吉林大学机械原理双语课件6.1gears-and-design

Chapter6Gearsanddesign(第6章齿轮机构及其设计)ApplicationTransmittingrotarymotionbetweentwoshafts,usuallywithaconstantspeedratio.6.1Applicationandclassificationofgears(齿轮机构的应用和分类)Classification)(2112是否为恒定值分按传动比i1.Gearswithconstantspeedratio（i12=常数C）2.变传动比齿轮机构（i12按一定规律变化）6.1.1Planargears(平面齿轮机构)Transmitmotionbetweenparallelshafts.1.Spurgears(直齿圆柱齿轮机构)Circulargears(圆形齿轮机构)Non-circulargears(非圆形齿轮机构)Spurgears1）externalgeartransmission2）internalgeartransmission3）pinionandracktransmission6.1.1Planargears1.Spurgeartransmission3.Herringbonegeartransmission2.Helicalgeartransmission6.1.2SpatialgearsTransmitthemotionandpowerbetweennonparallelshafts.1.Bevelgearing(锥齿轮传动)Transmitthemotionandpowerbetweenintersectantshafts.Types：1）straight(直齿)；2）helical(斜齿)；3）spiral(曲齿)。2.Crossedhelicalgeartransmission(螺旋齿轮传动)Transmitmotionbetweenspitialarbitrarycrossedshafts.3.Wormsandwormgearstransmission(蜗轮蜗杆传动)Transmitmotionbetweenspitialperpendicularshafts.1.Terminologyanddefinitionsz齿数齿顶圆draa()ra齿根圆drff()rf基圆drbb()rb分度圆dr()r任意圆drKK()rk齿厚sKsk齿槽宽eKek齿距周节()pKpkpseKKK齿顶高haha齿根高hfhf6.2Involutestandardspurgear(渐开线标准直齿轮)6.2.1Externalgear(外齿轮)Pinion,gear,wheel,gearset2.Parameters(1)Modulem当齿数为z,计算rK圆上周长为zpdzprKKKKππ2人为规定：πKKpm可见当z一定时，不同圆上的模数不等。mK是有理数，称为模数。dK=mKz规定：分度圆上的模数为标准值。mzdpm，π(2)PressureangleaKKrrbcosa规定：分度圆上的压力角为标准值。rrrrbbarccoscosaa或5.225.141520，，一般：a当rb一定时，不同圆上的压力角不等。Standardpitch/Referencecircle具有标准模数,标准压力角的圆。d=mz(3)coefficientofaddendumah正常齿制：短齿制：，1ah。8.0ah(4)coefficientofbottomclearancec正常齿制：短齿制：，25.0c。3.0c3.Calculation标准齿轮:具有标准齿廓参数且分度圆上的齿轮。se),,,(achma标准齿轮的基本参数:chmz,,,,aaacos22bffaaddhddhddmzd2ππ;)(faafaamesmphhhmchhmhh6.2.2Rack(齿条)“circle”“line”1.齿廓上各点压力角均相等，即ai=a;2.周节处处相等，即pi=p=mp。其他计算参照外齿轮尺寸计算公式。法线齿顶线齿根线分度线piai6.3.1FundamentalLawofGearing如图所示，任意齿廓在K点啮合的情况。P点为两齿廓啮合的瞬心。221121POPOvvPPPOPOi122112(齿廓啮合基本定律和齿廓曲线)6.3FundamentalLawofGearingandToothProfileCurvennPO1K(K1,K2)vK2K1vPO2vK2vK112FundamentalLawofGearingThetransmissionratiooftwomeshinggearsisinverselyproportionaltotheratiooftwolinesegmentscutfromthecenterlinebythecommonnormalofthetoothprofilesthroughthecontactpoint(互相啮合传动的一对齿轮在任一位置时的传动比，都与其连心线O1O2被其啮合齿廓在接触点处的公法线所分成的两线段成反比)。POPOi122112P——啮合节点，简称节点(pitchpoint).1)若P为定点，i12=C，P点的轨迹称为节圆(pitchcircle)。2)若P为动点，i12≠C，P点的轨迹为曲线(也称节线)(pitchcurve)。nnPO1K(K1,K2)vK2K1vPO2vK2vK112Choiceoftoothprofilecurve：1)Easytomanufactureandassemble(容易加工制造)；2)Easyinstallation(便于安装)；3)Goodexchangeability(互换性好)。本章主要介绍渐开线齿廓(involutetoothprofile)。Conjugate(共轭)6.3.2InvolutecurveanditsproperitesWhenthetoothprofilesareshapedsoastoproduceaconstantangularvelocityratiobetweenthetwoshafts,thenthetwomatingsurfacesaresaidtobeconjugate.Onepossiblechoiceforsuchconjugatesolutionsistheinvoluteprofilewhich,withfewexceptions,isinuniversaluseforgearteeth.1.Generationofinvolutecurvebasecircle基圆,generatingline发生线。oA基圆brKKBKa渐开线发生线rKK——渐开线展角Unfoldingangle。Ageneratinglineistangenttobasecircleandrollspurelyonit，thepathAKanarbitrarypointKongeneratinglineisaninvolutecurve.OAKKBKaGeneratinglineKrrb2.Propertiesofinvolutecurve；ABBK1)2)Normallineofapointoninvolutecurveistangenttobasecircle；3)PointBisthecenterofcurvatureofpointK，BKisthecurvatureradiusatpointK；4)Shapeofinvolutecurvedependsonsizeofbasecircle(lineisaspecialcaseofinvolutecurve）；5)Noinvolutecurveinbasecircle.Derivefromthepropertiesofinvolutecurve:normalpitch/法节=basepitch/基节pb=pcosa=mpcosaThebasepitchistheconstantandfundamentaldistancebetweenthesecurves,thatis,thedistancefromonetoothtothenext,measuredalongthecommonnormaltothetoothprofiles,whichisthelineofaction.K2K1bacdN2N1rb2rb1basepitchnormalpitch6.3.3InvoluteEquation(渐开线方程)1.PressureanglePointKonprofile,theanglebetweenitsforcedirectionandvelocitydirectionisaK.OAKBFvKaKaKKrbrKKKrrbcosabbbbtanrrrABrBKKKKaa2.Equation(polarequation)In△OBKOAKBFvKaKaKKrbrKUnfoldingangleK=tanaK-aK=invaKThepolarequationoftheinvoluteisthus:InengineeringfieldswesubstituteinvaKforK.invaK渐开线函数(involutefunction).KKKKKKrraaaataninvcosb1.两齿廓在K点啮合时,N1N2为两齿廓的公法线，N1N2与O1O2的交点为P。1.Toensureconstanttransmissionratio(保证定传动比传动)2.当两齿廓在K′点啮合时，rb1、rb2不变,N1N2仍为两齿廓的公法线；N1N2与O1O2的交点仍为P。即P为定点。常数）(122112CPOPOi结论：渐开线齿廓能满足定传动比传动。6.3.4MatingofinvoluteprofileO2O1KnN2nN1PK′rb121rb22.ActionLineofinvoluteprofileisastraightline(渐开线齿廓的啮合线为一直线)不变。不变时，、、当21212b1bNNOOrr∴传力方向不变。O2O1KnN2nN1PK′rb121rb2N1N2——啮合点的轨迹线，称为啮合线；也是啮合点的公法线；还是传力方向线；同时又是两基圆的内公切线。可以证明，当两齿轮中心距略有变化时，其传动比仍为两齿轮基圆半径反比。3.Separabilityofthecenterdistanceininvolutegearing(渐开线齿廓传动具有中心距可分性)1b2b1122122112rrNONOPOPOi可分性：当实际中心距与设计中心距略有变化时，其传动比仍然不变，这一特性称为渐开线齿廓传动的可分性。∵△O1N1P∽△O2N2PO2O1nN2nN1Prb121rb2注：此时传动比虽然不变，但啮合参数发生变化。6.4.1ConditionsofcorrectlymeshingforinvolutegearsK2K1bacdN2N1rb2rb1aacosπcosbmpp又6.4Meshingtransmissionsofinvolutespurgear(渐开线直齿圆柱齿轮啮合传动)2b1b21ppcdabKK∴correctmatingconditionpb1=pb2m1cosa1=m2cosa2Forstandardgearsm1=m2=ma1=a2=a6.4.2Centerdistanceandworkingpressureangle(中心距和啮合角)1.Externalgeartransmission(外啮合传动)(1)CenterdistanceBasicrequirementsa.Sta