齿轮传动及测量理论

Börner,TR-G,Folie1Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungPresentation介绍TheoryofGearingandMeasurement齿轮传动及测量理论Dr.JörgBörnerCorporateR&DZentraleForschungZFFriedrichshafenAGBörner,TR-G,Folie2Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungda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dadNa,dFaprefinishedcontour预加工轮廓dFa,mindNfdfdFfdNf,maxfinishedcontour精加工轮廓dfvBörner,TR-G,Folie3Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungThreadmodelStep1:Wrapathreadaroundthebasecircle,Step2:UnwindthethreadfromthebasecircleStep3: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Börner,TR-G,Folie4Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungStandardgeometryofgearteethFlanks=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Börner,TR-G,Folie5Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungRolldistanceEachcirclesegmentbelongstoaninvolutesegmentLengthofthecirclesegments=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Börner,TR-G,Folie6Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessung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Börner,TR-G,Folie7Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessung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Börner,TR-G,Folie8Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungWorkingpressureangleaw工作压力角awonlydefinedforagearpair只对一对齿轮定义awdependsonthecenterdistanceaw取决于中心距Workingpressureangle工作压力角awawBörner,TR-G,Folie9Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungPathofcontact(POC)duringmesh,thepointofcontactmovesalongthepathofcontact(POC)POCistangentialtothebasecirclesLengthofaction=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Börner,TR-G,Folie10Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungBasetangentlength公法线长度BasetangentlengthWk公法线长度Wkdependentonthenumberof取决于测量的齿数Kmeasuringteethk(picture:k=5)(图中k=5)Börner,TR-G,Folie11Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungPrefinishedcontour预加工轮廓PrefinishedgearsRootgeometryismanufacturedbyhobbingorcuttingBasetangentlengthofprefinishedgearsisdifferenttofinishedgearsAttention: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finishedcontour最终轮廓（精加工后）hobbedcontour滚齿后轮廓Börner,TR-G,Folie12Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungRollingabasicrackgeneratesagearThat‘stheprincipleofhobbingwormgrinding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Börner,TR-G,Folie13Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungTherootfilletisacycloid,generatedbythetooltipToolofprefinishprocess:hoborcutterUndercutisaspecialgeardesign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rararaBörner,TR-G,Folie14Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungOnebasicrackcangenerateseveralgearswiththesamebasecirclewiththesameinvolute,butdifferentpartsoftheinvolutechangingaddendummodification(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Börner,TR-G,Folie15Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungTableofaddendummodifications变位系数表Copyright©ZFFriedrichshafenAG2001Börner,TR-G,Folie16Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungVariationofprofileangle压力角的变化Börner,TR-G,Folie17Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungDuetothegeometricgenerationTheprobemoveslinearinthetransversplaneThegearrotatesDiagramofatrueinvoluteisaverticalline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Börner,TR-G,Folie18Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungProfileangledeviationfHa齿形角误差fHaDeviationinmicrometerµm千分尺的误差µmRelatedtothemeasurementrange与测量范围有关Profileformdeviationffa齿形轮廓误差ffaDeviationinmicrometerµm千分尺误差µmProfiledeviations齿形误差fHafHa-+ffaffa-+Börner,TR-G,Folie19Copyright©ZFFriedrichshafenAG2001GearingandMeasurementVerzahnungundMessungEvaluationrangeisusuallyequalto80%oftheprofilelengthEvaluationrangeisnotequaltotherequiredmeasurementrange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Börner,TR-G,Folie20Copyri