一种基于齿条法的螺杆转子型线设计方法

Design＆Research1006-2971201204-0001-06710049采用齿廓法线法，详细演示了齿条法这一转子型线设计方法，并推导出齿条上的典型基本曲线段对应展成的转子曲线段的方程。通过解析齿条法设计的代表型线，如Linde型线、Rinder型线和N型线，展示了齿条法设计的特点，为进一步设计高效型线提供参考。螺杆转子；型线设计；齿廓法线法；齿条法TH455AStudyonRotorProfileDesignofScrewCompressorsBasedUponRackGenerationMethodXUJianXULing-songYUXiao-lingFENGQuan-ke(SchoolofEnergyandPowerEngineeringXi’anJiaotongUniversityXi’an710049China)AbstractThispaperpresentsanewrotorprofilegenerationprocessorofscrewcompressorsusingrackgenerationprocedurebasedupontheLewistheoremanddemonstratesthestep-by-stepderivationoftheequationoftheprofilegeneratedbythebasiccurveplacedintherack.BytakingLindeProfileRinderProfileandNProfileasexampleswerevealthecharacteristicsofrackgenerationprocedurewhichprovidesreferenceforfurtherdevelopmentofrotorprofile.KeywordsscrewrotorprofilegenerationLewistheoremrackgenerationprocedure01。。。、。1-A-。。。1-A。。。234Design＆Research23402。、、。Linde1977[1]19722234777Rinder1984[2]1987[3]StosicN[45]。。。。“”。。2[6]。。。2OfxfyfOrxryrO1x1y1O2x2y2rj1、rj2、。、Orxryr、O1x1y1O2x2y2。1=2=L=0。[7]rj2rj1Oryr12=ω1ω2=rj2rj1=Z2Z1=i12,L=rj22=rj111OrxryrO2x2y2r2=M2rrrM2r=cos2-sin2rj2cos2+rj22sin2sin2cos2rj2sin2-rj22cos200000000000000000000000012OrxryrO1x1y1r1=M1rrrMlr=cos1sin1-rj1cos1-rj11sin1-sin1cos1rj1sin1-rj11cos100000000000000000000000013OrxryrOfxfyfrf=MfrrrMfr=10001-rj220000000000000000000000001=10001-rj1100000000000000000000000014willis[6]。xr-XrNx1=yr-YrNy155OrxryrxryrXrYr。Nx1Ny103234Design＆ResearchNr=rr(t)t×kr6rrtkr。xr3、4。3OrOrxryrrr(t)=tcosαtsinααααααααααααααααααααααα17tMM′。X。、rr(t)t=cosαsinααααααααααααααααααααααα08Nr=sinα-cosααααααααααααααααααααααα092OfXr=0,Yr=L107、9、105tcosαsinα=tsinα-L-cosαLsinα-t=01111(t)=trj1sinα122(t)=trj2sinα1312t1(t)。73O1x1y1r1t=tcosα-1ttt-rj1cos1t+1tsin1ttttsinα-1ttt+rj1sin1t-1tcos1tttαααααααααααααααααααααα11472O2x2y2r2t=tcosα+2ttt+rj2cos2t+2tsin2ttttsinα+2ttt+rj2sin2t-2tcos2tttαααααααααααααααααααααα115、α=0。α=π/2、12、13、14、151t=trj1162t=trj217r1t=-rj1cos1tttrj1sin1tttαααααααααααααααααααααα1=-rj1cost/rj1rj1sint/rj1αααααααααααααααααααααα118r2t=rj2cos2tttrj2sin2tttαααααααααααααααααααααα1=rj2cost/rj2rj2sint/rj2αααααααααααααααααααααα11974Ofxfyfrft=tcosα-tcos2α/sinααααααααααααααααααααααα12020。α=π/200[8]。′′′′′′4xrrrt=rcost+brsinttttttttttttttttttttttt121Nr=costsinttttttttttttttttttttttt02210、21、225rcost+bcost=rsint-Lsintbsint+Lcost=02311t=-brj1tant242t=-brj2tant25、r1t=bcos1ttt+rcost-1ttt-rj1cos1t+1tsin1ttttt-bsin1ttt+rsint-1ttt+rj1sin1ttt-1tcos1ttttttttttttttttttttttttttt126r2t=bcos2ttt+rcost+2ttt+rj2cos2t+2tsin2tttttbsin2ttt+rsint-2ttt+rj2sin2ttt-2tcos2ttttttttttttttttttttttttttt127b=0Oy24、25、26、271t=0282t=029r1t=rcost-rj1rsinttttttttttttttttttttttt130r2t=rcost+rj2rsinttttttttttttttttttttttt131Linde。5V、ω1、ω2、。54-6Linde。1Linde。6LindeDesign＆Research23404“”。“”。LindeA2、E2、F2G2D1。。A2ArAr′GrAr′ArBr。D1E2、D2E2D1E1“”“”。DrMr、MrEr。。、2。7a。7b。--。7、。[5]Rinder。Rinder“”。8Rinder42。、。9aRinderB2C2、E2F29bRinderB1C1、E1F19c5-6RinderRinder。（a）（b）abcd05234Design＆Research（c）abc5-6NikolaStosicN。10bDrErD2E2、D1E1CrDrC2D2、C1D1BrCrB2C2、B1C1FrGrF2G2、F1G1ErFrE2F2、E1F1。。Stosic“generalcircle”axp+byq=132p=q=2a=b=1/r32p=q=2a≠b32a、b……p、q。ArBrp=0.43q=1。HAHG。10dN5-7。N。、。Linde、RinderN。[1]LindeAktiengesellschaft.ScrewCompressorwithInvoluteProfiledTeeth:US，4，028，026[P].1977.[2]RinderL.SchraubenverdichterlaeuferMitEvolventenflanken（ScrewCompressorRotorwithInvoluteLobes）[C]，Proc.VDITagung“Schrauben-maschinen84”VDIBerichteNr.521Duesseldorf，1984.[3]RinderL.ScrewRotorProfileandMethodforGenerating:US，4，643，654[P].1987.[4]StosicN.PluralScrewPositiveDisplacementMachines:UK，9，610，289[P].1996.[5]StosicN，SmithIK，KovacevicA.ScrewCompressors:Math-ematicalModelingandPerformanceCalculation[M].Spri-nger-Verlag，Berlin，Heidelberg，2005.[6]徐健，余小玲，冯全科.螺杆压缩机转子型线设计方法[J].压缩机技术，2012（2）：1-6.[7]F.L.Litvin.GearGeometryandAppliedTheory[M].Cam-bridge：CambridgeUniversityPress，2004.[8]徐健，许岭松，余小玲，冯全科.圆弧-圆弧包络线啮合副在螺杆转子齿形中的应用[J].压缩机技术，2012（3）：1-6.。abcdDesign＆Research23406