包络法的资产负债螺杆压缩机转子外文文献翻译中英文翻译外文翻译Word格式文档下载.docx
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包络法的资产负债螺杆压缩机转子外文文献翻译中英文翻译外文翻译Word格式文档下载.docx
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A
EnvelopeMethodofGearing
FollowingStosic1998,screwcompressorrotorsaretreatedhereashelicalgearswithnonparallelandnonintersecting,orcrossedaxesaspresentedatFig.A.1.x01,y01andx02,y02arethepointcoordinatesattheendrotorsectioninthecoordinatesystemsfixedtothemainandgaterotors,asispresentedinFig.1.3.ΣistherotationanglearoundtheXaxes.Rotationoftherotorshaftisthenaturalrotormovementinitsbearings.Whilethemainrotorrotatesthroughangleθ,thegaterotorrotatesthroughangleτ=r1w/r2wθ=z2/z1θ,whererwandzarethepitchcircleradiiandnumberofrotorlobesrespectively.Inadditionwedefineexternalandinternalrotorradii:
r1e=r1w+r1andr1i=r1w−r0.ThedistancebetweentherotoraxesisC=r1w+r2w.pistherotorleadgivenforunitrotorrotationangle.Indices1and2relatetothemainandgaterotorrespectively.
Fig.A.1.Coordinatesystemofhelicalgearswithnonparallelandnonintersecting
Axes
Theprocedurestartswithagiven,orgeneratingsurfacer1(t,θ)forwhichameshing,orgeneratedsurfaceistobedetermined.Afamilyofsuchgener-atedsurfacesisgiveninparametricformby:
r2(t,θ,τ),wheretisaprofileparameterwhileθandτaremotionparameters.
r1=r1(t,θ)=[x1,y1,z1]
=x01cosθ-y01sinθ,x01sinθ+y01cosθ,p1θ](A,.1)
=(A.2)
(A.3)
(A.4)
(A.5)
Theenvelopeequation,whichdeterminesmeshingbetweenthesurfacesr1andr2:
(A.6)
togetherwithequationsforthesesurfaces,completesasystemofequations.Ifageneratingsurface1isdefinedbytheparametert,theenvelopemaybeusedtocalculateanotherparameterθ,nowafunctionoft,asameshingconditiontodefineageneratedsurface2,nowthefunctionofbothtandθ.Thecrossproductintheenvelopeequationrepresentsasurfacenormaland∂r2∂τistherelative,slidingvelocityoftwosinglepointsonthesurfaces1and2whichtogetherformthecommontangentialpointofcontactofthesetwosurfaces.Sincetheequalitytozeroofascalartripleproductisaninvariantpropertyundertheappliedcoordinatesystemandsincetherelativevelocitymaybeconcurrentlyrepresentedinbothcoordinatesystems,aconvenientformofthemeshingconditionisdefinedas:
(A.7)
Insertionofpreviousexpressionsintotheenvelopeconditiongives:
(A.8)
Thisisappliedheretoderivetheconditionofmeshingactionforcrossedhelicalgearsofuniformleadwithnonparallelandnonintersectingaxes.Themethodconstitutesageargenerationprocedurewhichisgenerallyapplicable.Itcanbeusedforsynthesispurposesofscrewcompressorrotors,whichareelectivelyhelicalgearswithparallelaxes.Formedtoolsforrotormanufacturingarecrossedhelicalgearsonnonparallelandnonintersectingaxeswithauniformlead,asinthecaseofhobbing,orwithnoleadasinformedmillingandgrinding.Templatesforrotorinspectionarethesameasplanarrotorhobs.Inallthesecasesthetoolaxesdonotintersecttherotoraxes.
Accordinglythenotespresenttheapplicationoftheenvelopemethodtoproduceameshingconditionforcrossedhelicalgears.Thescrewrotorgearingisthengivenasanelementaryexampleofitsusewhileaprocedureforformingahobbingtoolisgivenasacomplexcase.
TheshaftangleΣ,centredistanceC,andunitleadsoftwocrossedhelicalgears,p1andp2arenotinterdependent.Themeshingofcrossedhelicalgearsisstillpreserved:
bothgearrackshavethesamenormalcrosssectionprofile,andtherackhelixanglesarerelatedtotheshaftangleasΣ=ψr1+ψr2.Thisisachievedbytheimplicitshiftofthegearracksinthexdirectionforcingthemtoadjustaccordinglytotheappropriaterackhelixangles.Thiscertainlyincludesspecialcases,likethatofgearswhichmaybeorientatedsothattheshaftangleisequaltothesumofthegearhelixangles:
Σ=ψ1+ψ2.Furthermoreacentredistancemaybeequaltothesumofthegearpitchradii:
C=r1+r2.
Pairsofcrossedhelicalgearsmaybewitheitherbothhelixanglesofthesamesignoreachofoppositesign,leftorrighthanded,dependingonthecombinationoftheirleadandshaftangleΣ.
Themeshingconditioncanbesolvedonlybynumericalmethods.Forthegivenparametert,thecoordinatesx01andy01andtheirderivatives∂x01∂tand∂y01∂tareknown.Aguessedvalueofparameterθisthenusedtocalculatex1,y1,∂x1∂tand∂y1∂t.Arevisedvalueofθisthenderivedandtheprocedurerepeateduntilthedifferencebetweentwoconsecutivevaluesbecomessufficientlysmall.
Forgiventransversecoordinatesandderivativesofgear1profile,θcanbeusedtocalculatethex1,y1,andz1coordinatesofitshelicoidsurfaces.Thegear2helicoidsurfacesmaythenbecalculated.Coordinatez2canthenbeusedtocalculateτandfinally,itstransverseprofi
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