TheBasicsofSpiralBevelGears1GearingPrinciplesCylindricalandStraightBevelGearsThepurposeofgearsistotransmitmotionandtorquefromoneshafttoanother,Thattransmissionnormallyhastooccurwithaconstantratio,thelowestpossibledisturbancesderivedfromastraightrackwithstraighttoothprofile.Aparticulargear,rollingintherackwithconstantcenterdistancetotherack,requiresinvoluteflanksurfaces.Ashapingtoolwiththeshapeofrackcanmachineagearwithaperfectinvoluteflankform.Figure1showsacylindricalgearrollinginarack.Inthecaseofasingleindexfacemillingmethod,thetoothleadfunctioniscircular,asthebladeinthecutterperformsacircularmotion,whilethegeneratinggearrestsinafixedangularposition.Thetoothprofilingbetweenthecutterandthegeneratinggeardoesnotrequireanyrotationofthegeneratinggear.Thevirtualgeneratinggearisformedbythecutterheadinanon-generatingprocess.InFigure3,therotatingbladesinthecutterheadcanbeunderstoodtorepresentonetoothofthegeneratinggear.Asexplainedearlier,thegeneratinggearisthebevelgearequivalentofthestraightrackforgeneratingacylindricalgeartooth.Thepinionslotproducedinthatwayhastwodefects.First,theprofilewillnotallowrollingbetweenpinionandgeneratinggear(comparetotherackandcylindricalgeartoothinFigure1).Second,thepinionslotdoesnothavetheproperdepthalongthefacewidth.Assoonastheteethhaveaspiralangleandtheslotinclinestoanangleonanaxialplane,theteethwindaroundtheworkgearbody.Inafixedangularposition,justtheheelsection,forexample,iscuttotheproperdepth.Therollmotionrotatesthevirtualgeneratinggearandtheworkgearwiththeproperratiowhiletheyareengaged(similartothelinearmotionoftherack,Figure1,inconjunctionwiththegearrotation).Thatprocedurewasformachiningoneslot.Tomachinethenextslot,thecutterwithdraws,andtheworkindexesonepitch.Thespiralangleistheinclinationangleofthecurvedtoothtangenttotheradiusvectorfromtheintersectionpointofpinionandgearaxis(seeFigure4).Becauseofthecurvedshapeofthetoothlength,differentpointsalongthelacewidthhavedifferentspiralangles.Thenominalspiralangleofthespiralbevelgearorpinionistheanglemeasuredfromthecenterofthetooth.Itispossibletouseabevelgeneratinggearthatisidenticaltotileringgear.Filepinionisinthatcasegeneratedbyrollingwiththebevelgeneratinggear,andthegearismanufacturedsimplybyplungingthecuttertofulldepthwithoutrolling(non-generatedformcutting).Astraighttoothbevelgearsethascontactlinesthatareparalleltothepitchline(Figure5,top).Thefirstcontactbetweenageneratinggeartoothandapiniontoothstarts,forexample,intherootandmovesduringtherotationofthetwomatingmembersalongthepathofcontactstraightuptothetop.Thecontactlinesrepresentthemomentarycontactbetweenthetwoflanksinmesh.Withaspiralbevelgearsetthecontactlinesareinclinedrelativetothepitchlineorientation.Unlikethecontactlinesofthestraightbevelgearset,thecontactlinesofthespiralbevelgearsethavedifferentlengths.Thebottomoffigure5showsthemovementofthecontactfromheeltoptotoeroot.Theveryshortcontactlengthincreasesfromthebeginningoftherolltowardsthecenterofthefacewidthandreducesastherollapproachestheexitatthetoeend.Thecontactlinesbetweenpinionandgeneratinggearareidenticaltothecontactlinesbetweencutterbladesandpinionflanks.2SingleIndexProcess-FaceMillingInasingleindexprocess,justoneslotiscutatatime.Forthenon-generatedmemberonly,thecutterrotatesandisfedintotheworkgeartothefulldepth.Afterreachingthefulldepth,thecutterwithdrawsandtheworkindexesonepitchtothenextdesiredslotposition(Figure6,rightside).Theprocessrepeatsuntilallslotshavebeenmachined.Theresultingflankleadfunctionisacirculararc.Machiningageneratedmemberisdonebyplungingattheheelrollpositionfirst.Afterplunging,therollmotionbegins,andgeneratingoftheflanksfromheeltotoeoccurs.Theflankleadfunctionforafacemilled,generatedgearisacirculararcthatiswoundaroundaconicalsurface.Themanufacturing.ofafacemilledbevelgearpairispossibleinafive-cutprocessorinacompletingprocess.Thefive-cutprocessconsistsofthefollowingfiveindependentoperations:1.Gearroughing(alternateroughingblades),2.Gearfinishing(alternatefinishingblades),3.Pinionroughing(alternateroughingblades),4.Pinionfinishingconvex(innerbladesonly),and5.Pinionfinishingconcave(outerbladesonly).Acompletingprocessusestwocombinedoperations:1.Gearroughingandfinishing(alternateroughingfinishingblades)and2.Pinionroughingandfinishing(alternateroughingfinishingblades).3ContinuousIndexingProcess-FaceHobbingAcontinuouscuttingprocessconsistsofcontinuousrotationsandafeedmotiononly.Whileanouterandaninnerblademovethroughaslotoftheworkgear,theworkgearisrotatingintheoppositedirection,Therelationofthecutterrpmandtheworkrotationisequivalenttotheratiobetweenthenumberofworkgearteethandthenumbercutterheadbladegroups(starts).Theresultingflankleadfunctionisanepicycloid.Theeffectivecuttingdirectionofthebladesinthecutterheadisnotperpendiculartothecutterradiusvector(likeinthesingleindexingprocess).Thebladesaremovedinthecutterheadtangentiallytoanoffsetpositiontoaccommodatethecorrectorientationwithrespecttothecuttingmotionvector.Thepitchpointsonthecuttingedgeofinnerandouterbladehaveanidenticalradius.Therightslotwidthisachievedwiththeangulardistancebetweentheouterblade(first)andthefollowinginnerblade.TheleftportionofFigure6showsthekinematicrelationshipandtheorientationofthebladesrelativetocutterandcuttingmotion.Balancingofthetooththicknessesbetweenpinionandgearcanonlyberealizedbydifferentradiiofinnerandouterbladepitchpoints,sincethespacingbetweenthebladesisgivenbythecutterheaddesignandthereforeremainsconstant.Whileonebladegroup(likeshowninFigure6)ismovingthroughoneslot,theworkrotatesintheoppositedirection,suchthatthenextbladegroupentersthenextslot.Thatway,alltheslotsaroundtheworkgeararecutataboutthesametime.Thefeedmotiontofeedthecrittertothefulldepthpositionisthereforeslowerthaninthesingleindexprocess.Anon-generatedworkgearisfinishedwhenthefulldepthpositionisreached.Togetthehighestpossiblespacingaccuracy,adwelltimeisappliedtothenon-generatedmember.Theaimofthedwellmotionistoalloweachbladetomoveoncemoretoeachslot,whichtakesNslotstopassby,whereNisthenumberofcutterstartstimesthenumberof.gearteeth.Nisequivalenttoasmanyringgearrevolutionsasthecutterhasstarts.Forageneratedpinion,arollmotionfollowstheplungingcycleinthecenter,rollposition(thecutterdoesnotcutthefulldepthyet).Therollmotionafterplungingmovesthecuttingactiontotheheel；bothplungingandrollingtoheelispartoftheroughingcycle.Attheheelrollposition,thecutteradvancestothefulldepthposition,thecutterrpmincreasestoafinishingsurfacespeed,andaslowrollmotionfromheeltotoefollows.Whenarrivingatthetoe(endrollposition),allteethofthegeneratedworkgearorpinionarefinished(seeFigure7).4HeatTreatmentofBevelGearsHeattreatmentfollowsthesoftcuttingoperation.Thegenerallyusedlowcarbonsteelhastobecarburizedonthesurface,bycasehardeningforexample.Theheattreatmentisfinishedwiththequenchingoperationthatprovidesasurfacehardnessintherangeof60to63Rc(RockwellC)Thepinionmaybe3RcharderthantheringgeartoequalizethewearandreducetheriskofscoringThecorematerialstayssofterandmoreductile，withahardnessintherangeof30to40Rc.ThedistortionsfromheattreatmentarecriticaltothefinalhardfinishingoperationThekindofheattreatmentfacility(saltbath，furnaceorcontinuousfurnace)，aswellasthedifferencesbetweenthechargesofblankmaterial，hasasignificantinfluenceOnthegeardistortionThegear,whichismostlyshapedlikearing，losesitsflatness(itgetsafacerun-out)viathehardeningprocedureThepinion，inmostcases，isshapedlikealongshaftthatlosesitsstraightness(radialrunout)Inadditiontotheblankbodydistortions，heattreatingcausesadistortionoftheindividualteethThespiralanglechanges，theflanklengthcurvatureisreducedandthepressureanglechangesToachievethebestresults，attentionhastobepaidtoprocessingandhandlingofthepartsthroughthefurnace5HardFinishingofBevelGearsThefinalmachiningoperationafterheattreatmentshouldprovideagoodsurfacefinishandremoveflankdistortions.Themostcommonprocessusedislapping.Pinionandgeararebroughtintomeshandrolledunderlighttorque.Toprovideanabrasiveaction,amixtureofoilandsiliconcarbideispouredbetweentheteeth(Figure8).Arelativemovementofpinionandgearalongtheiraxesandamovementinoffsetdirectioniscreated,suchthatthecontactareamovesfromtoetoheelandbacknumeroustimes.Thelappingprocessimprovesthesurfacefinish，leavesadesirablemicro-structureontheflanksurfacesandremovesheattreatdistortionstosomeextent.Themetalremovalisnotuniforminthedifferentflanksectionsandvariesfromsettoset,sincethepinionandgearareusedastoolstohardfinisheachother.Thisisthereasonwhylappedsetshavetobebuiltasapair；lappedpinionsandgearsarenotinterchangeable.Thelappingsurfacestructureisnotorientedinthedirectionofthecontactlines,thusprovidingagoodhydrodynamicoilfilmbetweenthecontactareas.Thelappingstructurealsotendstodeliversidebandsinanoisefrequencyanalysis,whichmakesthegearsetappeartorollmorequietly.Duringthelappingprocess,apinionandageararealwaysmachinedandfinishedatthesametime.Thetimetolapapairisequaltoorshorterthanthetimetomachineonememberusinganotherfinishingmethod.Therefore,lappingisoftencalledthemosteconomicalbevelgearfinishingprocess.Anotherfinishingoptionisgrindingofbevelgears,whichislimitedtofacemilled(singleindex)bevelgears.Thegrindingwheelenvelopsasinglesideoranalternatecompletingcutter(Figure9).Todaystechnologydoesnotallowtheuseofagrindingtoolinacontinuousindexingprocess.Theadvantageofgrindingisthemanufacturingofanaccurateflanksurfacewithapredeterminedtopography.Theprocessallowstheconstantlyrepeatedproductionofequalpans.Buildinginpairsisnotnecessary.Lappedpairsusedinvehiclesrequireanoilchangeafterthefirst1,000milesbecauseofabrasiveparticlesintroducedtothetoothsurfacesduringlapping.Afurtheradvantageofgrindingoverlappingisthatsuchanoilchangeisunnecessarywithgroundspiralbevelgears.Aprocessbetweenlappingandgrindingwithrespecttosurfacespeedandrelativemotionishoning.Honingtrialsonbevelgearshavebeendone,buttheyhaventbeenprovensuccessful.Skivingisahardcuttingprocess.Atoolmaterialsuchascarbideorboroncarbonitrideisusedontilecuttingedge.Thecuttingmachinesetupisidenticaltothatforsoftmachining.Thebladepointdimensioniswiderthantheoneforsoftcutting,suchthata0.005-inchuniformstockremovalperflanktakesplace.Skivingdeliversahighqualitypartaccuracyandafinesurfacefinish.Skivingisappliedtosmallbatchesofmostlylargergearsets,Theadvantageofskivingistheuseofthesamecutterhead(onlywithdifferentblades)