机械类文献翻译包络法的资产负债.docx

机械类文献翻译包络法的资产负债.docx

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机械类文献翻译包络法的资产负债

英文原文

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,itstransverseprofilepointcoordinatesx2,y2canbeobtained.

Anumberofcasescanbeidentifiedfromthisanalysis.

（i）WhenΣ=0,theequationmeetsthemeshingconditionofscrewmachinerotorsandalsohelicalgearswithparallelaxes.Forsuchacase,thegearhelixangleshavethesamevalue,butoppositesignandthegearratioi=p2/p1isnegative.Thesameequationmayalsobeappliedforthegen-erationofarackformedfromgears.Additionallyitdescribestheformedplanarhob,frontmillingtoolandthetemplatecontrolinstrument.122AEnvelopeMethodofGearing

（ii）Ifadiscformedmillingorgrindingtoolisconsidered,itissuffcienttoplacep2=0.Thisisasingularcasewhentoolfreerotationdoesnotaffectthemeshingprocess.Therefore,areversetransformationcannotbeobtaineddirectly.

（iii）Thefullscopeofthemeshingconditionisrequiredforthegenerationoftheprofileofaformedhobbingtool.Thisisthereforethemostcompli-catedtypeofgearwhichcanbegeneratedfromit.

B

ReynoldsTransportTheorem

FollowingHanjalic,1983,ReynoldsTransportTheoremdefinesachangeofvariableφinacontrolvolumeVlimitedbyareaAofwhichvectorthelocalnormalisdAandwhichtravelsatlocalspeedv.Thiscontrolvolumemay,butneednotnecessarilycoincidewithanengineeringorphysicalmaterialsystem.Therateofchangeofvariableφintimewithinthevolumeis:

（B.1）

Therefore,itmaybeconcludedthatthechangeofvariableφinthevolumeViscausedby:

–changeofthespecificvariable

intimewithinthevolumebecauseofsources（andsinks）inthevolume,

dVwhichiscalledalocalchangeand

–movementofthecontrolvolumewhichtakesanewspacewithvariable

initandleavesitsoldspace,causingachangeintimeof

forρ

v.dAandwhichiscalledconvectivechange

Thefirstcontributionmayberepresentedbyavolumeintegral:

.

（B.2）

whilethesecondcontributionmayberepresentedbyasurfaceintegral:

（B.3）

Therefore:

（B.4）

whichisamathematicalrepresentationofReynoldsTransportTheorem.

AppliedtoamaterialsystemcontainedwithinthecontrolvolumeVmwhichhassurfaceAmandvelocityvwhichisidenticaltothefluidvelocityw,ReynoldsTransportTheoremreads:

（B.5）

IfthatcontrolvolumeischosenatoneinstanttocoincidewiththecontrolvolumeV,thevolumeintegralsareidenticalforVandVmandthesurfaceintegralsareidenticalforAandAm,however,thetimederivativesoftheseintegralsaredifferent,becausethecontrolvolumeswillnotcoincideinthenexttimeinterval.However,thereisatermwhichisidenticalforthebothtimesintervals:

（B.6）

therefore,

（B.7）

or:

（B.8）

Ifthecontrolvolumeisfixedinthecoordinatesystem,i.e.ifitdoesnotmove,v=0andconsequently:

（B.9）

therefore:

（B.10）

FinallyapplicationofGausstheoremleadstothecommonform:

（B.11）

Asstatedbefore,achangeofvariableφiscausedbythesourcesqwithinthevolumeVandinfluencesoutsidethevolume.Theseeffectsmaybeproportionaltothesystemmassorvolumeortheymayactatthesystemsurface.

Thefirsteffectisgivenbyavolumeintegralandthesecondeffectisgivenbyasurfaceintegral.

（B.12）

qcanbescalar,vectorortensor.

Thecombinationofthetwolastequationsgives:

Or:

（B.13）

Omittingintegralsignsgives:

（B.14）

Thisisthewellknownconservationlawformofvariable

.Sincefor

=1,thisbecomesthecontinuityequation:

finallyitis:

Or:

（B.15）

isthematerialorsubstantialderivativeofvariable

.Thisequationisveryconvenientforthederivationofparticularconservationlaws.Aspreviouslymentioned

=1leadstothecontinuityequation,

=utothemomentumequation,

=e,whereeisspecificinternalenergy,leadstotheenergyequation,

=s,totheentropyequationandsoon.

Ifthesurfaces,wherethefluidcarryingvariableΦentersorleavesthecontrolvolume,canbeidentified,aconvectivechangemayconvenientlybewritten:

（B.16）

wheretheoverscoresindicatethevariableaverageatentry/exitsurfacesections.Thisleadstothemacroscopicformoftheconservationlaw:

（B.17）

whichstatesinwords:

（rateofchangeofΦ）=（inflowΦ）−（outflowΦ）+（sourceofΦ）

中文译文

A

包络法的资产负债

螺杆压缩机转子Stosic1998年之后，被视为非平行不相交的螺旋齿轮，或在图的交叉轴。

A.1。

X01，y01和x02之前，y02是该点的坐标的坐标系统中的固定的主转子和闸转子的端部转子段，如示于图。

1.3。

Σ是绕X轴的旋转角度。

的转子轴的旋转，在其轴承是天然的转子运动。

虽然主旋翼旋转通过角度θ，闸转子的旋转通过角度τ=r1w/rwθ=z2/z1θ，其中rw和z是分别的转子叶片的节距圆的半径和数量。

此外，我们定义外部和内部的转子半径：

r1e=r1w+r1和r1i=r1W–r0。

转子轴之间的距离是C=r1W+r2W。

p是在给定的单元转子旋转角的转子引线。

标1和2分别涉及的主要和闸转子。

图。

A.1。

坐标系与非平行交错轴斜齿轮

与一个给定的，或产生表面R1（T，θ）的啮合，或产生的表面以确定，该程序开始。

一个集合中仍将产生表面参数形式：

R2（T，θ，τ），其中t是一个配置参数，θ和τ是运动参数。

包络面r1和r2之间的啮合方程，它决定：

r1=r1（t,θ）=[x1,y1,z1]

=x01cosθ-y01sinθ,x01sinθ+y01cosθ,p1θ]（A,.1）

=

（A.2）

（A.3）

（A.4）