渐开线标准直齿圆柱齿轮的传动和加工Transmission

渐开线标准直齿圆柱齿轮的传动和加工Transmissionandmachiningofinvolutestandardstraightcylindricalgears主讲人：张瑞静目录CONTENTS1234渐开线齿轮的正确啮合条件Correctmeshingconditionsforinvolutegears渐开线齿轮的连续传动条件Continuoustransmissionconditionsofinvolutegears渐开线齿轮的加工Machiningofinvolutegears根切现象与最少齿数Undercuttingphenomenonandminimumnumberofteeth1渐开线齿轮的正确啮合条件CorrectmeshingconditionsforinvolutegearsONE一、渐开线齿轮的正确啮合条件Correctmeshingconditionsforinvolutegears正确啮合是指齿轮副在传动时保证不出现重叠或侧隙过大而引起卡死或冲击现象，各轮齿依次啮合互不干扰，实现连续顺利传动。Correctmeshingreferstoensuringthatthegearpairdoesnotoverlaporhaveexcessivebacklashduringtransmission,causingjammingorimpact.Theteethofeachgearmeshinsequencewithoutinterferingwitheachother,achievingcontinuousandsmoothtransmission.一、渐开线齿轮的正确啮合条件CorrectmeshingconditionsforinvolutegearsPb1=Pb2Abletoengagecorrectly能正确啮合Pb1<Pb2Unabletoengagecorrectly不能正确啮合Pb1>Pb2Unabletoengagecorrectly不能正确啮合从外观看齿1比齿2小从外观看齿1比齿2大一、渐开线齿轮的正确啮合条件Correctmeshingconditionsforinvolutegears渐开线齿轮的正确啮合条件:Correctmeshingconditionsforinvolutegears:Pb1=Pb2Pb=πcosαπm1cosα1=πm2cosα2●模数相等，m=m1m2Equalmodulus,m=m1m2●分度圆上的齿形角相等，α1=α2Thetoothshapeanglesontheindexingcircleareequal,α1=α22渐开线齿轮的连续传动条件ContinuoustransmissionconditionsofinvolutegearsTWO二、渐开线齿轮的连续传动条件Continuoustransmissionconditionsofinvolutegears前一对轮齿尚未结束啮合，后继的一对轮齿已进入啮合状态。Thepreviouspairofteethhasnotyetfinishedmeshing,andthesubsequentpairofteethhasenteredameshingstate.二、渐开线齿轮的连续传动条件Continuoustransmissionconditionsofinvolutegears两轮连续传动的条件为B1B2≥PbTheconditionfortwowheelcontinuoustransmissionisB1B2≥Pb二、渐开线齿轮的连续传动条件Continuoustransmissionconditionsofinvolutegears一对齿轮的重合度:ε=B1B2/PbTheconditionfortwowheelcontinuoustransmissionisε=B1B2≥Pb一对齿轮的连续传动条件是:ε≥1Thecontinuoustransmissionconditionsforapairofgearsare:ε≥one从理论上讲，重合度为ε=1，齿轮副就能保证连续传动，但齿轮制造和安装有误差，实际上必须使重合度ε>1才能可靠保证传动的连续性。Intheory,thedegreeofoverlapisε=1.Thegearpaircanensurecontinuoustransmission,butthereareerrorsingearmanufacturingandinstallation,andinreality,theoverlapmustbeensuredε>1canreliablyensurethecontinuityoftransmission.二、渐开线齿轮的连续传动条件Continuoustransmissionconditionsofinvolutegears●重合度ε大，表示同时啮合的轮齿对数多，多对啮合的区间长，从而提高传动的承载能力，同时传动也平稳。CoincidencedegreeεLargeindicatesthattherearemanypairsofteethengagedsimultaneously,andthemeshingintervalbetweenmultiplepairsislong,therebyimprovingthebearingcapacityofthetransmissionandensuringsmoothtransmission.●实际重合度ε≥许用重合度。Actualoverlapε≥Permissibleoverlap.●中心距分离时，重合度会降低。Whenthecenterdistanceisseparated,theoverlapwilldecrease.3渐开线齿轮的加工MachiningofinvolutegearsTHREE三、渐开线齿轮的加工MachiningofinvolutegearsCastingmethod铸造法thermalbond热轧法Stampingmethod冲压法Powdermetallurgymethod粉末冶金法Dieforgingmethod模锻法Cuttingmethod(Mostcommonlyused)切削法（最常用）三、渐开线齿轮的加工Machiningofinvolutegears铣削milling拉削broaching滚齿hobbing插齿gearshaping仿形法Copyingmethod范成法generatingmethod切削法(最常用)Cuttingmethod(Mostcommonlyused)三、渐开线齿轮的加工Machiningofinvolutegears仿形法Copyingmethod在铣床上用具有渐开线齿形的成形铣刀直接切出齿形。Useaformingmillingcutterwithinvolutetoothprofiletodirectlycutthetoothprofileonamillingmachine.常用的铣刀有圆盘铣刀和指状铣刀。Thecommonlyusedmillingcuttersincludediscmillingcuttersandfingermillingcutters.三、渐开线齿轮的加工Machiningofinvolutegears进给feed分度360°/zIndexing360°/z圆盘铣刀加工Discmillingcutterprocessing仿形法Copyingmethod三、渐开线齿轮的加工Machiningofinvolutegears仿形法Copyingmethod指状铣刀加工适用于加工大模数m>20的齿轮和人字齿轮。Fingermillingcuttermachiningissuitableformachininggearswithlargemodulusm>20andherringbonegears.进给feed指状铣刀加工Fingermillingcutterprocessing分度360°/zIndexing360°/z三、渐开线齿轮的加工Machiningofinvolutegears仿形法Copyingmethod切齿方法简单，不需要专用机床，但生产率低，精度低，故仅适用单件或小批量生产及精度要求不高的齿轮加工。Thegearcuttingmethodissimpleanddoesnotrequirespecializedmachinetools,butithaslowproductivityandaccuracy,soitisonlysuitableforsinglepieceorsmallbatchproductionandgearprocessingwithlowaccuracyrequirements.三、渐开线齿轮的加工Machiningofinvolutegears范成法generatingmethod利用齿轮的啮合原理进行加工齿轮的一种方法。Amethodofmachininggearsusingthemeshingprincipleofgears.这种方法强制刀具同工件(轮坯)相对运动，同时进行切削。Thismethodforcesthetooltomoverelativetotheworkpiece(wheelblank)whilecutting.它们之间的运动关系同一对齿轮啮合一样，以此来保证齿形的正确和分齿的均匀。Themotionrelationshipbetweenthemisthesameasthemeshingofapairofgears,inordertoensurethecorrecttoothshapeandeventoothdivision.三、渐开线齿轮的加工Machiningofinvolutegears范成法

generatingmethod对于模数m和压力角α都相同而齿数不同的齿轮，可以用同一刀具进行加工。FormodulusmandpressureangleαGearswiththesamenumberofteethbutdifferentnumberscanbemachinedusingthesamecuttingtool.0302加工刀具类型如下：Thetypesofmachiningtoolsareasfollows:01齿轮滚刀Gearhob齿条插刀Rackcutter齿轮插刀Gearcutter三、渐开线齿轮的加工Machiningofinvolutegears范成运动generatingmotion加工原理processingprinciple让刀运动Maketheknifemove切削运动cuttingmotion●优点:用一把插刀可以加工出m、α相同，而齿数不同的各种齿轮(包括内齿轮)。Advantages:Usingacuttingtoolcanproducem、αVariousgears(includinginternalgears)withthesamenumberofteethbutdifferentnumbersofteeth.●缺点:切削不连续，生产效率较低。Disadvantages:Discontinuouscuttingandlowproductionefficiency.共轭齿廊互为包络线Conjugatetoothprofilesaremutuallyenvelopinglines三、渐开线齿轮的加工Machiningofinvolutegears(2)齿条插刀加工Rackandpinioncuttermachining齿条插刀齿廓的顶部比传动用的齿条高出c★m，以便切出传动时的径向间隙。Thetopofthetoothprofileoftherackandpinioncutterisc★mhigherthanthetransmissionrack,inordertocutouttheradialclearanceduringtransmission.三、渐开线齿轮的加工Machiningofinvolutegears●优点:用一把插刀可以加工出m、α相同，而齿数不同的齿轮。Advantages:Withasinglecuttingtool,mcanbemachinedαGearswiththesamenumberofteethbutdifferentnumbersofteeth.●缺点:不能加工内齿轮。切削不连续生产效率较低。Disadvantage:Unabletomachineinternalgears.Theproductionefficiencyofdiscontinuouscuttingislow.三、渐开线齿轮的加工Machiningofinvolutegears切削运动cuttingmotion让刀运动Maketheknifemove范成运动generatingmotion加工原理processingprinciple(3)齿轮滚刀加工Gearhobbing●优点:用一把插刀可以加工出m、α相同，而齿数不同的齿轮。切削连续，生产效率高。Advantages:Usingacuttingtoolcanproducem、αGearswiththesamenumberofteethbutdifferentnumbersofteeth.Continuouscuttingandhighproductionefficiency.●缺点:不能加工内齿轮。Disadvantage:Unabletomachineinternalgears.三、渐开线齿轮的加工Machiningofinvolutegears加工原理processingprinciple齿轮滚刀Gearhob4根切现象与最少齿数UndercuttingphenomenonandminimumnumberofteethFOUR用范成法加工齿轮时，当被加工齿轮的齿数较少时，其轮齿根部的渐开线尺廊被切去一部分的现象是根切现象。Whenusingthemethodofgeneratinggears,whenthenumberofteethinthegearbeingprocessedissmall,thephenomenonofaportionoftheinvoluteprofileattherootofthegearteethbeingcutoffiscalledrootcutting.四、根切现象与最少齿数Undercuttingphenomenonandminimumnumberofteeth渐开线齿廊的根切现象危害:Hazardsofundercuttingofinvolutetoothprofiles:●切掉部分齿廓;·Cutoffaportionofthetoothprofile·●削弱了齿根强度:Reducedtoothrootstrength:●严重时，切掉部分渐开线齿廓，降低重合度，影响了传动的平稳性。Inseverecases,cuttingoffaportionoftheinvolutetoothprofilereducestheoverlapandaffectsthesmoothnessofthetransmission.四、根切现象与最少齿数Undercuttingphenomenonandminimumnumberofteeth避免根切的措施:Measurestoavoidrootcutting:●z≥17(对于标准齿轮)Z≥17(forstandardgears)●变位Displacement变位:用齿条型刀具加工齿轮时，若不采用标准安装，而是将刀具远离或靠近轮坯回转中心，则刀具的分度线不再与被加工齿轮的分度圆相切。Displacement:Whenmachininggearswithrackandpinioncuttingtools,ifthestandardinsta