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1、TheBasicsofSpiralBevelGears1GearingPrinciplesCylindricalandStraightBevelGearsThepurposeofgearsistotransmitmotionandtorquefromoneshafttoanother,Thattransmissionnormallyhastooccurwithaconstantratio,thelowestpossibledisturbancesderivedfromastraightrackwithstraighttoothprofile.Aparticulargear,rollingint

2、herackwithconstantcenterdistancetotherack,requiresinvoluteflanksurfaces.Ashapingtoolwiththeshapeofrackcanmachineagearwithaperfectinvoluteflankform.Figure1showsacylindricalgearrollinginarack.Inthecaseofasingleindexfacemillingmethod,thetoothleadfunctioniscircular,asthebladeinthecutterperformsacircular

3、motion,whilethegeneratinggearrestsinafixedangularposition.Thetoothprofilingbetweenthecutterandthegeneratinggeardoesnotrequireanyrotationofthegeneratinggear.Thevirtualgeneratinggearisformedbythecutterheadinanon-generatingprocess.InFigure3,therotatingbladesinthecutterheadcanbeunderstoodtorepresentonet

4、oothofthegeneratinggear.Asexplainedearlier,thegeneratinggearisthebevelgearequivalentofthestraightrackforgeneratingacylindricalgeartooth.Thepinionslotproducedinthatwayhastwodefects.First,theprofilewillnotallowrollingbetweenpinionandgeneratinggear(comparetotherackandcylindricalgeartoothinFigure1).Seco

5、nd,thepinionslotdoesnothavetheproperdepthalongthefacewidth.Assoonastheteethhaveaspiralangleandtheslotinclinestoanangleonanaxialplane,theteethwindaroundtheworkgearbody.Inafixedangularposition,justtheheelsection,forexample,iscuttotheproperdepth.Therollmotionrotatesthevirtualgeneratinggearandtheworkgea

6、rwiththeproperratiowhiletheyareengaged(similartothelinearmotionoftherack,Figure1,inconjunctionwiththegearrotation).Thatprocedurewasformachiningoneslot.Tomachinethenextslot,thecutterwithdraws,andtheworkindexesonepitch.Thespiralangleistheinclinationangleofthecurvedtoothtangenttotheradiusvectorfromthei

7、ntersectionpointofpinionandgearaxis(seeFigure4).Becauseofthecurvedshapeofthetoothlength,differentpointsalongthelacewidthhavedifferentspiralangles.Thenominalspiralangleofthespiralbevelgearorpinionistheanglemeasuredfromthecenterofthetooth.Itispossibletouseabevelgeneratinggearthatisidenticaltotileringg

8、ear.Filepinionisinthatcasegeneratedbyrollingwiththebevelgeneratinggear,andthegearismanufacturedsimplybyplungingthecuttertofulldepthwithoutrolling(non-generatedformcutting).Astraighttoothbevelgearsethascontactlinesthatareparalleltothepitchline(Figure5,top).Thefirstcontactbetweenageneratinggeartoothan

9、dapiniontoothstarts,forexample,intherootandmovesduringtherotationofthetwomatingmembersalongthepathofcontactstraightuptothetop.Thecontactlinesrepresentthemomentarycontactbetweenthetwoflanksinmesh.Withaspiralbevelgearsetthecontactlinesareinclinedrelativetothepitchlineorientation.Unlikethecontactlineso

10、fthestraightbevelgearset,thecontactlinesofthespiralbevelgearsethavedifferentlengths.Thebottomoffigure5showsthemovementofthecontactfromheeltoptotoeroot.Theveryshortcontactlengthincreasesfromthebeginningoftherolltowardsthecenterofthefacewidthandreducesastherollapproachestheexitatthetoeend.Thecontactli

11、nesbetweenpinionandgeneratinggearareidenticaltothecontactlinesbetweencutterbladesandpinionflanks.2SingleIndexProcess-FaceMillingInasingleindexprocess,justoneslotiscutatatime.Forthenon-generatedmemberonly,thecutterrotatesandisfedintotheworkgeartothefulldepth.Afterreachingthefulldepth,thecutterwithdra

12、wsandtheworkindexesonepitchtothenextdesiredslotposition(Figure6,rightside).Theprocessrepeatsuntilallslotshavebeenmachined.Theresultingflankleadfunctionisacirculararc.Machiningageneratedmemberisdonebyplungingattheheelrollpositionfirst.Afterplunging,therollmotionbegins,andgeneratingoftheflanksfromheel

13、totoeoccurs.Theflankleadfunctionforafacemilled,generatedgearisacirculararcthatiswoundaroundaconicalsurface.Themanufacturing.ofafacemilledbevelgearpairispossibleinafive-cutprocessorinacompletingprocess.Thefive-cutprocessconsistsofthefollowingfiveindependentoperations:1.Gearroughing(alternateroughingb

14、lades),2.Gearfinishing(alternatefinishingblades),3.Pinionroughing(alternateroughingblades),4.Pinionfinishingconvex(innerbladesonly),and5.Pinionfinishingconcave(outerbladesonly).Acompletingprocessusestwocombinedoperations:1.Gearroughingandfinishing(alternateroughingfinishingblades)and2.Pinionroughing

15、andfinishing(alternateroughingfinishingblades).3ContinuousIndexingProcess-FaceHobbingAcontinuouscuttingprocessconsistsofcontinuousrotationsandafeedmotiononly.Whileanouterandaninnerblademovethroughaslotoftheworkgear,theworkgearisrotatingintheoppositedirection,Therelationofthecutterrpmandtheworkrotati

16、onisequivalenttotheratiobetweenthenumberofworkgearteethandthenumbercutterheadbladegroups(starts).Theresultingflankleadfunctionisanepicycloid.Theeffectivecuttingdirectionofthebladesinthecutterheadisnotperpendiculartothecutterradiusvector(likeinthesingleindexingprocess).Thebladesaremovedinthecutterhea

17、dtangentiallytoanoffsetpositiontoaccommodatethecorrectorientationwithrespecttothecuttingmotionvector.Thepitchpointsonthecuttingedgeofinnerandouterbladehaveanidenticalradius.Therightslotwidthisachievedwiththeangulardistancebetweentheouterblade(first)andthefollowinginnerblade.TheleftportionofFigure6sh

18、owsthekinematicrelationshipandtheorientationofthebladesrelativetocutterandcuttingmotion.Balancingofthetooththicknessesbetweenpinionandgearcanonlyberealizedbydifferentradiiofinnerandouterbladepitchpoints,sincethespacingbetweenthebladesisgivenbythecutterheaddesignandthereforeremainsconstant.Whileonebl

19、adegroup(likeshowninFigure6)ismovingthroughoneslot,theworkrotatesintheoppositedirection,suchthatthenextbladegroupentersthenextslot.Thatway,alltheslotsaroundtheworkgeararecutataboutthesametime.Thefeedmotiontofeedthecrittertothefulldepthpositionisthereforeslowerthaninthesingleindexprocess.Anon-generat

20、edworkgearisfinishedwhenthefulldepthpositionisreached.Togetthehighestpossiblespacingaccuracy,adwelltimeisappliedtothenon-generatedmember.Theaimofthedwellmotionistoalloweachbladetomoveoncemoretoeachslot,whichtakesNslotstopassby,whereNisthenumberofcutterstartstimesthenumberof.gearteeth.Nisequivalentto

21、asmanyringgearrevolutionsasthecutterhasstarts.Forageneratedpinion,arollmotionfollowstheplungingcycleinthecenter,rollposition(thecutterdoesnotcutthefulldepthyet).Therollmotionafterplungingmovesthecuttingactiontotheheel；bothplungingandrollingtoheelispartoftheroughingcycle.Attheheelrollposition,thecutt

22、eradvancestothefulldepthposition,thecutterrpmincreasestoafinishingsurfacespeed,andaslowrollmotionfromheeltotoefollows.Whenarrivingatthetoe(endrollposition),allteethofthegeneratedworkgearorpinionarefinished(seeFigure7).4HeatTreatmentofBevelGearsHeattreatmentfollowsthesoftcuttingoperation.Thegenerally

23、usedlowcarbonsteelhastobecarburizedonthesurface,bycasehardeningforexample.Theheattreatmentisfinishedwiththequenchingoperationthatprovidesasurfacehardnessintherangeof60to63Rc(RockwellC)Thepinionmaybe3RcharderthantheringgeartoequalizethewearandreducetheriskofscoringThecorematerialstayssofterandmoreduc

24、tile，withahardnessintherangeof30to40Rc.ThedistortionsfromheattreatmentarecriticaltothefinalhardfinishingoperationThekindofheattreatmentfacility(saltbath，furnaceorcontinuousfurnace)，aswellasthedifferencesbetweenthechargesofblankmaterial，hasasignificantinfluenceOnthegeardistortionThegear,whichismostly

25、shapedlikearing，losesitsflatness(itgetsafacerun-out)viathehardeningprocedureThepinion，inmostcases，isshapedlikealongshaftthatlosesitsstraightness(radialrunout)Inadditiontotheblankbodydistortions，heattreatingcausesadistortionoftheindividualteethThespiralanglechanges，theflanklengthcurvatureisreducedand

26、thepressureanglechangesToachievethebestresults，attentionhastobepaidtoprocessingandhandlingofthepartsthroughthefurnace5HardFinishingofBevelGearsThefinalmachiningoperationafterheattreatmentshouldprovideagoodsurfacefinishandremoveflankdistortions.Themostcommonprocessusedislapping.Pinionandgeararebrough

27、tintomeshandrolledunderlighttorque.Toprovideanabrasiveaction,amixtureofoilandsiliconcarbideispouredbetweentheteeth(Figure8).Arelativemovementofpinionandgearalongtheiraxesandamovementinoffsetdirectioniscreated,suchthatthecontactareamovesfromtoetoheelandbacknumeroustimes.Thelappingprocessimprovesthesu

28、rfacefinish，leavesadesirablemicro-structureontheflanksurfacesandremovesheattreatdistortionstosomeextent.Themetalremovalisnotuniforminthedifferentflanksectionsandvariesfromsettoset,sincethepinionandgearareusedastoolstohardfinisheachother.Thisisthereasonwhylappedsetshavetobebuiltasapair；lappedpinionsa

29、ndgearsarenotinterchangeable.Thelappingsurfacestructureisnotorientedinthedirectionofthecontactlines,thusprovidingagoodhydrodynamicoilfilmbetweenthecontactareas.Thelappingstructurealsotendstodeliversidebandsinanoisefrequencyanalysis,whichmakesthegearsetappeartorollmorequietly.Duringthelappingprocess,

30、apinionandageararealwaysmachinedandfinishedatthesametime.Thetimetolapapairisequaltoorshorterthanthetimetomachineonememberusinganotherfinishingmethod.Therefore,lappingisoftencalledthemosteconomicalbevelgearfinishingprocess.Anotherfinishingoptionisgrindingofbevelgears,whichislimitedtofacemilled(single

31、index)bevelgears.Thegrindingwheelenvelopsasinglesideoranalternatecompletingcutter(Figure9).Todaystechnologydoesnotallowtheuseofagrindingtoolinacontinuousindexingprocess.Theadvantageofgrindingisthemanufacturingofanaccurateflanksurfacewithapredeterminedtopography.Theprocessallowstheconstantlyrepeatedp

32、roductionofequalpans.Buildinginpairsisnotnecessary.Lappedpairsusedinvehiclesrequireanoilchangeafterthefirst1,000milesbecauseofabrasiveparticlesintroducedtothetoothsurfacesduringlapping.Afurtheradvantageofgrindingoverlappingisthatsuchanoilchangeisunnecessarywithgroundspiralbevelgears.Aprocessbetweenl

33、appingandgrindingwithrespecttosurfacespeedandrelativemotionishoning.Honingtrialsonbevelgearshavebeendone,buttheyhaventbeenprovensuccessful.Skivingisahardcuttingprocess.Atoolmaterialsuchascarbideorboroncarbonitrideisusedontilecuttingedge.Thecuttingmachinesetupisidenticaltothatforsoftmachining.Theblad

34、epointdimensioniswiderthantheoneforsoftcutting,suchthata0.005-inchuniformstockremovalperflanktakesplace.Skivingdeliversahighqualitypartaccuracyandafinesurfacefinish.Skivingisappliedtosmallbatchesofmostlylargergearsets,Theadvantageofskivingistheuseofthesamecutterhead(onlywithdifferentblades)andthepos

35、sibleuseofthesamecuttingmachine.Thatmakestheinvestmentinmachinesandtoolsaminimum.6SomeBevelGearConventionsTheexpressionbevelgearsisusedasageneraldescriptionforstraightandspiralbevelgearsaswellashypoidgearsets.Iftheaxesofthepinionandgeardonotintersectbuthaveadistanceinspace,thegearsetiscalledahypoidg

36、earset.Thenameisderivedfromthehyperbolicshapeofthepitchcones.Forsimplification,theblanksarestillmanufacturedwithaconicalshape.Theconvexgearflankrollswiththeconcavepinionflank.Thispairofflanksiscalledthedriveside.Thedirectionofrotationwherethoseflankscontactthepiniondrivesiscalledthedrivedirection.Th

37、edrivesidedirectionisalwaysusedinvehiclestodrivethevehicleforward.Thereversedirectionissubsequentlycalledthecoastside(vehiclerollsdownhill,footisoffthegaspedal,wheelsdrivetheengine).Insomecases,thecoastsideisusedtodrivethevehicle,butitisstillcalledthecoastside.Ease-offisthepresentationofflankformcorrectionsappliedtopinionand/orgear.Theease-offtopographyindefinedintheringgearcoordinatesystem,regardlessofwherethecorrectionsweredone(pinion,gearorboth).Protuberanceisaprofilereliefintherootareaoftheflank,whichpreventsflank