机械原理Chapter-6--Gear-Mechanisms-3

Chapter6GearMechanisms§6.7ManufacturingMethodsofInvoluteProfiles§6.8AddendumModificationonInvoluteGearsCuttingofToothProfiles•Therearevariousmethodsformanufacturingtoothprofiles,suchasdiecasting,precisionforging,powderprocess,moulding,cuttingandsoon.•Amongthem,cuttingisthemostwidelyused.•Therearegenerallytwotypesofcuttingmethods,•i.e.formcuttingandgeneratingcutting.FormCutting•Informcutting,thedesiredtoothprofileisproducedbypassingacutterthroughtheblank.•FormmillingwithadiskmillingcutterisshowninFig.•Thecutterrotatesandtheblankisfedaxially.FormCutting•Endmillingcuttersareusedforlargemodulesanddoublehelicalgears.•Thesectionofthecutterhastheshapeofthetoothspaceofthegeartobecut.FormCutting•Indexingisneededafteratoothspaceiscut•sotheaccuracyofthegeardependsontheaccuracyoftheindexplateaswellasthesectionshapeofthecutter.FormCutting•Astheshapeofaninvolutedependsonitsbaseradius,•adifferentcutterisrequiredforeachnumberofteeth•evenforthesamemoduleandsamepressureangle.rb=rcos=(mz/2)cosFormCutting•Thisisdivorcedfromreality:•inpractice,only8to26cuttersareavailableforeachmoduleandpressureangle.•Eachcutterisusedforseveraldifferentnumbersofteethandanerroristhereforeintroduced.FormCutting•Thecuttingprocessisinterruptedbytheindexingandtheproductionrateislowinformmilling.•Itsmainadvantageisthatitcanbeaccomplishedoncommonlyavailablemillingmachines.Broach(拉刀)--FormCuttingGeneratingCutting•Inageneratingcuttingmethod,theedgesofacuttertaketheformofagear(orrack)withthesamemoduleandpressureangleasthegeartobecut.•Thereisageneratingmotionbetweenthecutterandtheblankasifthecutterengagesasagearwiththegeartobecut.•Byaddingthecuttingmotionbetweenthecutterandtheblank,theprofileoftheteethisformedgraduallybyaseriesofcuts.Fig.6-22GeneratingCutting•Ifz0isthenumberofteethofthecutter•andzthenumberofteethofthegeartobecut,•theirtransmissionratioshouldbeFig.6-22•whichdefinesthegeneratingmotiontobeprovidedbythekinematicchaininthecuttingmachine.GeneratingCutting•Thecuttingmotionisthereciprocationofthecutter•whilethefeedisthemovementofthecuttertowardtheblank.Fig.6-22GeneratingCutting•Externalgearscanbecutwitharack-shapedshapercutter.•Theedgesofthecutterarenowstraightlineswhichcanbemadeaccurately.•Thatiswhyinvolutegearsareeasytomanufacture.Fig.6-23GeneratingCutting•ThecuttingmethodshowninFigisnotcontinuousintheshapingofagear.•Inmassproduction,hobbingisusedinsteadofshaping.Fig.6-23GeneratingCutting•Theshapeofahobislikeascrewwithsomeaxialslotstoformthecuttingedges.•Thecuttingedgetakestheshapeofarackandthehobisthereforearack-shapedcutter.GeneratingCutting•Therotationofthehobprovidesthecuttingmotionandisalsoequivalenttothecontinuoustranslationoftherack-shapedcutter.•Atthesametime,theblankisdrivenatacertaintransmissionratiotothecutterbythekinematicchaininthecuttingmachineandthisgivestherequiredgeneratingmotion.GeneratingCutting•Meanwhile,thehobisfedalongtheaxialdirectionoftheblanktocuttheteethforthewholefacewidth.•Cuttingiscontinuousandtheproductionrateisthereforeimproved.GeneratingCutting•Inthegeneratingmethod,onecutterisenoughforeachmoduleandpressureangle,inspiteofthenumberofteethofthegeartobecut.•Itisthereforethemostwidelyusedmethodtocutgears.CuttingaStandardGearwithStandardRack-shapedCutter•Theprofileofastandardrack-shapedcutterissimilartothatofastandardrack•butthetiplineisc*mhigherthantheaddendumlineforcuttingtheprofileattheroottoprovidethebottomclearance.ha*mc2*mmmah*=0.38m=0.38m*cm*hamah*m*cππ2mπ2mπ2mαρρρ=20°=20°αdedendumlinededendumlinereferencelineaddendumlinecuttertiplinereferencelineaddendumlineCuttingaStandardGearwithStandardRack-shapedCutter•Thecuttingedgebetweenthetiplineandtheaddendumlineisnotastraightline•andthecorrespondinggearprofilecutisnotinvolute.ha*mc2*mmmah*=0.38m=0.38m*cm*hamah*m*cππ2mπ2mπ2mαρρρ=20°=20°αdedendumlinededendumlinereferencelineaddendumlinecuttertiplinereferencelineaddendumlineCuttingaStandardGearwithStandardRack-shapedCutter•Therefore,indiscussingthegeneratingofaninvoluteprofile,wesimplyregardthestandardrack-shapedcutterashavingthesameprofileasthestandardrack.ha*mc2*mmmah*=0.38m=0.38m*cm*hamah*m*cππ2mπ2mπ2mαρρρ=20°=20°αdedendumlinededendumlinereferencelineaddendumlinecuttertiplinereferencelineaddendumlineCuttingaStandardGearwithStandardRack-shapedCutter•Tocutastandardgear,thetransmissionratioofthecutterandtheblankingeneratingmotionisthesameasthatoftherackandthegear.1rra1PVmah*αα'==ω11==1r'2b1r1N∞2N211vrCuttingaStandardGearwithStandardRack-shapedCutter•Furthermore,thereferencelineofthecuttershouldbetangenttothereferencecircleofthegearafterthefeedinghasfinished.1rra1PVmah*αα'==ω11==1r'2b1r1N∞2NCuttingaStandardGearwithStandardRack-shapedCutter•Thusthereferencelineofthecutterrollswiththereferencecircleofthegearwithoutslipping.1rra1PVmah*αα'==ω11==1r'2b1r1N∞2NCuttingaStandardGearwithStandardRack-shapedCutter•Therefore,thepitch,module,pressureangle,tooththicknessandspacewidthofthegearonthereferencecirclearethesameasthoseonthereferenceline.1rra1PVmah*αα'==ω11==1r'2b1r1N∞2NCuttingaStandardGearwithStandardRack-shapedCutter•Ast