設(shè)計（Design）何孔德三峽大學(xué)機械與材料學(xué)院M-261313872631306Thischaptermainlyintroducesthetypesofgearmechanisms,theinvolute(漸開線)anditsproperties,standardandhelicalinvolutegear,wormgearingandbevelgears（圓錐齒輪）.Emphases★：

theinvoluteanditsproperties,gearingofstandardinvolutespurgears,contactratioofaninvolutespurgearset.

Difficulties▲:AddendumModificationoninvolutegears,helicalgears,etc.Chapter2GEARMECHANISMS

齒輪機構(gòu)是用來傳遞任意兩軸間的運動和動力的，它是應(yīng)用最為廣泛的一種機械傳動機構(gòu)之一。齒輪傳動的特點1、主要優(yōu)點1)適用的圓周速度和功率范圍廣；2)機械效率高；3)可現(xiàn)準(zhǔn)確的傳動比、且傳動平穩(wěn)；4)壽命長；5)工作可靠；6)可實現(xiàn)空間任意兩軸（平行軸、相交軸、交錯軸）之間的傳動；7)結(jié)構(gòu)緊湊。2、主要缺點

1)要求有較高的制造和安裝精度，成本相對較高；

2)不適宜于遠(yuǎn)距離兩軸之間的傳動。Circulargears:constanttransmissionratio

non-circulargears:theratiovaries

Inthischapter,onlycirculargearsareconsidered.6.1TypesofGearMechanismsDependingontherelativeshaftspositions

parallelshafts→planargearmechanism(平面)

nonparallelshafts→spatialgearmechanism

(空間)6.1.1PlanarGearMechanismsExternalgearpair

Internalgearpair

Rackandpinion(齒條和齒輪)Externalgear:Spurgear(直齒輪)Helicalgear(斜齒輪)DoubleHelicalgear(人字齒輪)Internalgearpair:1.Spurinternalgear2.Helicalinternalgear6.1.2SpatialGearMechanisms1.Bevelgearmechanism(錐齒輪)

2.Crossedhelicalgearmechanism(螺旋齒輪機構(gòu))3.Wormandwormwheelmechanism(蝸桿蝸輪機構(gòu))6.2FundamentalsofEngagementofToothProfiles(齒廓嚙合基本定律)6.2.1FundamentalLawofGearing

VP1=VP2

1·O1P=2

·O2P

P12istheinstantcentreofthegears1and2.

P12P----------thepitchpoint(節(jié)點).Ifaconstanttransmissionratioi12isrequired.Wherever(無論何處)theteethcontact,thecommonnormaln-nofthetoothprofilesthroughthecontactpointmustintersectthecenterlineatafixedpoint。Pitchcircle(節(jié)圓):

thelocusofthepitchpointPonthemotionplaneofthepinionorthegear.

Pitchcirclesaretangentandrollwithoutslippingeachother純滾動.Thegearpairisrepresentedbytwochaindotted(點劃線)circlestangenttoeachother.動畫演示6.2.2ConjugateProfiles(共軛齒廓)

Meshing(嚙合的)profilesofteeththatcanyieldadesiredtransmissionratio(傳動比)aretermedconjugateprofiles.Foranyspecifictoothprofile,wecanfinditsconjugateprofile.

Involutes(漸開線)areusedmostwidelysincetheycanbemanufacturedandassembledeasily.兩頭牛背上的架子稱為軛，軛使兩頭牛同步行走。共軛即為按一定規(guī)律相配的一對。6.3TheInvolute(漸開線)andItsProperties6.3.1GenerationofInvolute

Aninvoluteisthecurvegeneratedbyanypointonastringwhichisunwrapped(展開)fromafixedcircle.

rb

——Theradiusofbasecircle（基圓）.n-n——Generatingline(發(fā)生線)

K

——unfoldingangle(展角)oftheinvoluteatpointK.

6.3.2PropertiesoftheInvolute

1.Thelengthofthegeneratingline(發(fā)生線)segmentunrolledfromthebasecircleisequaltothearclengthofthebasecirclerolled.

2.ThelengthofsegmentNKistheradiusofcurvatureoftheinvoluteatthepointK.

A=03.Thenormaldistancebetweentwoinvolutesofthesamebasecircleremainsthesame.4.Theshapeofaninvolutedependsonlyontheradiusofitsbasecircle.

Astheradiusrbofthebasecircleapproachesinfinity,theinvolutebecomesastraightline.5.Noinvoluteexistsinsideitsbasecircle.

6.3.3EquationoftheInvolute漸開線方程Pressureangle

K

FVK=NOKFVKThepolarparametricequationoftheinvolute漸開線方程with

Kasaparameteris6.3.4Gearing(嚙合)ofInvoluteProfilesInvolutegearshaveconstanttransmissionratio.constant

1.Locusofcontactpoint,thelineofaction(嚙合線)=commonnormaltotheinvoluteprofiles=thecommontangenttothebasecirclesCharacteristicsofthegearingoftheinvoluteprofile:SinceO1PN1O2PN2,2、Involutegearshaveseparability(可分離性)ofthecentredistance.Achangeincenterdistancedoesnotthereforeaffecttheconstanttransmissionratioofaninvolutegearpair.3、Workingpressureangle’α’isdefinedastheanglebetweenthevelocityofpitchpointP(onbothgears)andthelineofactionN1N2.

6.4.1.ExternalGears

6.4.StandardInvoluteSpurGearsThetoothnumberofagear----Z（齒數(shù)）Parametersofgear:

thefacewidth(齒寬)----Baddendumcircle(ortipcircle)（齒頂圓）----da,radedendumcircle(orrootcircle)（齒根圓）----df,rfbasecircle----db,rbanarbitrarycircle(任意圓)----di,riThetoothspace(齒槽)----thespacebetweentheprofilesoftwoadjacentteeth.Thespacewidth(齒槽寬)ei----thearclengthofthetoothspacealonganarbitrarycircle.Thetooththickness(齒厚)si----thearclengthofthetoothalonganarbitrarycircle.Thepitch(齒距，周節(jié))pi---arcdistancebetweencorrespondingpointsofadjacentteethalonganarbitrarycircle.pi=ei+sipressureangle

K

Differentpointontheinvolutehasdifferentpressureangle

K.

Thecirclethepointonwhichhas20°pressureangleisdefinedasreferencecircle(分度圓).FVKαKAnyparameteronthereferencecirclehasnosubscript(下標(biāo)),i.e.,r,e,s,p,=20°pi=ei+si

p=e+sThemodulem(模數(shù))----abasicparameteronthereferencecircle.Differentmoduleneedsdifferentcutter.Themodulemhasbeenstandardized.

m,Z,

arethreebasicparametersofagear.Tab6-1

modulesofInvoluteCylindricalGears

(GB/T1357-1987)Modulesofthefirstseriesarepreferable.

Firstseries0.1,0.12,0.15,0.2,0.25,0.3,0.4,0.5,0.6,0.8,1,1.25,1.5,2,2.5,3,4,5,6,8,10,12,16,20,25,32,40,

Secondseries0.35,0.7,0.9,1.75,2.25,2.75,(3.25),3.5,(3.75),4.5,5.5,(6.5),7,9,(11),14,18,22,28,(30),36,45Theaddendum(齒頂高)ha----radialdistancebetweenthereferencecircleandtheaddendumcircle.Thededendum(齒根高)hf----radialdistancebetweenthereferencecircleandthededendumcircle.Thetoothdepth(齒全高)h----radialdistancebetweenthededendumcircleandaddendumcircle.動畫演示Forstandardgears:c*----thecoefficientofbottomclearance(頂隙系數(shù)）ha*----thecoefficientofaddendum(齒頂高系數(shù)）ha*=1andc*=0.25forthenormaltooth(正常齒)ha*=0.8andc*=0.3fortheshortertooth(短齒)

c=c*m--------bottomclearance頂隙Basepitch(基節(jié))pb---thepitchonthebasecircle.Normalpitch(法節(jié))pn-------Thedistancebetweencorrespondingsidesofadjacenttoothprofilesalongthecommonnormal.pb=pnThefundamentalparameters:Z,m,

,ha*,c*Astandardgearmeans:m,

,ha*,c*takethestandardvaluesande=s一個齒輪：d=mzda=d+2ha=(z+2ha*)mdf=d-2hf=(z-2ha*-2c*)mdb=dcosαha=ha*mhf=(ha*+c*)mh=ha+hf=(2ha*+c*)mP=πm一對標(biāo)準(zhǔn)齒輪正常安裝：Involutesstraightlines6.4.2TheRack（齒條）

i

pipm

Thecharacteristicofrack:

Onthereferenceline(分度線),e=s.

Forstandardrack,ha=ha*m,hf=(ha*+c*)m6.4.3InternalGearsThetooththickness

thetoothspace——theactuallineofaction

——theoreticallineofaction

齒廓工作段theactualworkingprofile齒廓非工作段6.5GearingofInvoluteSpurGearsToensureacontinuoustransmission,theremustexistsuchsituationthattwopairsofteethcontactsimultaneously(同時地).

6.5.1ProperMeshingConditions(正確嚙合條件)forInvoluteGearsTwopairsofteethcontactsimultaneouslyatpointK1andK2K1K2=Pb1

K1K2=Pb2

∴Pb1=Pb2

Accordingtothepropertyoftheinvolute:Thepropermeshingconditionforinvolutegears:

Themodulesandpressureanglesoftwomeshinggearsarethesamerespectively.

6.5.2zerobacklash齒側(cè)間隙ofagearpairtherequirementsindesigningagearpair:Thebacklashshouldbezero.Tokeepzerobacklash,itholds:Thecentredistanceaisequalto(r1+r2),thereferencecirclescoincidewiththeirpitchcircles節(jié)圓.

Thetworeferencecircles分度圓aretangentandrollwithoutslipping.

6.5.3標(biāo)準(zhǔn)安裝Ifbothgearsarestandard,wehave:zerobacklash,無側(cè)隙嚙合標(biāo)準(zhǔn)安裝Thecentredistancea=r1+r2iscalledthereferencecentredistance(標(biāo)準(zhǔn)中心距).標(biāo)準(zhǔn)安裝Workingpressureangle’(嚙合角)標(biāo)準(zhǔn)安裝thebottomclearance(頂隙)c：theradialdistancefromthededendumcircleofonegeartotheaddendumcircleofanother標(biāo)準(zhǔn)安裝標(biāo)準(zhǔn)值Therefore,whentwostandardgearsareassembledatacentredistancea=r1+r2,notonlythebacklash=0,butalsobottomclearancec=c*m.

標(biāo)準(zhǔn)安裝Whentheactualcentredistancea’islargerthan(r1+r2),thereferencecircleswillseparate.Thetwopitchcircleswillbecomelargerandremaintangent.6.5.4非標(biāo)準(zhǔn)安裝a’只有增大——nonzerobacklash非標(biāo)準(zhǔn)安裝6.5.4transmissionratioconstantThepropermeshingconditionisNOTasufficientconditiontoensureacontinuoustransmission.

Thepropermeshingcondition:6.6ContactRatio(重合度)ofanInvoluteSpurGearSetGear1isadriver.6.6.1definitionofContactRatio

(重合度)ThemeshingbeginsatpointB2,KmovesalongthelineofactionandendsatpointB1ThesegmentB1B2iscalledtheactuallineofaction(實際嚙合線).IfTransmissioniscontinuousDefinethecontactratioas:TheconditionofcontinuousmotiontransmissionUsually,>[

]=1.2.Thevalueofthecontactratioindicatestheaverage(平均)numberoftoothpairsincontactduringacycletosharetheload.6.6.3CalculationofContactRatio(重合度)Forexternalgearpair:

dependsonZ1,Z2,a1,a2,’(2)rb1=ra1cos

a1,rb2=ra2cos

a2(6)Ifa’,thentan’and

.(5)IfZ,then

.Trytousesmallerm.(4)

isindependentofmodulem.(3)Ifra,thena

and

.短齒制缺點(1)6.7ManufacturingMethodsofInvoluteProfilesCuttingisthemostcommonmethodformanufactureofgears.

Therearevariousmethodsformanufacturingtoothprofiles,suchasdiecasting(模鑄),precisionforging(鍛造),punch沖壓,powder(粉末)process,cutting切削法andsoon.6.7.1CuttingofToothProfiles(1)Form(仿形法)Cutting(2)Generating(展成法或范成法)CuttingTherearegenerallytwotypesofcuttingmethods:FormCutting

Therearethreetypesofcutters:

Diskmillingcutter(盤形銑刀）Endmillingcutter(指狀銑刀)Broach(拉刀)DiskmillingcutterEndmillingcutters(端銑刀)areusedforlargemodulesanddoublehelicalgears.broach(拉刀)Characteristicsoftheformcutting:rb=rcos=(mZ/2)cosAstheshapeofaninvolutedependsonitsbaseradius,adifferentcutterisrequiredforeachnumberofteethevenforthesamemoduleandsamepressureangle.Formcuttingisnotagoodmethod.Itsmainadvantageisthatitcanbeaccomplishedoncommonlyavailablemillingmachines.(銑床)(2)GeneratingCutting(展成法或范成法加工)Inageneratingcuttingmethod,theedgesofacuttertaketheformofagear(orrack)withthesamemoduleandpressureangleasthegeartobecut1.Cuttingmotion3.Generatingmotion展成2.Retreatmotion退刀4.Feedmotion進給Externalgearscanbecutwitharack-shapedshapercutter(齒條插刀).TheedgesofthecutterarenowstraightlineswhichcanbemadeaccuratelyThecuttingprocessintheshaping(插齒)ofagearisnotcontinuous.

Inmassproduction,hobbing(滾齒)isusedinsteadofshaping.6.7.2CuttingaStandardGearwithStandardRack-shapedCutterThetiplineisc*mhigherthantheaddendumlineforcuttingtheprofileattheroottoprovidehfIndiscussingthegeneratingofaninvoluteprofile,wesimplyregardthestandardrack-shapedcutterashavingthesameprofileasthestandardrack.Tocutastandardgear,thereferencelineofthecuttershouldbetangenttothereferencecircleofthegearThem,

,ofthegearonthereferencecirclearethesameasthoseonthereferenceline.Asthes2ande2ofthecutteronthereferencelineareequaltoeachother,thegeariscutwiths=e=p/2=

m/2.Thededendumcircleofthegeariscutbythetiplineofthecutter.Theaddendumcircleofthegeariscutonalathe(車床).Itisnotcutbygearcutter!!6.7.3CutterInterference(根切現(xiàn)象)Somepartoftheinvoluteprofileneartherootportionisremovedinthegeneratingcutting.Thiswillreducethecontactratioaswellasthestrengthofthetoothandshouldbeavoidedorminimized.Thereasonforcutterinterference:

TheaddendumlineofthecutterpassesthelimitpointN1ofthelineofaction.Topreventcutterinterference:短齒制：ha*=0.8，a=20°，Zmin=146.8AddendumModificationonInvoluteGears

齒輪變位6.8.1IntroductionofAddendumModificationDisadvantagesofstandardgears:1.ZZmin2.a’=a3.Thestrengthofthepinionismuchlowerthanthatofthegear.——外嚙合

無法安裝；

Correctedgears變位齒輪Incuttingthecorrectedgear,therackshapedcutterislocatedadistancexmfromthepositionusedforcuttingthestandardgear.xm——thedistancebetweenthepitchlineandthereferencelinex——modificationcoefficient

正變位

零變位

負(fù)變位

Onlythepositionofthecuttermaybechanged----thereferencelineofthecuttermaynotbetangenttothereferencecircleofthegear.Thegear-cuttingmachines,thecuttersandthetransmissionratiobetweenthecutterandtheblankremainsunchanged.Comparisonbetweenacorrectedgearandthestandardgear:1.ParametersZ,m,r(=mZ/2),

,andrb=(rcos

)arethesame.2.Parametersdf,da,s,emaychange.Thismeansthatdifferentportionsofthesameinvoluteareemployedfortheprofilesofthestandardgearandthecorrectedgear6.8.2GeometricDimensionsofCorrectedGears

Topreventcutterinterference：最小變位系數(shù)正變位

負(fù)變位

1、分度圓上的齒厚見圖：刀具節(jié)線的齒槽寬比中線齒槽寬，∴被切齒輪分度圓上的齒厚增加在△IJK中：

分度圓的齒厚：

2、齒頂高和齒根高

齒根高h(yuǎn)f：刀具加工節(jié)線到頂刃線之間的距離

對正變位：x>0，hf比標(biāo)準(zhǔn)減小xm

對負(fù)變位：x<0，hf比標(biāo)準(zhǔn)增加xm

∴變位齒輪的齒根圓半徑：

齒頂高：

∵變位齒輪的分度圓與相應(yīng)標(biāo)準(zhǔn)齒輪的分度圓一樣，∴變位齒輪的齒頂高僅決定于輪坯頂圓的大小。

為保證齒全高

由于所以6.8.3GearingofaCorrectedGearPairTokeepzerobacklash,itholds:Itcanbeshownthatthisresultsin:Thisisthegearingequationwithoutbacklash(無側(cè)隙嚙合方程).節(jié)圓與分度圓重合，a’=a節(jié)圓與分度圓不重合，a’≠a中心矩變動系數(shù)y:6.8.4TypesofCorrectedGearPairs(2)Heightcorrectiongearpair(等變位傳動):Standardgeardrive(零變位：標(biāo)準(zhǔn)傳動):x1＝0，x2=0，’＝＝20°,a’=a

互換性好，>1.2.x1=-x2>0(x1+x2=0),’＝＝20°,a’=a,r1’=r1,r2’=r2Z1maylessthan17.(Z1+Z2)mustbelargerthan34.

a’=a,Twogearsmayhavesamestrengths.suitableforanya’.Disadvantages:

(3)Angularcorrectiongearpairwithx1+x2

0anda’a.Positivegearing(正傳動)：x1+x2>0

’>＝20°,a’>a,r1’>r1,r2’>r2Thegearmaybenegativemodified(負(fù)變位).Advantages:(Z1+Z2)maybelessthan34.StrengthofgearsDisadvantages:

StrengthofgearsAdvantages:

(b)Negativegearing(負(fù)傳動):x1+x2<0’<＝20°,a’<a,r1’<r1,r2’<r2Pinionmaybepositivemodified(正變位).suitableforanya’.Negativegearing(負(fù)傳動）isnotrecommended(推薦).6.9HelicalGearsforParallelShafts(斜齒輪傳動)6.9.1GenerationandCharacteristicsofHelicalTeethSpurgearThetoothsurfaceofthespurgearisthereforeaninvolutecylinder(漸開線柱面).

Thetoothsurfacesofspurgearscontactonastraightlineparalleltotheaxesofthegears.suddenloadingandsuddenunloadingonteethVibrationandnoiseIngenerationofthetoothprofileofahelicalgear,thestraightlineKKonthegeneratingplaneisnolongerparalleltotheaxisofthegear.EverypointonthestraightlineKKwillproduceaninvolute.Thecurveconnectingthestartingpointsoftheinvolutesonthebasecylinderisahelix(螺旋)AA.Thesurfaceprofileofahelicalgeariscalledaninvolutehelicoid(漸開線螺旋面)1Thetoothsurfacesoftwoengaginghelicalgearscontactonastraightlineinclined.漸開線螺旋面齒廓的特點②端面（垂直于齒輪軸線的面）與齒廓曲面的交線為漸開線。③與基圓柱同軸的圓柱面與漸開線螺旋面的交線為一螺旋線。不同面→螺旋角不同斜齒輪的嚙合特點：（1）兩斜齒齒廓的公法面既是兩基圓柱的公切面，又是傳動的嚙合面（2）兩齒廓的接觸線與軸線夾角βbThelengthofthecontactlinechangesgraduallyfromzerotomaximumandthenfrommaximumtozero.Theloadingandunloadingoftheteethbecomegradualandsmooth.Thatiswhyhelicalgearscanoperateatahigherspeed.6.9.2ParametersofHelicalGears1、斜齒輪的切削加工：①仿形法；②范成法：滾齒（用仿形法加工斜齒輪時，銑刀是沿螺旋齒槽的方向進刀的）1.Onthetransverseplane(端面)(withsubscript“t”)⊥軸線的面Thetransverseprofileofahelicalgearisaninvolute.Twosetsofparameters:2.Onthenormalplane(法面)（withsubscript“n”)垂直于分度圓柱面螺旋線的切線的平面Parametersonthenormalplanearethestandardvalues.

Theyaredeterminedbycutter.進刀方向⊥法面

刀具的齒形應(yīng)于斜齒輪的法面齒形相同，→法面上的模數(shù)和壓力角為標(biāo)準(zhǔn)值。mnisstandardized.

n=20

t20三維圖???mn,han*andcn*takethestandardvaluesasforspurgears.螺旋角β：

螺旋線的導(dǎo)程

Pz:螺旋線繞一周時它沿軸線方向前進的距離

（上式表明，不同圓柱面的螺旋角不等）

ThereferencediameterandcentredistanceshouldbecalculatedonthetransverseplaneasReferencecentredistanceacanbeadjustedbychangingthehelixangle(螺旋角)

.Standardhelicalgeardrivecansuitanycentredistance.6.9.3ProperMeshingConditionsforHelicalGearsReview:Accordingtothepropermeshingconditionsofspurgeardrive,6.9.4ContactRatioforaHelicalGearPairThelengthoftheactuallineofactionincreasesbyL.

iscalledthetransversecontactratio(端面重合度).

iscalledtheoverlapratio(軸向重合度).Thetransversecontactratio

canbecalculatedwiththeparametersonthetransverseplane.軸向重合度

Dueto

,thecontactratioofahelicalgearpairismuchhigherthanthatofaspurgearpair.Alargecontactratiomeansthatmoregearteethareengagedatthesametimewhichgiveshighstrengthtothegears.

6.9.5VirtualNumberofTeeth(當(dāng)量齒數(shù))forHelicalGearsTocalculatethestrengthofthetooth,andtochoosethetypeofthecuttingtool,thevirtualgear(當(dāng)量齒輪)ofthehelicalgearisintroduced.Thevirtualgear(當(dāng)量齒輪)ofthehelicalgearisaspurgear,thetoothprofileofwhichisequivalenttothatofahelicalgearonthenormalplane.

當(dāng)量齒輪：以ρ為分度圓半徑，用斜齒輪的mn和αn分別為模數(shù)和壓力角作一虛擬的直齒輪，其齒形與斜齒輪的法面齒形最接近。這個齒輪稱斜齒輪的當(dāng)量齒輪，齒數(shù)ZV稱當(dāng)量齒數(shù)。Thevirtualnumberofteeth(當(dāng)量齒數(shù))forthehelicalgear------thenumberZvofteethofthevirtualgear.Zvisusedtocalculatethestrengthofthetooth.

已知mn、

n、Z、

的斜齒輪法面齒形

以mn為模數(shù)、以

n為壓力角、以Zv為齒數(shù)的直齒輪齒形。Furthermore,theminimumnumberofteethofthestandardhelicalgearwithoutcutterinterferencecanbederivedasAdvantageofhelicalgears：Helicalgearsoperatemoresmoothly.Havehigherstrength.Theworkingcentredistanceofahelicalgearpaircanbeadjustedbythehelixangle

.比直齒輪小，機構(gòu)更緊湊制造成本與直齒輪相同Helicalgearsarethereforewidelyusedforhighspeedorheavyloadtransmission.Themaindisadvantageofhelicalgearsis:Theyproduceanaxialthrust(軸向推力).HelicalgearsThehelixangleisthereforelimitedtowithin8

to20.

DoubleHelicalgears6.10.1WormGearinganditsCharacteristicsWormgeardrivesareusedtotransmitmotionandpowerbetweennon-intersectingandnon-parallelshafts,usuallycrossingatarightangle.6.10WormGearing(蝸桿傳動)Wormsareakindofscrew,usuallyrighthanded(右旋)forconvenienceofcutting,orlefthanded(左旋)ifnecessary.Wormsareusuallydriverstoreducethespeed.Directionof

1?Directionofhelixoftheworm?Wormwheels(蝸輪)arethematinggearsoftheworms.Maincharacteristicsofwormgeardrives:(1)Smoothsilentoperationasscrewdrives.(2)Greaterspeedreduction.(3)Iftheleadangle(導(dǎo)程角)

1

ofawormislessthantheequivalentfrictionangle(當(dāng)量摩擦角)

V,theback-drivingisself-lockingtg

V=fV(當(dāng)量摩擦系數(shù))(4)Lowerefficiency(效率)<70%6.10.2TypesofWorms(1)Straightsidedaxialworms圓柱蝸桿-------ZA-worm阿基米德蝸桿Thetransversesection(橫切面)isArchimedesspiral(螺旋線).Theaxialsectionisinvoluterack.(2)Involutehelicoidworms----ZI-worm漸開線蝸桿螺旋面(3)Arc-contactworms-----ZC-worm圓弧齒蝸桿Smallerstress(4)Envelopingworm(包絡(luò)蝸桿),moreteethengaged.(5)Spiroid錐蝸桿6.10.3ProperMeshingConditionsforWormDrivesThemid-plane主平面----Thetransverseplaneofawormwheelpassingthroughtheaxisoftheworm.Theengagement(嚙合)betweenaArchimedeswormandawormwheelonthemid-planecorrespondstothatofaninvoluterackandpinion.Necessaryconditionsforawormandawormwheeltomeshproperly.Thewormwheelshouldbecutbyacutterwiththesameshapeasthoseofthematingworm.6.10.4MainParametersandDimensionsforWormDrives1）Theaxialpressureangleofworm

x1is20

.Thiscanbeincreasedto25

inpowertransmissionordecreasedto15

or12

inindexingdevices(分度裝置).2)Themodulem----standardvaluesTheseriesofmodulesforwormsissomehowdifferentfromthoseforgears.Table6-2m11.251.622.53.15Mid-diameterd1182022.42028(18)22.4(28)35.5(22.4)28(35.5)45(28)35.5(45)56m456.381012.5Mid-diameterd1(31.5)40(50)71（40）50（63）90（50）63（80）112（63）80（100）140（71）90（112）160（90）112（140）200Table6.2ModulesandReferenceDiametersofWorms(mm)(GB10085-88)3)Thenumberofthreads(頭數(shù))ofthewormZ1Z1,theni.Z1,thenefficiency

Z1=1,2,4,6arepreferable.ThenumberofteethofawormwheelZ2.

Z2=27~804)Theleadangle(導(dǎo)程角)

1oftheworm.標(biāo)準(zhǔn)化table6-2直徑系數(shù)Theefficiencyincreaseswithincreaseof

1.If

1islessthantheequivalent(當(dāng)量)frictionangle

v,thewormgearpairisself-locking(自鎖)inback-driving.4)Themid-diameterd1ofworm(蝸桿中徑）4)Themid-diameterd1ofworm(蝸桿中徑）d1isstandardizedtoreducethenumberofcuttersandshouldbechosentogetherwiththemodulem.d1mZ1!!!!m11.251.622.53.15Mid-diameterd1182022.42028(18)22.4(28)35.5(22.4)28(35.5)45(28)35.5(45)56m456.381012.5Mid-diameterd1(31.5)40(50)71（40）50（63）90（50）63（80）112（63）80（100）140（71）90（112）160（90）112（140）200Table6.3ModulesandReferenceDiametersofWorms(mm)(GB10085-88)Thereferencediameter(分度圓直徑)d2ofwormwheel.d2=mZ26)Thecentredistancea’ofthewormgearpair.Sincetheshapeofthewormshouldbethesameasthestandardwormwheelcutter,thewormshouldnotbemodified.Advantages:Disadvantages:Lowerefficiencyduetothegreaterrelativeslidingspeedbetweentheteeth.Thefrictionlossmayresultinoverheating(過熱)andseriouswear.SmoothsilentoperationGreaterspeedreduction.Iftheleadangleofawormislessthanthe

equivalent(當(dāng)量)frictionangle,theback-drivingisself-locking.6.11BevelGears(錐齒輪)Bevelgearsareusedtotransmitmotionandpowerbetweenintersectingshafts.6.11.1TypesandApplicationsofBevelGearsTheteethofabevelgeararedistributedonthefrustum(截錐體)ofacone(圓錐體).正確嚙合條件：軸角傳動比：錐頂角：δ，錐頂距RParametersanddimensionsatthelargeendaretakentobestandardvalues.Parametersanddimensionsatthelargeendaretakentobestandardvalues.Theshaftangleofabevelgearpaircanbeanyrequiredvalue.Inmostcases,thetwoshaftsintersectatarightangle直角.Therearestraight,helicalandspiral(直齒、斜齒、曲齒)bevelgears.Attention:

Modulesofb