齿轮传动及测量理论

齿轮传动及测量理论

GearingandMeasurement VerzahnungundMessungda

齿顶圆直径

tipdiameterdNa,dFa,dab

有效齿顶圆直径

effectivetipdiameterdFa,min

最小有效齿顶圆直径

min.effectivetipdiameterdNf,max

最大有效齿顶圆直径

max.SAPdiameterdNf

SAP直径

SAPdiameterdFf

齿根形状直径

rootformdiameter

df

根圆直径

rootdiameterdfv砂轮齿顶位置（假想齿根圆直径） SAP:startofactiveprofile

SAP:有效齿形的起点Diameters

直径da

dNa,dFa

prefinishedcontour预加工轮廓dFa,min

dNf

df

dFf

dNf,max

finishedcontour精加工轮廓dfv

GearingandMeasurement VerzahnungundMessungThreadmodelStep1:Wrapathreadaroundthebasecircle,Step2:Unwindthethreadfromthe

basecircleStep3:Fixedtothethread,apenpaints

theinvolute.Fadenmodel第一步:沿基圆绕线第二步:将线展开拉直第三步:将笔固定于线，可画出渐开线

Developing

展成

GearingandMeasurement VerzahnungundMessungStandardgeometryofgearteethFlanks=involutes.Tooththickness

sb.Tipcircleandrootcirclelimit

thestandardtooth.轮齿的标准几何外形齿侧面=渐开线齿厚

sb.齿顶圆和齿根圆限定了标准齿的形状.Standardtooth

标准齿

GearingandMeasurement VerzahnungundMessungRolldistanceEachcirclesegmentbelongs

toaninvolutesegmentLengthofthecirclesegments

=lengthofthethread

=rolldistance滚动距离每段圆弧都属于一个渐开线段圆弧长度=线的长度=滚动距离

Rolldistance

滚动距离

GearingandMeasurement VerzahnungundMessungOnebasecirclegenerates

manyinolutes.Basepitch=distance

betweentheinvolutes.一个基圆展成许多渐开线基节=渐开线间的距离Basepitch

基节

GearingandMeasurement VerzahnungundMessungMainadvantage

ofinvolutegears: Independentfromthechange

ofthecenterdistance渐开线齿轮的主要优点:

与中心局的改变无关Changeofcenterdistance

中心距的改变

GearingandMeasurement VerzahnungundMessungWorkingpressureangleaw

工作压力角aw

onlydefinedforagearpair

只对一对齿轮定义awdependsonthecenterdistance

aw

取决于中心距Workingpressureangle

工作压力角awaw

GearingandMeasurement VerzahnungundMessungPathofcontact(POC)duringmesh,thepointofcontact

movesalongthepathofcontact(POC)POCistangentialtothebasecirclesLengthofaction=Distanceonthe

POCbetweenthetipcircles

啮合轨迹啮合过程中，接触点沿啮合轨迹移动啮合轨迹与基圆相切啮合长度=齿顶圆之间啮合轨迹线的距离Pathofcontact(POC)

啮合轨迹POC

啮合轨迹

GearingandMeasurement VerzahnungundMessungBasetangentlength

公法线长度BasetangentlengthWk

公法线长度Wk

dependentonthenumberof

取决于测量的齿数K

measuringteethk

(picture:k=5) (图中k=5)大家学习辛苦了，还是要坚持继续保持安静

GearingandMeasurement VerzahnungundMessungPrefinishedcontour

预加工轮廓PrefinishedgearsRootgeometryismanufactured

byhobbingorcuttingBasetangentlengthofprefinished

gearsisdifferenttofinishedgearsAttention: Changeofhoborcutter

canmakeproblems预加工的齿轮滚齿或铣齿加工得到齿根轮廓预加工后的基圆切线长度与最终的基圆切线长度是不一样的注意:更换滚刀或铣刀可能出现问题

finishedcontour最终轮廓（精加工后）hobbedcontour滚齿后轮廓

GearingandMeasurement VerzahnungundMessungRollingabasicrack

generatesagearThat‘stheprincipleofhobbingwormgrinding

滚动齿条可以生成齿轮这就是滚齿和蜗杆磨的原理Basicrack

齿条basecircle

基圆

GearingandMeasurement VerzahnungundMessungTherootfilletisacycloid,

generatedbythetooltipToolofprefinishprocess:

hoborcutterUndercutisaspecialgeardesign齿根修形是由刀头加工得到的圆滚线粗加工的刀具：滚刀或铣刀根切是一种特殊的齿轮设计Rootfillet

齿根修形Cycloid

圆滚线Tooltip

刀头rarara

GearingandMeasurement VerzahnungundMessung Onebasicrackcangenerateseveralgearswiththesamebasecirclewiththesameinvolute,butdifferentpartsoftheinvolutechangingaddendummodification(pro)

一个齿条可以生成多个齿轮有同样的基圆有相同的渐开线，但属于渐开线的不同部分更换变位系数（齿形改变）Addendummodification

齿顶修形

GearingandMeasurement VerzahnungundMessungTableofaddendummodifications

变位系数表Copyright©ZFFriedrichshafenAG2001

GearingandMeasurement VerzahnungundMessungVariationofpro

压力角的变化

GearingandMeasurement VerzahnungundMessungDuetothegeometricgenerationTheprobemoveslinearinthe transversplaneThegearrotatesDiagramofatrueinvolute

isaverticalline根据几何结构探头在横截面线性移动齿轮转动一条无误差的渐开线的图是一条垂线Measurementofinvoluteprofiles

渐开线齿形的测量

GearingandMeasurement VerzahnungundMessungProdeviationfHa

齿形角误差fHaDeviationinmicrometerµm

千分尺的误差µmRelatedtothemeasurementrange

与测量范围有关

Prodeviationffa

齿形轮廓误差ffaDeviationinmicrometerµm

千分尺误差µmPro

齿形误差fHafHa-+ffaffa-+

GearingandMeasurement VerzahnungundMessungEvaluationrangeisusually

equalto80%oftheproEvaluationrangeisnotequal

totherequiredmeasurementrange计量范围通常在齿形长度的80%以内计量范围不等同于要求的测量范围Evaluationrange

计量范围pro

齿形测量100%80%

GearingandMeasurement VerzahnungundMessungTypicalpro

典型齿形图Examplesofpro

齿形测量的实例

GearingandMeasurement VerzahnungundMessungUnderload

加载时deformationofthegearteeth

轮齿变形entryimpact

啮入冲击modificationsareusedtoavoid

通过修形来避免啮入冲击

theentryimpact

Proload

加载时的齿形

主动轮从动轮主动轮从动轮

GearingandMeasurement VerzahnungundMessungHelicalgearsScrewedtransversecut.involuteineachtransversecut.sameKsheetasspurgears.

斜齿轮螺旋横切.各个横截面中的渐开线.同直齿轮一样的跨测齿数表（K表）Helicalgears

斜齿轮

GearingandMeasurement VerzahnungundMessungTransversecutBasecircledb

dependsonhelixangleb.Differentbgeneratesdifferentinvolutes

inthetransverscuts.Pictureshowstransversecutswith

samebasicrackbutdifferenthelixangles

横截面基圆db取决于螺旋角b不同的b

在横截面上生成不同的渐开线如图所示，横截面上有相同的齿条，但是螺旋角不同Influenceofhelixangle

螺旋角的影响

GearingandMeasurement VerzahnungundMessungTwogearsinmesh

啮合的一对齿轮twobasecylinders

两个基圆柱closedthread,

绕圆柱，有闭合的曲线

wrappedaroundthecylinders Basecylinder

基圆柱

GearingandMeasurement VerzahnungundMessungHelicalgears

斜齿轮Propertiesofthecylindersurface

圆柱面的特征可以展开到平面上

canbetransformedintoaplane Thecylindercanbethe

这个圆柱可以是节圆，也可以是基圆

pitchcylinderorbasecylinder Developingintotheplane

展开到平面

GearingandM