54883《机械原理（英语）（第2版）》基本课件Chapter 7 Design of Gear Mechanisms

Chapter7DesignofGearMechanisms1.ParallelShaftGears(1)SpurgearsTheteetharestraightandparalleltothegearaxis.Thisgearisspurgear.Ifthegearshaveexternalteethontheoutersurfaceofthecylinders,theyrotateintheoppositedirection,asshowninFig7-1a.Aninternalgearcanmeshwithaexternalpiniononlyandtheyrotateinthesamedirection,asshowninFig7-1b.Thepinionandrackcombinationconvertsrotarymotionintotranslationalmotionorviceversa,asshowninFig7-1c.

7.1ClassificationofGearMechanismsFig.7-1Spurgears(直齿圆柱齿轮)Fig.7-2Helicalgears(斜齿圆柱齿轮)(2)HelicalgearsLikespurgears,helicalgearscanalsobeusedtoconnectparallelshafts,buttheirteetharenotparalleltotheirshaftsaxes,eachbeinghelicalinshape.Twomeshinggearshavethesamehelixangle,buthaveteethofoppositehands,asshowninFig7-2.Helicalgearcanalsobeclassifiedasexternalcontact,internalcontact,helicalpinionandrack.Fig.7-3Herringbonegears(人字齿轮)(3)HerringbonegearsHerringbonegearsareequivalenttoapairofhelicalgearswithoppositehelixanglesmountedsidebyside,asshowninFig7-3.Theaxialthrustforcesofthetworowsofteethcanceleachother.Sotheycanbeusedathighspeedswithlessnoiseandvibrations.2.SpatialGears(1)IntersectingshaftgearsIftheteethareformedontheconesurface,thisgeariscalledabevelgear.Iftheteetharestraightandcoincidentwiththeirconeelements,thisgeariscalledstraightteethbevelgearshowninFig7-4a.Whentheteethofbevelgearareinclinedatanangletothefaceofbevel,thisgearisknownashelicalbevelgearorspiralbevelgear,asshowninFig7-4b.Thecurvedteethbevelgearhasteeththatarecurved,butwithazerodegreespiralangle,asshowninFig7-4c.

Fig.7-4Bevelgears(锥齿轮)Fig.7-6Wormgears(蜗轮蜗杆)(2)SkewshaftgearsTotransmitmotionbetweentheskewshafts,thespiralgearsorcrossedhelicalgears,wormgearsandHypoidgearsareoftenusedinmachines.Thespiralgearsorcrossedhelicalgearsarelimitedtohighload,andtheirshaftscanbesetatanyangle,asshowninFig7-5.

(3)WormgearsFig7-6showswormgearsinwhichafewteethofthesmallergeararewrappedarounditscircumferenceanumberoftimesandformscrewthreads,andthelargerwheelhasconcaveshapeinitsdiameterdirectionsothattoenvelopetheportionofthesmallergear.Thesmallergeariscalledworm;thelargergeariscalledwormgear.Fig.7-5Crossedhelical

gears(交错轴斜齿轮)1.LawofGearingFig.7-7Fundamentallawofgearing(齿廓啮合的基本定律)7.2FundamentalLawofGearing[Duringmeshingofgears,theprofileofatoothongear1ismeshingatpointKwithanotherprofileonthatgear2toproducearotarymotion.Fig7-7showstwocontactingprofileswithcommonnormaln—n,andthisnormalintersectsthelineofthetwogearcentersO1O2atpointP.

Ifthepitchpointvariesforallphaseofthegearing,theratioisnotaconstant.Thistypeofgeariscallednoncirculargears.Fig7-8showsapairofnoncirculargears.Fig.7-8Noncirculargears(非圆齿轮)2.ConjugateProfilesWhenallthecommonnormallinesforeveryinstantaneouspointofcontactcanpassthroughthepitchpoint,thisisthefundamentallawofgearing;anymeshingprofileswhichsatisfythelawofgearingcanbecalledtheconjugateprofiles.

Inordertomaintainthefundamentallawofgearingtobetrue,thegeartoothprofilesonmeshinggearsmustbeconjugateofoneanother.Thereareinfinitenumbersofpossibleconjugatepairsthatcanbeused,butonlyafewcurveshavebeenpracticallyappliedasgearteeth.Thecycloidprofileisstillusedinwatchesandclocksasatoothform,butmostothergearsusetheinvolutecurvefortheirshape.1.Involute(1)DevelopmentoftheinvoluteFig7-9showsaninvolutegeneratedbyalinerollingonthecircumferenceofacirclewithcenteratO;Whenthelinerolls,thepathgeneratedbythepointKonthelineistheinvolutecurve.

7.3InvolutePropertiesandInvoluteToothProfilesFig.7-9Developmentofthe

involute(渐开线的形成)(2)Involuteproperties1)Thelengthofthegeneratinglineisequaltothearclengthwhichthegeneratinglinerollswithoutslippingonthebasecircle.2)Thegeneratinglineisalwaystangenttothebasecircle,anditisalwaysanormaloftheinvoluteatapointK.3)ThelengthNKisthecurvatureradiusoftheinvoluteatpointK.PointNisthecenterofthecurvatureoftheinvoluteatpointK.

4)Theshapeoftheinvolutedependsupontheradiusofthebasecircle.Thesmallertheradiusofthebasecircleis,thesteepertheinvoluteis.Iftheradiusofthebasecircleisinfinite,theinvolutecurvebecomesastraightline.ThisisshowninFig7-10.Fig.7-10Shapeofinvolutes

andradiusofbasecircles

(渐开线的形状与基圆半径)2.MeshingofInvoluteProfiles(1)TheinstantaneousangularvelocityratioisconstantFig7-11showstwobasecircleswithcentersatO1,O2andradiirb1,rb2.

(2)SeparabilityofthecenterdistanceAnychangeincenterdistancewillhavenoeffectupontheinvoluteprofiles;thegearratiocannotbevaried.

(3)StationaryactionforceThelineofactionincaseofinvoluteteethisalongthecommonnormalatthecontactpoint,andthecommonnormalisthecommontangentofthebasecircles.Fig.7-11Gearingofinvoluteprofiles

(渐开线齿廓的啮合)Fig.7-12Spurgearnomenclatures(渐开线直齿圆柱齿轮名词术语)7.4NomenclaturesofStandardSpurGearandGearSizes1.GearTeethNomenclatures(1)AddendumcircleItisacirclepassingthroughthetopesoftheteeth.Theradiusanddiameteraredenotedasraandda.(2)DedendumcircleItisacirclepassingthroughtherootsoftheteeth.Theradiusanddiameteraredenotedasrfanddf.

(3)ReferencecircleItisadatumcircleingeardesignandmeasurement.Theradiusanddiameteraredenotedasrandd.Notethatthesubscriptwillbeomittedwhenexpressingthedimensionsofagear,suchasr,d,p,etc.(4)BasecircleItisacirclegeneratingtheinvolutecurves.Theradiusanddiameteraredenotedasrbanddb.(5)Tooththickness,spacewidthandcircularpitchThetooththicknessisthethicknessofthetoothmeasuredalongthecircumference,suchassK.Thespacewidthisthespacebetweentheadjacentteethmeasuredalongthecircumference,suchaseK(6)Addendum,dedendumandfulldepthTheaddendumistheradialheightfromthereferencecircletotheaddendumcircle,denotedasha.Thededendumistheradialheightfromthereferencecircletotherootcircle,denotedashf.Thefulldepthistheradialdistancebetweentheaddendumcircleandtherootcircle,denotedashf.(7)NormalpitchItisthecircularpitchmeasuredalongtheirnormal,denotedaspb.Itisequaltothecorrespondingpitchonthebasecircle.(8)FacewidthItisthelengthofthetoothparalleltothegearaxis,denotedasB.2.ParametersofInvoluteGear(1)NumberofteethItisthetotalnumberoftheteeththegearpossesses,anditisalwaysaninteger,denotedasz.

(2)ModuleThelengthofcircumferenceofthereferencecircleisequaltothesumofthenumberofthecircularpitchesonthereferencecircle,sowehave:πd=pz.(3)PressureangleThedefinitionofpressureanglehasbeendemonstratedandherewe

Fig.7-13Gearsizewithsamenumber

ofteethanddifferentmoduleofteeth

(同齿数、不同模数齿轮尺寸)emphasizethattherearedifferentanglesonthedifferentcircumferencesofthegear.

(4)CoefficientofaddendumAstandardvalueoftheaddendumisha=h*am.h*aiscalledthecoefficientofaddendum,usually,h*a=1,fornormalteeth;h*a=0.8,forshorterteeth.

(5)Coefficientofclearance3.GeometricalSizesofStandardSpurGears

Ifagearhasthestandardmoduleandpressureangleonthereferencecircle,standardaddendumanddedendum,alsothetooththicknessisequaltothespacewidthonthereferencecircle,itiscalledthestandardgear.

Tab7-2showstheformulaofcalculatingthesizesofstandardgears.4.ToothThicknessAlonganArbitraryCircle

Ingeardesignandmanufacturing,thetooththicknessonthearbitrarycircle,suchastooththicknessonthegeartop,sometimesmaybenecessary.Fig7-14showsageartooththathasthicknesssKatradicallocationrK.Fig.7-14Tooththicknessalonganarbitrarycircle(任意圆齿厚)5.TerminologyforInternalGears

Aninternalgearhasitsteethcutontheinsideoftherimratherthanontheoutside,andithasconcavetoothprofiles,whilethetoothprofilesoftheexternalgearareconvex.Fig7-15showsatypicalinternalgear,andthefollowingsaredifferentfromtheexternalgear.Fig.7-15Terminologyforinternal

gears(渐开线内齿圆柱齿轮术语)6.TerminologyforaRackArackisaportionofagearhavinganinfinitebasediameter,thusitsreferencecircle,addendumcircle,dedendumcircleareallstraightlines.Theinvoluteprofileoftherackbecomesastraightlineandisperpendiculartothelineofaction,seetheFig7-16.

Fig.7-16Terminologyforarack(齿条术语)Thecharacteristicsofarackareasfollows.1)Theprofilesareallskewlines,andtheyareparallelonthesamesideoftheteeth.Thepressureanglesatdifferentpointontheprofileareallthesameandtheyareequaltothenominalpressureangleof20°.2)Thepitchremainsunchangeableonthereferenceline,addendumline,andsoon.Itsvalueisp=πm;thebasepitchispb=πmcosα.3)Theaddendumanddedendumarethesamewiththeexternalgears.

1.ConditionsofCorrectlyMeshingforInvoluteGears7.5MeshingDriveofStandardSpurGearsFig.7-17Meshingofteeth(齿轮啮合)Gearstransmitmotionbymeansofsuccessivelyengagingteeth,butnotbothgearsaretobemeshedtogethercorrectly.Fig7-17showsapairofmeshinggearsinwhichallthecontactpointsbetweenthetwogearswiththeinvoluteprofilesmustlieonthelineofaction,sothatthepitchpointremainfixed.2.ConditionsofContinuousTransmissionofGears(1)MeshingprocessofapairofgearsInFig-7-18,twogears1and2withrotatingcentersatO1andO2respectivelyareincontactatpointB2andK.

(2)Conditionsofcontinuoustransmissionofgears

Fig7-18showsthatthelaterpairofteethisjustcomingintocontactattheinitialpointB2andthepreviouspairofteethisincontactatthepointK,andthecontactwillnotyethavereachedfinalpointB1.Thus,forashorttimetherewillbetwopairsofteethincontact,thecontinuoustransmissionissatisfied.

Fig.7-18Meshingprocessofteeth(轮齿的啮合过程)1)Contactratioforexternalspurgears.Fig7-19showsapairofmeshinggearshavinginvoluteteeth.ThelengthB2B1canbecalculatedfromthefollowingrelationship.Fig.7-19Contactratioforexternal

gears(外啮合齿轮重合度计算)(3)ValueofcontactratioRearrangingtheaboveequations,weobtain:2)Contactratioforinternalspurgears.ThecontactratioforinternalgearisillustratedinFig7-20.Inthesamemethod,wecanobtainthefollowingformula.Fig.7-20Contactratioforinternalgear

(内啮合齿轮重合度计算)3)Contactratioforapinionandarack.ThecontactratioforapinionandarackisillustratedinFig7-21.WherePB1isasthesameasbeforeandPB2dependsupontherelativepositionofthepinionandtherack.Ifthepinionmesheswitharackwithoutchangingthedistanceofthecenter,thatistosay,thereferencelineoftherackistangenttothereferencecircleofthepinion,thelengthofPB2isasfollows:Fig.7-21Contactratioforapinionand

arack(齿轮齿条啮合的重合度计算)Fig.7-22Natureofteethaction(重合度的意义)Thecontactratiomeanstheaveragenumberofpairsofteethwhichareincontactusuallyisnotaninteger.Iftheratiois12,asshowninFig7-22,itdoesnotmeanthatthereare12pairsofteethincontact.Itmeansthattherearealternatelyonepairandtwopairsofteethincontact,oronepairofteethisalwaysincontact,andtwopairsofgearsareincontact20percentoftimes.FromFig7-22,weknowthattherearetwopairsofteethincontactonthesegmentsofB2K′andKB1,andonthesegmentKK′onlyonepairofteethisincontact.3.RelativeSlideBetweenContactTeeth

FromFig7-22weknowthattheworkingprofileofgear1isfrompointB2toitstoothtop,andtheworkingprofileofgear2isfrompointB1toitstoothtop.Whenthepairofteethcontactsatanarbitrarypoint,suchaspointK′,theslidewilloccurbetweentheteethsurfacesalongtheirtangentdirection.ThisisbecausethatthevelocityofpointK′isnotthesameonthetwogears.4.CenterDistanceofGearsWhentheshaftsofapairofgearsaremountedcorrectly,thefollowingconditionsmustbesatisfied.1)Theradicalclearancebetweentheaddendumcircleofagearandthededendumcircleofthemeshinggearmustbethestandardvalue,thatisc=c*m;seetheFig7-23.

Fig.7-23Normalcenterdistance(无侧隙啮合的径向间隙)2)Thebacklashmustbezerotheoretically;thetooththicknessonthepitchcircleisequaltothespacewidthonthepitchcircleofthemeshinggear.5.PinionandRackExample7-1Twoinvolutegearsinmeshhaveamoduleof2.5mmandapressureangleof20°.Thenumbersofteetharez1=22,z2=33.Thecoefficientofaddendumish*a=1,andc*=0.25.Findthefollowings:1)Sizesofthetwogears;2)Contactratio;3)Ifthecenterdistanceisincreased1mm,findthecontactratio.

Fig.7-24Meshingofapinionandarack(齿轮与齿条啮合)1.GearTeethForming(1)FormingCuttingProbablytheoldestmethodofcuttinggearteethismilling.Aformmillingcuttercorrespondingtotheshapeofthetoothspaceisusedtocutonetoothspaceatatime,afterthegearisindexedthroughonecircularpitchtothenextposition.Therearetwokindsofmillingcutter:oneisthedisccuttershowninFig7-25a;theotheristhefingercuttershowninFig7-25b.

7.6FormingandUndercuttingofGearTeethFig.7-25Formingcutting(仿形加工)(2)GeneratingCuttingIngenerating,atoolhavingashapedifferentfromthetoothprofileismovedrelativetothegearblanktoobtainthepropertoothshape.Themostcommonmethodsofgeneratinggearteethareshapingmethodandhobbingmethod.1)Shapingteeth.Shapingisahighlyfavoredmethodofgeneratingteethofgear.Thecuttingtoolusedintheshapingmethodiseitherarackcutterorapinioncutter.Fig7-26showsshapingteethwithapinioncutter;Fig7-27showsshapingteethwitharackcutter.Fig.7-26Shapingteethwith

apinioncutter(齿轮插刀)Fig.7-27Shapingteethwith

arackcutter(齿条插刀)Fig.7-28Hobbingteeth(滚齿加工)2)Hobbingteeth.Fig7-28illustratesthegeneratingprocesswithahob.Ahobisacylindricalcutterwithoneormorehelicalthreadsquitelikeascrewthreadtap,andhasstraightsideslikearack.Thehobandtheblankarerotatecontinuouslyattheproperangularvelocityratio,andthehobisthenfedslowlyacrossthefaceoftheblankfromoneendofteethtotheother.Allteethhavebeencut.Fig.7-29Undercutting(根切现象)2.Undercutting

Whengearteethareproducedbyageneratingprocess,thetopofcuttingtoolremovestheportionoftheinvoluteprofileneartherootteeth.Thisiscalledundercutting.TheundercuttingweakensthetoothbyremovingmaterialatitsrootshowninFig7-29.Severeundercuttingwillpromoteearlytoothfailure.Itmayalsoreducethelengthofcontactandresultinrougherandnoisiergearaction.Inmachinedesign,theundercuttingmustbeavoidedoreliminatedbythedesigner.Fig.7-30Rackcutterprofile

(齿条插刀的齿廓)(1)CausationofundercuttingThedifferencebetweentherackcutterandtherackisthattheaddendumoftherackcutterisgreaterthanthatoftherack,adistancec*m,asshowninFig7-30.Fig.7-31Undercuttingprocess(根切的形成)Fig7-31illustratesageneratingprocessofastandardgearwiththerackcutter.TheinitialpointofcuttingisatpointB1whichistheintersectionbetweenthelineofactionandtherightedgeoftherackcutter.Whentherackcutterismovedfromposition1toposition2,theinvoluteprofileofthegearwillcompletelybecut.BecausetheaddendumlineoftherackexceedstheextremepointN,thegeneratingprocesscannotbestopped,suchasatposition3,obviously,theinvoluteprofileoftheroottoothontheleftedgeofthecutterwillbecutaway.(2)MinimumnumberofteethtoavoidundercuttingThemethodstoeliminateundercuttingareasfollows:1)Reducetheheightofthetoothofthecutter.ThesegearstobecutarecalledshorttoothgearsFig.7-32Minimumnumberofteethtoavoid

undercutting(避免根切的最少齿数);theyhaveasmallcontactratio.2)Increasethepressureangle.Thisresultsinasmallerbasecircle,sothatmoreofthetoothprofilebecomesinvolute.3)Reducethenumberofteeth.Whenthenumberofteethofageartobecutisreduced,theradiusofbasecircleisreducedtoo,andtheextremepointNislikelytofallontherightofthepointB2wheretheaddendumlineoftherackcutterintersectsthelineofaction.SeetheFig7-32.1.ConceptofNonstandardGears7.7NonstandardSpurGearsIngeneratingastandardgearwitharackcutter,iftheaddendumlineoftherackcutterexcessestheextremepointNwheretheaddendumlineofthecutterintersectsthelineofaction,theundercuttingwilloccur.Tosolveit,therackcuttercanbemovedadistancexmoutwardsuntiltheaddendumlineofthecutterfallsdowntheextremepointN,asshowninFig7-33.Inthiscase,thereferencelineisnolongertangenttothereferencecircleofthegear,thelinewhichistangenttothereferencecircleofthegearisthepitchline,andthetooththicknessandtoothspaceonthepitchlineoftherackisnotequal.Thetooththicknessandtoothspaceonthereferencecircleofthegeartobecutisnotequaltoo.Thisgeariscalledthenonstandardgearormodifiedgear.

2.MinimumCoefficientofOffsetFig.7-33Smallestcoefficientofoffset(最小变位系数)WhentheaddendumlinepassesthroughtheextremepointN,thereisjustnoundercuttingtooccur,asshowninFig7-33.Therefor,wehave:3.ComparisonofStandardGearandNonstandardGear(1)NovariedsizesThebasecircle,referencecircle,circularpitchandbasepitcharenotvaried.Theinvolutecurveisnotchanged;itisusedonthedifferentportionoftheinvolute.

Fig.7-34Tooththicknessofapositivemodifiedgear(正变位齿轮齿厚)(2)VariedsizesThetooththicknessandwidthspacearevaried.Fig7-34showsageneratingprocessofastandardgearandapositivemodifiedgear.Theaddendumanddedendumarevaried.FromtheFig7-35,wecanobservethattheaddendumofapositivemodifiedgearislargerthanthatofthestandardgear,anditsdedendumissmallerthanthatofthestandardgear.Inthesamemethod,wecanfindthedifferencebetweenthestandardgearandnegativemodifiedgearintheiraddendumanddedendum.Fig.7-35Toothprofilesofthestandardgearand

modifiedgears(变位齿轮与标准齿轮的齿廓)4.BriefIntroductionofNonstandardGears

Supposingthatthecoefficientsofoffsetofthetwogearsarex1andx2,thetypesofgeartransmissioncanbeclassifiedasfollows.1)Thecoefficientsofoffsetx1andx2areallzero,thatis:x1+x2=0，andx1=x2=0.Itisapairofstandardgears.2)Thecoefficientsofoffsetx1andx2areequalinmagnitudebutoppositeindirection;thatis:x1+x2=0，andx1=-x2≠0.

3)Thesumofthecoefficientsofoffsetx1andx2isnotequalzero,thatis:x1+x2≠01.ShapeoftheToothofHelicalGearFig.7-36Toothsurfaceofaspurgearandahelicalgear(渐开线圆柱齿轮和斜齿轮轮齿的齿面)7.8ParallelHelicalGears

IfaplaneSrollsonabasecylinder,alineKK′paralleltotheaxisofthecylinderintheplanewillgenerateaninvolutesurfaceofaspurgearonthecylinder,showninFig7-36a.Thus,whenapairofspurgearsisinmesh,contactbetweentheteethisalongthelineparalleltotheaxis.However,ifthelineintheplaneisinclinedanangleβbtotheaxisofthecylinder,itwillgeneratesaninvolutehelicoids,asshowninFig7-36b.2.BasicParametersofaHelicalGear(1)HelixangleFig7-37ashowsahelicalgearwithrighthandthread.Ifweextendthewidthofthehelicalgearuntilitisequaltotheleadofthehelix,thendevelopthebasecylinderandreferencecylinder;thehelixanglescanbedeterminedfromFig3-37b.

Fig.7-37Helixangles(螺旋角)(2)NormalmoduleandtransversemoduleThetransverseplaneofahelicalgearisperpendiculartoitsaxis,anditisacirclewhichisusedtocalculateitsgeometricalsizes.Thenormalplaneisperpendiculartoitstooththread;itisanellipsewhichisusedtoanalyzeforceaction.Therefore,theparametersofthehelicalgearcanbedividedintothatofthetransverseplaneandnormalplane.Fig.7-38Helicalgeartoothrelations(斜齿轮模数关系)Fig.7-39Normalpressureangle

andtransversepressureangle

(法向压力角和端面压力角)

(3)Normalandtransversecoefficientsofaddendum(4)Normalandtransversecoefficientsofclearance(5)NormalandtransversepressureanglesThespurgearsareidentifiedbymeansofonepressureangle;thegeometryofhelicalgearsrequiresthetwopressureangles.Fig7-39showsthetoothprofileofahelicalrackonthetransverseplaneandnormalplane.4.ConditionsofCorrectlyMeshingforHelicalGears

Theconditionsofcorrectlyengagingforapairofhelicalgearsarethatthenormalmoduleandnormalpressureangleofthetwomeshinggearsmustbethesamerespectively,orthetransversemoduleandtransversepressureangleofthetwomeshinggearsmustbethesamerespectively;theirhelixanglesmustbeequalandhaveoppositehelicaldirections.Theyare:mn1=mn2或mt1=mt2

αn1=αn2或αt1=αt2

β1=-β2（“-”代表旋向相反）5.ConditionsofContinuousTransmissionofGearsFig.7-40Contactratioforhelicalgears(斜齿轮传动重合度)Thecontactratioofapairofhelicalgearsisgreaterthanthatofspurgears.ThiscanbeillustratedinFig7-40.Theupperfigureisadevelopedbasecylinderofaspurgearinwhichthetransverseplaneiscoincidentwiththenormalplane;thelineB1B2representsthecontactlengthofthegears.Thecontactratiois:ε=εa+εβTheFig7-whichhasthesamenumberofteethandthetransversemodulewiththeFig7-40aspurgear.6.EquivalentSpurGear

Inordertounderstandthetoothshapeofthenormalplaneofahelicalgear,ahelicalgearcanbecutbytheobliqueplanewhichisperpendiculartothetoothdirection,asshowninFig7-41.Theintersectionoftheobliqueplaneandthereferencecylinderproducesanellipsewhosesemimajoraxisisa,andsemiminoraxisisb.Fig.7-41Equivalentspurgear

(当量齿轮)7.AdvantagesandDisadvantagesofHelicalGears

Helicalgearsaremoreexpensivethanspurgearsbutoffersomeadvantages.Theyoperatequieterthanspurgearsbecauseofsmoothandgradualcontactbetweentheiranglesurfacesastheteethcomeintomesh.Spurgearteethmeshalongtheirentirefacewidthatonce;thesuddenimpactoftoothontoothcausesvibration.Also,forthesamegeardiameterandmodule,ahelicalgearisstrongerduetotheslightlythickertoothforminaplaneperpendiculartothegearaxis.

Theoneofthedisadvantagesofhelicalgearsisthattheyproduceanaxialthrustforcewhichisharmfultothebearings.Therefore,thehelixangleislimitedfrom8°~15°.1.CharacteristicsofWormGearsFig.7-42Wormandwormgear(蜗轮蜗杆)7.9WormandWormGearsWormandwormgearareusedtotransmitmotionbetweentwoshaftswhicharenonparallel,nonintersecting,usuallyatashaftangleof90°,asshowninFig7-42.2.TypesofWormGears

Fig.7-43WormTypes(蜗杆传动类型)3.ParametersandSizesofWormGears(1)ParametersofwormgearsInthemainsectionwhichisperpendiculartotheaxisofthewormgearandcontainstheaxisofthecylindricalworm,theconjugateactionofwormsisthesameasarackand