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.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・Iflheradiiofthepitchcirclesareaandb,thedistancebetweenthegearshaftsisa+b.Intheactionofthegears,thepitchcirclesrollononeanotherwithoutslipping.Toensurethis,thegearteethmusthaveapropershapesothatwhenthedrivinggearmovesuniformly,sodoesthedrivengear.Thismeansthatthelineofpressure,normaltothetoothprofilesincontact,passesthroughthepitchpoint.Then,thetransmissionofpowerwillbefreeofvibrationandhighspeedsarepossible・Wewon'ttalkfurtheraboutgearteethhere・havingstatedthisfundamentalprincipleofgearing・
IfagearofpitchradiusahasNteeth,thenthedistancebetweencorrespondingpointsonsuccessiveteethwillbe2jra/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.Ifoneofthegearsisintenuil(havingteethonitsinnerrim),thenthevelocityratioispositive,sincethegearswillrotateinthesamedirection.
Theusualinvolutegearshaveatoothshapethatistolerantofvariationsinthedistancebetweentheaxes,sothegearswillrunsmoothlyifthisdistanceisnotquitecorrect.Thevelocityratioofthegearsdoesnotdependontheexactspacingoftheaxes,butisfixedbythenumberofteeth・orwhatisthesamething,bythepitchdiameters・Slightlyincreasingthedistanceaboveitstheoreticalvaluemakesthegearsruneasier,sincetheclearancesarelarger.Ontheotherhand,backlashisalsoincreased,whichmaynotbedesiredinsomeapplications・
Anepicyclicgeartrainhasgearshaftsmountedonamovingarmorcarrierthatcanrotateabouttheaxis,aswellasthegearsthemselves・Thearmcanbeaninputelement,oranoutputelement,andcanbeheldfixedorallowedtorotate・Theoutergearistheringgearorannulus.Asimplebutverycommonepicyclictrainisthesun-and-planetepicyclictrain,showninthefigureattheleftThreeplanetarygearsareusedformechanicalreasons;theymaybeconsideredasoneindescribingtheactionofthegearing・Thesungear,thearm・ortheringgearmaybeinputoroutputlinks.
Ifthearmisfixed,sothatitcannotrotate,wehaveasimpletrainofthreegears.Then・nz/n】=・N1/N2,ns/nz=+N2/N3.andnVni=-N1/N3.Thisisverysimple,andshouldnotbeconfusing.Ifthearmisallowedtomove,figuringoutthevelocityratiostaxesthehumanintellect.Attemptingthiswillshowthetmthofthestatement;ifyoucanmanageit,youdeservepraiseandfame.ItisbynomeansimpossibleJustinvoved・Howeverthereisaveryeasywaytogetthedesiredresult・First,justconsiderthegeartrainlocked,soitmovesasarigidbody,armandall.Allthreegearsandthearmthenhaveaunityvelocityratio.
Thetrickisthatanymotionofthegeartraincancarriedoutbyfirstholdingthearmfixedandrotatingthegearsrelativetooneanother,andthenlockingthetrainandrotatingitaboutthefixedaxis.Thenetmotionisthesumordifferenceofmultiplesofthetwoseparatemotionsthatsatisfiestheconditionsoftheproblem(usuallythatoneelementisheldfixed).Tocarryoutthisprogram,constructatableinwhichtheangularvelocitiesofthegearsandarmarelistedforeach,foreachofthetwocases.Thelockedtraingives1,1,1,1forarm,gearI,gear2andgear3.Armfixedgives0.1,-N1/N2,-N1/N3.Supposewewantthevelocityrationbetweenthearmandgear1・whengear3isfixed・Multiplythefirstrowbyaconstantsothatwhenitisaddedtothesecondrow,thevelocityofgear3willbezero・ThisconstantisN】/N3・Now.doingonedisplacementandthentheothercorrespondstoaddingthetworows.WefindN1/N3,1+N1/N3,N1/N3-Ni/N2.
Thefirstnumberisthearmvelocity,thesecondthevelocityofgear1,sothevelocityratiobetweenthemisNi/(Ni+N3),aftermultiplyingthroughbyN3.TliisisthevelocityratioweneedfortheTamiyagearbox,wheretheringgeardoesnotrotate,thesungearistheinput,andthearmistheoutput.Theprocedureisgeneral,however.andwillworkforanyepicyclictrain.
OneoftheTamiyaplanetarygearassemblieshasN1=N2=16,N3=48,whiletheotherhasNi=12,N2=1&N3=48.Becausetheplanetarygearsmustfitbetweenthesunandringgears.theconditionN3=Ni+2N?
mustbesatisfied.Itisindeedsatisfiedforthenumbersofteethgiven.Thevelocityratioofthefirstsetwillbe16/(48+16)=1/4.Thevelocityratioofthesecondsetwillbe12/(48+12)=1/5.Bothratiosareasadvertised・Notethatthesungearandarmwillrotateinthesamedirection・
Thebestgeneralmethodforsolvingepicyclicgeartrainsisthetabularmethod,sinceitdoesnotcontainhiddenassumptionslikeformulas,norrequiretheworkofthevectormethod.Thefirststepistoisolatetheepicyclictrain,separatingthegeartrainsforinputsandoutputsfromit.Findtheinputspeedsorturns,usingtheinputgeartrains・Thereare,ingeneraltwoinputs,oneofwhichmaybezeroinsimpleproblems.Nowpreparetworowsofthetableofturnsorangularvelocities・Thefirstrowcorrespondstorotatingaroundtheepicyclicaxisonce・andconsistsofalll's.Writedownthesecondrowassumingthatthearmvelocityiszero,usingtheknowngearratios.Therowthatyouwantisalinearcombinationofthesetworows,withunknownmultipliersxandy.Summingtheentriesfortheinputgearsgivestwosimultaneouslinearequationsforxandyintermsoftheknowninputvelocities・Nowthesumofthetworowsmultipliedbytheirrespectivemultipliersgivesthespeedsofallthegearsofinterest.Finally,findtheoutputspeedwiththeaidoftheoutputgeartrain.Becarefultogetthedirectionsofrotationcorrect,withrespecttoadirectiontakenaspositive・
TheTamiyaGearboxKit
Thepartsarebestcutfromthesprueswithaflush-cutterofthetypeusedinelectronics・TheverysmallbitsofplasticremainingcanthenberemovedwithasharpX-actoknife・Carefullyremoveallexcessplastic,astheinstnictionssay.
Readtheinstructionscarefullyandmakesurethatthingsaretherightwayupandinthecorrectrelativepositons.Thegearboxunitsgotogethereasilywithlightpressure・Notethatthebrownonesmustgotogetherinthecorrectrelativeorientation・The4mmwashersaretheonesofwhichtwoaresupplied,andthereisalsoafull-sizedrawingofoneintheinstnictions・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・Nowputthemotorterminalsinaverticalcolunin.andpressonthemotorclamp・
Thereverseoftheinstnictionsshowhowtoattachthedrivearmandgivessomehintsonuseofthegearbox・Igotanextraspringpin.andtwoextra3mmwashers.Ifyouhavesomesmallwashers,theycanbeusedonthemachinescrewsholdingthegearboxtogether.Enoughtorqueisproducedattheoutputtodamagethings(upto6kg-cm),s
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