ML17318A706

Last-Stage Blades of Large Steam Turbines.

ML17318A706
Person / Time
Site:	Cook
Issue date:	03/17/1980
From:	HOHN A, NOVACEK P BBC BROWN BOVERI, INC. (FORMERLY BROWN BOVERI CORP.
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ML17318A689	List: ML17318A688 ML17318A690 ML17318A691 ML17318A693 ML17318A706 ML17318A707
References
CH-T-060040-E, CH-T-60040-E, NUDOCS 8004220034
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IluteBROWNBOVERILast-SteBladesofLargeSteamTurbinesPublication No.CM-T060040EA.IfohnandP.¹vacekThepresentarticledealswiththebladesihthelastrotatingrowinlargesteamturbines, consfdering themasamachineelement.Thestaticanddynamicstressesoccurring inservicearediscussed andtheireffectonthedesignofthebladesisdemonstrated.

Somemethodsoftestfngwhichareusedinthedesignofprototypes areexplained astheyenablebladesdesignedonpuretheorytobetestedunderconditions comparable withthoseexperienced"in service,therebyenablingthebehaviour ofthebladesinservicetobepre-dicted.¹wadaysthfsperformance lsfromtimetotimecheckedlnservfcefnpowerstations; thearticleprovidessomeinformation regarding testproceduresandtheresultsobtained.

Inconclusion theauthorsdiscussfuturedevelop-mentslnbladeeonstructfon.

Introduction Afeatureofthelasttenyearsintheconstruction ofsteamturbineswasthemarkedriscintheunitratingsofma-:chines.Atthebeginningof the1960'sthemajorityoflargethermalmachinesinEuropeaninstallations weremainlyinthe125to150MWrange.Today,bothinEuropeandinAmerica,machineswithanoutputofmorcthan1000MWarebeinginstalled.

Inthemthevolumeofsteamthathastobchandledonemergingfromtheblading(last-stage) maybeoftheorderofmagnitude of10000m'/s (fossilfuelledplants)upto25000ms/s(innuclearpowerplantswithturbinesemploying saturated steam).In.ordertohandlesuchenormousquantities ofsteaminareason-ablenumberofflows,thecross-section offlowinthebladeductshastobelargeandthelaststagecorrespondingly long.Ontheotherhand,inthclastrowofbladesoflargesteamturbinesabout6%ofthetotalheatdropofthesteamflowingthroughtheturbineisconverted intome-chanicalenergy.Sincethesetwofactors-highoutputand qualityoftheenergyconversion

-arealsoinfluenced bythelaststage,particular attention hasbeenpaidtothesebladesduringthepasttenyears.Here,developments incomputerapplications provedofgreatassistance totheengineers concerned withstrengthandflowproblems.

Ontheonehand,thebladeanglesandprofileshadtobedetermined withtheaidofath~imensional flowcal-culation; ontheotherhand,theaptitudeofthctwistedlast-stage bladeshadtobcprovedunderservicecondi-tions.Thecostofproducing thclast-stage bladesforlargeturbinesishigh.Therefore, theturbinemanufacturers endeavour tomarketaproductwhichwillperformitsdutieswithoutanytrbubleformanyyears.Comparing newdesignsoflast-stage bladeswiththoseofthepast,itisstrikingly evidentthatmechanically sounddesignstodaydispcnscwithformsof"aidstosurvival".

Dampingwiresandinsomecasescoverstripsarenowathingofthepastforlargeturbinesrunningatconstantspeed.Apartfromreducingcostsandobtaining abetterefficiency bythismeans,themachineisalsomademorereliablebecausethcunsupported bladeismountedunderverydefiniteconditions whichmakescalculation simpler.Furthermore, withthemethodsofmeasuring nowavail-ablethcresultsobtainedbycalculation caneasilybecheckedandcalibrated inservice.StaticStressesoftheBladeThecross-secuon ofabladevariesconsiderably frombottomtotop,themainaxisofinertiaofthcindividual cross-sections beingtwistedfromonetoanotherascanbeseeninFig.1and2.Thepathtakenbydevelopment can,beseeninFig.3whereabladeusedfortyyearsagoforaspeedof1200rev/min,whichwasslightlytaperedandhardlytwistedatall,iscomparedwithamoderntypeofbladefroma400MW(3000rev/min)turbine.Whatismoststrikingisthcdiffer-enceintheshapeofthecross-sections alongthcradiusinthetwodesigns.Sincethecentrifugal stressaz(seeTableI)isresponsible forthegreaterpartofthetotalstress,evenintwistedblades(Fig.4),itmaybeadoptedasaroughguidetothecross-section oftheblade.UsingthenotationfromFig.4wethenobtain:Differential centrifugal forcerdK-qrco~F(r)dr "I4CNPyIslilI~44*I,,40V'4*gEcc4gj,sfrle'.PC~t+actl+4t44~sc$V,+4LocalbladestressRffNtttaF(r)drRsF(R)(2)IfF(r)~Fisconstant, aswasapproximately thecaseintheolderbladesillustrated inFig.3,therelationship be-tweenthetensionduetocentrifugal forceintermsoftheradiusisgivenbyntoaaz=(Rt'ra)2(3)Thestressin'hebladeinthiscaseincreases quadratically fromthetiptothebaseandattainsitsmaximumvalueinthetransition frombladetoroot(Fig.5).Withthisshapingthcdesignerhasnotmadethebestuseofthematerials andtheattainable peripheral speedstherefore remainconsiderably belowthoseoftaperedblades.Ifontheotherhand,anattemptismadetokeepthetensilestressduetocentrifugal forceconstantoverthcgrcatcrpartofthelengthofthebladebydifferentiating equation(2)dF(r)ntnsrdrF(r)azthefollowing solutionisobtained:

-(R4s-+tte4F(r)~Fte(5)~Modernlast-stage bladeshaveacross-section whichroughlycomplieswithequation(5)(seeFig.4):azisal-mostconstantalongthelengthoftheblade.Fromequa-tion(5)itisapparentthatthevariation incross-section ofthebladeisonlydependent onthematertalchosen(n,az),thespeed(nt)andthegeometry(R',r).Thissituation isillustrated inFig.6forthebladeaccording'to Fig.2madefromthreedifferenmaterials.

Inservice,however,thesebladesarealsosubjected tootherstressesbesidesaz(TableI):~Iecclseve%144%NFig.I-Last-stage bladesofa600MWturbineintheassetnbled state-Duetoinaccuracy inmanufacture orductodeliberate deviation ofthelincconnecting thecentresofgravityofthevariouscross-sections fromtheradial,thebladeissubjected tobendingduetocentrifugal force(as),whichmaybeaddedtoorsubtracted fromazaccording toitssign.Intheolderdesigns(cylindrical blades)azandattarethesolestresscomponents producedinthebladebyrotation.

Consequently, calculation ofthestressesductorotationiseasyforsuchbladesandcanbereadilyanalysed.

-Inmodern,long,last-stage blades,however,apartfromthechangeinprofiledownthelengthofthcblade,the TableI:Stressesinthetlast-stage bladesofturbinesinserviceTypeofstressCauseStatic1Constanttensionduetocentrifugal forcetrzCentrifugal forceproducedbytheblademasssituatedabovethegivencrosssection2Flexuralstressduetocentrifugal forceurnThedeparture:

ofthelinejoiningthecentreofgravityofthesections.romtheradial3Untwisting normalstresstra4Untwisting sheerstressrg5FlexuralstressduetosteamforcetrnThetwistingofthebladeduetocentrifugal forceThetwistingofthebladeduetocentrifugal forceSteamforceactingonthebladeDynamic6Alternating flexuralstressesawSteamflowdeviations fromthepreceding stationary blading,detachment, asymmetry (disturbances) inthedesign(atthehorizontal joint),disturbing internals suchasprobes,criticalspeeds,shortcircuitatthegenerator Fig.2-Shapeofprofileandvelocitytriangles ofalast~gobladel000mmlongU>>Peripheral speedCi>>AbsolutevelocityofthesteamenteringthebladeFig.3-Comparison betweenlastwtage bladesasmadeinl930(nl200rev/min)andinl965(n3000rev/min)UIU>>605m/sI.III~465IIIII322CaCICItaAtrIV'1iaai1I>>c!4*EI'aowNcove%isoessI~MIll~

individual cross-sections aresubjected tosuccessive twistinordertoallowforthcchangeinperipheral speedovertheheightoftheduct.Duetorotationoftheseblades,twoadditional stresscomponents occur:thenorinalstresstrRandthesheerstressrltduetothebladeuntwisting.

Ahelpfulmodelwhichshowshowthesestressesarepro-ducedcanbeseeninFig.7.Thisshowsthatwhenthebladeuntwistsundertheeffectofacentrifugal forcecom-pressionstressesarcproducedintheoutersectionswhilethcmiddlesectionissubjected totensionandtorsion.-Apartfromthesestresscomponents producedbyrota-tionthebladeisalsosubjected totheforcesproducedbythefiowingmedium.Hereadistinction mustbemadebe-tweenthestaticcomponent andadynamiccomponent ofstressaw.TableIprovidesinformation aboutthecausesleadingtothesestresses.

Itisquiteevidentthatforcalculation ofthestressesofthetwistedtaperedbladeitisessential tousecomputers be-causethestressesIto5inTableIatdifferent pointsontheedgesoftheprofilehavetobecalculated fordifferencross-sections.

Fig.4showsthcresultofsuchastresscal-Fig.6-Distribution ofthecombinedstressacrosstheblade,showingtherelationship bctwecnthcsumevofallstresscomponents according toTableltothemaximumvalueevws*Ft~Reference a~ion(sceot.SlRt~HubradiusRsRadiusatthetipR'Radiusol'hereference cross-section r~Coordinates evRcfcrcnce stress-as~Tensionduetocentrifugal foNeFt~37culation.

Thereinthercfcrence stresstrv~sumofthe'tress components, was.determined according tothesheerstresshypothesis

[I].Forpractical applications itisextremely important tochecktheresultsofthestresscalculations byrandommeasurements, becausewhenmoreisknownaboutthestressesitispossibleforoptimumutilization ofthcmaterialtobcachieved.

Herethefollowing checksarepossible.

-Thestressesintherotatingbladesaremeasuredwhen,thebladedrotorisoverspeed tested.Groupsofstraingaugesareattachedtotheblade;thereadingsusuallybeingtransmitted torecorders byasystemofsliprings.

-Itis,ofcourse,possiblethattheactualmeasurement ofthebladestresscannotbeundertaken becausenomeansoftransmitting themeasurement canbeattachedtotherotatingrotor.Usuallytheemployment ofaslipringsys-temtotransmitthcmeasurement requiresdrillings intherotorbodyfortheleads,whichinturnresultsinunde-siredstressconcentration.

Theuseofatelemetry systemalsoimposescertainrestrictions onthegeometryoftherotorwhichhavetobetakenintoaccountwhenitisdesigned.Therefore, whendirectstressmeasurement isnotpossible, forthereasonsgiven,thebladefittedwithstraingaugesmayberunuptooverspeed instagesandaftereachrunexaminedatstandstill tocheckforlocalexceed-ingoftheyieldpointbymeasuring thcchangeintheelectrical resistance ofthestraingaugecomparedwiththeinitialvalue.However,sincethisisonlyameansofcali-bratingthecalculation, itisimmaterial whetherthebladeconsistsoflow-alloy annealedmaterial.

-Afurthercheckistomeasurethcangleofplasticun-twist.Whereaslonglast-stage bladesuntwistelastically.

inservicebybetween5to8',underexperimental conditions thebladescanbebroughttosuchperipheral speedsthatplasticuntwistoccurstoanextentthatcanbemeasured.

Byextrapolation tozeroplastification thespeedcanbcdetermined atwhichtheblade"stilljust"remainselastic.Thcspeeddetermined inthiswayatwhichplastification beginsrepresents theupperlimitatwhichthetestblademaybeusedandfromtherelationship

+v/+Vtnss0,70,76trvisalsoapplicable tobladeshavingthesamegeometrybutotherstrengthvalues.Attachment oftheBladestotheShaft0.620,9~0,20,rg0,etgoc8005OY/dvressI0,55I>~~~anowN aovrteleeesstThebladesofthelaststageoflargeturbinesdevelopcentrifugal forcesofsomehundredsoftonswhenrunning.Forthisreasononlyveryefficienmethodsofattachment canbcconsidered.

Amongthesystemsinuseatpresent,suchasrhombusfixinginaperipheral slot,finger-shaped boltedfixing,straightorcurvedfir-treeroots,thelastmentioned isanidealmeansofattachment becauseitpermitsveryclosestaggering ofthebladecascadeandthecentrifugal forceisproducedinanoptimummannerinthcshaftteeth.Thisdesignisillustrated in.Fig.l.Forreliability considerations itisessential toknowtheexactlimitsoftheselectedmethodofattachment; there-fore,inadditiontocalculations, photoelastic investiga-0,5aze<z0,40.3Ft0,2CICIO,I0.5iIIII32l0F/FtIaaowueovsnt100000~IFig.6-Variation ol'tionsofabladegivenbyequation(5)l'orditfcrent typesofmaterialA~SteelB~Titaniutn CFibre-reinforced plasticF'romcction RsWKIWNCOVtN100000IFig.5-Stressdistribution inahst-stage section0~SpeciActnassofthebladematerialUsPeripheral speedatbladetipOthernotationseeFig.4.bladewithconstantcross-Fig.y-Modeltoexplainunwind-ingstressAB~Paitf~ZlW3BladetipFixingPressureTorsionTensionLeadingedgeCentralclementofthecross-scctionTrailingedge10000rI tionsandpullouttestsondummybladesarenormally'erformed.

Fig.8isaschematic illustration ofsuchatestbedonwhichBrownBoveriperformfull-scale testsuptoaforceof2000t.Inthccourseofthesetestsnotonlythecurveofdeformation againstforcewasplottedbutalsothenotchstressatthebottomoftheindentation inthefir-treeroot.Usingstraingaugeswithagridof04mmlocaldeformation wasdetermined exactlytowithinafewpercent.Effective Vibration 00OotcoosaIFig.Sa-Put&outtestonabenttir-treeroot,withdeformation diagramA~Workingpoint(ratedspeed)BFractureP~TensionS~Clearance atthcbottomofthcgroove,varyingwithtensionThelast-stage bladeissubjected toforcedvibration whenrunning;thesourcesofdisturbance arelistedinTableLThcmagnitude oftheforcesactingonthcbladeinscrviccis,however,largelyunknown.Consequently, theresultsofcalculations ofthealternating stressescausedbytheforcedvibrations areopentoconsiderable doubt.Forthisreasonithasbecomenormalpracticetojudgetheme-chanicalqualityofthebladesaccording tothemagnitude ofthestaticstressesIto5(TableI)andthenaturalfre-quenciesofthcbladeinrelationtotheexcitingfrequencies (multiples ofthespeed).Withtheaidstocalculation thatareavailablc todaythelowernaturalfrequencies ofthebladecanbccalculated sufllcientiy accurately toavoidFig.Sb-RotorsegmentusedforpuuwuttestFig.Sc-Bladerootindentations sheeredotrinpWlwuttestIttttISIitI8sr"4"tIIIIIIIOIOWIIevce resonance withpossibl'llatingsteamforces.Here,though,thefollowing factsmustbeborneinmind.-Adecisivefactorforassessing thevibration behaviour ofthebladeisitsfrequencies atoperating speed.AscanbeseeninFig.9,thecentrifugal forcehasastiffening effectontheblade,withtheresultthatthenaturalfre-quencyincreases withthespeedofrotation.

Thisriseisdifferent forthevariousordersanddependsontheshapeoftheoscillation.

Thestifiening effectisgreaterwithflexuralthanwithtorsional vibration oftheblade(seenodallinesinFig.9).-Differences ilgwumaterialqualityandtolerable devia-tionsingeomet~tof individual bladesresultinascatterbandateachorderofnaturalfrequency.

Simpliftcations andapproximations whichhave"tobetakenintoaccountwhensettingupamodelforcalculation resultindiscrepancies fromreality.Forthesereasonsthecalculation hastoberecalibrated forthedevelopment ofnewbladeswhoseshapediffersfromthatofexistingdesigns.Theprocedure adoptedisroughlyasfollows:Havingcalculated thefirstnaturalfrequencies intermsofFig.9-Naturall'requencies Fofthcbladeplottedagainstspeedn(rev/min)Nodallinesatthellrstfournaturall'requencies.

A.B.C,DPermhtedscatterbandsoffrequencies forzerospeedmeasurement a.b,c,...Permincdscatterbandsol'bladefrequencies atoperating speedE~SpccdrangeinwhichthetbdngrigidityisinQuenced bycentrifugal lorco6Usualscauerband(precision forgedblade)HForbidden l'requency rangeformeasurements atz<<roandnormalspeednI~Speedinrev/s~Valuesmeasuredforzerospeedvibration Valuesmeasuredatdilfcrcnt speedsFig.l0-Arrangement ofthetelemetry systemformeasurement ofvibra-tiononlaststagebladesinserviceDStraingaugeonthebladelY~Shah$~Transmitter APick-upring400/v//I9nsgus3007/ls)511s200Df3H'3ItsHl00281znl00020003000tMCQO~1eaoWNaovznl100100I Ospeedforbladeswiththedesireddimensions andmaterialqualities, eachmanufactured bladeischeckedatzerospeed.Bymeasuring thenaturalfrequencies ofsomebladesduringoverspeed testingitispossibletocheckwhethertheriseinfrequency asafunctionofthcspeedwascalculated correctly.

Herethebladeismadetovibratebydisturbance forces(excitation plates)manytimeslargerthanthedisturbance forcesactuallyexperienced inservice.Oncompletion ofthistestwhichhastobecarriedoutonceforeveryprototype last-stage blade,aneconomicselection ofthemanufactured bladescanbeperformed bycheckingatzerospeed(rr=0)alone.InFig.9thefrequency rangesa,b,c...arcpermissible atscrviccspeed,therangeHisforbidden.

Thusthepermitted frequency rangesA,B,CatzerospeedarefixetLToalimitedextentcompleted bladeswhoseroutinezerospeedmeasurement producesnaturalfrequency valuesoutsidetherangesA,B,Ccanbebroughtinsidetheserangesbysubsequent machining withinthedimensional tolerance.

However,itmustberemembered thatthissubsequent machining changesallthenaturalfrequencies.

Theseriesoftestsisconcluded bymeasurements inservice.In1968BrownBovericheckeda600MWmachinebytelemetry andwasabletoestablish thedynamicbehav-iouroflast-stage blades1000mmlongthroughout theentireloadrange.Themainobstacles werethedevelop-mentofawatertight anderosionproofmeansofstickingandcoveringthestraingaugesandthedevelopment ofelectronic equipment capableofwithstanding centrifugal

'ccelerations upto7000gandtemperatures upto150'Cforlongperiods.Fig.10showsthemeasuring setup.Thesemeasurements wererepeatedsuccessfully in1969and1971ona300MWmachineinwhichthesteamhadahighmoisturecontent.Suchmeasurements arenowadaysdesirable forvariousreasonsandarcgaininginsignifi-cancebecause:Fig.11showsthearrangement ofthestraingaugesonone.ofthebladesexamined..

Itwasimportant toattachthestraingaugesatpointswheretherewasarelatively highamplitude ofvibration inorderthattheresultofmeasure-mentatsuchpointscouldbecomparedwiththeresultsofcalculations andsothatconclusions couldbcdrawnregarding themaximumstressestowhichthebladewassubjected.

Fig.II-StraingaugesNo.5l,52.53.6I,62and63ontherearofatestbladeI'ormeasuring naturalfrequencies inservice52.62635I,6I-Littleisknownaboutthestimulation whichcausesthebladetovibrateinscrvicc.-Thclengthofthebladesinthclaststagesofsteamturbineshasbeenincreased inrecentyearsbyallmanu-facturers andwillcontinuetoincreaseasunitoutputsareraised.Thiswillmakethebladesflexumlly softerandtheywillrespondtoexternalinfluences bymorepronounced vibration.

-Inmanyplacestodaythcuseofriverwaterforcoolingthecondensers isnolongerpermitted.

Theuscofcoolingtowers,however,resultsinwarmercoolingwaterandconsequently ahigherpressureinthecondenser comparedwiththefreshwatercooling.Therefore, itisnecessary tocheckwhethertheforcestowhichthefinal-stage bladesareexposedasaresultofthehigherexhaustpressuredonotrepresent anunreasonable strain.Duringsuchmeasurements thcfollowing operational conditions wereexamined:

-Whilethemachinewasrunningup,theresonance oftheblades(damping) wastested.Thevacuumwasvariedbe-tween30and250mbar.-Thevibration ofthefinal-stage bladewasexaminedatdilferent loadsandexhaustpressures upto250mbar.-Bymeansofshutdowntestswithpartialandfullvacuumbreakagethebehaviour ofthefinalwtage bladeswasalsotestedundertheseabnormalconditions.

te4141I Theresultsofthesemea.entscanbesummarized asfollows:-Thebladesaresufficiently proofagainstvibration frac-turebutonlywhenthenaturalfrequencies arenotmul-tiplesofthespeedofrotation.

-Theaerodynamic excitation forcesareverysmallpro-videdstepsaretakentoavoidobvioussourcesofdistur-bancewhendesigning andmanufacturing theturbine.-Theexcitation forcesresulting fromerrorsinthepitchofthestationary bladesegmentsoroftheactualstationary bladesthemselves, occuratsuchhighfrequencies thattheydonotrepresent adirecthazardfortheblades.-Iftheaboverequirements aretakenintoaccount,themaximumalternating stressesthroughout theentireopera-tionalrangeandattheexhaustpressures inusenowadaysareonlyafractionofthestrengthofthebladematerial.

-Athighexressurestheamplitudes ofvibration maybeexpectedtoincrease.

Theyarehighestatnoload,becauseheretheaerodynamic conditions areunfavour-ablefortheblades.Forthatpointonthebladewhichismostseverelystressed, alternating stressesmayoccurwhichreachsuchahighlevelinrelationtothefatiguestrengthofthebladematerial, eveningooddesigns,thattheycannolongerbeignored.Fig.12givessomeideaofthevibration ofthebladesduringashutdownwithfullvacuumbreakage.

Thereintheincreaseintheexhaustpressurepagainsttimefcanbeseen,alsotheresultant dropinspeedrtoftheshaftduetoincreased ventilation, thecurveofthetemperature Tintheexhaustareaaswellasthecurveofthenaturalfrequency Fandtheamplitude Aofthebladevibration atpoint63inFig.11.FixingandDamping20Hx3000lgI60IIIIIIIIisoIIr20min600mmHg400Fig.12-Measuremcnt ofbladevibration duringrun-outofthemachinefollowing fullvacuumbreakageFNaturalI'requency ofthetestbladeAAmplitude measuredbystraingaugeNo.63inFIg.IIatfre-quencyFT~Temperature inexhaustregionnSpeedoftheturbineshaA'~Pressureinexhaustregionr~TltncInthediscussion ofbladevibration thequestionoftenarisesregarding theinfluence oftheflexibility ofthebladefixingandofthedampingonthevibration oftheblade.Owingtotheenormouscentrifugal forcesactingonthebladeinservice,amounting tosomehundredsoftons,thecontactsurfacesbetweenthebladeandtheshaftarepressedagainstoneanothersostronglythatnottheslightest movementcanoccuratthesepointsandtherefore thereisnovariation inthenaturalfrequencies ofthebladewhichmayberegardedasrigidlymounted.However,theindentations intheshaftandthefootofthebladehavetheirownehsticity valueswhichdivergefromtherigid,idealcase.AscanbeseeninFig.13,thisinfluence onthenaturalfrequency ofthebladeisnegligibly small,becausecurrentdesignspossessrigidityvalueswhichcomefairlyclosetotheabsolutely rigidfixing[2].Thedampingiscomposedofcomponents whichdependonthemethodofrootfixing,theambientmediumandthematerialfromwhichthebladeismade.Inpracticethisdampingismeasuredbyrecording thelogarithmic decre-ment.AsFig.14shows,thedampingchangeswiththeamplitude ofthealternating stress.Atstressvalueswhichcaninfactoccurinturbines, itreachesanorderofmag-nitudeatwhichadistinctchangeintheresonantfrequency canbedetected.

IIOOAl40IIOimm/mmI000[QpqylIleelesI200ErosionThelaststagesoflargecondensing turbinesoperateinthewetsteamregion,wherethesteamcontains5to12%moisture.

Mainlyresponsible forerosionisthewaterwhichseparates outintheoutermost thirdofthelastrowofstationary blades.Dropbydropthiswateristomoff 895QmVlChIItIII///IIIO986'D>>0D<<0,02D<<0,05D<<O.lD>>O.I5I500HzPO,l0,90,95I,oI,05IoooD5000,050iO'O~'iO'O~IO'10I01lensesIO,OI0I00,200300400XleolosIFig.I3-Inliuence oftheelasticity oi'hebladeibungonthenaturalfre.qucncyA>>FixinginthehalfplanehfRigidityof AxingPt<<-<<IO'kpcmYoung'smodulusE<<2I.Io'picmchf8Theoretical equivalent AxingmodelPsrn<<Rigidequivalent Axingwithaeromassn<<Inclination acpointofAxingduetohfC<<Curveoffrequencies PagainscAxingrigidityPt,Pc,Ps<<Naturalfrequencies ofArsttothirdorderD<<Rigidity ofcommonkindsoi'bladeAxingsFig.I4-Incremental functionanddampingofavibrating bladey<<Incremental functionrr<<Frequency ratio:Excitingfrequency toresonancfrequency D<<Lehr'scoeAicient ofdamping2nDLogarithmic dccremenc d(I-DXAmplitude ofalternating stress(kp/cmt)ADisplacement orthcpeakfrequency fory[y(r/)1.,duetodamping10-thctrailingedgeofthestarybladesandaccelerated bythcflowofsteam.ThcKrops,whichmaybeupto02mmacross,reachvelocities inthespacebetweenthestationary andmovingbladeswhichdifferconsiderably fromthoseofthesteamflow[3).Thisimpliesthatthereisarelatively largedifference betweentheperipheral speedofthebhdetipandtheperipheral component ofdropletspeed,asaresultofwhichthedropletsstriketheleadingedgeofthebladewithanabrasiveefl'ectknownaserosion.Turbinemanufacturers protectbladesagainsterosionbyarmouring theleadingedge.Thiscanbedoneeitherbyhardening thebasicmaterial(themethodadoptedbyBrownBoveri)orbysoldering onplatesofStellite.

Thetotalamountofmateriallostbyerosionisaloga-rithmicfunctionoftime;whereastheerosionrateishighduring-the initialperiodofservice,italmostceasesafteraboutoneyear[4).Anexplanation forthisisthattheporesinthesurfaceofthebladewhereerosionhastakenplacearepartlyfllledwithwater,sothattheimpactforcesofthedropsstrikingthebladesareonlytransferred tothematerialinadampedform(Fig.15).FutureProssItisthesizeofmodernpowerstationturbineswhichistheirmostimpressive feature.Machineswithunitratingsofover1000MWarebeingbuilt;theyhaveatotallengthofabout70m,thediameteroftherotormeasuredacrossthetipsofthefinal-stage bladevariesbetween45and55m,depending onthemanufacturer, whilethecasingsurrounding thelow-pressure rotorisalmostasbigasaprivatehouse.Sincethetrendtowardfurtherincreases inunitcapacities iscontinuing stepsarealreadybeingtakentodeveloplast-stage bladestoevenlargersizesinordertocopewiththeenormoussteamvolumes-ina1100MWmachinetheamount'is about30000m'/swithacondenser vacuumof005bar-inareasonable numberofflows.Herethestressestowhichtherotorissubjected areofparticular signiflcance.

Sincetherotordiscsaremadeofmaterialwhoseyieldpointcannotbeextendedmuchfurther,anattemptismadetoenlargetheoutletareabyreducingthcspeedoftherotorandbyemploying asuit-ablematerialforthelast-stage blades.Since,incurrentdesigns,thecentrifugal forcesofthelast-stage bladesFig.tS-Erodedleadingedgeol'abladeMagniAeation 20xFig.l6-CarbonAbresbeforebeinginsertedIntheplasticmatrixMagniAeatton 4SOx producestressesinthesectionoftherotor,whichmayamountto35%ofthetotalrotorstress,thegcncraltrendistowardsbladematerials withhigherstrengths butalowerspecificweight.Foremostamongsuch,materials istitanium.

Inrecentyears,however,reinforced materials (plastics) havefoundnewfieldsofapplication.

Amongthem,plasticsreinforced withboronandcarbonfibresexhibitproperties whicharequiteequaltothoseofahigh-alloy steel.Theplasticbladetherefore hasacertainchanceofbeingemployedatthccoldendofpowerstationturbines, providedtheverysevereproblemoferosioncanbeover-come.TableIIshowstheproperties ofamaterialofthiskind.Thccarbonfibresembeddedinthematrixhaveadiameterofabout5IO'm.Fig.16and17respectively showsuchfibresbeforebeinginsertedintheplasticmatrixandthesurfaceofafracturethroughsuchacomposite bar.Thelargesteamturbinesbeingbuilttodayarenormallyemployedasbase-load machinesandtheyareexpectedtoobtainaveryhighavailability.

Asitisunderstandable thattheindkvidual elementshavetobecarefully examinedTableII:Properties ofaplasticmaterialreinforced withcarbonfibresMatrix:Fibre:DensityTensilestrengthYoung'smodulusHeattransfercoclficient Coclficient ofthermalexpansion EpoxyresinCarbon(60%byvolume)16Longitudinal 7500Longitudinal 24..10'ongitudinal 34Transverse 29Longitudinal Transverse

-07.10e28.IO'eg/cmakp/cm'p/ctn'/m

'CW/m'C/'C/Oeeveninthedesignstage,wemakeeveryefforttoutilize.moderncomputerandtestfacilitics asfaraspossible.

Theaimofalltheseefiortsistoensurethatfuturelargema-chineswithratingsabove1000MWwillbejustasreliableandcompact.Intheattainment ofthisaimsizeandqualityofthelast-stage bladesplaysanimportant part.Fig.l7-Fractured surfaceofacompoundmaterhlemploying carbonabtereinforcement Mattniacation lI00tcBibliography

[I]J.MontoyaGarcfatCoupledbendingandtorsional vibrations inatwisted,rotatingblade.BrownBoveriRev.1966$3(3)216-230.[2]F.VagttObcrdieBerechnung derFundamcntdefor-mation.Published byNorskeVidenskaps Aka'demi, 1925.4.1V~"-4I[3]G.Gyarmathyt Grundlage einerTheoricderNass-dampfturbine.

Mitteilung Nr.6published bytheInsti-tuteforThermalTurbo-Machines, SwissFederalInstitute ofTechnology, Zurich.[4]J.Hossli:Problemsintheconstruction ofturbinesfornuclearpowerplants.BrownBoveriPublication 3340E(1967).[5]A.Hohn,P.¹vacektDicEndschaufeln grosserDampfturbinen ausmechanischer Sicht.Schweiz.Bauztg1970BB(30)673-678.BBCBROWNBOVERIBBCBrown,BoveflgCompany.Ltd.,CH-5401Baden/Switzerland printedInSwltrertand frtl2-7504ICtasaittcauon No.0101