VariableArcGearPrincipleandtheFormationofTangWei2008-1-28AbstractToaclassofvariablearcgear.Useofdeviationfunction,giventhetoothprofileofthestructuralintegrityoftheprocess,proveditstoothprofileengagementtomeetthebasiclawoftoothprofileequationderivedbasicformula,discussedthechangingarcofthegear,giventhechangingarctoothProfileexamples；suchgearhasahighcarryingcapacity,especiallyforhigh-speed,high-precisionCNCmachining,itwillbeoccasionsintheheavytransmissionapplications.Keywords：gear,profile,deviationfunction,engagementprinciple,gearstrengthIntroductionWiththedevelopmentofscienceandtechnology,todrivetherequirementshavebeenincreased,particularlyintheareaofheavyandsmallisparticularlyprominent.Atpresent,thegearusedinthedesignofainvolutesline,andcycloidarctoothprofilethreeofthem,involutesgearduetomanufacturingsimpledeviationfromtheCentrenotsensitivetotheadvantagesofwidelyused,butitbearerLessandlessforheavytransmission；cyclonicalgearcontactstresssmall,toothprofileofthecoincidenceoflargeandisconducivetotheimprovementofbendingstrength,butthemeshingofgearsprecisionmanufacturingandassemblyhigher；lastcentury1950sthearcgearbendingstrengthisnothigh,inordertoachievecontinuouscontacttobemadegenerallyhelicalgears,andsmallmanufacturersintheareahavebeengreatlyrestricted.Inordertoincreasethecarryingcapacityofgears,theresearchersputforwardanumberofnewtoothprofile,forexample:micro-segmentgearprofile,dual-bandinvolutesgear,thegearincreasetheintensitycouldplayarole,butthesenewteethProfileinthemanufacturingorassemblyareastherearestillcertaindeficiencies.Thisdeviationfromtheconceptoffunction,anewtypeofgear-gearchangearc.Thepaperintroducedthearcgearchangetheformationofprinciple,derivedToothformula,discussedthechangingarcofthegearisgiventoothprofileexamples.1Avariablearctoothprofileofaprinciple1.1VariablearctoothprofileofaprincipleBelowD.C.H.YangaccordingtoAmericanscholars,suchasthedeviationfunction(DF),variablearctoothprofileontheformationofprinciple.P1isaradiusofacircleofthegearsection,1forthecornertoe(1)radius,evenlydistributedinthecenterofaround,paintedaseriesofround,asshowninFigure1(herefore(11)=0rCOS(21)；Whene(1)boundtomeetcertainconditions,thisseriesofroundenvelopecantosmooththetoothprofileg1(1),canbeseenfromthemap,e1(1)=|P(1)-g(1)|,saide(1)forthedeviationfunctionandwewillmeettheaboveprincipleofformationofatoothprofilecollectivelyreferredtoasvariableenvelopearctoothprofile,referredtoasvariablearctoothprofile,ItconstitutesachangeofgearknownastheArcgear.Whenthedeviationfromfunctione（1）=r1cos（）,thechangeisthecommonarctoothprofileoftheinvolutestoothprofile,andwhenthedeviationfunctionfor)2sin(2)(10101rrreThenchangedthearctoothprofileCycloidisthetoothprofile,andthegeneralarcgear,theequivalentofdeviationfunctione(1)onlyincertaindiscretepointsvalue.1.2arctoothprofilechangethecalculationCanbeseenfromFigure2,thecomponentthatcoordinateswiththegearchangearctoothprofileoftheequationforP1)cos()cos(1111ergx(1)sin()sin(1111ergy(2)-In,definedasthepointgtoothprofileofthenormallinewiththeanglebetweenthex-axis,whichisafunctionof1fromFigure2that1ee11rL)(tan2211erebacbacoaooao11111)()2/0(1（3）Inordertogetthetoothprofiletothepracticalapplication,thedeviationmustalsofunctione(1)thechoicetodocertainrestrictions(1)Toensurethetoothprofileofnon-crossingto|)cos(|11re（4）(2)Toensurethatequation(3)Solutionfor212re（5）(3)ToensurethecontourofCcontinuous,inthesectionwitharoundp1Toothg1attheintersectionofCp,e(cp)mustbezero.(4)ToensureToothfairing,ine(1)minimum,betweenthemaximumchangemustbemonotonous.(5)InordertogearteethN1forintegerandensuringthatacertainoverlapfactor,themeetingpointbetweenthepointofviewofthe1shouldmeet.11n2gearchangearctoothprofileoftheengagementprincipleForachangeofgeararctoothprofileofmutualengagement,asshowninFigure3,inoneinstant,thisconjugategear1oand2osTooth1cand2cgpointinth