何孔德设计双语版-第二章

设计（Design）何孔德三峡大学机械与材料学院M-261313872631306Thischaptermainlyintroducesthetypesofgearmechanisms,theinvolute(渐开线)anditsproperties,standardandhelicalinvolutegear,wormgearingandbevelgears（圆锥齿轮）.Emphases★：

theinvoluteanditsproperties,gearingofstandardinvolutespurgears,contactratioofaninvolutespurgearset.

Difficulties▲:AddendumModificationoninvolutegears,helicalgears,etc.Chapter2GEARMECHANISMS

齿轮机构是用来传递任意两轴间的运动和动力的，它是应用最为广泛的一种机械传动机构之一。齿轮传动的特点1、主要优点1)适用的圆周速度和功率范围广；2)机械效率高；3)可现准确的传动比、且传动平稳；4)寿命长；5)工作可靠；6)可实现空间任意两轴（平行轴、相交轴、交错轴）之间的传动；7)结构紧凑。2、主要缺点

1)要求有较高的制造和安装精度，成本相对较高；

2)不适宜于远距离两轴之间的传动。Circulargears:constanttransmissionratio

non-circulargears:theratiovaries

Inthischapter,onlycirculargearsareconsidered.6.1TypesofGearMechanismsDependingontherelativeshaftspositions

parallelshafts→planargearmechanism(平面)

nonparallelshafts→spatialgearmechanism

(空间)6.1.1PlanarGearMechanismsExternalgearpair

Internalgearpair

Rackandpinion(齿条和齿轮)Externalgear:Spurgear(直齿轮)Helicalgear(斜齿轮)DoubleHelicalgear(人字齿轮)Internalgearpair:1.Spurinternalgear2.Helicalinternalgear6.1.2SpatialGearMechanisms1.Bevelgearmechanism(锥齿轮)

2.Crossedhelicalgearmechanism(螺旋齿轮机构)3.Wormandwormwheelmechanism(蜗杆蜗轮机构)6.2FundamentalsofEngagementofToothProfiles(齿廓啮合基本定律)6.2.1FundamentalLawofGearing

VP1=VP2

1·O1P=2

·O2P

P12istheinstantcentreofthegears1and2.

P12P----------thepitchpoint(节点).Ifaconstanttransmissionratioi12isrequired.Wherever(无论何处)theteethcontact,thecommonnormaln-nofthetoothprofilesthroughthecontactpointmustintersectthecenterlineatafixedpoint。Pitchcircle(节圆):

thelocusofthepitchpointPonthemotionplaneofthepinionorthegear.

Pitchcirclesaretangentandrollwithoutslippingeachother纯滚动.Thegearpairisrepresentedbytwochaindotted(点划线)circlestangenttoeachother.动画演示6.2.2ConjugateProfiles(共轭齿廓)

Meshing(啮合的)profilesofteeththatcanyieldadesiredtransmissionratio(传动比)aretermedconjugateprofiles.Foranyspecifictoothprofile,wecanfinditsconjugateprofile.

Involutes(渐开线)areusedmostwidelysincetheycanbemanufacturedandassembledeasily.两头牛背上的架子称为轭，轭使两头牛同步行走。共轭即为按一定规律相配的一对。6.3TheInvolute(渐开线)andItsProperties6.3.1GenerationofInvolute

Aninvoluteisthecurvegeneratedbyanypointonastringwhichisunwrapped(展开)fromafixedcircle.

rb

——Theradiusofbasecircle（基圆）.n-n——Generatingline(发生线)

K

——unfoldingangle(展角)oftheinvoluteatpointK.

6.3.2PropertiesoftheInvolute

1.Thelengthofthegeneratingline(发生线)segmentunrolledfromthebasecircleisequaltothearclengthofthebasecirclerolled.

2.ThelengthofsegmentNKistheradiusofcurvatureoftheinvoluteatthepointK.

A=03.Thenormaldistancebetweentwoinvolutesofthesamebasecircleremainsthesame.4.Theshapeofaninvolutedependsonlyontheradiusofitsbasecircle.

Astheradiusrbofthebasecircleapproachesinfinity,theinvolutebecomesastraightline.5.Noinvoluteexistsinsideitsbasecircle.

6.3.3EquationoftheInvolute渐开线方程Pressureangle

K

FVK=NOKFVKThepolarparametricequationoftheinvolute渐开线方程with

Kasaparameteris6.3.4Gearing(啮合)ofInvoluteProfilesInvolutegearshaveconstanttransmissionratio.constant

1.Locusofcontactpoint,thelineofaction(啮合线)=commonnormaltotheinvoluteprofiles=thecommontangenttothebasecirclesCharacteristicsofthegearingoftheinvoluteprofile:SinceO1PN1O2PN2,2、Involutegearshaveseparability(可分离性)ofthecentredistance.Achangeincenterdistancedoesnotthereforeaffecttheconstanttransmissionratioofaninvolutegearpair.3、Workingpressureangle’α’isdefinedastheanglebetweenthevelocityofpitchpointP(onbothgears)andthelineofactionN1N2.

6.4.1.ExternalGears

6.4.StandardInvoluteSpurGearsThetoothnumberofagear----Z（齿数）Parametersofgear:

thefacewidth(齿宽)----Baddendumcircle(ortipcircle)（齿顶圆）----da,radedendumcircle(orrootcircle)（齿根圆）----df,rfbasecircle----db,rbanarbitrarycircle(任意圆)----di,riThetoothspace(齿槽)----thespacebetweentheprofilesoftwoadjacentteeth.Thespacewidth(齿槽宽)ei----thearclengthofthetoothspacealonganarbitrarycircle.Thetooththickness(齿厚)si----thearclengthofthetoothalonganarbitrarycircle.Thepitch(齿距，周节)pi---arcdistancebetweencorrespondingpointsofadjacentteethalonganarbitrarycircle.pi=ei+sipressureangle

K

Differentpointontheinvolutehasdifferentpressureangle

K.

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

p=e+sThemodulem(模数)----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(齿顶高)ha----radialdistancebetweenthereferencecircleandtheaddendumcircle.Thededendum(齿根高)hf----radialdistancebetweenthereferencecircleandthededendumcircle.Thetoothdepth(齿全高)h----radialdistancebetweenthededendumcircleandaddendumcircle.动画演示Forstandardgears:c*----thecoefficientofbottomclearance(顶隙系数）ha*----thecoefficientofaddendum(齿顶高系数）ha*=1andc*=0.25forthenormaltooth(正常齿)ha*=0.8andc*=0.3fortheshortertooth(短齿)

c=c*m--------bottomclearance顶隙Basepitch(基节)pb---thepitchonthebasecircle.Normalpitch(法节)pn-------Thedistancebetweencorrespondingsidesofadjacenttoothprofilesalongthecommonnormal.pb=pnThefundamentalparameters:Z,m,

,ha*,c*Astandardgearmeans:m,

,ha*,c*takethestandardvaluesande=s一个齿轮：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一对标准齿轮正常安装：Involutesstraightlines6.4.2TheRack（齿条）

i

pipm

Thecharacteristicofrack:

Onthereferenceline(分度线),e=s.

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

thetoothspace——theactuallineofaction

——theoreticallineofaction

齿廓工作段theactualworkingprofile齿廓非工作段6.5GearingofInvoluteSpurGearsToensureacontinuoustransmission,theremustexistsuchsituationthattwopairsofteethcontactsimultaneously(同时地).

6.5.1ProperMeshingConditions(正确啮合条件)forInvoluteGearsTwopairsofteethcontactsimultaneouslyatpointK1andK2K1K2=Pb1

K1K2=Pb2

∴Pb1=Pb2

Accordingtothepropertyoftheinvolute:Thepropermeshingconditionforinvolutegears:

Themodulesandpressureanglesoftwomeshinggearsarethesamerespectively.

6.5.2zerobacklash齿侧间隙ofagearpairtherequirementsindesigningagearpair:Thebacklashshouldbezero.Tokeepzerobacklash,itholds:Thecentredistanceaisequalto(r1+r2),thereferencecirclescoincidewiththeirpitchcircles节圆.

Thetworeferencecircles分度圆aretangentandrollwithoutslipping.

6.5.3标准安装Ifbothgearsarestandard,wehave:zerobacklash,无侧隙啮合标准安装Thecentredistancea=r1+r2iscalledthereferencecentredistance(标准中心距).标准安装Workingpressureangle’(啮合角)标准安装thebottomclearance(顶隙)c：theradialdistancefromthededendumcircleofonegeartotheaddendumcircleofanother标准安装标准值Therefore,whentwostandardgearsareassembledatacentredistancea=r1+r2,notonlythebacklash=0,butalsobottomclearancec=c*m.

标准安装Whentheactualcentredistancea’islargerthan(r1+r2),thereferencecircleswillseparate.Thetwopitchcircleswillbecomelargerandremaintangent.6.5.4非标准安装a’只有增大——nonzerobacklash非标准安装6.5.4transmissionratioconstantThepropermeshingconditionisNOTasufficientconditiontoensureacontinuoustransmission.

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

(重合度)ThemeshingbeginsatpointB2,KmovesalongthelineofactionandendsatpointB1ThesegmentB1B2iscalledtheactuallineofaction(实际啮合线).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

.短齿制缺点(1)6.7ManufacturingMethodsofInvoluteProfilesCuttingisthemostcommonmethodformanufactureofgears.

Therearevariousmethodsformanufacturingtoothprofiles,suchasdiecasting(模铸),precisionforging(锻造),punch冲压,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(盘形铣刀）Endmillingcutter(指状铣刀)Broach(拉刀)DiskmillingcutterEndmillingcutters(端铣刀)areusedforlargemodulesanddoublehelicalgears.broach(拉刀)Characteristicsoftheformcutting:rb=rcos=(mZ/2)cosAstheshapeofaninvolutedependsonitsbaseradius,adifferentcutterisrequiredforeachnumberofteethevenforthesamemoduleandsamepressureangle.Formcuttingisnotagoodmethod.Itsmainadvantageisthatitcanbeaccomplishedoncommonlyavailablemillingmachines.(铣床)(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进给Externalgearscanbecutwitharack-shapedshapercutter(齿条插刀).TheedgesofthecutterarenowstraightlineswhichcanbemadeaccuratelyThecuttingprocessintheshaping(插齿)ofagearisnotcontinuous.

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

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

m/2.Thededendumcircleofthegeariscutbythetiplineofthecutter.Theaddendumcircleofthegeariscutonalathe(车床).Itisnotcutbygearcutter!!6.7.3CutterInterference(根切现象)Somepartoftheinvoluteprofileneartherootportionisremovedinthegeneratingcutting.Thiswillreducethecontactratioaswellasthestrengthofthetoothandshouldbeavoidedorminimized.Thereasonforcutterinterference:

TheaddendumlineofthecutterpassesthelimitpointN1ofthelineofaction.Topreventcutterinterference:短齿制：ha*=0.8，a=20°，Zmin=146.8AddendumModificationonInvoluteGears

齿轮变位6.8.1IntroductionofAddendumModificationDisadvantagesofstandardgears:1.ZZmin2.a’=a3.Thestrengthofthepinionismuchlowerthanthatofthegear.——外啮合

无法安装；

Correctedgears变位齿轮Incuttingthecorrectedgear,therackshapedcutterislocatedadistancexmfromthepositionusedforcuttingthestandardgear.xm——thedistancebetweenthepitchlineandthereferencelinex——modificationcoefficient

正变位

零变位

负变位

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

,andrb=(rcos

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

Topreventcutterinterference：最小变位系数正变位

负变位

1、分度圆上的齿厚见图：刀具节线的齿槽宽比中线齿槽宽，∴被切齿轮分度圆上的齿厚增加在△IJK中：

分度圆的齿厚：

2、齿顶高和齿根高

齿根高hf：刀具加工节线到顶刃线之间的距离

对正变位：x>0，hf比标准减小xm

对负变位：x<0，hf比标准增加xm

∴变位齿轮的齿根圆半径：

齿顶高：

∵变位齿轮的分度圆与相应标准齿轮的分度圆一样，∴变位齿轮的齿顶高仅决定于轮坯顶圆的大小。

为保证齿全高

由于所以6.8.3GearingofaCorrectedGearPairTokeepzerobacklash,itholds:Itcanbeshownthatthisresultsin:Thisisthegearingequationwithoutbacklash(无侧隙啮合方程).节圆与分度圆重合，a’=a节圆与分度圆不重合，a’≠a中心矩变动系数y:6.8.4TypesofCorrectedGearPairs(2)Heightcorrectiongearpair(等变位传动):Standardgeardrive(零变位：标准传动):x1＝0，x2=0，’＝＝20°,a’=a

互换性好，>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(正传动)：x1+x2>0

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

StrengthofgearsAdvantages:

(b)Negativegearing(负传动):x1+x2<0’<＝20°,a’<a,r1’<r1,r2’<r2Pinionmaybepositivemodified(正变位).suitableforanya’.Negativegearing(负传动）isnotrecommended(推荐).6.9HelicalGearsforParallelShafts(斜齿轮传动)6.9.1GenerationandCharacteristicsofHelicalTeethSpurgearThetoothsurfaceofthespurgearisthereforeaninvolutecylinder(渐开线柱面).

Thetoothsurfacesofspurgearscontactonastraightlineparalleltotheaxesofthegears.suddenloadingandsuddenunloadingonteethVibrationandnoiseIngenerationofthetoothprofileofahelicalgear,thestraightlineKKonthegeneratingplaneisnolongerparalleltotheaxisofthegear.EverypointonthestraightlineKKwillproduceaninvolute.Thecurveconnectingthestartingpointsoftheinvolutesonthebasecylinderisahelix(螺旋)AA.Thesurfaceprofileofahelicalgeariscalledaninvolutehelicoid(渐开线螺旋面)1Thetoothsurfacesoftwoengaginghelicalgearscontactonastraightlineinclined.渐开线螺旋面齿廓的特点②端面（垂直于齿轮轴线的面）与齿廓曲面的交线为渐开线。③与基圆柱同轴的圆柱面与渐开线螺旋面的交线为一螺旋线。不同面→螺旋角不同斜齿轮的啮合特点：（1）两斜齿齿廓的公法面既是两基圆柱的公切面，又是传动的啮合面（2）两齿廓的接触线与轴线夹角βbThelengthofthecontactlinechangesgraduallyfromzerotomaximumandthenfrommaximumtozero.Theloadingandunloadingoftheteethbecomegradualandsmooth.Thatiswhyhelicalgearscanoperateatahigherspeed.6.9.2ParametersofHelicalGears1、斜齿轮的切削加工：①仿形法；②范成法：滚齿（用仿形法加工斜齿轮时，铣刀是沿螺旋齿槽的方向进刀的）1.Onthetransverseplane(端面)(withsubscript“t”)⊥轴线的面Thetransverseprofileofahelicalgearisaninvolute.Twosetsofparameters:2.Onthenormalplane(法面)（withsubscript“n”)垂直于分度圆柱面螺旋线的切线的平面Parametersonthenormalplanearethestandardvalues.

Theyaredeterminedbycutter.进刀方向⊥法面

刀具的齿形应于斜齿轮的法面齿形相同，→法面上的模数和压力角为标准值。mnisstandardized.

n=20

t20三维图???mn,han*andcn*takethestandardvaluesasforspurgears.螺旋角β：

螺旋线的导程

Pz:螺旋线绕一周时它沿轴线方向前进的距离

（上式表明，不同圆柱面的螺旋角不等）

ThereferencediameterandcentredistanceshouldbecalculatedonthetransverseplaneasReferencecentredistanceacanbeadjustedbychangingthehelixangle(螺旋角)

.Standardhelicalgeardrivecansuitanycentredistance.6.9.3ProperMeshingConditionsforHelicalGearsReview:Accordingtothepropermeshingconditionsofspurgeardrive,6.9.4ContactRatioforaHelicalGearPairThelengthoftheactuallineofactionincreasesbyL.

iscalledthetransversecontactratio(端面重合度).

iscalledtheoverlapratio(轴向重合度).Thetransversecontactratio

canbecalculatedwiththeparametersonthetransverseplane.轴向重合度

Dueto

,thecontactratioofahelicalgearpairismuchhigherthanthatofaspurgearpair.Alargecontactratiomeansthatmoregearteethareengagedatthesametimewhichgiveshighstrengthtothegears.

6.9.5VirtualNumberofTeeth(当量齿数)forHelicalGearsTocalculatethestrengthofthetooth,andtochoosethetypeofthecuttingtool,thevirtualgear(当量齿轮)ofthehelicalgearisintroduced.Thevirtualgear(当量齿轮)ofthehelicalgearisaspurgear,thetoothprofileofwhichisequivalenttothatofahelicalgearonthenormalplane.

当量齿轮：以ρ为分度圆半径，用斜齿轮的mn和αn分别为模数和压力角作一虚拟的直齿轮，其齿形与斜齿轮的法面齿形最接近。这个齿轮称斜齿轮的当量齿轮，齿数ZV称当量齿数。Thevirtualnumberofteeth(当量齿数)forthehelicalgear------thenumberZvofteethofthevirtualgear.Zvisusedtocalculatethestrengthofthetooth.

已知mn、

n、Z、

的斜齿轮法面齿形

以mn为模数、以

n为压力角、以Zv为齿数的直齿轮齿形。Furthermore,theminimumnumberofteethofthestandardhelicalgearwithoutcutterinterferencecanbederivedasAdvantageofhelicalgears：Helicalgearsoperatemoresmoothly.Havehigherstrength.Theworkingcentredistanceofahelicalgearpaircanbeadjustedbythehelixangle

.比直齿轮小，机构更紧凑制造成本与直齿轮相同Helicalgearsarethereforewidelyusedforhighspeedorheavyloadtransmission.Themaindisadvantageofhelicalgearsis:Theyproduceanaxialthrust(轴向推力).HelicalgearsThehelixangleisthereforelimitedtowithin8

to20.

DoubleHelicalgears6.10.1WormGearinganditsCharacteristicsWormgeardrivesareusedtotransmitmotionandpowerbetweennon-intersectingandnon-parallelshafts,usuallycrossingatarightangle.6.10WormGearing(蜗杆传动)Wormsareakindofscrew,usuallyrighthanded(右旋)forconvenienceofcutting,orlefthanded(左旋)ifnecessary.Wormsareusuallydriverstoreducethespeed.Directionof

1?Directionofhelixoftheworm?Wormwheels(蜗轮)arethematinggearsoftheworms.Maincharacteristicsofwormgeardrives:(1)Smoothsilentoperationasscrewdrives.(2)Greaterspeedreduction.(3)Iftheleadangle(导程角)

1

ofawormislessthantheequivalentfrictionangle(当量摩擦角)

V,theback-drivingisself-lockingtg

V=fV(当量摩擦系数)(4)Lowerefficiency(效率)<70%6.10.2TypesofWorms(1)Straightsidedaxialworms圆柱蜗杆-------ZA-worm阿基米德蜗杆Thetransversesection(横切面)isArchimedesspiral(螺旋线).Theaxialsectionisinvoluterack.(2)Involutehelicoidworms----ZI-worm渐开线蜗杆螺旋面(3)Arc-contactworms-----ZC-worm圆弧齿蜗杆Smallerstress(4)Envelopingworm(包络蜗杆),moreteethengaged.(5)Spiroid锥蜗杆6.10.3ProperMeshingConditionsforWormDrivesThemid-plane主平面----Thetransverseplaneofawormwheelpassingthroughtheaxisoftheworm.Theengagement(啮合)betweenaArchimedeswormandawormwheelonthemid-planecorrespondstothatofaninvoluterackandpinion.Necessaryconditionsforawormandawormwheeltomeshproperly.Thewormwheelshouldbecutbyacutterwiththesameshapeasthoseofthematingworm.6.10.4MainParametersandDimensionsforWormDrives1）Theaxialpressureangleofworm

x1is20

.Thiscanbeincreasedto25

inpowertransmissionordecreasedto15

or12

inindexingdevices(分度装置).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(头数)ofthewormZ1Z1,theni.Z1,thenefficiency

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

Z2=27~804)Theleadangle(导程角)

1oftheworm.标准化table6-2直径系数Theefficiencyincreaseswithincreaseof

1.If

1islessthantheequivalent(当量)frictionangle

v,thewormgearpairisself-locking(自锁)inback-driving.4)Themid-diameterd1ofworm(蜗杆中径）4)Themid-diameterd1ofworm(蜗杆中径）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(分度圆直径)d2ofwormwheel.d2=mZ26)Thecentredistancea’ofthewormgearpair.Sincetheshapeofthewormshouldbethesameasthestandardwormwheelcutter,thewormshouldnotbemodified.Advantages:Disadvantages:Lowerefficiencyduetothegreaterrelativeslidingspeedbetweentheteeth.Thefrictionlossmayresultinoverheating(过热)andseriouswear.SmoothsilentoperationGreaterspeedreduction.Iftheleadangleofawormislessthanthe

equivalent(当量)frictionangle,theback-drivingisself-locking.6.11BevelGears(锥齿轮)Bevelgearsareusedtotransmitmotionandpowerbetweenintersectingshafts.6.11.1TypesandApplicationsofBevelGearsTheteethofabevelgeararedistributedonthefrustum(截锥体)ofacone(圆锥体).正确啮合条件：轴角传动比：锥顶角：δ，锥顶距RParametersanddimensionsatthelargeendaretakentobestandardvalues.Parametersanddimensionsatthelargeendaretakentobestandardvalues.Theshaftangleofabevelgearpaircanbeanyrequiredvalue.Inmostcases,thetwoshaftsintersectatarightangle直角.Therearestraight,helicalandspiral(直齿、斜齿、曲齿)bevelgears.Attention:

Modulesofb