机械设计---mecysueducn

第六章Toothedgearing齿轮传动,3-1Generalconsiderations概述3-2Materials,typesoffailureanddesigncriteria齿轮材料、失效形式和计算准则3-3Loadsincylindricalgearing圆柱齿轮传动载荷计算3-4Strengthofspurcylindricalgearing直齿圆柱齿轮传动强度计算3-5Strengthofhelicalcylindricalgearing斜齿圆柱齿轮传动强度计算Toothedgearingdesignexample齿轮传动设计实例3-6Straightbevelgearing直齿圆锥齿轮传动,6-1Generalconsiderations概述,Characteristicsandapplications特点和应用Typesofthetoothedgearing齿轮分类,BACK,一、Characteristicsandapplications特点和应用1、Advantages优点Longservicelifeandhighreliability工作可靠，寿命长Constantspeedratio传动比恒定Highefficiency工作效率高Smalloverallsize结构紧凑,2、Shortcomings缺点Highcost成本高Noiseinoperationatconsiderablespeedsorlowprecisioninmanufacture制造精度低或者高速运转时，振动噪音大Theyareunsuitablefordutyovermediumandlongdistances不适合大的中心距,3、Applications应用,二、Typesoftoothedgearing齿轮分类,1、Accordingtothedifferencebetweentherelativepositionsoftheshafts：按轴布置方式分Toothedgearingbetweenparallelshafts平行轴齿轮传动（Cylindricalgearing圆柱齿轮传动）,SpurCylindricalgearing直齿圆柱齿轮传动HelicalCylindricalgearing斜齿圆柱齿轮传动Herringbonegearing人字齿圆柱齿轮传动,Toothedgearingbetweenintersectingshafts相交轴齿轮传动（Bevelgearing圆锥齿轮传动）,Toothedgearingbetweencrossedshafts：交错轴齿轮传动,直齿圆锥齿轮传动斜齿圆锥齿轮传动曲齿圆锥齿轮传动,Crossedhelicalgearing螺旋齿轮传动,Skewbevelgearing,Straightbevelgearing,Spiralbevelgearing,2、Accordingtothedifferenceoperatingconditions：按工作条件分Closedgearing闭式齿轮传动Opengearing开式齿轮传动Partlyopengearing半开式齿轮传动,3-2Materials,typesoffailuresanddesigncriteriaofgears齿轮材料、失效形式和计算准则,Materialsofgears齿轮材料Typesoffailures失效形式Designcriteria计算准则,一、Materialsofgear齿轮材料Requirements基本要求：Enoughimpacttoughness一定的冲击韧性(Ensuresufficientbeamstrengthinbendingundervariableload)（保证变载荷下，弯曲疲劳强度较高),Enoughhardness一定的硬度（Ensuresufficientenduranceoftheirsurfacelayers保证抗齿面失效的能力）Highmanufacturabilityandlowcost工艺性好、成本低,1、Forgedsteel锻钢（Wideapplication常用）Underordinaryservicecondition一般场合：Lowerhardnessoftoothsurface软齿面（HB350）齿轮材料Processingprocedure工艺过程：Medium-carbonsteels(45)中碳钢、Medium-carbonalloysteels(40Cr)中碳合金钢Structuralimprovementandnormalization调质或正火Cutting切齿,Forgearswithlowerhardnessoftoothsurface,thehardnessdifferencebetweensmallgeartoothsurfaceandlargegearoneisrequired:软齿面大小齿轮之间要求具有一定的硬度差：HBHB1HB23050,Criticalgears重要应用：,Processingprocedure工艺过程：Cuttingteeth切齿Hardening淬火Grinding磨削2、Caststeel铸钢（Forgearsoflargediameters尺寸较大、不容易锻造时选用da400mm）,Higherhardnessoftoothsurface选硬齿面（HB350）齿轮材料,3、Castiron铸铁Greyiron灰口铸铁（HT200HT400)：Easytomanufactureandlowcost工艺性好、价格低；However,thestrengthandtoughnessisconsiderablylessthanthatofsteels但冲击韧性差、强度低Forlow-speed,large-sizegearingwithoutimpact.低速、无冲击、大尺寸齿轮,High-strengthcastiron球墨铸铁（QT5005、QT6002等)：HighstrengthandtoughnessTakingtheplaceofcaststeelgears强度高、冲击韧性好、代替铸钢,4、Plastics非金属材料（Caprolonandpolyformaldehydeetc夹布胶木和尼龙等,）：Self-lubricationandnoiselessoperation具有自润滑性、工作噪音低Forgearsofhighspeed,lightloadandlowaccuracyrequirement用于高速、小功率、精度要求不高时,BACK,二、Typesoffailure失效形式Toothbreakage轮齿折断Failureoftoothsurfacelayers齿面损伤：Fatiguepitting,seizing,abrasivewearandplasticflowofmaterial点蚀、胶合、磨损和塑性变形,三、Designcriteria计算准则,1、Closegearing闭式齿轮传动：Theprincipaltypesoffailurearepitting,toothbreakageandseizingoftheteeth.Andseizingoftheteethoccursunderheavyloadandcalculationincheckingforthepossibilityoftoothseizureisnoteffective.Hence,onlycalculationsofthecontactingfatiguestrengthandbendingfatiguestrengtharecarriedout.以点蚀、轮齿折断和胶合失效形式为主，其中胶合发生于重载，而且计算方法不成熟，所以一般只进行齿面接触疲劳强度和齿根弯曲疲劳强度计算。,Lowhardnessgearing软齿面齿轮传动：Theprincipaltypeoffailureispitting以点蚀失效为主,Designingonthebasicofthecalculatingofcontactfatiguestrengthoftheworkingsurfacesoftheteeth按齿面接触疲劳强度设计Checkingthebendingfatiguestrengthoftheteethroot按齿根弯曲疲劳强度校核,Highhardnessgearing：硬齿面齿轮传动Theprincipaltypeoffailureistoothbreakage以轮齿折断失效为主,Designingonthebasicofthecalculatingofthebendingfatiguestrengthoftheteethroot按齿根弯曲疲劳强度设计Checkingthecontactfatiguestrengthoftheworkingsurfacesoftheteeth按齿面接触疲劳强度校核,BACK,2、Opengearing开式齿轮传动：Theprincipaltypesoffailureareabrasivewearandtoothbreakage.Uptillnow,calculationforanassessmentoftheservicelifeofgearssubjecttosubstantialwearisnoteffective.Hence,thedesigniscarriedoutonthebasicofthecalculationsofthebendingfatiguestrength,thenmodulemisincreasedby10to15%totakeintoaccounttheinfluenceofwear.以磨损和轮齿折断失效为主，其中磨损无可靠计算方法，所以按弯曲疲劳强度设计，然后考虑磨损因素，将模数m增加1015。,6-3Loadsincylindricalgearing圆柱齿轮传动载荷计算,Forcesinspurcylindricalgearing直齿圆柱齿轮传动受力分析Forcesinhelicalcylindricalgearing斜齿圆柱齿轮传动受力分析计算载荷,BACK,一、Forcesinspurcylindricalgearing直齿圆柱齿轮传动受力分析,1、Relationshipbetweenforcesactingondrivinganddrivengears,Magnitudeofforces,Drivinggear（resistanceforce):Itsdirectionisoppositetothedirectionofrotationofdrivinggear.Drivengear(drivingforce):Itsdirectionissamewiththedirectionofrotationofdrivengear.,Directingfromthepitchpointtotherotatingcentre,二、Forcesinhelicalcylindricalgearing斜齿圆柱齿轮传动受力分析,Relationshipbetweenforcesactingonthedrivinganddrivengears,Resolveinto,Magnitudeofforces,Directionofforces,Asbefore,Helixdirection:lefthandforleft-handhelixgearandrighthandforright-handhelixgear.,Rotatingdirection:thebendingdirectionoffourfingers.,Thesamedirectionofthumbing,Theoppositedirectionofthumbing,三、Designload计算载荷Fnd=KFnKLoadfactor载荷系数（Takeintoaccounttheinfluenceofmultiformfactorsontheload考虑各种因素对载荷实际影响）,K=KAKvKK,KAServicefactor使用系数,Motor原动机Operatingmachine工作机,性能不稳,附加外部动载荷,Unsteadyperformance,Loadgrowinstantly载荷瞬时增大,Additionalexternaldynamics,KA,KvDynamicloadfactor动载系数,Errorsinmanufactureandassembly制造安装误差Deflectionsoftheteethunderload轮齿变形,Errorsinengagement啮合误差Instantaneousangularacceleration瞬时角加速度：,Additionalinternaldynamicload附加内部动载荷,Loadgrowinstantly载荷瞬时增大,Kv,Decreaseinvelocity,increaseinaccuracyofgearmanufacture速度v降低,精度增高Modificationofthetoothfaceprofile齿顶修形,Decreaseindynamicload动载荷减小,KVDrops,KFactorofloaddistributionamongtheteeth齿间载荷分配系数Errorsinmanufacture由于误差,K,载荷在各啮合齿对间分配不均Nouniformloaddistributionamongtheteeth,某对齿所受载荷高于平均值Loadactingonsomegearismorethantheaverageload,KFactorofthenonuniformloadingalongthefacewidth齿向载荷分配系数,Bendingandtorsiondeformationoftheshaft轴弯曲、扭转变形Elasticdisplacementofbearings轴承弹性位移Errorsinmanufactureandassembly制造安装误差,齿轮副相倾斜、轮齿扭曲Thegearsareinmisalignmentwithrespecttoeachother,Theloadisdistributednonuniformlyalongthefacewidth载荷沿接触线分布不均,Loadactingonsomepartoftheteethalongthefacewidthincrease载荷局部增大,K,Makingtheteethwithataperedcrown鼓形齿,Properfacewidth齿宽合理,Loadconcentrationcanbereducedby:,Locatingthegearsfavorablybetweenthebearings齿轮布置合理Increasingtherigidityoftheshaftandbearings增加轴和轴承座刚度Raisingtheaccuracyofmanufactureandassembly提高制造、安装精度,Loadconcentrationisreduced偏载降低,KDecreased,由上述五点,InfluenceofbendingdeformationoftheshaftonK,InfluenceoftorsiondeformationoftheshaftonK,InfluenceoftotaldeformationoftheshaftonK,6-4Strengthcalculationsforspurgears直齿圆柱齿轮传动强度计算,Contactfatiguestrengthcalculation齿面接触疲劳强度计算Beamfatiguestrengthcalculation齿根弯曲疲劳强度,BACK,一、Contactfatiguestrengthcalculation齿面接触疲劳强度计算1、Formulas公式推导TheHertzformulaandstrengthcondition：赫兹公式与强度条件,Characteristicpoint计算特征点：Pitchpoint节点（Duetopittingbeginsatthelinepassingthroughthispointwhereloadistransmittedbyasinglepairofteeth.Anotherreasonistosimplifycalculation.此处为单对齿啮合，最易发生点蚀；此处计算过程简化.）,Thecontactstressdependonloadandtheradiiofcurvatureofthecontactpointoftheteeth.Andthecontactstressvariesalongwiththechangeofthecontactpoint.,Equivalentradiusofcurvature综合曲率半径,Radiusofcurvatureofgear,Equivalentradiusofcurvature,Influencesofradiusofcurvature,Changesofcontactstress,Lengthofthelineofcontact接触线长度L,Facewidthoftooth齿宽b,Load,Contactratiofactor,Thefacecontactratio,Substituting、into：,Factortakingintoaccountthemechanicalpropertiesofthegearmaterials,Factortakingintoaccounttheshapeofthecontactingsurfaces,Forchecking,Facewidthfactor,Weobtain:,Fordesign,Itissubstitutedintofollowingequation,1、Formula1）Basichypotheses基本假设Geartoothistreatedasacantileverandthewholeforceisappliedtothetopofthetooth轮齿视为悬臂梁，全部载荷作用于齿顶,二、Beamfatiguestrengthoftoothroot齿根弯曲疲劳强度,BACK,Thestrengthisdeterminedforthesideoftheteethsubjecttotensilestress以受拉边为计算依据,Thedangerouscrosssectionistakenby30tangenttotheaxisofthetooth危险截面AB（30切线法）Onlyconsideringperipheralcomponentoftheforce(compressionstresscausedbyverticalcomponentislessthan10%ofbendingstress)仅计水平力FncosF（仅为b百分之几）,2）Introduction推导过程Onthedangerouscrosssection：危险截面处,Toothformfactor,计入,Loadfactor载荷系数KStressconcentrationfactor应力修正系数YSa(应力集中）Contactratiofactor重合度系数Y（Loadistransmittedbymorethanonepairofteeth载荷不只一对齿承担）,Fordesign,Forchecking,Substitutingbandd1intoaboveformula:,Moduleincreases模数m增大Fdecrease：Contactratiofactor重合度系数,2、Notes,Bendingstrengthmainlydependonm.弯曲强度主要取决于m（Forpowerdrives:动力传动m1.52mm）,ToothformfactorYFaisindependentofm,onlydependontoothform齿形系数YFa：P59图3-21与模数m无关，仅取决于齿形（Z，x）ZYFaF1F2UsuallyF1F2*Bendingstrengthofthepinionandgearshouldbecalculatedrespectivelyorcarriedoutforthetoothedgearwiththehigherratioof大小齿轮弯曲强度应该分别计算，或取中大者计算。,FAllowablebendingstress许用弯曲应力FlimBendingendurancelimitofgearstestedwith1offatiguepossibilities失效概率为1时，试验齿轮弯曲疲劳强度P67图328.SFSafetymargin安全系数（一般SF1）KFNServicelifefactor寿命系数KFNf（N）P65图326,Z1（Numberoftheteethofthepinion小齿轮齿数）Lowhardnessclosegearing:(Overallsizeofthedrivemainlydependsoncontactstrength,whilebendingstrengthofthedriveissufficient.)闭式软齿面齿轮：（传动尺寸主要取决于接触强度，弯曲强度较富裕）,Whend1=constandbendingstrengthisensured,itissuggestedthatalargernumberoftheteethofthepinionshouldbetaken.在d1=const时，并满足弯曲强度前提下，尽量取多的齿数（Z1，m相应，d1=mZ1）,齿根弯曲应力变化规律,单侧受载,双侧受载,6-5Strengthforhelicalcylindergearing斜齿圆柱齿轮传动强度计算,Contactingfatiguestrengthofthetoothsurface齿面接触疲劳强度计算Bendingstrength弯曲强度计算,BACK,一、Contactingfatiguestrengthofthetoothsurface齿面接触疲劳强度计算1、Formula按节点处法面当量直齿圆柱齿轮计算。,Thelengthofthelineofcontact接触线长度L（Varies）,Axialcontactingratio,F,Substituting、代入into，andfavorableinfluenceofthelineofcontactinclinedtotherootoftheteethonthecontactingstrengthofthegearsisconsideredbyhelixangerfactor此外，计入螺旋角系数以考虑接触线倾斜对接触强度的有利影响,Factortakingintoaccountthemechanicalpropertiesofthegearmaterials,Factortakingintoaccounttheshapeofthecontactingsurfaces,Forchecking,Fordesign,2、NotesHelicalgearsarestrongerthanspurgearsforthefollowingreason斜齿轮相对于直齿轮承载能力:,nL,BACK,Advantagesisnotobvious优点不明显FaServicelifeofthebearing轴承寿命,Usually825（Herringbonegears：2035）,二、Bendingstrength弯曲强度计算,1、Formula：Helicalteethcanbeassumedtoconformedwiththetoothofaequivalentspurgearinacrosssectionnormaltothetooth.Thestrengthcalculationisdoneagainsttheequivalentspurgear按法面当量直齿圆柱齿轮计算,BACK,Basicparametersoftheequivalentspurgear当量齿轮的基本参数：Modulemn、Equivalentnumberofteeth当量齿数,FavorableinfluenceofthelineofcontactinclinedtotherootoftheteethonthebendingstrengthofthegearsistakenintoaccountbyhelixangerfactorY引入螺旋角系数Y考虑接触线倾斜对弯曲强度的有利影响,Spurgear,Helicalgear,Forchecking,Byanalogywithspurgearing：采用比较法,Fordesign,intoaboveformula:,Substituting,YFa、YSaTakenbyequivalentnumberofteeth据当量齿数查取,2、Notes,Helixangerfactor,Helicalgearsarestrongerthanspurgearsinbendingstrength斜齿轮和直齿轮相比，弯曲强度增大.（Y1，ZvYFaF）,6-6Spurbevelgearingdrive直齿圆锥齿轮传动（Usually=901+2）,Specialfeaturesofthebevelgearingascomparedwithcylindricalgearing和圆柱齿轮相比，锥齿轮的特点Geometricalrelationshipandbasicparametersoftheequivalentgearforbevelgearing几何关系和当量齿轮基本参数Forcesinbevelgearing受力分析Contactstrength接触强度Bendingstrength弯曲强度Notes说明Problems思考题,BACK,一、Specialfeature