Gear 513分析和总结分析和总结.docx

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5.1.3 Kinematicphenomenaofbevelgearhobbingmachines

Inadditiontotheknowneffectsofthenonlinearspecialkinematicsandthetiltedmillingspindle，thebevelgeargeneratingprocesshasthepotential，evenwithaplanegeneratingaxoid，tochangethekinematicrelationshipsinacontrolledmannerthroughchangesincutterheadandworkgearpositionrelativetotherollingcradleaxis/5.9/.

AdesignprinciplefromF.L.LiNin，1985,wasdrawnfromrecentliterature/5.6/(Figure6).Avisualizeddisplacementoftherollingcradleaxisandthecutterheadaxisinequalamountsinthesamedirectionleadstoanincreaseincutterheadradius.Thetransferredradius

remainsexactlythesameinthevalidityrangeoftheparallelogramafterchangingthemachinesetting.

Figure6:The“Litvinianparallelogram”forgenerationofcontactlinecrowningwithoutrotationalerror

TheradiusdifferenceΔRresultsfromthemeantoothwidthandthedesiredcontactline

crowningΔZG,accordingtoformula(5.9)withLB=ΔZG(greatestordinatevalue).ThemachinecorrectionvaluesarepresentedinFigure7，nexttotheconstructionofthe“Litvinianparallelogram”.

Becausetherollingcradleaxis cannotbedisplacedto，onlythecutterheadradius

RCOWchangesintheupperportionofthefigure.Inordertoobtainthepositionchangeoftheworkgearrelativetothecutterheadandtherollingcradle，theworkgearisdisplacedaxiallybyATXTM，andthecutterheadmovedinbyATYMM.

TheLitviniancorrectionproceduredeliversasomewhatalteredflanklinediagramalongthegeneratingaxis(i.e.transversepathofcontact),whichisdesignatedasthe“normalsangleerror”inFigure7.Thisnormalerrorbecomessmallerwithincreasingspiralangle，andismaximalwithZerolgears.Theeffect,however,isexactsincetheparallelogramconditionalongthe“lineofequalmeshingangles”(seeFigure7)leadstothesamecontactrelationshipsasthoseoftheoriginaldesign