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翻译部分英文原文GearmechanismsGearmechanismsareusedfortransmittingmotionandpowerfromoneshafttoanotherbymeansofthepositivecontactofsuccessivelyengagingteeth.Inabout2,600B.C.,ChineseareknowntohaveusedachariotincorporatingacomplexseriesofgearslikethoseillustratedinFig.2.7.Aristotle,inthefourthcenturyB.C.wroteofgearsasiftheywerecommonplace.InthefifteenthcenturyA.D.,LeonardodaVincidesignedamultitudeofdevicesincorporatingmanykindsofgears.Incomparisonwithbeltandchaindrives,geardrivesaremorecompact,canoperateathighspeeds,andcanbeusedwhereprecisetimingisdesired.Thetransmissionefficiencyofgearsisashighas98percent.Ontheotherhand,gearsareusuallymorecostlyandrequiremoreattentiontolubrication,cleanliness,shaftalignment,etc.,andusuallyoperateinaclosedcasewithprovisionforproperlubrication.Gearmechanismscanbedividedintoplanargearmechanismsandspatialgearmechanisms.Planargearmechanismsareusedtotransmitmotionandspatialgearmechanisms.Planargearmechanismsareusedtotransmitmotionandpowerbetweenparallelshafts,andspatialgearmechanismsbetweennonparallelshafts.Typesofgears1Spurgears.ThespurgearhasacylindricalpitchsurfaceandhasstraightteethparalleltoitsaxisasshowninFig.2.8.Theyareusedtotransmitmotionandpowerbetweenparallelshafts.Thetoothsurfacesofspurgearscontactonastraightlineparalleltotheaxesofgears.Thisimpliesthattoothprofilesgointoandoutofcontactalongthewholefacewidthatthesametime.Thiswillthereforeresultinthesuddenloadingandsuddenunloadingonteethasprofilesgointoandoutofcontact.Asaresult,vibrationandnoiseareproduced.2Helicalgears.ThesegearshavetheirtoothelementsatanangleorhelixtotheaxisofthegearFig.2.9.Thetoothsurfacesoftwoengaginghelicalgearsinnplanargearmechanismscontactonastraightlineinclinedtotheaxesofthegears.Thelengthofthecontactlinechangesgraduallyfromzerotomaximumandthenfrommaximumtozero.Theloadingandunloadingoftheteethbecomegradualandsmooth.HelicalgearsmaybeusedtotransmitmotionandpowerbetweenparallelshaftsFig.2.9aorshaftsatanangletoeachotherFig.2.9d.AherringbonegearFig.2.9cisequivalenttoarighthandandalefthandhelicalgearplacedsidebyside.Becauseoftheangleofthetooth,helicalgearscreateconsiderablesidethrustontheshaft.Aherringbonegearcorrectsthisthrustbyneutralizingit,allowingtheuseofasmallthrustbearinginsteadofalargeoneandperhapseliminatingonealtogether.Oftenacentralgrooveismadearoundthegearforeaseinmachining.3Bevelgars.Theteethofabevelgeararedistributedonthefrustumofacone.Thecorrespondingpitchcylinderincylindricalgearsbecomespitchcone.Thedimensionsofteethondifferenttransverseplanesaredifferent.Forconvenience,parametersanddimensionsatthelargeendaretakentobestandardvalues.Bevelgearsareusedtoconnectshaftswhicharenotparalleltoeachother.Usuallytheshaftsare90deg.toeachother,butmaybemoreorlessthan90deg.Thetwomatinggearsmayhavethesamenumberofteethforthepurposeofchangingdirectionofmotiononly,ortheymayhaveadifferentnumberofteethforthepurposeofchangingbothspeedanddirection.Thetoothelementsmaybestraightorspiral,sothatwehaveplainandspiralbevelgears.Hypoidcomesfromthewordhyperboloidandindicatesthesurfaceonwhichthetoothfacelies.Hypoidgearsaresimilartobevelgears,butthetwoshaftsdonotintersect.Theteetharecurved,andbecauseofthenonintersectionoftheshafts,bearingscanbeplacedoneachsideofeachgear.Theprincipaluseofthidtypeofgearisinautomobilerearendsforthepurposeofloweringthedriveshaft,andthusthecarfloor.4Wormandwormgears.Wormgeardrivesareusedtotransmitmotionandowerbetweennonintersectingandnonparallelshafts,usuallycrossingatarightangle,especiallywhereitisdesiredtoobtainhighgearreductioninalimitedspace.Wormsareakindofscrew,usuallyrighthandedforconvenienceofcutting,orlefthandeditnecessary.Accordingtotheenvelopingtype,wormscanbedividedintosingleanddoubleenveloping.Wormsareusuallydriverstoreducethespeed.Ifnotselflocking,awormgearcanalsobethedriverinasocalledbackdrivingmechanismtoincreasethespeed.Twothingscharacterizewormgearingalargevelocityratios,andbhighslidingvelocities.Thelattermeansthatheatgenerationandpowertransmissionefficiencyareofgreaterconcernthanwithothertypesofgears.5Racks.Arackisagearwithaninfiniteradius,oragearwithitsperimeterstretchedoutintoastraightline.Itisusedtochangereciprocatingmotiontorotarymotionorviceversa.Alatherackandpinionisgoodexampleofthismechanism.GeometryofgeartoothThebasicrequirementofgeartoothgeometryistheprovisionofangularvelocityrationsthatareexactlyconstant.Ofcourse,manufacturinginaccuraciesandtoothdeflectionswellcauseslightdeviationsinvelocityratiobutacceptabletoothprofilesarebasedontheoreticalcurvesthatmeetthiscriterion.Theactionofapairofgearteethsatisfyingthisrequirementistermedconjugategeartoothaction,andisillustratedinFig.2.12.Thebasiclawofconjugategeartoothactionstatesthatasthegearsrotate,thecommonnormaltothesurfacesatthepointofcontactmustalwaysintersectthelineofcentersatthesamepointPcalledthepitchpoint.Thelawofconjugategeartoothcanbesatisfiedbyvarioustoothshapes,buttheonlyoneofcurrentimportanceistheinvolute,or,moreprecisely,theinvoluteofthecircle.Itslastimportantcompetitorwasthecycloidalshape,usedinthegearsofModelTFordtransmissions.Aninvoluteofthecircleisthecurvegeneratedbyanypointonatautthreadasitunwindsfromacircle,calledthebasecircle.ThegenerationoftwoinvolutesisshowninFig.2.13.Thedottedlinesshowhowthesecouldcorrespondtotheouterportionoftherightsidesofadjacentgearteeth.Correspondingly,involutesgeneratedbyunwindingathreadwrappedcounterclockwisearoundthebasecirclewouldfortheouterportionsoftheleftsidesoftheteeth.Notethatateverypoint,theinvoluteisperpendiculartothetautthread,sincetheinvoluteisacirculararcwitheverincreasingradius,andaradiusisalwaysperpendiculartoitscirculararc.Itisimportanttonotethataninvolutecanbedevelopedasfarasdesiredoutsidethebasecircle,butaninvolutecannotexistinsideitsbasecircle.Letusnowdevelopamatingpairofinvolutegearteethinthreestepsfrictiondrive,beltdrive,andfinally,involutegeartoothdrive.Figure2.14showstwopitchcircles.Imaginethattheyrepresenttwocylinderspressedtogether.Ifslippagedoesnotoccur,rotationofonecylinderpitchcirclewillcauserotationoftheotheratanangularvelocityratioinverselyproportionaltotheirdiameters.Inanypairofmatinggears,thesmallerofthetwoiscalledthepinionandthelargeronethegear.Thetermgearisusedinageneralsensetoindicateeitherofthemembers,andalsoinaspecificsensetoindicatethelargerofthetwo.Usingsubscriptspandgtodenotepinionandgear,respectively.Inordertotransmitmoretorquethanispossiblewithfrictiondrivealone,wenowaddabeltdriverunningbetweenpulleysrepresentingthebasecircles,asinFig2.15.Ifthepinionisturnedcounterclockwiseafewdegrees,thebeltwillcausethegeartorotateinaccordancewithcorrectvelocityratio.Ingearparlance,angleΦiscalledthepressureangle.Fromsimilartriangles,thebasecircleshavethesameratioasthepitchthus,thevelocityratioprovidedbythefrictionandbeltdrivesarethesame.InFig.2.16thebeltiscutatpointc,andthetwoendsareusedtogenerateinvoluteprofilesdeandfgforthepinionandgear,respectively.ItshouldnowbeclearwhyΦiscalledthepressureangleneglectingslidingfriction,theforceofoneinvolutetoothpushingagainsttheotherisalwaysatanangleequaltothepressureangle.AcomparisonofFig.2.16andFig.2.12showsthattheinvoluteprofilesdoindeedsatisfythefundamentallawofconjugategeartoothaction.Incidentally,theinvoluteistheonlygeometricprofilesatisfyingthislawthatmaintainsaconstantpressureangleasthegearsrotate.Noteespeciallythatconjugateinvoluteactioncantakeplaceonlyoutsideofbothbasecircles.NomenclatureofspurgearThenomenclatureofspurgearFig.2.17ismostlyapplicabletoallothertypeofgears.Thediameterofeachoftheoriginalrollingcylindersoftwomatinggearsiscalledthepitchdiameter,andthecylinderssectionaloutlineiscalledthepitchcircle.Thepitchcirclesaretangenttoeachotheratpitchpoint.Thecirclefromwhichtheinvoluteisgeneratediscalledthebasecircle.Thecirclewherethetopsoftheteethlieiscalledthededendumcircle.Similarly,thecirclewheretherootsoftheteethlieiscalledthededendumcircle.Betweentheaddendumcircleandthededendumcircle,thereisanimportantcirclewhichiscalledthereferencecircle.Parametersonthereferencecirclearestandardized.Themodulemofagearisintroducedonthereferencecircleasabasicparameter,whichisdefinedasmp/π.Sizesoftheteethandgearareproportionaltothemodulem.Theaddendumistheradialdistancefromthereferencecircletotheaddendumcircle.Thededendumistheradialdistancefromthereferencecircletothededendumcircle.Clearanceisthedifferencebetweenaddendumanddedenduminmatinggears.Clearancepreventsbindingcausedbyanypossibleeccentricity.Thecircularpitchpisthedistancebetweencorrespondingsideofneighboringteeth,measuredalongthereferencecircle.Thebasepitchissimilartothecircularpitchismeasuredalongthebasecircleinsteadofalongthereferencecircle.Itcaneasilybeseenthatthebaseradiusequalsthereferenceradiustimesthecosineofthepressureangle.Since,foragivenangle,theratiobetweenanysubtendedarcanditsradiusisconstant,itisalsotruethatthebasepitchequalsthecircularpitchtimesthecosineofthepressureangle.Thepressureangleistheanglebetweenthenormalandthecircumferentialvelocityofthepointonaspecificcircle.Thepressureangleonthereferencecircleisalsostandardized.Itismostcommonly20ºsometimes15º.Thelineofcentersisalinepassingthroughthecentersoftwomatinggears.Thecenterdistancemeasuredalongthelineofcentersequalsthesumofthepitchradiiofpinionandgear.Tooththicknessisthewidthofthetooth,measuredalongthereferencecircle,isalsoreferredtoastooththickness.Widthofspaceisthedistancebetweenfacingsideofadjacentteeth,measuredalongthereferencecircle.Tooththicknesspluswidthofspaceequalsthecircularpitch.Backlashisthewidthofspaceminusthetooththickness.Facewidthmeasurestoothwidthinanaxialdirection.Thefaceofthetoothistheactivesurfaceofthetoothoutsidethepitchcylinder.Theflankofthetoothistheactivesurfaceinsidethepitchcylinder.Thefilletistheroundedcorneratthebaseofthetooth.Theworkingdepthisthesumoftheaddendumofagearandtheaddendumofitsmatinggear.Inordertomateproperly,gearsrunningtogethermusthaveathesamemodulebthesamepressureanglecthesameaddendumanddedendum.Thelastrequirementisvalidforstandardgearsonly.GeartoothstrengthHavingdealtwithgeargeometry,wenowturntothequestionofhowmuchpowerortorqueapairofgearswilltransmitwithouttoothfailure.Figure2.18showsaphotoelasticpatternofgeartoothstresses.Thedetailsofthisexperimentalstressanalysisprocedurearebeyondthescopeofthisbook,anditissufficientheretonotethatthehigheststressesexistwherethelinesarebunchedclosesttogether.Thisoccursattwolocationsathepointofcontactwiththematinggear,whereforceisacting,andbinthefilletatthebaseofthetooth.Inordertoensureworkingsafetyandreliability,weshouldconductstrengthcalculationsofthegeartooth,includingtoothbendingstrength,toothbendingfatiguestrength,andtoothsurfacecontactfatiguestrength.Ingeardesigning,thecalculatingstressmustbelessthanallowablestresswhichdependsonseveralfactors,suchas,material,heattreatment,manufacturingprocess,requiredlifeandtherelevantfactorofsafetyagainsttoothfailure.Fordesignpurposes,theallowablestressisselectedaccordingtocorrespondingstandardsandpastexperiences.
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