displacement (mm)250, 150 1001 _o_ -50[- _ -100[ i -150! -. -20O_ -- -250:........................... -1.5 -1 -0.5 0 0.5 1 1.5 Displacement (mm) 2OO 150 100 50zv _o,? -5O -100 -150I z Sti"nessI -200' ........ 1.5 1 0.5 0 0.5 1 1.5 Displacement (mm)20........._---,, .....,.--_....._....... Txxstiffness15__ _1oi._.,_. , -0.15-0.1-0.05 00.050.10.150.20.25 Rotation (rad) E -4 i i-8 -I -12 Eo -16 i -20 -24' -0.07-0.06-0.05-0.04-0.03-0.02-0.01 00.0t Rotation (rad/0....... _ -r.... : -4-2[Tzzstiffness I, -6 zE_8 _-10-12 -14 -16 -18 -20'-............................ -0.05 -0.04 -0.03 -0.02 -0.01 Rotation (rad) Figure7:Hingeresponse insixstiffness tests. NASA/CP--2002-211506 42
Thein-plane shearstiffness, Kyy,andtheoutofplaneshearstiffness, Kzz,werepredicted byconsidering therolamite andtape-spring partsofthehingeastwoseparate built-inbeams. Hence: Kyy=2Erbrd3rL_ +212EtlZZL3 12EtlyyKzz=2--Erb3dr +2-- L3 L3 Thetorsional stiffness, Txx,waspredicted byconsidering theenddeflections, inthez-direction forthe rolamite andthey-direction forthetapes,induced byaunittorsional rotation ofthehinge.Eachdeflection causes associated shearforcesintheequivalent beamsdefined above,fromwhichtherequired twisting moment is: Txx=2Erb3drh2 12h2Etlzz 2L3+22L3 Thein-plane bending stiffness, Tyy,waspredicted byconsidering thataunitrotation aboutycauses extension andcompression ofthetape-springs. Therolamite haszerostiffness onitsown,asthisisthe direction offreerotation, butitprovides anelasticconstraint forthetapesprings actingasasinglebeam, whichleadstoanadditional stiffness contribution. HenceTyyis: L 4I4_rwE_ )(__)-1] -1AtEts2 Tyy=2brdrEr {- In 1+ d2+----wE_ Qr 2L Theout-of-plane bending stiffness, Tzz,waspredicted byconsidering thataunitrotation aboutzputsa pairofrolamite wheels intotension andtheotherpairintocompression, whilstthetape-spring was considered asabuilt-inbeamsubject toanendrotation. Theresulting expression is:: d2[L 4(4_rwE_ )]-1 Tzz=-_-2brdrE_ r4- In 1+2stlzzwE_ Qr L Moment-Rotation Properties Themoment-rotation relationship ofTSRhingesisrequired inordertomodelthedynamic deployment of anysystem utilizing thesehinges. SeffenandPellegrino (1999)havedeveloped analytical expressions for thekeyparameters determining themoment-rotation behavior oftape-springs. Fromtheseexpressions, the"steady-state" deployment moment ofaTSRhingewithasinglepairoftapesprings isgivenby: M-Ett3a 6(1-v2) Where tandvarethethickness andPoisson's ratio,respectively, ofatapespringandatheangle subtended byitscross-section, inradians. Notethatthisexpression doesnotinclude theeffects of contact between thetwotapesprings andoftheconstraint imposed bytherolamite wheels; hencethe actualdeployment moment isusually largerandalsonon-uniform. Greater accuracy requires afullynon-linear numerical formulation tobeadopted. Hence, aquasi-static simulation ofthefoldingofaTSRhingewasmadewiththefinite-element package Abaqus (Hibbitetal. 2000).Thepurpose oftheFEmodelling wastoaccurately simulate thesnap-through deformation ofthe tapesprings andtoderivethefullbending moment-rotation relationship ofthehinge,including the buckling moment. NASA/C Pm2002-211506 43
Table2:TermsusedinAnalytical Expressions. Term At br d dr Er Er* Et h lyy Izz L Qr r ,.s wDefinition Value Units Cross-sectional areaoftape Widthofequivalent rolamite beam(zdirection) Center-to-center distance between rolamite wheels andtapes Depthofequivalent rolamite beam(ydirection) Young's modulus ofrolamite wheels (Delrin) Contact modulus --Er/2(1-v2) Young's modulus oftape(steel) Widthofrolamite hinge 2n_moment ofareaforonetape(y-axis) 2n_moment ofareaforonetape(z-axis) Lengthoftapeandequivalent rolamite beam Contact forcebetween rolamite wheels Radiusofrolamite wheels Separation oftapeneutralaxes Widthofrolamite contact area2.5 10 11 8 3.1 1.6 210 35 95 95 88 20-800 28.1 12.5 10mm mm mm mm kN/mm2 kN/mm2 kN/mm2 mm mm4 mm4 4 mm N mm mm mm Therefore, afull3Dmodelwassetup,Figure8.Thetapesprings weremodelled using50x12,4-node doublycurvedgeneral-purpose shellelements (s4)foreachspring.Theseelements weregenerated with logarithmic biasalongthetapelengthsothatthefinermeshisconcentrated inthemiddleofthetapes, wheremostofthedeformation beforethesnapandthecontact between thetapestakeplace. f --.- J / \ / \ / \,','e_ ,.a........ :::_-:::::::-: :: '';'_:•:: ',', ', _- ^/'/,,,,,,ji,rii'it.Ii'.l]lh'lll.!lliiii.iii:;:.,:_._.i_. -.,-.,i..,.,i,_.:,,:,,:,,,-,.'..nI ___.a_=./...... _'.......... _,-_._,4_. _'S •, I'-' '_ .__ I /\ Figure8.Finiteelement modelofTSRhinge TherollingpartoftheTSRhingewasmodelled asasetoftworigidarms,usingrigidbeamelements. The armsconnect thecenters ofrotation, BandC,tonodesAandD,andmulti-point constraints weredefined between thesenodesandthenodesattheendofthetapes.NodesBandCarefixedinalldirections and canonlyrotatearound anaxisparallel toy.Inordertosimulate thehingedeformation, equalclockwise andanti-clockwise rotations ofupto90degwereapplied tonodesBandC,respectively. Contact between thetapeswasmodelled asasurface tosurface contact. TheRikssolution procedure wasinitially chosen, inordertotracethecomplete equilibrium pathofthe hinge,including unstable parts. However, therewereproblems withconvergence afterthefirstsnapthrough point,hencearotation controlled solution procedure hadtobeadopted instead. The"Stabilize" function available inAbaqus wasused,whichautomatically switches toapseudo-dynamic simulation whenaninstability isdetected. Thismethod gavethedesired convergence, butitshould benotedthat unstable partsoftheresponse cannotbepredicted bythismethod. Thefiniteelement predictions werevalidated against experimental resultsobtained fromanESHTorsion Machine. Figure9(a)showsthetestingarrangement; theheadofthetestingmachine applies arotation to thecenterofoneoftherolamite wheels, whilstmeasuring themoment, andthecenteroftheotherwheel isheldinabearing coaxial withthewheel.Themeasured response ofthehingeduringfolding and unfolding hasbeenplotted inFigure9(b)alongwiththeFEpredictions. Themeasured peakbuckling NASA/CP--2002-211506 44
moment---notshowninthefigure---was13Nm,whichcompareswithapredictionof19Nm.However, duringdeployment themaximum moment was1Nm,muchlowerthanthe12Nmpredicted bytheFE simulation. (a) (b) 8oo 6o0 ,,-.,. E zE400v .,,w., t" _20o0 -200 0............:  •.:.... ,.....i.......\............_.;......:....:\.:..... /:FEPrediction Deployment k.}..:....:....:......:....... 4080120160200 Rotation(deg) Figure9.Moment-rotation testset-upandresults Damping Damping canhavetwofunctions inahinge;toslowthetimerequired fordeployment andtoreduce the shockarisingfromlocking. Inordertotesttheeffectiveness ofdifferent damping methods, amock-up ofa deployable panelsystem onasatellite wasmadefromtwoidentical aluminium honeycomb panels. Panel 1isattached toarigidbase;panel2isconnected topanel1bytwoidentical TSRhinges. Eachpanelhas dimensions of1mby0.5m,andweighs 1.67kgincluding hingesandhingefittings. Thewholesetupis showninFigure10. Deployment testswereconducted forthreedifferent damping configurations, asshownbelow: 1.Noadditional damping. 2.TwobrownOasisfoamblocksplaced between thetwopanels, asshown inFigure11(a),to absorbenergy bycrushing thefoamduringthefinalapproach phase. 3.Singlelayerof3M434sounddamping tapeapplied tobothsidesofeachtapespring,asshown inFigure1l(b). Deployment Tests Thedeployment ofthepanelwasrecorded usingaKodakEKTAPRO HS4540high-speed videocamera anddigitized toobtainrotation vs.timegraphs. Theresults canbeseeninFigure 12forcase1 (undamped) andcase3.Case2givesexactlythesameresultsascase1,asthefoamdoesnotaffectthe large-scale rotation behavior. Itcanbeseenthatthedamping layersmakeanegligible difference tothe rotation vs.timeresponse. Amodelofthedeployment ofthepanelwasmadeusingPro/Mechanica Motion (Parametric Technology Corp.,2001),arigid-body dynamic analysis program. Theloadsapplied tothismodelwerethosefound fromtheAbaqus modelofthehinge,takingintoaccount thedirection ofmotionandthestate---i.e.,fully unfolded ornot---ofthehinge. NASA/CP--2002-211506 45
Figure 10.Deployable panel (a) (b) Figure11. Damping foamanddamping tape 180............... , 160 140 120  undamped 100 g -_80 damped "_ _'40 20. 000.20.40.60.811.21.41.61.8 Time(s) Figure12.Deployment ofpanelwithdamped andundamped hinges NASA/CP--2002-211506 46