機(jī)械畢業(yè)設(shè)計(jì)英文外文翻譯63超高速行星齒輪組合中內(nèi)部齒輪的有限元分析

11英文原文FiniteElementAnalysisofinternalGearinHigh-SpeedPlanetaryGearUnitsAbstract:Thestressandtheelasticdeflectionofinternalringgearinhigh-speedspurplanetarygearunitsareinvestigated.Arimthicknessparameterisdefinedastheflexibilityofinternalringgearandthegearcase.ThefiniteelementmodelofthewholeinternalringgearisestablishedbymeansofPro/EandANSYS.Theloadsonmeshingteethofinternalringgearareappliedaccordingtothecontactratioandtheload-sharingcoefficient.Withthefiniteelementanalysis(FEA),theinfluencesofflexibilityandfittingstatusonthestressandelasticdeflectionofinternalringgeararepredicted.Thesimulationrevealsthattheprincipalstressanddeflectionincreasewiththedecreaseofrimthicknessofinternalringgear.Moreover,largerspringstiffnesshelpstoreducethestressanddeflectionofinternalringgear.Therefore,theflexibilityofinternalringgearmustbeconsideredduringthedesignofhigh-speedplanetarygeartransmissions.Keywords:planetarygeartransmissions;internalringgear;finiteelementmethodHigh-speedplanetarygeartransmissionsarewidelyusedinaerospaceandautomotiveengineeringduetotheadvantagesoflargereductionratio,highloadcapacity,compactnessandstability.Greatattentionhasbeenpaidtothedynamicpredictionofgearunitsforthepurposeofvibrationreductionandnoisecontrolinthepastdecades(1-^8ksoneofthekeyparts,internalgearmustbedesignedcarefullysinceitsflexibilityhasastronginfluenceonthegeartrain'performance.studieshaveshownthattheflexibilityofinternalgearsignificantlyaffectsthedynamicbehaviorsofplanetarygeartrains(9).inordertogetstressesanddeflectionsofringgear,severalfiniteelementanalysismodelswereproposed(10-14).however,mostofthemodelsdealtwithonlyasegmentoftheinternalringgearwithathinrim.thegearsegmentwasconstrainedwithcorrespondingboundaryconditionsandappointloadwasexertedonasingletoothalongthelineofactionwithoutconsideringthechangeoverbetweenthesingleanddoublecontactzoneinacompletemeshcycleofagiventooth.Afiniteelement/semi-analyticalnonlinearcontractmodelwaspresentedtoinvestigatetheeffectofinternalgearflexibilityonthequasi-staticbehaviorofaplanetarygearset(15).Byconsideringthedeflectionsofallgearsandsupportconditionsofsplines,thestressesanddeflectionswerequantifiedasafunctionofrimthickness.Comparedwiththepreviouswork,thismodelconsideredthewholetransmissionsystem.However,themethoddescribedinRef.(15)requiresahighlevelofexpertisebeforeitcanevenbesuccessful.Thepurposeofthispaperistoinvestigatetheeffectsofrimthicknessandsupportconditionsonthestressandthedeflectionofinternalgearinahigh-speedspurplanetarygeartransmission.Firstly,afiniteelementmodelforacompleteinternalgearfixedtogearcasewithstraightsplinesiscreatedbymeansofPro/EandANSYS.Then,properboundaryconditionsareappliedtosimulatingtheactualsupportconditions.Meanwhilethecontactratioandloadsharingareconsideredtoapplysuitableloadsonmeshingteeth.Finally,withthecommercialfiniteelementcodeofAPDLinANSYS,theinfluencesofrimthicknessandsupportconditiononinternalringgearstressanddeflectionareanalyzed.finiteelementmodelexamplesystemAthree-planetplanetarygearset(quenchedandtemperedsteel5140)definedinTab.1istakenasanexampletostudytheinfluenceofrimthicknessandsupportconditions.Tab.1ParametersofexamplesystemIlcmSunRingI'cizthnumber■2367MuJule/工工m3FrWiiurcangl<^Q202020YDun^'jimndul<rFa—-Prbtio—03-l?cnsily/(trn—7.R-AsshowninFig.1,threeplanetsareequallyspacedaroundthesungearwith120?apartfromeachother.Here,allthegearsinthegearunitarestandardinvolutespurgears.Thesungearischosenastheinputmemberwhilethecarrier,whichisnotindicatedinFig.1forthesakeofclarity,ischosenastheoutputmember.Theinternalringgearissetstationarybyusing6splinesevenlyspacedroundtheoutercircletoconstraintherigidbodymotionofringgear.

Fig.1DiagramofexamplesystemAdimensionlessinternalgearrimthicknessparameter九isdefinedastheratioofrimthicknesstothetoothheightasfollows:Wherer,r,raretheouter,dedendumandaddendumradiusofinternalgear,respectively.Asmaller九ernalgearswithdifferentvaluesof九=1.0,1.5,2.025areinvestigatedinthispaper.Inallthesecases,thewidthsofringgearare44mm,andtheconnectingsplinesare34mminlengthand14mminwidth,whiletheheightsofsplinesineachcaseare5mm,6mm,7mmand8mm,respectively.Afiniteelementmodelfortheinternalgearwith九=1.5isshowninFig.2,whichcontains69813elementsand112527nodes.Fig.2FiniteelementmodelofinternalringgearloadsandboundaryconditionsTheinternalgearisfixedtogearcasethroughsplinesandmesheswithplanetgears.Assumingthattheloadisevenlydistributedtoeachplanetandallfrictionsarenegligible,themeshingforcebetweeneachplanetandtheringisasfollows:如;cosaWhereTistheoveralloutputtorque;iistheoverallreductionratio;ristheradiusofsuncscsgear;npdenotesthenumberofplanets;isthepressureangle.Inaddition,byconsideringthecontactratioandloadsharingfactors,wecanfinallydeterminethemeshpositionsandtheproportionsoftheloadcarriedbyeachtoothofthering.TheloadstateoftheringisshowninFig.3.Fig.3LoadstateofinternalringgearHere,thephaseanglebetweeneachplanetis120。and耳(1,???.,6)isthenormalmeshingforceactingontheteethofinternalgear.Forclaritypurpose,onlytheteethinmeshareplottedinFig.3.afterobtainingthemeshingforcesactingoninternalgear,wecanapplythemtothefiniteelementmodel.Tobespecific,themeshingforcesareevenlydistributedtothecorrespondingnodesalongthelineofengagement.Assupportconditionscanbeverycomplicatedifconsideringthecontactproblems,specialsubstitutemustbemadetomodeltheactualcontactsatthesplines.Inthispaper,thesplinesarecoupledwiththeringbytheoverlappednodesandsixspringsequallyspacedbetweentheoutersurfaceoftheringandthehousingsurfaceareappliedtosimulatingthesupportconditions.Thesupportconditionbetweentheringandthehousingisindicatedthroughthestiffnessofthesesprings.Theprocesscanbedetailedasfollows.Asinglenodeneedstobedefinedforeachspline-to-housingconnection.ThisisachievedsuingCOMBINE14elementsateachsplineposition,whichconnectthesplinestothepointsatthehousingsurfacewithaninfinitestiffness.Alldegreeoffreedoms(DOFs)ofthesepredefinednodesareconstrained.AttheotherendofeachspringelementisacommonnodeconnectedwithsplinewhoseDOFsexceptinradialdirectionareallconstrained.Inaddition,thenodesontheloadedsurfaceofeachsplineareconstrainedincircumferentialDOF.AndtheaxialDOFoftheringisconstrained.ThesupportconditionsimulatedwithspringsisshownasFig.4Fig.4SupportconditionsimulatedthroughspringsFEAresultsByapplyingproperloadsandboundaryconditions,afiniteelementanalysiscanbeconductedtofigureouttheeffectsofrimthicknessandsupportconditionsoninternalgearstressanddeflection.Astotheexamplesystem,thestressanddeflectionarepredictedat24discreteangularpositionswithanincrementof5。,whichspana120?-rotationofthecarrier.thisensuresthatanytoothofinternalgeargoesthroughacompletemeshingcyclebecausethenumberofplanetsis3.2.1effectofrimthicknessoninternalgearstressanddeflectionInFig.5,themaximumprincipalstress(Misesstress)oftheringateachdiscretepositionisplottedagainstthecarrierrotationangleforfourdifferentringrimthickness(=1.0,1.5,2.0,2.5).here,thespringstiffnessis33N/mm.

Fig.5MiiximumMisesstressesofringunderdifferent丸vidliesFig.5MiiximumMisesstressesofringunderdifferent丸vidliesFig.6showsthedeflectionshapesofringswithdifferentrimthickness.Theringdeflectionsfor九=1.0and九=2.0aredemonstratedinFig.7withthesamedeflectionmagnificationfactorof50.(b)A=2.0.0(b)A=2.0Fig.6DeilectionshapesofringwithdiilerentAvaluesObviously,when九increases,thedeflectionofringdecreases.Theamountofradialdeflectionoftheringinbothoutwardandinwarddirectionisplottedasafunctionof九inFig.7.here,thepositiveamountsdenotetheoutwarddeflectionswhilethenegativeonesdenotetheinwarddeflection.When九=1.0,themaximumout-wardandinwardradialdeflectionsarepredictedtobe0.139and0.122mm,respectively.Iftheringsipermittedtodeflectsomuch,thosemanufacturingerrorsassociatedwiththeinternalgearsuchasthe

roundnesserrorandrun-outerrorcanbetoleratedaslongastheirmagnitudesarelesstheamountofdeflection.Fig.7Maximumradialdeilectionsofringasafunction□f2valuesFig.7Maximumradialdeilectionsofringasafunction□f2values冒mEmu斗LPPIlnpF」EnuHXEWeffectofspringstiffnessoninternalgearstressanddeflectionThemaximumprincipalstressoftheringwithvariedspringstiffnesskisshowninFig.8.here,theunitofstiffnessisN/mm.obviously,themaximumprincipalstressoftheringwith九=1.0ismuchmoresensitivetothesupportstiffnessthanthatoftheringwith九=2.5.andforaringwithagiven九,themaximumprincipalstressincreaseswiththedecreaseofspringstiffness.QnV2?;1ETJ5踣首mdTmhicllWJ9ullrsFQnV2?;1ETJ5踣首mdTmhicllWJ9ullrsF<duCarriernotationil'；A=I.Ur?2.-

Ar1各SMa^iniutnMi&csstressesairingunderdiilercidspringstiirncssFig.9demonstratestheinfluenceofspringstiffnessonthemaximumradialdeflectionofthering.Similarlythemaximumradialdeflectionsoftheringwith九=1.0ismuchmoresensitivetothesupportstiffnessthanthatoftheringwith九=2.5.andforaringwithagiven九,themaximumdeflectionincreasewiththedecreaseofspringstiffness.nlri.--=:*'".-,JTT-vp一上ELLEVEy卻nlri.--=:*'".-,JTT-vp一上ELLEVEy卻4L)刪豹II1-012ftCarrjtrroLaliorLangLuf)(a)4=1.1)2fl4(i6U闕ldO12DCarrh^r^otHLLonanple/4j250sQ5ulli/n.2gDu-p「-5PIS_umul-suwi：h';.-1=J.?Fig.9MaximumradialdeilectionofringunderdiilerentspringstillnessconclusionsInthispaper,afiniteelementanalysismodelisemployedtoinvestigatetheeffectofflexibilityofinternalringgearonstressesanddeflections.Basedontheresultspresentedabove,someconclusionsareasfollows.Therimthicknessofringisinfluentialtoitsstresses.Withthedecreaseofrimthickness,themaximumprincipalstressofinternalringgearincreasesandthecriticalpointatwhichthemaximumstressoccursmovesfromfilletregiontotherootoftooth.Therimthicknessalsoinfluencesinternalringgeardeflections.Aringwithathinrimproduceslargerdeflectionsthanaringwiththickrim.Whenthedeflectionislargeenough,somemanufacturingerrorsassociatedwithinternalringgearsuchasroundnesserrorandrun-outerrorcanbetolerated.1111Thespringstiffnessbothaffectsthestressanddeflectionofinternalringgear.Aninternalgearringwithlargerspringstiffnesstendstoproducesmallerstressanddeflection.Analternativewayofusinggearstotransmittorqueistomakeoneormoregears,i.e.,planetarygears,rotateoutsideofonegear,i.e.sungear.Mostplanetaryreductiongears,atconventionalsize,areusedaswell-knowncompactmechanicalpowertransmissionsystems[1].TheschematicoftheplanetarygearsystememployedisshowninFigureoSinceSUMMiTVdesignsarelaidoutusingAutoCAD2000,theFigure1isgeneratedautomaticallyfromthelayoutmasks(Appendix[1]).Oneunitoftheplanetarygearsystemiscomposedofsixgears:onesungear,a,threeplanetarygears,b,onefixedringgear,c,onerotatingringgear,d,andoneoutputgear.Thenumberofteethforeachgearisdifferentfromoneanotherexceptamongtheplanetarygears.Aninputgearisthesungear,a,drivenbythearmconnectedtothemicro-engine.Therotatingringgear,d,isservedasanoutputgear.Forexample,ifthearmdrivesthesungearintheclockwisedirection,theplanetarygears,b,willrotatecounter-clockwiseattheirownaxisandatthesametime,thosewillrotateaboutthesungearinclockwisedirectionresultinginplanetarymotion.Duetotherelativemotionbetweentheplanetarygears,b,andthefixedringgear,c,therotatingringgear,d,willrotatecounterclockwisedirection.Thisissocalleda3Kmechanicalparadoxplanetarygear[1].中文超高速行星齒輪組合中內(nèi)部齒輪的有限元分析摘要：超高速行星齒輪組合中內(nèi)部齒輪的應(yīng)力和彈性變形的調(diào)查。環(huán)的厚度參數(shù)的定義是內(nèi)部齒圈和齒輪箱的彈性。整個(gè)內(nèi)部齒圈的有限元模型是用Pro/EandANSYS的方式確定的。內(nèi)部齒圈輪齒的載荷取決于嚙合系數(shù)和載荷分布系數(shù)。依靠有限元分析（有限元分析），可以預(yù)測內(nèi)部齒圈的應(yīng)力和彈性變形對其靈活性和裝配情況的影響。模擬表明，主應(yīng)力和撓度隨著內(nèi)齒圈齒厚的減少而增加的。此外，較大的彈簧剛度有助于減少內(nèi)部齒圈的應(yīng)力和撓度。因此，在設(shè)計(jì)的高速行星齒輪傳動(dòng)時(shí)，內(nèi)部齒圈的彈性必須加以考慮。關(guān)鍵詞：行星齒輪傳動(dòng)；內(nèi)部齒圈;有限元方法由于大減速比，高承載能力，高壓實(shí)度和高穩(wěn)定性的優(yōu)勢，超高速行星齒輪傳動(dòng)被廣泛應(yīng)用于航空航天和汽車工程。動(dòng)態(tài)預(yù)測齒輪單位為目的的減振及噪音管制在過去數(shù)十年已經(jīng)被給予高度重視。（1-8）作為其中的關(guān)鍵部件，內(nèi)部的齒輪設(shè)計(jì)必須小心，因?yàn)樗撵`活性，對齒輪傳動(dòng)系的性能，具有很強(qiáng)的影響。研究表明，內(nèi)部齒輪的彈性對行星齒輪系的動(dòng)態(tài)行為有顯著的影響（9）。為得到齒圈應(yīng)力和撓度，提出了幾個(gè)有限元分析模型（10月14日）。不過，大部分模型只能處理薄環(huán)內(nèi)齒圈的一段。齒輪部分受相應(yīng)的邊界情況約束，在沒有考慮到一個(gè)假設(shè)輪齒完整的嚙合循環(huán)中的單、雙接觸帶完全不同時(shí)，額定載荷等于線運(yùn)動(dòng)中單個(gè)輪齒受到的載荷。有限元/半解析非線性接觸模式被提交去調(diào)查準(zhǔn)靜態(tài)行為的行星齒輪組中的內(nèi)部齒輪的靈活性的影響?？紤]到所有齒輪的撓度和齒條的支撐情況，其應(yīng)力和撓度是關(guān)于環(huán)厚度的一個(gè)函數(shù)。與過去的工作相比，這種模式被考慮成整個(gè)傳動(dòng)系統(tǒng)。不過，標(biāo)準(zhǔn)的描述方法（15），需要一個(gè)高層次的專業(yè)知識(shí)，才可以更成功。本文件的目的是調(diào)查環(huán)的厚度和支撐條件對一個(gè)高速的行星齒輪傳動(dòng)的內(nèi)部齒輪應(yīng)力和撓度影響。首先，一個(gè)完整的內(nèi)部齒輪用直齒條固定齒輪箱上的有限元模型是依靠Pro/E和ANSYS的方式創(chuàng)造的。其次，適當(dāng)?shù)倪吔鐥l件適用于模擬實(shí)際的支撐條件。同時(shí)，嚙合系數(shù)和載荷分布系數(shù)被認(rèn)為同樣適用于相嚙合輪齒的載荷。最后，借助于ANSYS中的商業(yè)有限元APDL編碼，可以分析環(huán)厚度和支撐情況對內(nèi)齒圈應(yīng)力和撓度的影響。1有限元模型1.1系統(tǒng)舉例表1所示的3個(gè)行星輪的行星齒輪組（調(diào)制鋼5140）用來舉例研究環(huán)厚度和支撐情況的影響。表1為系統(tǒng)參數(shù)項(xiàng)目太陽輪行星輪內(nèi)齒圈齒數(shù)232267模數(shù)/mm333壓力角/（?）202020楊氏模量/GPa—205—泊松比—0.3—密度/(t?m3)—7.8—如圖1,3個(gè)行星輪兩兩間距120度圍繞太陽輪等空間布置。這里的所有齒輪都是標(biāo)準(zhǔn)的漸開線齒輪。太陽輪作為輸入件的同時(shí)，為表達(dá)清晰，圖1沒有表示出作為輸出件的支撐件。內(nèi)齒圈外圓均勻布置的可約束齒圈剛性運(yùn)動(dòng)的6齒花鍵使其得以固定。圖1為系統(tǒng)圖例平面內(nèi)齒圈環(huán)厚系數(shù)九被定義為環(huán)厚與輪齒高度的比，如下［包(1)r,r,r分別為內(nèi)齒圈的分度圓、齒根高和齒頂高。0fa九值越小說明齒圈越靈活，九值越大說明齒圈越不靈活。本文章研究九取不同值時(shí)九=1.0,1.5,2.0,2.5的內(nèi)齒圈.在所有這些情況下，內(nèi)齒圈的寬為44毫米，連接花鍵長34毫米、寬14毫米、高度分別為5、6、7、8毫米。圖2所示的九=1.5的內(nèi)齒圈有限元模型包含了69813個(gè)元件和112527個(gè)節(jié)點(diǎn)。圖2。內(nèi)齒圈有限元模型1.2載荷和邊界條件1111~~內(nèi)齒圈通過鍵與箱體連接，與行星輪嚙合。假設(shè)每個(gè)行星輪上的載荷是均勻分布的，而且所有的摩擦力可以忽略，那么每個(gè)行星輪和太陽輪間的嚙合力如下：如;cosaT是輸出的扭矩和，i是全部減速比，r是內(nèi)齒圈半徑，n是行星輪個(gè)數(shù)，Cscsp是壓力角。此外，考慮到嚙合系數(shù)以及載荷分布因數(shù)，最后確定嚙合的位置和齒圈每個(gè)齒的承載比例。圖3所示為環(huán)的受載狀態(tài)。圖3為內(nèi)齒圈的受載狀態(tài)這里，每兩個(gè)行星輪的相位角是120度。F(l,???.,6)是作用在內(nèi)齒圈輪i齒上正常嚙合力。為明確的目的，只有輪齒畫在圖3中。得到內(nèi)齒圈輪齒嚙合力后，我們可以將其加到有限元模型中。具體說，嚙合力是均勻分布在沿嚙合線上相應(yīng)的節(jié)點(diǎn)上的。因?yàn)橹吻闆r特別復(fù)雜，如果考慮到接觸問題，必須建立鍵實(shí)際接觸的特殊代替模型。這里，用交替的節(jié)點(diǎn)和6個(gè)空間均勻布置的鍵與內(nèi)齒圈聯(lián)合在一起，在內(nèi)齒圈外表面和機(jī)架表面間模擬支撐狀況。內(nèi)齒圈與機(jī)架間的支撐狀況說明了這些凸起的剛度。其過程可詳列如下。單一的節(jié)點(diǎn)需要詳細(xì)說明每個(gè)內(nèi)齒圈與機(jī)架的連接。在每個(gè)鍵的位置用14個(gè)聯(lián)合元件完成，在無限剛度的機(jī)架表面，聯(lián)合元件與鍵是點(diǎn)連接。這些定義節(jié)點(diǎn)的自由度是受約束的。在每個(gè)彈性元件的令一端是徑向自由度全部受約束鍵連接的常見節(jié)點(diǎn)。此外，每個(gè)鍵的受載荷表面上的節(jié)點(diǎn)是受圓周自由度的約束的。環(huán)的軸向自由度也是受約束的。模擬環(huán)的支撐情況如圖4所示。

圖4為鍵支撐情況示意圖2有限元分析的結(jié)果運(yùn)用適當(dāng)?shù)妮d荷和邊界條件，有限元分析可以計(jì)算出內(nèi)齒圈厚度和支撐情況對應(yīng)力和撓度的影響。以系統(tǒng)為例，可以預(yù)測在旋轉(zhuǎn)支座120度范圍內(nèi)，以5度增量的24個(gè)離散角度位置的應(yīng)力和撓度。行星輪數(shù)目為3,這將保證內(nèi)齒圈的每個(gè)輪齒都能有一個(gè)完整的嚙合周期。2.1齒環(huán)厚度對內(nèi)齒圈應(yīng)力和撓度的影響在圖5中，每一個(gè)離散的位置的最大主應(yīng)力（Mises應(yīng)力）在機(jī)架的旋轉(zhuǎn)角度的四種不同的環(huán)厚度（九=1.0,1.5,2.0,2.5）的繪圖。在這里，彈簧剛度是33n/mm。Ed^fLRLKuJlliF:?」?uLXEdE3EEXJ嚴(yán)Ed^fLRLKuJlliF:?」?uLXEdE3EEXJ嚴(yán)圖5為不