齒輪系統(tǒng)動(dòng)力學(xué)剛體模型

齒輪系統(tǒng)動(dòng)力學(xué)剛體模型第一頁，共十四頁，編輯于2023年，星期六齒輪動(dòng)力學(xué)模型建立—葛銀明第二頁，共十四頁，編輯于2023年，星期六1.齒輪模型發(fā)展歷史Fromthe1920sto1930softhelastcentury,aprimarygoalofengineersistoanalyzetheengagingdynamicproblemsinordertoquantifytheentityofteethloadingsbymeansofbothanalyticalandexperimentalmethodologies.Fromthe1950s,verysimpli?edlumpedparameterssystems(asmass-springsystems)havebeensetuptostudydynamiceffectsongears,becomingmoreandmoresophisticated.Duringthe1970sand1980s,lumpedparametersmodelsmayincludecomplexeffectsasthetridimensionalstiffnessofteeth,nonlinearitiesofthesystem,dampingandfrictionparameters.第三頁，共十四頁，編輯于2023年，星期六1.齒輪模型發(fā)展歷史Nowadays,referencemodelsavailabletakethepeculiarityintoaccountglobaldynamicphenomenaastorsion,?exuralandaxialvibrations,allowingtoobtainbothtransitoryandoperatingresponses,alsoifdifferenttypologiesofengagingerrorsareconsidered.Aimofthepresentworkistosetupacombinedmultibody/FEMnumericaltechnique,onthebasisofacommercialcode,inordertosimulatetheengagingphenomenoninaerospacegears,whosepeculiarityisahigh?exibilityofthebodygearwithrespectteethring第四頁，共十四頁，編輯于2023年，星期六Thelastoneisprobablythebestwaytoanalyzethegeardynamics,butthecomputationaleffortrequiredisveryhigh,sointhepresentpaper,theRFLEXapproachsimplemented.Allthe?exibilityfeaturesofbodiesarederivedusingFEapproach.第五頁，共十四頁，編輯于2023年，星期六FullRigidModel(FRM)

（1）theRecurdynToolkitGear

（2）thestiffnessvalueoftheteethiscomputedusingananalyticalapproachbasedontheHertzianformulationorFEA

2.1直齒輪剛體動(dòng)力學(xué)模型第六頁，共十四頁，編輯于2023年，星期六FlexTeethModel(FTM)（1）aBushingForceelementsetsthestiffnessvaluesofthethreetorsionalspringsthatlinkthetooth.（2）theQFBGeartoolofRecurdyn（3）thetoothcomplianceparameterintheBushingForcesiscomputedimposingatorquetoagearsectorandmeasuringthede?ectionofeachtooth2.1直齒輪剛體動(dòng)力學(xué)模型第七頁，共十四頁，編輯于2023年，星期六斜齒輪斜齒輪彎一扭一軸禍合分析模型2.2斜齒輪動(dòng)力學(xué)模型第八頁，共十四頁，編輯于2023年，星期六2.2斜齒輪動(dòng)力學(xué)模型第九頁，共十四頁，編輯于2023年，星期六（1）模態(tài)分析阻尼C=0及激勵(lì)P=0時(shí)進(jìn)行模態(tài)分析（2）響應(yīng)求解方法結(jié)構(gòu)復(fù)雜，解析方法求解困難，多用數(shù)值方法求解。常見的數(shù)值求解方法：逐步積分法（Newmark法，Wilson—θ，中央差分法）和精細(xì)積分法2.2斜齒輪動(dòng)力學(xué)模型第十頁，共十四頁，編輯于2023年，星期六2.3圓錐齒輪動(dòng)力學(xué)模型第十一頁，共十四頁，編輯于2023年，星期六2.3圓錐齒輪動(dòng)力學(xué)模型第十二頁，共十四頁，編輯于2023年，星期六3.齒輪柔體動(dòng)力學(xué)Theconventional?niteelementanalysesrequireaprohibitivelyre?nedmeshtoaddresstheseproblemswhenoneseeksdynamicresponse.Thesemi-analytical?niteelementanalyses

Contactparameterssolvedbyusingtheanalyticalmethod，andsubstitutedintotheFEMFlexibilityofbodiescouldbeconsideredintwodifferentways,usingthemodalsuperposition(RFLEX,reduced?exibilitymodel)orconsideringtheoverallbody?exibilitybymeansofthediscretizedmassandstiffnessmatricesofthebody(FFLEX,full?exibilitymodel).

第十三頁，共十四頁，編輯于2023年，星期六FullFlexibleModel(FFM)The?exibilityofthegearsiscomputedbymeansof