螺旋锥齿轮的无根切最小变位系数

:199810293,471039,1000443HfmaxD,,,:,,,,,Z2,1965(AGMA)B=35,DHfmax[1]Z2min[2],,HfmaxD,,1,,,,[3,4]DHfmax:,,r=r(u,U,W)(1)uUW19997304©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1f(u,U,W)=nõv12=0(2),vr2=vr1+v12=0(3),1,DHfmax:sin2A0sinScsinA0-sinHfcosA0-(cos2Hf+c2-2ccosHfsinB)1ö2(sinA0sinS1+cosA0sinUtanHf)=0(4)csinA0-sinHfcosA02sin3A0cosA0sinScosScosHfsinDb-csinA0-sinHfcosA02sin2A0sinScosHfcosDb(1-cos2A0cos2S)+csinA0-sinHfcosA0(cos2Hf+c2-2ccosHfsinB)1ö2sin2A0cosA0sinS(sinDcosS1+cosUcosScosDbsinHf)+sinA0cosDbcosHf(sinS1+cos2A0sinScosUtan2Hf)+cosA0cosSsinS1cosDbsinHf-(cos2Hf+c2-2ccosHfsinB)1ö2cos2A0cosDbsinS1(sinHf+cosHftanA0cosS)csinA0-sinHfcosA0cosA0cosS+(cos2Hf+c2-2ccosHfsinB)1ö2cosUtanHf=0(5)S=U-q+WS1=q-WDb=D-Hfc=rcRcosq=(cosHf-csinB)(cos2Hf+c2-2ccosHfsinB)1ö2(6)sinq=ccosB(cos2Hf+c2-2ccosHfsinB)1ö2(7)(4)(5)HfUWcA0BD,UWc,,ABDHf,A0BDHf(4)(5),HfUWc[3],,Hf,Hfmax2minU=Hf+1D2j=1[Hj]2+D8i=11Gi(8),Hj(4)(5),GiHfUWc,364:©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2DHfmaxDA0BDHfmax,2A0=141525,B=35AGMA209103[1]DHfmax,,,,[5]DHfmaxtanHz=(1+4tan2Dsin2Acos2A)1ö2-12tanDcos2A(9)Hz(9)3HzHfmaxDHfmaxDHzHfmax(3),(D)=Hz-Hfmax=A1D2-A2D(10)A1A2Hfmax=Hz-A1D2+A2D(11)DHfmax,DHfmaxA1A2,11HfmaxAö()Bö()A1A2Aö()Bö()A1A2141535010395060101732920300105354001011395163501046100010185002035010624220101850620150103566201008339204001071959010290612020010428290100957922153501071350010165052025010476670100973225350107924201011993DHfmax0101801077,(11),xmin=ha3+c3-z2sinDtan(Hz-A1D2+A2D)(12)ha3c3z461999©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.3(1),(2)DHfmax,,1AGMA209.03.SystemforSpiralBevelGears,1965.2AGMA209.04.SystemforSpiralBevelGears,1982.35..,,.:,1968.138151,4124384..,1966.5AGMA208.03.SystemforStraightBevelGears,1965.6,.GleasonDHfmax.,1988,1(2):1427THEMINIMUMMODIFICATIONCOEFFICIENTOFSPIRALBEVELGEARWITHOUTUNDERCUTYangBoyuanLiangGuiming(LuoyangInstituteofTechnology)GuoKai(NorthJiaotongUniversity)AbstractSpiralbevelgearisaveryimportantelementindrivelinesofvariousmachinessuchastractors,trucksetc.Itisagoodmethodtousenon2zeromodificationtoincreasetoothstrengthortoimprovegearingpropertiesindesignofspiralbevelgears.Toavoidundercutisthemostbasicrequirement.Thustheminimummodificationcoefficientfornon2undercutgearsmustbedetermined.Howeverthereisnotaclearandaccurateformulaforcalculatingitsparameterseveninstandardsofmodernindustrialcountries.Inthispaper,basedonthetheoryofthreedimensionalgearing,theD2HfmaxcurveswithoutundercutforGleasontypespi2ralbevelgearsarederivedbytheoptimummethodofpenaltyfunction.Theformulaforcal2culatingtheminimummodificationcoefficientattheconditionofnon2undercutisgiventhroughthemathematicaltreatmentoftheresults.Itisprovedthattheresultsofcalculatingbytheprincipleofgearingaretrueandreliable.Owingtotheirgoodaccuracy,theyareuse2fultoboththemanualdesignandCADandprovideafoundationindesignofspiralbevelgearswithoutundercut.KeywordsSpiralbevelgear,Undercut,Modification564:©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.