齿轮传动及测量理论ppt课件

.,Presentation介绍,TheoryofGearingandMeasurement齿轮传动及测量理论Dr.JrgBrnerCorporateR&DZentraleForschungZFFriedrichshafenAG,.,da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.SAPdiameterdNfSAP直径SAPdiameterdFf齿根形状直径rootformdiameterdf根圆直径rootdiameterdfv砂轮齿顶位置（假想齿根圆直径）SAP:startofactiveprofileSAP:有效齿形的起点,Diameters直径,dfv,.,ThreadmodelStep1:Wrapathreadaroundthebasecircle,Step2:UnwindthethreadfromthebasecircleStep3:Fixedtothethread,apenpaintstheinvolute.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,.,StandardgeometryofgearteethFlanks=involutes.Tooththicknesssb.Tipcircleandrootcirclelimitthestandardtooth.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,.,RolldistanceEachcirclesegmentbelongstoaninvolutesegmentLengthofthecirclesegments=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,.,Onebasecirclegeneratesmanyinolutes.Basepitch=distancebetweentheinvolutes.一个基圆展成许多渐开线基节=渐开线间的距离,Basepitch基节,.,Mainadvantageofinvolutegears:Independentfromthechangeofthecenterdistance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,.,Workingpressureangleaw工作压力角awonlydefinedforagearpair只对一对齿轮定义awdependsonthecenterdistanceaw取决于中心距,Workingpressureangle工作压力角,.,Pathofcontact(POC)duringmesh,thepointofcontactmovesalongthepathofcontact(POC)POCistangentialtothebasecirclesLengthofaction=DistanceonthePOCbetweenthetipcircles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,.,Basetangentlength公法线长度,BasetangentlengthWk公法线长度Wkdependentonthenumberof取决于测量的齿数Kmeasuringteethk(picture:k=5)(图中k=5),.,Prefinishedcontour预加工轮廓,PrefinishedgearsRootgeometryismanufacturedbyhobbingorcuttingBasetangentlengthofprefinishedgearsisdifferenttofinishedgearsAttention:Changeofhoborcuttercanmakeproblems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,.,RollingabasicrackgeneratesagearThatstheprincipleofhobbingwormgrinding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,.,Therootfilletisacycloid,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,ra,ra,ra,.,Onebasicrackcangenerateseveralgearswiththesamebasecirclewiththesameinvolute,butdifferentpartsoftheinvolutechangingaddendummodification(profileshift)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,.,Tableofaddendummodifications变位系数表,CopyrightZFFriedrichshafenAG2001,.,Variationofprofileangle压力角的变化,.,DuetothegeometricgenerationTheprobemoveslinearinthetransversplaneThegearrotatesDiagramofatrueinvoluteisaverticalline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,.,ProfileangledeviationfHa齿形角误差fHaDeviationinmicrometerm千分尺的误差mRelatedtothemeasurementrange与测量范围有关Profileformdeviationffa齿形轮廓误差ffaDeviationinmicrometerm千分尺误差m,Profiledeviations齿形误差,.,Evaluationrangeisusuallyequalto80%oftheprofilelengthEvaluationrangeisnotequaltotherequiredmeasurementrange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,profilemeasurement齿形测量,.,Typicalprofilecharts典型齿形图,Examplesofprofilemeasurement齿形测量的实例,.,Underload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,Profileunderload加载时的齿形,.,HelicalgearsScrewedtransversecut.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,.,TransversecutBasecircledbdependsonhelixangleb.Differentbgeneratesdifferentinvolutesinthetransverscuts.Pictureshowstransversecutswithsamebasicrackbutdifferenthelixangles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,.,Twogearsinmesh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,.,Helicalgears斜齿轮Propertiesofthecylindersurface圆柱面的特征可以展开到平面上canbetransformedintoaplaneThecylindercanbethe这个圆柱可以是节圆，也可以是基圆pitchcylinderorbasecylinder,Developingintotheplane展开到平面,.,Helicalgear斜齿轮Thecontactlinesarestraightlines.啮合线是直线Advantage:smoothentrance优点：啮入平稳Contactratioispartofgeardesign啮合比是齿轮设计的重要部分,Contactline啮合线,.,Measurementkinematics测量运动学probemoveslinear探头线性运动Thegearrotates齿轮旋转Diagramofanidealhelix理想的螺旋线图是一条直线isaline,Measurementofthelead齿向的测量,.,Profilecontactratioea齿形接触比,ea=ga/pet,b-Facewidth齿宽ga-Pathofcontact啮合轨迹pet-basepitch基节,ea=1,6,ea=2,b,.,Overlapratioeb重合比,eb=1,b,eb=0,8,b-Facewidth齿宽b-helixangle螺旋角bb-basehelixangle基圆螺旋角mn-Normalmodule法向模数pet-basepitch基节,.,Contactlinesathelicalgear斜齿轮的啮合线,Startofcontact啮合起点,Endofcontact啮合终点,Gearrotation(drivinggear)齿轮转动（主动轮）,Contactline啮