1、VariableArcGearPrincipleandtheFormationofTangWei2008-1-28AbstractToaclassofvariablearcgear/Useofdeviationfunction/giventhetoothprofileofthestructuralintegrityoftheprocess/proveditstoothprofileengagementtomeetthebasiclawoftoothprofileequationderivedbasicformula/discussedthechangingarcofthegear/givent
2、hechangingarctoothProfileexamples；suchgearhasahighcarryingcapacity/especiallyforhigh-speed/high-precisionCNCmachining/itwillbeoccasionsintheheavytransmissionapplications/Keywords：gear/profile/deviationfunction/engagementprinciple/gearstrengthIntroductionWiththedevelopmentofscienceandtechnology/todri
3、vetherequirementshavebeenincreased/particularlyintheareaofheavyandsmallisparticularlyprominent/Atpresent/thegearusedinthedesignofainvolutesline/andcycloidarctoothprofilethreeofthem/involutesgearduetomanufacturingsimpledeviationfromtheCentrenotsensitivetotheadvantagesofwidelyused/butitbearerLessandle
4、ssforheavytransmission；cyclonicalgearcontactstresssmall/toothprofileofthecoincidenceoflargeandisconducivetotheimprovementofbendingstrength/butthemeshingofgearsprecisionmanufacturingandassemblyhigher；lastcentury1950sthearcgearbendingstrengthisnothigh/inordertoachievecontinuouscontacttobemadegenerally
5、helicalgears/andsmallmanufacturersintheareahavebeengreatlyrestricted/Inordertoincreasethecarryingcapacityofgears/theresearchersputforwardanumberofnewtoothprofile/forexample/micro-segmentgearprofile/dual-bandinvolutesgear/thegearincreasetheintensitycouldplayarole/butthesenewteethProfileinthemanufactu
6、ringorassemblyareastherearestillcertaindeficiencies/Thisdeviationfromtheconceptoffunction/anewtypeofgear-gearchangearc/Thepaperintroducedthearcgearchangetheformationofprinciple/derivedToothformula/discussedthechangingarcofthegearisgiventoothprofileexamples/1Avariablearctoothprofileofaprinciple1/1Var
7、iablearctoothprofileofaprincipleBelowD/C/H/YangaccordingtoAmericanscholars/suchasthedeviationfunction(DF)/variablearctoothprofileontheformationofprinciple/P1isaradiusofacircleofthegearsection/1forthecornertoe(1)radius/evenlydistributedinthecenterofaround/paintedaseriesofround/asshowninFigure1(herefo
8、re(11)=0rCOS(21)；Whene(1)boundtomeetcertainconditions/thisseriesofroundenvelopecantosmooththetoothprofileg1(1)/canbeseenfromthemap/e1(1)=|P(1)-g(1)|/saide(1)forthedeviationfunctionandwewillmeettheaboveprincipleofformationofatoothprofilecollectivelyreferredtoasvariableenvelopearctoothprofile/referred
9、toasvariablearctoothprofile/ItconstitutesachangeofgearknownastheArcgear/Whenthedeviationfromfunctione（1）=r1cos（）/thechangeisthecommonarctoothprofileoftheinvolutestoothprofile/andwhenthedeviationfunctionfor)2sin(2)(10101rrreThenchangedthearctoothprofileCycloidisthetoothprofile/andthegeneralarcgear/th
10、eequivalentofdeviationfunctione(1)onlyincertaindiscretepointsvalue/1/2arctoothprofilechangethecalculationCanbeseenfromFigure2/thecomponentthatcoordinateswiththegearchangearctoothprofileoftheequationforP1)cos()cos(1111ergx(1)sin()sin(1111ergy(2)-In/definedasthepointgtoothprofileofthenormallinewiththe
11、anglebetweenthex-axis/whichisafunctionof1fromFigure2that1ee11rL)(tan2211erebacbacoaooao11111)()2/0(1（3）Inordertogetthetoothprofiletothepracticalapplication/thedeviationmustalsofunctione(1)thechoicetodocertainrestrictions(1)Toensurethetoothprofileofnon-crossingto|)cos(|11re（4）(2)Toensurethatequation(
12、3)Solutionfor212re（5）(3)ToensurethecontourofCcontinuous/inthesectionwitharoundp1Toothg1attheintersectionofCp/e(cp)mustbezero/(4)ToensureToothfairing/ine(1)minimum/betweenthemaximumchangemustbemonotonous/(5)InordertogearteethN1forintegerandensuringthatacertainoverlapfactor/themeetingpointbetweenthepo
13、intofviewofthe1shouldmeet/11n2gearchangearctoothprofileoftheengagementprincipleForachangeofgeararctoothprofileofmutualengagement/asshowninFigure3/inoneinstant/thisconjugategear1oand2osTooth1cand2cgpointinthemesh/accordingtotoothprofileengagementprinciple/Conjugatetoothprofileequationcanbewritten)cos()cos(1111ergx（6）)sin()sin(1111ergy（7）)(tan)(2211111ere)2/(1（8）)cos()cos(2222ergx（9）)sin()sin(2222ergy（10）
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