翻譯部分英文原文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.Typesofgears(1)Spurgears.ThespurgearhasacylindricalpitchsurfaceandhasstraightteethparalleltoitsaxisasshowninFig.2.8.Theyareusedtotransmitmotionandpowerbetweenparallelshafts.Thetoothsurfacesofspurgearscontactonastraightlineparalleltotheaxesofgears.Thisimpliesthattoothprofilesgointoandoutofcontactalongthewholefacewidthatthesametime.Thiswillthereforeresultinthesuddenloadingandsuddenunloadingonteethasprofilesgointoandoutofcontact.Asaresult,vibrationandnoiseareproduced.(2)Helicalgears.Thesegearshavetheirtoothelementsatanangleorhelixtotheaxisofthegear(Fig.2.9).Thetoothsurfacesoftwoengaginghelicalgearsinnplanargearmechanismscontactonastraightlineinclinedtotheaxesofthegears.Thelengthofthecontactlinechangesgraduallyfromzerotomaximumandthenfrommaximumtozero.Theloadingandunloadingoftheteethbecomegradualandsmooth.HelicalgearsmaybeusedtotransmitmotionandpowerbetweenparallelshaftsFig.2.9(a)orshaftsatanangletoeachotherFig.2.9(d).AherringbonegearFig.2.9(c)isequivalenttoaright-handandaleft-handhelicalgearplacedsidebyside.Becauseoftheangleofthetooth,helicalgearscreateconsiderablesidethrustontheshaft.Aherringbonegearcorrectsthisthrustbyneutralizingit,allowingtheuseofasmallthrustbearinginsteadofalargeoneandperhapseliminatingonealtogether.Oftenacentralgrooveismadearoundthegearforeaseinmachining.(3)Bevelgars.Theteethofabevelgeararedistributedonthefrustumofacone.Thecorrespondingpitchcylinderincylindricalgearsbecomespitchcone.Thedimensionsofteethondifferenttransverseplanesaredifferent.Forconvenience,parametersanddimensionsatthelargeendaretakentobestandardvalues.Bevelgearsareusedtoconnectshaftswhicharenotparalleltoeachother.Usuallytheshaftsare90deg.toeachother,butmaybemoreorlessthan90deg.Thetwomatinggearsmayhavethesamenumberofteethforthepurposeofchangingdirectionofmotiononly,ortheymayhaveadifferentnumberofteethforthepurposeofchangingbothspeedanddirection.Thetoothelementsmaybestraightorspiral,sothatwehaveplainandspiralbevelgears.Hypoidcomesfromthewordhyperboloidandindicatesthesurfaceonwhichthetoothfacelies.Hypoidgearsaresimilartobevelgears,butthetwoshaftsdonotintersect.Theteetharecurved,andbecauseofthenonintersectionoftheshafts,bearingscanbeplacedoneachsideofeachgear.Theprincipaluseofthidtypeofgearisinautomobilerearendsforthepurposeofloweringthedriveshaft,andthusthecarfloor.(4)Wormandwormgears.Wormgeardrivesareusedtotransmitmotionandowerbetweennon-intersectingandnon-parallelshafts,usuallycrossingatarightangle,especiallywhereitisdesiredtoobtainhighgearreductioninalimitedspace.Wormsareakindofscrew,usuallyrighthandedforconvenienceofcutting,orlefthandeditnecessary.Accordingtotheenvelopingtype,wormscanbedividedintosingleanddoubleenveloping.Wormsareusuallydriverstoreducethespeed.Ifnotself-locking,awormgearcanalsobethedriverinasocalledback-drivingmechanismtoincreasethespeed.Twothingscharacterizewormgearing(a)largevelocityratios,and(b)highslidingvelocities.Thelattermeansthatheatgenerationandpowertransmissionefficiencyareofgreaterconcernthanwithothertypesofgears.(5)Racks.Arackisagearwithaninfiniteradius,oragearwithitsperimeterstretchedoutintoastraightline.Itisusedtochangereciprocatingmotiontorotarymotionorviceversa.Alatherackandpinionisgoodexampleofthismechanism.GeometryofgeartoothThebasicrequirementofgear-toothgeometryistheprovisionofangularvelocityrationsthatareexactlyconstant.Ofcourse,manufacturinginaccuraciesandtoothdeflectionswellcauseslightdeviationsinvelocityratio；butacceptabletoothprofilesarebasedontheoreticalcurvesthatmeetthiscriterion.Theactionofapairofgearteethsatisfyingthisrequirementistermedconjugategear-toothaction,andisillustratedinFig.2.12.Thebasiclawofconjugategear-toothactionstatesthatasthegearsrotate,thecommonnormaltothesurfacesatthepointofcontactmustalwaysintersectthelineofcentersatthesamepointPcalledthepitchpoint.Thelawofconjugategear-toothcanbesatisfiedbyvarioustoothshapes,buttheonlyoneofcurrentimportanceistheinvolute,or,moreprecisely,theinvoluteofthecircle.(Itslastimportantcompetitorwasthecycloidalshape,usedinthegearsofModelTFordtransmissions.)Aninvolute(ofthecircle)isthecurvegeneratedbyanypointonatautthreadasitunwindsfromacircle,calledthebasecircle.ThegenerationoftwoinvolutesisshowninFig.2.13.Thedottedlinesshowhowthesecouldcorrespondtotheouterportionoftherightsidesofadjacentgearteeth.Correspondingly,involutesgeneratedbyunwindingathreadwrappedcounterclockwisearoundthebasecirclewouldfortheouterportionsoftheleftsidesoftheteeth.Notethatateverypoint,theinvoluteisperpendiculartothetautthread,sincetheinvoluteisacirculararcwitheverincreasingradius,andaradiusisalwaysperpendiculartoitscirculararc.Itisimportanttonotethataninvolutecanbedevelopedasfarasdesiredoutsidethebasecircle,butaninvolutecannotexistinsideitsbasecircle.Letusnowdevelopamatingpairofinvolutegearteethinthreesteps:frictiondrive,beltdrive,andfinally,involutegear-toothdrive.Figure2.14showstwopitchcircles.Imaginethattheyrepresenttwocylinderspressedtogether.Ifslippagedoesnotoccur,rotationofonecylinder(pitchcircle)willcauserotationoftheotheratanangularvelocityratioinverselyproportionaltotheirdiameters.Inanypairofmatinggears,thesmallerofthetwoiscalledthepinionandthelargeronethegear.(Theterm“gear”isusedinageneralsensetoindicateeitherofthemembers,andalsoinaspecificsensetoindicatethelargerofthetwo.)Usingsubscriptspandgtodenotepinionandgear,respectively.Inordertotransmitmoretorquethanispossiblewithfrictiondrivealone,wenowaddabeltdriverunningbetweenpulleysrepresentingthebasecircles,asinFig2.15.Ifthepinionisturnedcounterclockwiseafewdegrees,thebeltwillcausethegeartorotateinaccordancewithcorrectvelocityratio.Ingearparlance,angleiscalledthepressureangle.Fromsimilartriangles,thebasecircleshavethesameratioasthepitch；thus,thevelocityratioprovidedbythefrictionandbeltdrivesarethesame.InFig.2.16thebeltiscutatpointc,andthetwoendsareusedtogenerateinvoluteprofilesdeandfgforthepinionandgear,respectively.Itshouldnowbeclearwhyiscalledthepressureangle:neglectingslidingfriction,theforceofoneinvolutetoothpushingagainsttheotherisalwaysatanangleequaltothepressureangle.AcomparisonofFig.2.16andFig.2.12showsthattheinvoluteprofilesdoindeedsatisfythefundamentallawofconjugategear-toothaction.Incidentally,theinvoluteistheonlygeometricprofilesatisfyingthislawthatmaintainsaconstantpressureangleasthegearsrotate.Noteespeciallythatconjugateinvoluteactioncantakeplaceonlyoutsideofbothbasecircles.NomenclatureofspurgearThenomenclatureofspurgear(Fig.2.17)ismostlyapplicabletoallothertypeofgears.Thediameterofeachoftheoriginalrollingcylindersoftwomatinggearsiscalledthepitchdiameter,andthecylinderssectionaloutlineiscalledthepitchcircle.Thepitchcirclesaretangenttoeachotheratpitchpoint.Thecirclefromwhichtheinvoluteisgeneratediscalledthebasecircle.Thecirclewherethetopsoftheteethlieiscalledthededendumcircle.Similarly,thecirclewheretherootsoftheteethlieiscalledthededendumcircle.Betweentheaddendumcircleandthededendumcircle,thereisanimportantcirclewhichiscalledthereferencecircle.Parametersonthereferencecirclearestandardized.Themodulemofagearisintroducedonthereferencecircleasabasicparameter,whichisdefinedasm=p/.Sizesoftheteethandgearareproportionaltothemodulem.Theaddendumistheradialdistancefromthereferencecircletotheaddendumcircle.Thededendumistheradialdistancefromthereferencecircletothededendumcircle.Clearanceisthedifferencebetweenaddendumanddedenduminmatinggears.Clearancepreventsbindingcausedbyanypossibleeccentricity.Thecircularpitchpisthedistancebetweencorrespondingsideofneighboringteeth,measuredalongthereferencecircle.Thebasepitchissimilartothecircularpitchismeasuredalongthebasecircleinsteadofalongthereferencecircle.Itcaneasilybeseenthatthebaseradiusequalsthereferenceradiustimesthecosineofthepressureangle.Since,foragivenangle,theratiobetweenanysubtendedarcanditsradiusisconstant,itisalsotruethatthebasepitchequalsthecircularpitchtimesthecosineofthepressureangle.Thepressureangleistheanglebetweenthenormalandthecircumferentialvelocityofthepointonaspecificcircle.Thepressureangleonthereferencecircleisalsostandardized.Itismostcommonly20(sometimes15).Thelineofcentersisalinepassingthroughthecentersoftwomatinggears.Thecenterdistance(measuredalongthelineofcenters)equalsthesumofthepitchradiiofpinionandgear.Tooththicknessisthewidthofthetooth,measuredalongthereferencecircle,isalsoreferredtoastooththickness.Widthofspaceisthedistancebetweenfacingsideofadjacentteeth,measuredalongthereferencecircle.Tooththicknesspluswidthofspaceequalsthecircularpitch.Backlashisthewidthofspaceminusthetooththickness.Facewidthmeasurestoothwidthinanaxialdirection.Thefaceofthetoothistheactivesurfaceofthetoothoutsidethepitchcylinder.Theflankofthetoothistheactivesurfaceinsidethepitchcylinder.Thefilletistheroundedcorneratthebaseofthetooth.Theworkingdepthisthesumoftheaddendumofagearandtheaddendumofitsmatinggear.Inordertomateproperly,gearsrunningtogethermustha