机械设计双语版 第6章.ppt

Thischaptermainlyintroducesthetypesofgearmechanisms theinvoluteanditsproperties standardandhelicalinvolutegear wormgearingandbevelgears Emphases theinvoluteanditsproperties gearingofstandardinvolutespurgears contactratioofaninvolutespurgearset Difficulties AddendumModificationoninvolutegears helicalgears etc Chapter6GEARMECHANISMS circulargears constanttransmissionratio non circulargears theratiovaries Inthischapter onlycirculargearsareconsidered 6 1TypesofGearMechanisms Dependingontherelativeshaftspositions parallelshafts planargearmechanism 平面 nonparallelshafts spatialgearmechanism 空间 6 1 1PlanarGearMechanisms Externalgearpair Internalgearpair Rackandpinion 齿条和齿轮 Externalgear Spurgear 直齿轮 Helicalgear 斜齿轮 DoubleHelicalgear 人字齿轮 Internalgearpair 1 Spurinternalgear2 Helicalinternalgear 6 1 2SpatialGearMechanisms 1 Bevelgearmechanism 锥齿轮 2 Crossedhelicalgearmechanism 螺旋齿轮机构 3 Wormandwormwheelmechanism 蜗杆蜗轮机构 6 2FundamentalsofEngagementofToothProfiles 齿廓啮合基本定律 6 2 1FundamentalLawofGearing VP1 VP2 1 O1P 2 O2P P12istheinstantcentreofthegears1and2 P12 P thepitchpoint 节点 Ifaconstanttransmissionratioi12isrequired Wherever 无论何处 theteethcontact thecommonnormaln nofthetoothprofilesthroughthecontactpointmustintersectthecenterlineatafixedpoint Pitchcircle 节圆 thelocusofthepitchpointPonthemotionplaneofthepinionorthegear Pitchcirclesaretangentandrollwithoutslippingeachother纯滚动 Thegearpairisrepresentedbytwochaindotted 点划线 circlestangenttoeachother 6 2 2ConjugateProfiles 共轭齿廓 Meshing 啮合的 profilesofteeththatcanyieldadesiredtransmissionratio 传动比 aretermedconjugateprofiles Foranyspecifictoothprofile wecanfinditsconjugateprofile Involutes 渐开线 areusedmostwidelysincetheycanbemanufacturedandassembledeasily 6 3TheInvolute 渐开线 andItsProperties 6 3 1GenerationofInvolute Aninvoluteisthecurvegeneratedbyanypointonastringwhichisunwrapped 展开 fromafixedcircle rb Theradiusofbasecircle 基圆 n n Generatingline 发生线 K unfoldingangle 展角 oftheinvoluteatpointK 6 3 2PropertiesoftheInvolute 1 Thelengthofthegeneratingline 发生线 segmentunrolledfromthebasecircleisequaltothearclengthofthebasecirclerolled 2 ThelengthofsegmentNKistheradiusofcurvatureoftheinvoluteatthepointK A 0 3 Thenormaldistancebetweentwoinvolutesofthesamebasecircleremainsthesame 4 Theshapeofaninvolutedependsonlyontheradiusofitsbasecircle Astheradiusrbofthebasecircleapproachesinfinity theinvolutebecomesastraightline 5 Noinvoluteexistsinsideitsbasecircle 6 3 3EquationoftheInvolute渐开线方程 Pressureangle K F VK NOK Thepolarparametricequationoftheinvolute渐开线方程with Kasaparameteris 6 3 4Gearing 啮合 ofInvoluteProfiles Involutegearshaveconstanttransmissionratio constant 1 Locusofcontactpoint thelineofaction 啮合线 commonnormaltotheinvoluteprofiles thecommontangenttothebasecircles Characteristicsofthegearingoftheinvoluteprofile Since O1PN1 O2PN2 2 Involutegearshaveseparability 可分离性 ofthecentredistance Achangeincenterdistancedoesnotthereforeaffecttheconstanttransmissionratioofaninvolutegearpair 3 Workingpressureangle isdefinedastheanglebetweenthevelocityofpitchpointP onbothgears andthelineofactionN1N2 6 4 1 ExternalGears 6 4 StandardInvoluteSpurGears Thetoothnumberofagear Z 齿数 Parametersofgear thefacewidth 齿宽 B addendumcircle ortipcircle 齿顶圆 da ra dedendumcircle orrootcircle 齿根圆 df rf basecircle db rb anarbitrarycircle 任意圆 di ri Thetoothspace 齿槽 thespacebetweentheprofilesoftwoadjacentteeth Thespacewidth 齿槽宽 ei thearclengthofthetoothspacealonganarbitrarycircle Thetooththickness 齿厚 si thearclengthofthetoothalonganarbitrarycircle Thepitch 齿距 周节 pi arcdistancebetweencorrespondingpointsofadjacentteethalonganarbitrarycircle pi ei si pressureangle K Differentpointontheinvolutehasdifferentpressureangle K Thecirclethepointonwhichhas20 pressureangleisdefinedasreferencecircle 分度圆 K Anyparameteronthereferencecirclehasnosubscript 下标 i e r e s p 20 pi ei si p e s Themodulem 模数 abasicparameteronthereferencecircle Differentmoduleneedsdifferentcutter Themodulemhasbeenstandardized m Z arethreebasicparametersofagear Tab6 1modulesofInvoluteCylindricalGears GB T1357 1987 Modulesofthefirstseriesarepreferable Theaddendum 齿顶高 ha radialdistancebetweenthereferencecircleandtheaddendumcircle Thededendum 齿根高 hf radialdistancebetweenthereferencecircleandthededendumcircle Thetoothdepth 齿全高 h radialdistancebetweenthededendumcircleandaddendumcircle Forstandardgears c thecoefficientofbottomclearance 顶隙系数 ha thecoefficientofaddendum 齿顶高系数 ha 1andc 0 25forthenormaltooth 正常齿 ha 0 8andc 0 3fortheshortertooth 短齿 c c m bottomclearance顶隙 Basepitch 基节 pb thepitchonthebasecircle Normalpitch 法节 pn Thedistancebetweencorrespondingsidesofadjacenttoothprofilesalongthecommonnormal pb pn Thefundamentalparameters Z m ha c Astandardgearmeans m ha c takethestandardvaluesande s 一个齿轮 d mzda d 2ha z 2ha mdf d 2hf z 2ha 2c mdb dcos ha ha mhf ha c mh ha hf 2ha c mP m 一对标准齿轮正常安装 Involutes straightlines 6 4 2TheRack 齿条 i pi p m Thecharacteristicofrack Onthereferenceline 分度线 e s Forstandardrack ha ha m hf ha c m 6 4 3InternalGears Thetooththickness thetoothspace theactuallineofaction theoreticallineofaction 齿廓工作段theactualworkingprofile齿廓非工作段 6 5GearingofInvoluteSpurGears Toensureacontinuoustransmission theremustexistsuchsituationthattwopairsofteethcontactsimultaneously 同时地 6 5 1ProperMeshingConditions 正确啮合条件 forInvoluteGears TwopairsofteethcontactsimultaneouslyatpointK1andK2 K1K2 Pb1 K1K2 Pb2 Pb1 Pb2 Accordingtothepropertyoftheinvolute Thepropermeshingconditionforinvolutegears Themodulesandpressureanglesoftwomeshinggearsarethesamerespectively 6 5 2zerobacklash齿侧间隙ofagearpair therequirementsindesigningagearpair Thebacklashshouldbezero Tokeepzerobacklash itholds Thecentredistanceaisequalto r1 r2 thereferencecirclescoincidewiththeirpitchcircles节圆 Thetworeferencecircles分度圆aretangentandrollwithoutslipping 6 5 3标准安装 Ifbothgearsarestandard wehave zerobacklash 无侧隙啮合 标准安装 Thecentredistancea r1 r2iscalledthereferencecentredistance 标准中心距 标准安装 Workingpressureangle 啮合角 标准安装 thebottomclearance 顶隙 c theradialdistancefromthededendumcircleofonegeartotheaddendumcircleofanother 标准安装 标准值 Therefore whentwostandardgearsareassembledatacentredistancea r1 r2 notonlythebacklash 0 butalsobottomclearancec c m 标准安装 Whentheactualcentredistancea islargerthan r1 r2 thereferencecircleswillseparate Thetwopitchcircleswillbecomelargerandremaintangent 6 5 4非标准安装 a 只有增大 nonzerobacklash 非标准安装 6 5 4transmissionratio constant ThepropermeshingconditionisNOTasufficientconditiontoensureacontinuoustransmission Thepropermeshingcondition 6 6ContactRatio 重合度 ofanInvoluteSpurGearSet Gear1isadriver 6 6 1definitionofContactRatio 重合度 ThemeshingbeginsatpointB2 Kmovesalongthelineofaction andendsatpointB1 ThesegmentB1B2iscalledtheactuallineofaction 实际啮合线 IfTransmissioniscontinuous Definethecontactratioas Theconditionofcontinuousmotiontransmission Usually 1 2 Thevalueofthecontactratioindicatestheaverage 平均 numberoftoothpairsincontactduringacycletosharetheload 6 6 3CalculationofContactRatio 重合度 Forexternalgearpair dependsonZ1 Z2 a1 a2 2 rb1 ra1cos a1 rb2 ra2cos a2 6 Ifa thentan and 5 IfZ then Trytousesmallerm 4 isindependentofmodulem 3 Ifra then a and 短齿制缺点 1 6 7ManufacturingMethodsofInvoluteProfiles Cuttingisthemostcommonmethodformanufactureofgears Therearevariousmethodsformanufacturingtoothprofiles suchasdiecasting 模铸 precisionforging 锻造 punch冲压 powder 粉末 process cutting切削法andsoon 6 7 1CuttingofToothProfiles 1 Form 仿形法 Cutting 2 Generating 展成法或范成法 Cutting Therearegenerallytwotypesofcuttingmethods FormCuttingTherearethreetypesofcutters Diskmillingcutter 盘形铣刀 Endmillingcutter 指状铣刀 Broach 拉刀 Diskmillingcutter Endmillingcutters 端铣刀 areusedforlargemodulesanddoublehelicalgears broach 拉刀 Characteristicsoftheformcutting rb rcos mZ 2 cos Astheshapeofaninvolutedependsonitsbaseradius adifferentcutterisrequiredforeachnumberofteethevenforthesamemoduleandsamepressureangle Formcuttingisnotagoodmethod Itsmainadvantageisthatitcanbeaccomplishedoncommonlyavailablemillingmachines 铣床 2 GeneratingCutting 展成法或范成法加工 Inageneratingcuttingmethod theedgesofacuttertaketheformofagear orrack withthesamemoduleandpressureangleasthegeartobecut 1 Cuttingmotion 3 Generatingmotion展成 2 Retreatmotion退刀 4 Feedmotion进给 Externalgearscanbecutwitharack shapedshapercutter 齿条插刀 Theedgesofthecutterarenowstraightlineswhichcanbemadeaccurately Thecuttingprocessintheshaping 插齿 ofagearisnotcontinuous Inmassproduction hobbing 滚齿 isusedinsteadofshaping 6 7 2CuttingaStandardGearwithStandardRack shapedCutter Thetiplineisc mhigherthantheaddendumlineforcuttingtheprofileattheroottoprovidehf Indiscussingthegeneratingofaninvoluteprofile wesimplyregardthestandardrack shapedcutterashavingthesameprofileasthestandardrack Tocutastandardgear thereferencelineofthecuttershouldbetangenttothereferencecircleofthegear Them ofthegearonthereferencecirclearethesameasthoseonthereferenceline Asthes2ande2ofthecutteronthereferencelineareequaltoeachother thegeariscutwiths e p 2 m 2 Thededendumcircleofthegeariscutbythetiplineofthecutter Theaddendumcircleofthegeariscutonalathe 车床 Itisnotcutbygearcutter 6 7 3CutterInterference 根切现象 Somepartoftheinvoluteprofileneartherootportionisremovedinthegeneratingcutting Thiswillreducethecontactratioaswellasthestrengthofthetoothandshouldbeavoidedorminimized Thereasonforcutterinterference TheaddendumlineofthecutterpassesthelimitpointN1ofthelineofaction Topreventcutterinterference 短齿制 ha 0 8 a 20 Zmin 14 6 8AddendumModificationonInvoluteGears齿轮变位 6 8 1IntroductionofAddendumModification Disadvantagesofstandardgears 1 Z Zmin 2 a a 3 Thestrengthofthepinionismuchlowerthanthatofthegear 外啮合 无法安装 Correctedgears变位齿轮 Incuttingthecorrectedgear therackshapedcutterislocatedadistancexmfromthepositionusedforcuttingthestandardgear xm thedistancebetweenthepitchlineandthereferenceline x modificationcoefficient 正变位 零变位 负变位 Onlythepositionofthecuttermaybechanged thereferencelineofthecuttermaynotbetangenttothereferencecircleofthegear Thegear cuttingmachines thecuttersandthetransmissionratiobetweenthecutterandtheblankremainsunchanged Comparisonbetweenacorrectedgearandthestandardgear 1 ParametersZ m r mZ 2 andrb rcos arethesame 2 Parametersdf da s emaychange Thismeansthatdifferentportionsofthesameinvoluteareemployedfortheprofilesofthestandardgearandthecorrectedgear 6 8 2GeometricDimensionsofCorrectedGears Topreventcutterinterference 最小变位系数 正变位 负变位 1 分度圆上的齿厚 见图 刀具节线的齿槽宽比中线齿槽宽 被切齿轮分度圆上的齿厚增加 在 IJK中 分度圆的齿厚 2 齿顶高和齿根高 齿根高hf 刀具加工节线到顶刃线之间的距离 对正变位 x 0 hf比标准减小xm 对负变位 x 0 hf比标准增加xm 变位齿轮的齿根圆半径 齿顶高 变位齿轮的分度圆与相应标准齿轮的分度圆一样 变位齿轮的齿顶高仅决定于轮坯顶圆的大小 为保证齿全高 由于 所以 6 8 3GearingofaCorrectedGearPair Tokeepzerobacklash itholds Itcanbeshownthatthisresultsin Thisisthegearingequationwithoutbacklash 无侧隙啮合方程 节圆与分度圆重合 a a 节圆与分度圆不重合 a a 中心矩变动系数y 6 8 4TypesofCorrectedGearPairs 2 Heightcorrectiongearpair 等变位传动 Standardgeardrive 零变位 标准传动 x1 0 x2 0 20 a a互换性好 1 2 x1 x2 0 x1 x2 0 20 a a r1 r1 r2 r2 Z1maylessthan17 Z1 Z2 mustbelargerthan34 a a Twogearsmayhavesamestrengths suitableforanya Disadvantages 3 Angularcorrectiongearpairwithx1 x2 0anda a Positivegearing 正传动 x1 x2 0 20 a a r1 r1 r2 r2 Thegearmaybenegativemodified 负变位 Advantages Z1 Z2 maybelessthan34 Strengthofgears Disadvantages Strengthofgears Advantages b Negativegearing 负传动 x1 x2 0 20 a a r1 r1 r2 r2 Pinionmaybepositivemodified 正变位 suitableforanya Negativegearing 负传动 isnotrecommended 推荐 6 9HelicalGearsforParallelShafts 斜齿轮传动 6 9 1GenerationandCharacteristicsofHelicalTeeth Spurgear Thetoothsurfaceofthespurgearisthereforeaninvolutecylinder 渐开线柱面 Thetoothsurfacesofspurgearscontactonastraightlineparalleltotheaxesofthegears suddenloadingandsuddenunloadingonteeth Vibrationandnoise Ingenerationofthetoothprofileofahelicalgear thestraightlineKKonthegeneratingplaneisnolongerparalleltotheaxisofthegear EverypointonthestraightlineKKwillproduceaninvolute Thecurveconnectingthestartingpointsoftheinvolutesonthebasecylinderisahelix 螺旋 AA Thesurfaceprofileofahelicalgeariscalledaninvolutehelicoid 渐开线螺旋面 1Thetoothsurfacesoftwoengaginghelicalgearscontactonastraightlineinclined 渐开线螺旋面齿廓的特点 端面 垂直于齿轮轴线的面 与齿廓曲面的交线为渐开线 与基圆柱同轴的圆柱面与渐开线螺旋面的交线为一螺旋线 不同面 螺旋角不同 斜齿轮的啮合特点 1 两斜齿齿廓的公法面既是两基圆柱的公切面 又是传动的啮合面 2 两齿廓的接触线与轴线夹角 b Thelengthofthecontactlinechangesgraduallyfromzerotomaximumandthenfrommaximumtozero Theloadingandunloadingoftheteethbecomegradualandsmooth Thatiswhyhelicalgearscanoperateatahigherspeed 6 9 2ParametersofHelicalGears 1 斜齿轮的切削加工 仿形法 范成法 滚齿 用仿形法加工斜齿轮时 铣刀是沿螺旋齿槽的方向进刀的 1 Onthetransverseplane 端面 withsubscript t 轴线的面 Thetransverseprofileofahelicalgearisaninvolute Twosetsofparameters 2 Onthenormalplane 法面 withsubscript n 垂直于分度圆柱面螺旋线的切线的平面 Parametersonthenormalplanearethestandardvalues Theyaredeterminedbycutter 进刀方向 法面 刀具的齿形应于斜齿轮的法面齿形相同 法面上的模数和压力角为标准值 mnisstandardized n 20 t 20 三维图 mn han andcn takethestandardvaluesasforspurgears 螺旋角 螺旋线的导程Pz 螺旋线绕一周时它沿轴线方向前进的距离 上式表明 不同圆柱面的螺旋角不等 Thereferencediameterandcentredistanceshouldbecalculatedonthetransverseplaneas Referencecentredistanceacanbeadjustedbychangingthehelixangle 螺旋角 Standardhelicalgeardrivecansuitanycentredistance 6 9 3ProperMeshingConditionsforHelicalGears Review Accordingtothepropermeshingconditionsofspurgeardrive 6 9 4ContactRatioforaHelicalGearPair Thelengthoftheactuallineofactionincreasesby L iscalledthetransversecontactratio 端面重合度 iscalledtheoverlapratio 轴向重合度 Thetransversecontactratio canbecalculatedwiththeparametersonthetransverseplane 轴向重合度 Dueto thecontactratioofahelicalgearpairismuchhigherthanthatofaspurgearpair Alargecontactratiomeansthatmoregearteethareengagedatthesametimewhichgiveshighstrengthtothegears 6 9 5VirtualNumberofTeeth 当量齿数 forHelicalGears Tocalculatethestrengthofthetooth andtochoosethetypeofthecuttingtool thevirtualgear 当量齿轮 ofthehelicalgearisintroduced Thevirtualgear 当量齿轮 ofthehelicalgearisaspurgear thetoothprofileofwhichisequivalenttothatofahelicalgearonthenormalplane 当量齿轮 以 为分度圆半径 用斜齿轮的mn和 n分别为模数和压力角作一虚拟的直齿轮 其齿形与斜齿轮的法面齿形最接近 这个齿轮称斜齿轮的当量齿轮 齿数ZV称当量齿数 Thevirtualnumberofteeth 当量齿数 forthehelicalgear thenumberZvofteethofthevirtualgear Zvisusedtocalculatethestrengthofthetooth 已知mn n Z 的斜齿轮法面齿形 以mn为模数 以 n为压力角 以Zv为齿数的直齿轮齿形 Furthermore theminimumnumberofteethofthestandardhelicalgearwithoutcutterinterferencecanbederivedas Advantageofhelicalgears Helicalgearsoperatemoresmoothly Havehigherstrength Theworkingcentredistanceofahelicalgearpaircanbeadjustedbythehelixangle 比直齿轮小 机构更紧凑制造成本与直齿轮相同 Helicalgearsarethereforewidelyusedforhighspeedorheavyloadtransmission Themaindisadvantageofhelicalgearsis Theyproduceanaxialthrust 轴向推力 Helicalgears Thehelixangleisthereforelimitedtowithin8 to20 DoubleHelicalgears 6 10 1WormGearinganditsCharacteristics Wormgeardrivesareusedtotransmitmotionandpowerbetweennon intersectingandnon parallelshafts usuallycrossingatarightangle 6 10WormGearing 蜗杆传动 Wormsareakindofscrew usuallyrighthanded 右旋 forconvenienceofcutting orlefthanded 左旋 ifnecessary Wormsareusuallydriverstoreducethespeed Directionof 1 Directionofhelixoftheworm Wormwheels 蜗轮 arethematinggearsoftheworms Maincharacteristicsofwormgeardrives 1 Smoothsilentoperationasscrewdrives 2 Greaterspeedreduction 3 Iftheleadangle 导程角 1ofawormislessthantheequivalentfrictionangle 当量摩擦角 V theback drivingisself lockingtg V fV 当量摩擦系数 4 Lowerefficiency 效率 70 6 10 2TypesofWorms 1 Straightsidedaxialworms圆柱蜗杆 ZA worm阿基米德蜗杆 Thetransversesection 横切面 isArchimedesspiral 螺旋线 Theaxialsectionisinvoluterack 2 Involutehelicoidworms ZI worm渐开线蜗杆螺旋面 3 Arc contactworms ZC worm圆弧齿蜗杆Smallerstress 4 Envelopingworm 包络蜗杆 moreteethengaged 5 Spiroid 锥蜗杆 6 10 3ProperMeshingConditionsforWormDrives Themid plane主平面 Thetransverseplaneofawormwheelpassingthroughtheaxisoftheworm Theengagement 啮合 betweenaArchimedeswormandawormwheelonthemid planecorrespondstothatofaninvoluterackandpinion Necessaryconditionsforawormandawormwheeltomeshproperly Thewormwheelshouldbecutbyacutterwiththesameshapeasthoseofthematingworm 6 10 4MainParametersandDimensionsforWormDrives 1 Theaxialpressureangleofworm x1is20 Thiscanbeincreasedto25 inpowertransmissionordecreasedto15 or12 inindexingdevices 分度装置 2 Themodulem standardvaluesTheseriesofmodulesforwormsissomehowdifferentfromthoseforgears Table6 2 Table6 2ModulesandReferenceDiametersofWorms mm GB10085 88 3 Thenumberofthreads 头数 ofthewormZ1 Z1 theni Z1 thenefficiency Z1 1 2 4 6arepreferable ThenumberofteethofawormwheelZ2 Z2 27 80 4 Theleadangle 导程角 1oftheworm 标准化table6 2 直径系数 Theefficiencyincreaseswithincreaseof 1 If 1islessthantheequivalent 当量 frictionangle v thewormgearpairisself locking 自锁 inback driving 4 Themid diameterd1ofworm 蜗杆中径 4 Themid diameterd1ofworm 蜗杆中径 d1isstandardizedtoreducethenumberofcuttersandshouldbechosentogetherwiththemodulem d1 mZ1 Table6 3ModulesandReferenceDiametersofWorms mm GB10085 88 Thereferencediameter 分度圆直径 d2ofwormwheel d2 mZ2 6 Thecentredistancea ofthewormgearpair Sincetheshapeofthewormshouldbethesameasthestandardwormwheelcutter thewormshouldnotbemodified Advantages Disadvantages Lowerefficiencyduetothegreaterrelativeslidingspeedbetweentheteeth Thefrictionlossmayresultinoverheating 过热 andseriouswear SmoothsilentoperationGreaterspeedreduction Iftheleadangleofawormislessthantheequivalent 当量 frictionangle theback drivingisself locking 6 11BevelGears 锥齿轮 Bevelgearsareusedtotransmitmotionandpowerbetweenintersectingshafts 6 11 1TypesandApplicationsofBevelGears Theteethofabevelgeararedistributedonthefrustum 截锥体 ofacone 圆锥体 正确啮合条件 轴角 传动比 锥顶角 锥顶距R Parametersanddimensionsatthelargeendaretakentobestandardvalues Parametersanddimensionsatthelargeendaretakentobestandardvalues Theshaftangleofabevelgearpaircanbeanyrequiredvalue Inmostcases thetwoshaftsintersectatarightangle直角 Therearestraight helicalandspiral 直齿 斜齿 曲齿 bevelgears Attention ModulesofbevelgearsmustbechosenfromTable6 3 notTable6 1 1 Straightbevelgears 2 helical 螺旋状的 bevelgearmechanism 3 Spiralbevelgear 弧形锥齿轮 mechanism 6 11 2Ba