2018第三屆國(guó)際機(jī)械透平學(xué)術(shù)citc中文稿件

PaperID:CITC ProceedingsofThirdInternationalTurbomachineryConferenceCITC,April12,2018;Chong李濤11，2減振效果；在所研究的參數(shù)中存在一個(gè)最優(yōu)的接觸角使得減振效果最佳；而摩擦系數(shù)主要影響葉片的StudyonVibrationReductionCharacteristicsoftheRotatingFlexibleBladewithTaoLi HouXin-(1.SchoolofMechanicalEngineering&Automation,NortheasternUniversity；2.KeyLaboratoryofVibrationandControlofAero-PropulsionSystemsMinistryofEducationof ,NortheasternUniversity):Inthispaper,theshroudedbladewastakenastheresearchobject,andthedynamicmodelofthethree-dimensionalrotatingbladewithshroudswasestablished.ThedifferentialequationofmotionofthebladewassolvedbyLagrangeequationanddiscretizedbyGalerkinmethod.Finally,theinfluenceofspeed,contactangle,clearanceandcoefficientoffrictiononthevibrationresponsewasstudiedbynumericalsolution.Theresultsrevealthatthereisanobviouseffectofvibrationreductionbytheshroud.Andthereisabestcontactangleinthestudiedparameterstogetthebesteffectofvibrationreduction.Thefrictioncoefficientmainlyaffectstheresonancepeakoftheblade.Whenthefrictioncoefficientisbigger,thedameffectismoreobvious.Theclearancehasaninfluenceontheresonancefrequencyandtheresonancepeak.However,whentheclearanceistoosmall,thedameffectisnolongerobvious.TheseconclusionscanprovideareferenceforthedesignofShroudedblades.:Shroudedblades;Vibrationdam;Contacttheory;Dryfriction;NonlinearNumerical 惡劣，經(jīng)常出現(xiàn)疲勞現(xiàn)象，為了使旋轉(zhuǎn)葉片能夠有更高

1OXYZ為整

究工作。等人[2]針對(duì)帶凸肩的平板葉片，分析了凸肩的結(jié)構(gòu)參數(shù)對(duì)葉片非線性響應(yīng)的影數(shù)片特影。人4了徑5夠考慮接觸面摩擦運(yùn)動(dòng)過(guò)程中正壓力隨時(shí)間變化的微滑移moka等人6和m等人7ang89。

Fig.1SchematicdiagramoftherotatingshroudedbladeinconstantspeedT1a

y

x z ]

定義：rRx00T，δuv 響。Hunt等人[16]認(rèn)為接觸力應(yīng)和相對(duì)位移n次方成正比 而言，n取1.5。本文基于Hunt[16]接觸理論，建立了接觸力模

量r為：Rdxrr

=4211 1Tva 2 1 2 1 20 =1L

[u2

2Rx22Rxu2u22v2

w為葉片側(cè)向穩(wěn)態(tài)振動(dòng)位移，為接觸角，即 2Rx2，2Rxu在運(yùn)動(dòng)方程中不出現(xiàn)，故略去

kh為彈性力學(xué)中的接觸剛度。當(dāng)凸肩工作面接觸時(shí)中間葉片承受著來(lái)自左或右端葉片的干摩擦力FfFN

x

2 Lc

z

U EA()dx EI(x2)dx f()22

1LEI(2w)dxLf(w)dx y2 2 0c 片y向截面慣性矩；fc(x)為離心力，表達(dá)式為：f(x)Ldf(x)1A2(L22RL2Rxx2 )n

2Fig2simplifiedmodelofshroudedu(x,t)(x)U

i1 nini

其中，XT=U(t)V(t)W(t)T為位移向量，M為質(zhì)量 Fk(vsinwcos

kc(d

kcdFf1=F

kd

FF

kcdFN kcdFN

肩結(jié)構(gòu)和無(wú)凸肩結(jié)構(gòu)葉片的葉尖幅頻曲線圖，從圖3個(gè)狀態(tài)下的葉尖幅頻曲線都隨著轉(zhuǎn)速的增加，其頻率不 FvF

Fw

FvF FwF

由式14和式15可知凸肩接觸面產(chǎn)生的正壓力和摩擦1Table.1Theparametersofrotatingblade 350 150 60 7 200 泊松比 7850 摩擦剪切剛度(kc 接觸剛度(kh 接觸角 Fig.3Theamplitude-frequencycurvesofbladeatdifferentrotatingspeeds

3045從減振角度考慮，較為理Fig.4Theamplitude-frequencycurvesofbladeatdifferentcontactangle51000rad/s0、0.1、0.5和1.0時(shí)的葉尖幅頻曲線圖，其他參數(shù)均采用振幅；但是頻率隨摩擦系數(shù)的增加有小幅度的減小。因 Fig.5Theamplitude-frequencycurvesofbladeatdifferentfrictioncoefficient

(4)當(dāng)接觸發(fā)生時(shí)，葉片幅值隨間隙的減小而降低，,.,.0.5mm、1.0mm和2.0mm時(shí)的葉尖幅頻曲線圖，其

隙減小到0.1mm后，葉片的最大幅值不再減小，頻率

,,,[J].,2006,,,,0.1mm

王延慶

等. Fig.6Theamplitude-frequencycurvesofbladeatdifferent

上官博,徐自力,等.一種正壓力隨時(shí)間變化的微[J].,2016,TomiokaT,KobayashiY,YamadaG. ysisofvibrationofrotatingdisk–bladecoupledsystemsbyusingartificialspringsandorthogonalpolynomials[J].JournalofSound&Vibration,1996,191(1):53-73.LimHS,ChungJ,HongHY.Modalysisofarotatingmulti-packetbladesystem[J].JournalofSound&Vibration,2009,325(3):513-531.ItsApplicationtotheDesignofShroudContact[J].TransactionsofASMEJournalofEngineeringforGasTurbinesandPower,1997,119:958-963YangBD，ChenJJ，MengCH.PredictionofResonantResponseofShroudedBladeswithThree-DimensionalShroudConstraint[J].TransactionsofASMEJournaloyEngineeringforGasTurbinesandPower,1999，121：HerbertRG,McwhannellDC.ShapeandFrequencyCompositionofPulsesFromanImpactPair[J].JournalofEngineeringforIndustry,1977,99(3):513.LankaraniHM,NikraveshPE.AContact WithHysteresisDamforImpactysisofMultibodySystems[J].JournalofMechanicalDesign,1990,112(3):369-376.IwanWD.Thedynamicresponseofbilinearhystereticsystems.CaliforniaInstituteofTechnology,1966MenqCH,GriffinJH.AComparisonofTransientandSteadyStateFiniteElementysesofthe ResponseofaFrictionallyDampedBeam[J].JournalofVibration&Acoustics,1985,107(1):106-106.GriffinJH.AReviewofFrictionDamofTurbineBladeVibration[J].InternationalJournalofTurbo&JetEngines,1990,7(3-4):297-308.P?stL,Pe?ekL,RadolfováA.Bladecouplewithdryfrictionconnection[J].Applied&ComputationalMechanics,2015.HuntKH,CrossleyFRE.CoefficientofRestitutionInterpretedasDaminVibroimpact[J].JournalofAppliedMechanics,1975,42(2):440-445.作者簡(jiǎn)介：（1994年，男，東學(xué)，機(jī)械通訊作者簡(jiǎn)介：(1980年)，男，東