行星齿轮减速器中英文翻译英文资料.docx

行星齿轮减速器中英文翻译英文资料.docx

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行星齿轮减速器中英文翻译英文资料

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英文原文

PlanetaryGears

Introduction

TheTamiyaplanetarygearboxisdrivenbyasmallDCmotorthatrunsatabout10,500rpmon3.0VDCanddrawsabout1.0A.Themaximumspeedratiois1:

400,givinganoutputspeedofabout26rpm.Fourplanetarystagesaresuppliedwiththegearbox,two1:

4andtwo1:

5,andanycombinationcanbeselected.Notonlyisthisagooddriveforsmallmechanicalapplications,itprovidesanexcellentreviewofepicyclegeartrains.Thegearboxisaverywell-designedplastickitthatcanbeassembledinaboutanhourwithveryfewtools.ThesourceforthekitisgivenintheReferences.

Let'sbeginbyreviewingthefundamentalsofgearing,andthetrickofanalyzingepicyclicgeartrains.

EpicyclicGearTrains

Apairofspurgearsisrepresentedinthediagrambytheirpitchcircles,whicharetangentatthepitchpointP.Themeshinggearteethextendbeyondthepitchcirclebytheaddendum,andthespacesbetweenthemhaveadepthbeneaththepitchcirclebythededendum.Iftheradiiofthepitchcirclesareaandb,thedistancebetweenthegearshaftsisa+b.Intheactionofthegears,thepitchcirclesrollononeanotherwithoutslipping.Toensurethis,thegearteethmusthaveapropershapesothatwhenthedrivinggearmovesuniformly,sodoesthedrivengear.Thismeansthatthelineofpressure,normaltothetoothprofilesincontact,passesthroughthepitchpoint.Then,thetransmissionofpowerwillbefreeofvibrationandhighspeedsarepossible.Wewon'ttalkfurtheraboutgearteethhere,havingstatedthisfundamentalprincipleofgearing.

IfagearofpitchradiusahasNteeth,thenthedistancebetweencorrespondingpointsonsuccessiveteethwillbe2πa/N,aquantitycalledthecircularpitch.Iftwogearsaretomate,thecircularpitchesmustbethesame.Thepitchisusuallystatedastheration2a/N,calledthediametralpitch.Ifyoucountthenumberofteethonagear,thenthepitchdiameteristhenumberofteethtimesthediametralpitch.Ifyouknowthepitchdiametersoftwogears,thenyoucanspecifythedistancebetweentheshafts.

Thevelocityratiorofapairofgearsistheratiooftheangularvelocityofthedrivengeartotheangularvelocityofthedrivinggear.Bytheconditionofrollingofpitchcircles,r=-a/b=-N1/N2,sincepitchradiiareproportionaltothenumberofteeth.Theangularvelocitynofthegearsmaybegiveninradians/sec,revolutionsperminute（rpm）,oranysimilarunits.Ifwetakeonedirectionofrotationaspositive,thentheotherdirectionisnegative.Thisisthereasonforthe（-）signintheaboveexpression.Ifoneofthegearsisinternal（havingteethonitsinnerrim）,thenthevelocityratioispositive,sincethegearswillrotateinthesamedirection.

Theusualinvolutegearshaveatoothshapethatistolerantofvariationsinthedistancebetweentheaxes,sothegearswillrunsmoothlyifthisdistanceisnotquitecorrect.Thevelocityratioofthegearsdoesnotdependontheexactspacingoftheaxes,butisfixedbythenumberofteeth,orwhatisthesamething,bythepitchdiameters.Slightlyincreasingthedistanceaboveitstheoreticalvaluemakesthegearsruneasier,sincetheclearancesarelarger.Ontheotherhand,backlashisalsoincreased,whichmaynotbedesiredinsomeapplications.

Anepicyclicgeartrainhasgearshaftsmountedonamovingarmorcarrierthatcanrotateabouttheaxis,aswellasthegearsthemselves.Thearmcanbeaninputelement,oranoutputelement,andcanbeheldfixedorallowedtorotate.Theoutergearistheringgearorannulus.Asimplebutverycommonepicyclictrainisthesun-and-planetepicyclictrain,showninthefigureattheleft.Threeplanetarygearsareusedformechanicalreasons;theymaybeconsideredasoneindescribingtheactionofthegearing.Thesungear,thearm,ortheringgearmaybeinputoroutputlinks.

Ifthearmisfixed,sothatitcannotrotate,wehaveasimpletrainofthreegears.Then,n2/n1=-N1/N2,n3/n2=+N2/N3,andn3/n1=-N1/N3.Thisisverysimple,andshouldnotbeconfusing.Ifthearmisallowedtomove,figuringoutthevelocityratiostaxesthehumanintellect.Attemptingthiswillshowthetruthofthestatement;ifyoucanmanageit,youdeservepraiseandfame.Itisbynomeansimpossible,justinvoved.However,thereisaveryeasywaytogetthedesiredresult.First,justconsiderthegeartrainlocked,soitmovesasarigidbody,armandall.Allthreegearsandthearmthenhaveaunityvelocityratio.

Thetrickisthatanymotionofthegeartraincancarriedoutbyfirstholdingthearmfixedandrotatingthegearsrelativetooneanother,andthenlockingthetrainandrotatingitaboutthefixedaxis.Thenetmotionisthesumordifferenceofmultiplesofthetwoseparatemotionsthatsatisfiestheconditionsoftheproblem（usuallythatoneelementisheldfixed）.Tocarryoutthisprogram,constructatableinwhichtheangularvelocitiesofthegearsandarmarelistedforeach,foreachofthetwocases.Thelockedtraingives1,1,1,1forarm,gear1,gear2andgear3.Armfixedgives0,1,-N1/N2,-N1/N3.Supposewewantthevelocityrationbetweenthearmandgear1,whengear3isfixed.Multiplythefirstrowbyaconstantsothatwhenitisaddedtothesecondrow,thevelocityofgear3willbezero.ThisconstantisN1/N3.Now,doingonedisplacementandthentheothercorrespondstoaddingthetworows.WefindN1/N3,1+N1/N3,N1/N3-N1/N2.

Thefirstnumberisthearmvelocity,thesecondthevelocityofgear1,sothevelocityratiobetweenthemisN1/（N1+N3）,aftermultiplyingthroughbyN3.ThisisthevelocityratioweneedfortheTamiyagearbox,wheretheringgeardoesnotrotate,thesungearistheinput,andthearmistheoutput.Theprocedureisgeneral,however,andwillworkforanyepicyclictrain.

OneoftheTamiyaplanetarygearassemblieshasN1=N2=16,N3=48,whiletheotherhasN1=12,N2=18,N3=48.Becausetheplanetarygearsmustfitbetweenthesunandringgears,theconditionN3=N1+2N2mustbesatisfied.Itisindeedsatisfiedforthenumbersofteethgiven.Thevelocityratioofthefirstsetwillbe16/（48+16）=1/4.Thevelocityratioofthesecondsetwillbe12/（48+12）=1/5.Bothratiosareasadvertised.Notethatthesungearandarmwillrotateinthesamedirection.

Thebestgeneralmethodforsolvingepicyclicgeartrainsisthetabularmethod,sinceitdoesnotcontainhiddenassumptionslikeformulas,norrequiretheworkofthevectormethod.Thefirststepistoisolatetheepicyclictrain,separatingthegeartrainsforinputsandoutputsfromit.Findtheinputspeedsorturns,usingtheinputgeartrains.Thereare,ingeneral,twoinputs,oneofwhichmaybezeroinsimpleproblems.Nowpreparetworowsofthetableofturnsorangularvelocities.Thefirstrowcorrespondstorotatingaroundtheepicyclicaxisonce,andconsistsofall1's.Writedownthesecondrowassumingthatthearmvelocityiszero,usingtheknowngearratios.Therowthatyouwantisalinearcombinationofthesetworows,withunknownmultipliersxandy.Summingtheentriesfortheinputgearsgivestwosimultaneouslinearequationsforxandyintermsoftheknowninputvelocities.Nowthesumofthetworowsmultipliedbytheirrespectivemultipliersgivesthespeedsofallthegearsofinterest.Finally,findtheoutputspeedwiththeaidoftheoutputgeartrain.Becarefultogetthedirectionsofrotationcorrect,withrespecttoadirectiontakenaspositive.

TheTamiyaGearboxKit

Thepartsarebestcutfromthesprueswithaflush-cutterofthetypeusedinelectronics.TheverysmallbitsofplasticremainingcanthenberemovedwithasharpX-actoknife.Carefullyremoveallexcessplastic,astheinstructionssay.

Readtheinstructionscarefullyandmakesurethatthingsaretherightwayupandinthecorrectrelativepositons.Thegearboxunitsgotogethereasilywithlightpressure.Notethatthebrownonesmustgotogetherinthecorrectrelativeorientation.The4mmwashersaretheonesofwhichtwoaresupplied,andthereisalsoafull-sizedrawingofoneintheinstructions.Thesmallerwasherswillnotfitovertheshaft,anyway.Theoutputshaftismetal.Uselargerlong-noseplierstopresstheE-ringintopositioninitsgrooveinfrontofthewasher.Thereisapictureshowinghowtodothis.TherewasanextraE-ringinmykit.Thethreeprongsfitintothecarriersfortheplanetarygears,andaredrivenbythem.

Nowstackupthegearboxunitsasdesired.Iusedallfour,beingsuretoputa1:

5unitontheendnexttothemotor.Therefore,Ineededthelongscrews.Presstheorangesungearforthelast1:

5unitfirmlyonthemotorshaftasfarasitwillgo.Ifitisnotwell-seated,themotorclipwillnotclose.Itmightbeagoodideatoputsomelubricantonthisgearfromthetubeincludedwiththekit.Ifyouuseadifferentlubricant,testitfirstonapieceofplasticfromthekittomakesurethatitiscompatible.Adrygraphitelubricantwouldalsoworkquitewell.Thisshouldspreadlubricantonallpartsofthelastunit,whichistheonesubjecttothehighestspeeds.Putthemotorinplace,gentlybutfirmly,wigglingitsothatthesungearmeshes.Ifthesungearisnotmeshed,themotorclipwillnotclose.Nowputthemotorterminalsinaverticalcolumn,andpressonthemotorclamp.

Thereverseoftheinstructionsshowhowtoattachthedrivearmandgivessomehintsonuseofthegearbox.Igotanextraspringpin,andtwoextra3mmwashers.Ifyouhavesomesmallwashers,theycanbeusedonthemachinescrewsholdingthegearboxtogether.Enoughtorqueisproducedattheoutputtodamagethings（upto6kg-c