清華機(jī)械工程專業(yè)電子版機(jī)械設(shè)計(jì)基礎(chǔ)

Chapter6GearsObjectsofthischapter1.Computetheforcesexertedongearteethastheyrotateandtransmitpower.2.Describesuitablemetallic（金屬的）materialsfromwhichtomakethegears,inordertoprovideadequate（適當(dāng)?shù)?、足夠的）performanceforbothstrengthandpitting（點(diǎn)蝕）resistance（抵抗力）.3.UsetheGBasthebasisforcompletingthedesignofthegears.Chapter6

Gears1.Loadsexertedongearteeth2.Failuresofgearsanddesignrules3.Bendingstressingearteeth4.Contactstressongearteeth5.Choiceofspurgearparameters（參數(shù)）6.Structure（結(jié)構(gòu)）designofwheelsandgearslubrication7.CADindesignofgearpair1.Loadsexertedongearteeth

Hypothesis（假設(shè)）:ConcentrationforceactingonthemidpointoftoothwidthIgnoring（忽略）frictionforcebetweenmeshingteethForceinmeshFrictionforceAccessional（附加的）forceLoadsinmesh（嚙合）SpurGear（直齒圓柱齒輪）Tangentialload切向力Radialload徑向力Normalload法向力NominalTorsionkWr/minNmmDirectionofloadsFig6-10p191DriverGear

(主動(dòng)輪-1）ωHelicalGear（斜齒輪）Question:HowtoJudgetheAxialLoadDirectionActingontheHelicalWheel?Principlesofleftorrighthand(Driving（主動(dòng)）Gear)DeterminethehelicaldirectionofdrivergearteethPutoutyour“right”handandholdtheaxes,thenmakesurefourfingersexceptthethumb（大拇指）tothedirectionoftherotation.Atlast,yourthumbpointsthedirectionoftheaxial（軸向）force.TRYBYYOURSELF!!StraightBevelGear（直齒錐齒輪）DirectionofAxialLoad:pointtolargetransverseplane2.FailuresofgearsanddesignrulesBulk（體積）orbodyofgeartoothtoothbreakageskin-deep（表面）ofgeartoothFatiguefailureoccursonlyonoringearteethtoothbreakage1）Bulk（體積）orbodyofgeartoothtoothbreakageskin-deep（表面）ofgeartoothabrasionOpeningGearTransmissionNolubricationisusedLubricatingconditionEnclosed（被裝入箱子的）GearTransmissionusinglubricationpittingSoftskinofteeth軟齒面（350HBW）——收斂性點(diǎn)蝕Hardskinoftooth硬齒面（>350HBW）——擴(kuò)展性點(diǎn)蝕Onlycanbefoundintheenclosedgearboxesscoringandscuffing（膠合）Highspeed,Heavyload,orLowspeed,Heavyloadplasticdeformation3）Majorinfluencefactorsofgearfailuresfluctuated（變化的）stresses；relativeslidingvelocity（速度）ofmeshteeth；Materialsandtheirheatingtreatment;lubricatingconditionabrasion（磨損），pitting（點(diǎn)蝕），scoringandscuffing（膠合），plasticdeformation（塑性變形）用35年對931各齒輪失效各種情況進(jìn)行了統(tǒng)計(jì)（上世紀(jì)70年代——以軟齒面材料為主）序號(hào)齒輪失效類型占總失效的百分比%1疲勞斷齒32.82過載斷齒19.53輪齒碎裂4.34輪轂撕裂4.65表面疲勞20.36表面磨損13.27齒面塑性變形5.3Reference:《齒輪的失效分析》郭志德等，機(jī)械工業(yè)出版社，19924）Improvementstrategies（措施、策略）forgearteethfatiguefailureMaterialsandtheirheatingtreatment;p181~185LubricationGearwithaddendummodification（變位齒輪）Gearprecision（精度）

P179~181—Pleaselearnitbyyourselves精度等級GB/T10095.1-2001和GB/T10095.2-2001規(guī)定，齒輪精度分為13級，按0～12數(shù)序排列，0級最高，12級最低。0～2級為待發(fā)展的特高精度等級。3～5級為高精度等級，用于精密傳動(dòng)，如：航空、船用等6～8級為中等精度等級，用于汽車、機(jī)床傳動(dòng)鏈等9～12級為低精度等級，重載、低速不重要的齒輪，如農(nóng)機(jī)。PrecisionStandardofinvolutegearandbevelgear

Handbook:p125~p140（錐齒輪標(biāo)準(zhǔn)不同）精度的選擇用途、工作條件、傳遞功率和圓周速度的大小及其它技術(shù)要求等來選擇精度等級圓柱齒輪傳動(dòng)直齒斜齒5級以上>20>406級＜15＜307級＜10＜158級＜6＜109級＜2＜45)DesignRules

（準(zhǔn)則）toothbreakageBendingStressesEq.(6-9)PittingfailureContactStressesQuestion:

Howtodealwithotherskin-deepfatigue?

GB/T6413-1986漸開線圓柱齒輪膠合承載能力計(jì)算方法

Abrasivefatigueisconsideredbyenlargingthevalueofm.

2.Isitnecessarytocalculatebothbendingandcontactstressesingeardesign?

accordingtothefailurestyleofgearsa)OpeningGearTransmissionMainfailuresarewearandtoothbreakage:JustneedtocalculatebendingstressF.b)EnclosedGearTransmissionusinglubricationSoftskinofteethPittingFatigue:FirstcalculateH,thentestF.(Hardnessofsmallgearisoften30~50HBSlargerthanbigone.)HardskinoftoothToothBreakage:FirstcalculateF,thentestH.

GB/T10062.1-2003通用機(jī)械漸開線圓柱齒輪承載能力簡化計(jì)算方法2.Failuresofgearsanddesignrules1)Bulk（體積）orbodyofgeartoothtoothbreakage2)skin-deep（表面）ofgeartooth3)Majorinfluencefactorsofgearfailures4)Improvementstrategies（措施、策略）forgearteethfatiguefailure5)DesignRules（準(zhǔn)則）3.BendingstressingearteethHypothesis（假設(shè)）AlltransmittingloadsactingononepairofmeshingteethMovetheloadcomponentstothetoothtipUsingthebendingofacantilevered(懸臂）beamtosimulate（模擬）thestressactingonageartoothapproximately（近似地）.Spurgear2)Determinationthecritical（危險(xiǎn)）sectionofthemaximalbendingstress-Lewis（劉易斯）equation（30°切線法）Causenormalstressonthetooth,whichisoftenneglectedFn3)DeterminationofthemaximalbendingstressFWidthofgearLoadfactor(p186~190)Table6-7Fig.6-7Fig.6-8Table6-8應(yīng)力修正系數(shù)Fig.6-19重合度系數(shù)Fig.6-20Allowablebendingstress許用彎曲應(yīng)力(testequation)Allowable（許用）BendingStress[]FLimitbendingstress

，P207，208,Fig.6-24Safetyfactor，P209,Table6-12Lifefactor，P209,Table6-13Sizefactor，P210,Fig.6-25Stressfactorofbendingtestinggear，equalto2.CyclicnumberN:（p206）Contacttimeofsamesideofgeartoothperturningcircle4)Designequationforpreventing（防止）gearfromtoothbreakagefailureWidthFactor，F(xiàn)ig.6-10IfandWecanobtainfromEq.(6-11):

GB/T1357-1987漸開線圓柱齒輪模數(shù)(p177表6-1)

第一系列0.11100.121.25120.151.5160.22200.252.5250.33320.44400.55500.660.88第二系列0.35(6.5)0.770.991.75(11)2.25142.7518(3.25)223.528(3.75)(30)4.5365.545Attention:Thecalculatingmodulus（模數(shù)）misenlargedto10%~15%inordertoconsideratethewearinfluenceontheopentransmissiongearteethThemodulusvalueisgeneralequaltoorlargerthan1.5~2mmofpowertransmissiongear.SpurgearTestequationofbendingstressDesignequationofbendingstressHelicalgears—p2171）Basicideatodealwiththebendingstressinhelicalgeartooth：ResultantforceFnactsonthenormalplane（法面）--zv,mnTheeffectofhelixangle(螺旋角）willbeconsidered--Y

2）Testequationofbendingstrength:3）Designequationofbendingstrength:Fig6-29Bevelgears--p2251）Basicideatodealwiththebendingstressinbevelgeartooth：ResultantforceFnactsontheequivalentspurgearofmid-plane（齒寬中點(diǎn)的當(dāng)量直齒輪）--zv,mm,TvBecauseoflowmanufacturalprecision,K=1andY=1Transformmm

intostandardmodulemGeometricalcalculationofbevelgearonpage2233）Designequationofbendingstrength:2）Testequationofbendingstrength:WidthfactorAttention:Usingthesametablesandfiguresofspurgear,butusingtheequivalent（當(dāng)量）geometrical（幾何的）parameters.ThemodulusvaluemcanbeobtainedfromGB/T12368-1990BriefSummary1）彎曲疲勞強(qiáng)度設(shè)計(jì)建模方法2）工程簡化和不確定因素的處理方法3）從特殊到一般的思想方法4）影響齒根彎曲疲勞應(yīng)力的主要因素分析4.ContactstressongearteethHertziancontactpressure-p38~40(2-41)Where:E1,E2—modulusofelasticityoftwocontactcylinders1,2

—poisson’sratiooftwocontactcylinders1)HypothesisTwocontactgearteethissimulatedbytwocontactcylindersunderaradialload.Usingpitchpointinsteadofmaximumcontactstresspointtoconsiderthegearcontactstrength

Spurgearsa)Lengthofcontactlineb)Loadc)EquivalentcurvatureradiusContactstressonpitchpointFactorofcontactratioFig.6-132)CalculationofcontactstressGearratioElasticfactorTable6-94)TestequationofcontactstrengthFactorofpitchregionFig.6-145)Designequationofcontactstrength6)Allowablecontactstress[]HLimitcontactstress，F(xiàn)ig.6-22SafefactorofcontactstrengthTable6-12Workhardeningfactor,Table6-23LifefactorofcontactstrengthTable6-11Helicalgears—p214~2161）BasicideatodealwiththecontactstressonhelicalgearsResultantforceFnactsonthenormalplane（法面）--zv,mnTheinfluenceofhelixangle(螺旋角）willbeconsidered--Z

2）Testequationofcontactstrength:3）Designequationofcontactstrength:Factorofhelixangle,Fig.6-28Bevelgears--p223~2251）Basicideatodealwiththecontactstressonbevelgears：ResultantforceFnactsontheequivalentspurgearofmid-plane（齒寬中點(diǎn)的當(dāng)量直齒輪）--zv,mm,TvBecauseoflowmanufacturalprecision,K=1andZ=12）Testequationofcontactstrength:3）Designequationofbendingstrength:齒輪強(qiáng)度計(jì)算小結(jié)疲勞強(qiáng)度類型針對的對象應(yīng)力的性質(zhì)一對齒輪應(yīng)力大小的特點(diǎn)主要影響參數(shù)彎曲單個(gè)齒輪的輪齒內(nèi)應(yīng)力兩個(gè)齒輪彎曲應(yīng)力不一定相等模數(shù)m接觸一對齒輪的齒面表面應(yīng)力兩個(gè)齒輪表面接觸應(yīng)力相等節(jié)圓直徑d1思考題：已知兩對標(biāo)準(zhǔn)直齒圓柱齒輪的工作參數(shù)、材料、使用壽命及寬度等均相同，其余幾何參數(shù)不同：第一對：z1=20,z2=40,m=3mm；第二對：z1=30,z2=60,m=2mm。試分析：兩對齒輪的接觸疲勞應(yīng)力是否相同？兩對齒輪相應(yīng)齒輪的彎曲疲勞應(yīng)力是否相同？通過計(jì)算結(jié)果說明齒輪的彎曲疲勞應(yīng)力和接觸疲勞應(yīng)力的主要影響參數(shù)是什么？5.Choiceofgearparameters2）teethnumberofpinion(小齒輪）z1

softtoothsurface(350HBS)andclosettransmission–pittingfatigueismajorfailurestyle.Openingtransmission，wearandteethbreakageismajorfailurestyle1）gearratio：SpurgearsHelicalgearsBevelgearsu≤7u≤5u≤33）widthfactor：

Table6-10，forspurgears,thewidthofpinionisoften5to10mmlargerthangearwheel(大齒輪).4）modificationcoefficientofgearsFig.6-21PurposeofusingmodificationcoefficientingeardesignAvoidundercutting(根切),Increasingstrength,Satisfyingthedemandofspeedratioandcenterdistance

Influenceonthecontactstrength(synthesisinfluenceof（x1+x2）)1、x1+x2=0,Hisfixedness.2、x1+x2>0,Hdecreasing3、x1+x2<0,HincreasingInfluenceonthecontactstrength1、x>0，F(xiàn)decreasing2、x<0，F(xiàn)increasing5）ChoiceofgearprecisionTable6-3漸開線圓柱齒輪和漸開線錐齒輪精度選擇Table6-4常用精度等級圓柱齒輪的應(yīng)用范圍和加工方法6.Structuredesignofwheelsandgears

lubrication1)CompositionofawheelFlange輪緣Spoke輪輻Hub輪轂2)ConsiderationofwheelstructuredesignOrientationandfixationNointerferencewithnearbypartsCapabilityofbearingloadsandenoughworklifeAcceptableprecisionManufacturable3)Typicalstructureofspokesp404~408a)WheelandaxelBevelgears（pinions)：b)solidc)ventro-board

腹板式e)Assemblagemuchlargerdiameterofgearsinordertosavethemateriald)Spoke

輪輻式Spurgears：GearaxelSolidwheelsofbevelgear,cylindricalgearandsprocketWheelwithventro-boardofbevelgearWheelwithventro-boardofcylindricalgear（foundry-鑄造)SpokewheelofcylindricalgearAssemblagegear4)LubricatingmethodsofgearboxGenerallubricants:baste（油脂）andlubrication（潤滑油）Generallubricatingmethodsofgearboxandselectivemethods:table16-4,p498Lubricatingmethodsofgearboxlieonthevelocityofgears!表16-4閉式齒輪潤滑方式的選擇齒輪節(jié)圓速度v/(m/s)潤滑方式＜0.8＜10~123~1212~15脂潤滑（涂抹或充填）浸油潤滑飛濺潤滑（齒輪箱軸承需靠齒輪浸油飛濺時(shí)）壓力噴油、噴霧潤滑Viscosityoflubricationa)Absolute(ordynamic)viscosity—?jiǎng)恿︷ざ?

平行板間液體的層流流動(dòng)模型ShearstressAbsoluteviscosityVelocitygradsNewtonEquationSIUnit:Pa·s非SI單位：泊，P(dyn·s/cm2)b)Kinematicviscosity—運(yùn)動(dòng)黏度

Inmanysituationsitisveryconvenienttousekinematicviscosityratherthandynamicviscosity.—Forexample,measuringthevalueofviscosityDefinition:DensityofmineraloilUnit:m2/s溫度計(jì)溫度計(jì)攪拌器試液杯外容器計(jì)尖釘潤滑油水木塞流出短管接受瓶水平調(diào)節(jié)螺釘三角支架恩氏粘度計(jì)基本結(jié)構(gòu)非SI單位：斯，St(cm2/s)c)TemperatureandpressureeffectsonViscosityTheviscosityofmineraloilsandsyntheticoilsdecreaseswiththeincreasingtem