ML17318A693
| ML17318A693 | |
| Person / Time | |
|---|---|
| Site: | Cook  |
| Issue date: | 03/17/1980 |
| From: | HOHN A BBC BROWN BOVERI, INC. (FORMERLY BROWN BOVERI CORP. |
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| ML17318A689 | List: |
| References | |
| CH-T-060-053-E, CH-T-60-53-E, NUDOCS 8004220027 | |
| Download: ML17318A693 (16) | |
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BBCBROWNBQVERIRotorsorLargeSteamTurbinesPublicationNo.CH-T060053E RotorsforLargeSteamTurbinesA.HohnAstheunitcapacityofsteamturbosetsIncreases,sotoodoesthesfseoftherotor,andhencealsothestressesappliedtoit.Thevariousdesignsofrotorarediscussedandresultsofstresscalculationsgiven.Rotormaterialsareconsideredbriefly,followedbycommentonthefuturedevelopmentofrotordesignforlargesteamturbines.RotorConfigurationsThedesignscurrenttodayarerestrictedtotheformsshowninFig.l:-Diagramashowstworotors,eachproducedfromasingleforging.-Shrinkingdiscsontoacentralshai?whichtransmitsthetorquegivesrisetothecompositeconstructionofdiagramb.-Indiagramc,separatediscshavebeenweldedtogethertoformadrum.typerotor[I],Eachconfigurationhasitsownadvantagesanddisad-vantagesasregardsproductionofthe'teel,heattreatment,machiningandtesting,butthesewillnotbedealtwithspecificallyhere.Distinctivedifferencesinthematterofstressesareconsideredinthefollowing'twosectlolls.StaticsofRotorsundertheInfluenceofSpeed,DiscGeometryandTemperatureTheDiscundertheinfluenceofRotationintroductionSteamturbinestodayareremarkableparticularlyfortheirsize:unitcapacitiesofmorethanl000MWarenowtobefoundbothinconventionalpowerstationswithfossil-fuelledboilersandalsoinnuclearpowerplant.Foranumberofreasons,unitcapacitieswillriseevenfurtherinfuture,anditwouldbcprematureatthemomenttospeakofanylimit.Machinesofthissizerepresentasubstantialfinancialcommitmentandinthceventoffailurecauseseriousdisruptionofthepowersupplytobothdomesticandindustrialusers.Itisthereforeunder-standablethatthemanufacturerofsuchmachinesdoesasmuchasthelateststateofthetechnologywillallowinordertoensurethattheselargemachinesarereliableinservice.Thisarticleisconcernedwiththeheartofthemachine,therotor,andreferenceismadetothevariousrotordesignsandthedifiercncesbetweenthem.Fulltreatmentofthesubjectwouldhavetoincludethcstaticbehaviourinsteady-stateoperationandundertransientconditions,andalsothedynamicsoftherotorundertheinfluenceoftheflowofsteam.This,however,wouldgobeyondthcscopeofanarticle,andthereforethemainfocusofattentionhereisonsteady-stateoperationwhichatalleventsconstitutesthebasisofthemechanicaldesign,andonwhichallotherphenomenaarcsuperimpose*Csticot(3-.')o~Ci~a8Disregardinganyexternaltensionforthctimebeing,thecurvesofradialandtangentialstressarefoundtobeasfollowsfor:a.asoliddisc:t.~'(3+v)(..8(2)Alldesignersofturbomachinesusethcrotatingdiscinoncformorthcotherasabasiccomponentoftherotor.Thefollowingremarksontherotatingdisc,whicharcofanelementarynatureandcanbepursuedfurtherin(2,3,4]forexample,arethereforeapplicabletoall,withaccounttakenoftheboundaryconditionsparticulartoaspecificdesign.Iftheequilibriumofforcesintheradialdirectionistakenonarotatingdiscelementofconstantthickness,al-lowanceismadefortherelationshipbetweenradialandtangentialexpansioninthcdiscandHooke'slawforbiaxialstressisintroduced,weobtainthediflerentialequationofthe'rotatingdiscintermsofa<withthegeneralsolution:
dandsincecrt=-(rrtr)+(2r'o'l'2cos(3~<<)/I+3<<2rt~rr'Z8(3+.b.aperforateddisc:(2cos(3+<<)tIrXr22trrr2qr2rr(4)sI.rztscos(3+<<)I2,rt's'-;3<<I."'+"'*+sI"3+.centreofthesoliddisc,i.e.witherr--clt=(lrs'co'3+<<)/8.ThcresultcanbeseeninFig.2.Toillustratemoreclearlythemutualinfiuencesofradialandtangentialstress,Fig.2alsoincludesthedimensionlesscomparativestressSvonthcassumptionofconstantworkofdeformation,thus:;-y;*+;*-;.,utldSv~8clv(2rs'o'3+2)FromFig.2wccandrawafirstconclusion:Inordertoshowequations(2)to(5)ingeneralformtheyaremadedimensionlesswiththestressprevailingattheForthesamedimension(rs),thesamematerial((2)andthcsamespeed(co),theperforateddiscwillexhibitaFig.I-DlirerenttypesofrotorconstructionFig.2-Dimensionlessradial,tangentialandcombinedstressesol'iscsofequalwidth2,01,8'tOl02030405r2-~0,6St126'rlSttSv1,41,2rs1.00,90,8070,60.50,40.30,2O,IO,lSrtrs0,20.4osr06/r8or---Sr~eraer(3+v)8ov---Sv~0r22ars(3+r)0.10,20,30,40.50,60.70,80.91,0rs8orOrser(3+<<)
higherloadingthanthesoliddisc.Ameasureofthisisthemeantangentialstress.Thisresultalsoremainsessentiallyunchangedwhentheadditionalloadscausedbybladetension,steampressureandshrinkagearesuperimposedontherotationalStreSseS.TheconsiderationspresentedsofararesuFIcientfordeterminingtherotationalstressesinthecaseofasoliddisc.Fortheperforatedandshrunk-ondiscofFig.lb,however,deformationalsohastobetakenintoaccount,owingtothediFerentstiffnessofthecentralshaftandthedisc.Onlythencanoncdefinetherequireddegreeofshrinkage,whichinturnhasaninfiuenceonthechoiceofmaterial.DeformationAffectingthePerforatedDiscHerewecanagainstartfromEq.(I)anddeterminetheintegrationconstantsC<andCtappropriatetotheboundaryconditions.Withthcaidofthccalcuhtedstressesitispossibletodeterminetheradialexpansion,andhencealsothcradialdisplacementUforanyradiusofthecentralshaAoroftheshrunk-ondisc.OfparticularinterestaretherelativedisplacementsUtofshaAanddiscatthepointofattachmentwithradiusr1.ThcresultofconsideringdeformationinthiswaycanbcreadfromthcTable.Thus,anyexpansionofdiscorshaAisproportion-altotheforces.artandarswhichcauseit.Thereisasquare-lawrelationshipbetweentheexpansionandrota-tionru.Hereitmustbcnotedthatfordifferentspeedsthcexternaltensionarsalsovariesasthesquareofthespeed.Theshrunkwnbodyhastosatisfythefollowingcondi-tions:atthepointofcontactbetweendiscandshaAatradiusrtthesumofdisc,expansionandshaltcompres-sionmustequalthedegreeofshrinkagedu,i.e.rtw-rtsUtw+UtsWiththisitisnowpossibletoconstructa"springdiagram"oftheshrunkjoint(Fig.3),andwithinthistherelativedegreeofshrinkagehrjrcanbcdeterminedforagivengeometry(rt,r1)andadesiredshrinkageforceo<t.Thcshrinkageforceischoseninthelightofthetwofollowingpoints:-Expansionofthediscduetorotationmayonlybelargeenoughto<<nsurethatapositivefixingismaintainedwhenrunatoverspeed(normallyl2xoperatingspeed),i.e.thediscmustnotcomeloose.PublicationsbymanufacturersofthistypeofconstructionindicatethattheliAwFspeed(zero-shrinkage)liesapproximatefy35%abovethenormaloperatingspeed[5).-Itmustalsobeascertainedwhether,atnormaloperat-ingspeed,thcshrunk-ondiscisf'ullycapableoftrans-ferringthcbhdetorquetothccentralshaft.Generallyspeaking,thisrequirementisalwaysmetiftheoverspeedconditionissatisfied.Ourconsiderationsregardingtheshrunkwndisccanthusbcsummarizedasfollows:Atstandstillthediscisstretchedbecauseitwasundersizewhenfittedon-theshaft,andtheshaAiscompressedbythcshrinkage.Owingto'tsownrotationandthetensileforceexertedbythebladesthediscexpandsmorethanthecentralshaft.Theshrinkageforceisthusreduced.Aresidualdegreeofshrinkagemustberetainedwhentherotorisrunatovcrspeed.ExpansionofshaftanddiscShrinkagforceRotationExternaltensionNON>I~8)B)COmruii(tt1)er1icu'(I-r)riJuan,4aDiscriix(I-r)+-(I+r)r11I'iiX[-(S+r)+(I-rtrli Figurc3showstheserelauonshipsforstandstill(co=0),operatingspeed(co),overspeed(co~co')andliftofspeed(co'I35co)foradiscofuniformwidthwitharadiusratioofrr/ri~3.InthisdiagramthcelasticitypropertiesofthediscandthccentralshafthavebeendeterminedinaccordancewiththeTable.Ontheabscissathcpointoforiginisthedesireddegreeofshrinkage(&/ri)o,whichisselectedaccordingtotheresidualshrinkage(ordinate)desiredattheoverspeedcondition.Theindividualcom-ponentsofthediscandshaftexpansionduetorotationandexternaltensionorehavealsobeentakenfromtheTable.Inordertoestablishtheorderofmagnitudeofthecompressiveforcesoriinvolved,andalsotheresidualshrinkage,thediagramwascompiledusingrealisticconditionssuchasoccurinthecaseofI.p.rotorsforhalf-speedsteamturbines:n1500rev/min,equivalenttoco=157s-',overspeedco'12co;bladetensionerisbeingtakenas8kgf/mrnaatthenormaloperatingspeed.TheresidualshrinkageforanyspeedscanbeobtaineddirectlyfromFig.3bymeansofthcfollowingconversionfromthestationaryshrinkagediagram.Thebasicprin-ciplesofthisareexplainedin[6].octE2,$~IO32,0I,OO,SI2Uisps34IUswrIUsripgWehave:(9)Sincetheresidualshrinkageduatoperatingspeedcoisgivenbyco~0(10)fortheresidualshrinkageweobtainI-co~cu'II)Fig.3-ShrinkagediagramforshrunkendiscsunderdlirerenioperatingeondiiionsThusitcanbeseenfromFig.3thatanextremelylargedegreeofshrinkage(415x10-')isnecessarytoachievealift-offspeedofco'I35co,takingintoaccountthebladetension.IffortheexampleinFig.3ithadbeenstipulatedthatliiboffistooccurat135%ofoperatingspeedwithoutallowancefortheexternaltensionetre(i.e.withoutblad-ing),thiswouldresultinthestandstillshrinkagediagramshownbythebrokenlineinFig.3,withastandstillshrinkageof26x10-s.Inthiscase,however,thebladedrotorwouldloseitsresidualshrinkageevenatsmalloverspeeds(9%inthisinstance),owingtothebladetension,andsomemeanssuchaskeyswouldbeneededtopreventthediscfromslipping.ThereserveofspeeduptoliftwifmentionedhereisdeterminedbythcresidualshrinkageobtainedwithEq.(11).influenceofDiscGeometryTheabovestatementsareofafundamentalnatureandaidone'sunderstandingwhencomparingdificrentdesigns.Butinpracticetheshrunk-ondiscisnotofconstantwidth.Thediscmeridianwillthereforebeshapedinsomeway,itwillbeformedtoyieldadiscofuniformstrengthortheperforateddiscwillbegivenahyperbolicmeridiansimilartoy=c/rn,inordertomakethebestpossibleuscofthematerial.ThisthenresultsinamoregentledisccharacteristicthanshowninFig.3,andhenceinareductionofthenecessaryshrinkageforce.Buthere,too,averytightshrinkfitwillstillbeneededforagreatvarietyofdiscmeridianshapes,whichisonereasonwhyhighlytemperedmaterialsarechosenforthediscs.Thereareanumberofmethods(e.g.[2])forcalculatingthestressinadiscofanytechnicallyfeasiblecontour.Themethodoffiniteelementshasrecentlycometobeusedforthispurpose,evengoingtotheextentofnotonlydeterminingthestressconditionsintheindividualparts(discs)oftherotor,butalsoofconsideringtherotorasanentityandtakingintoaccounttheinteractionsbe-tweenneighbouringpartsofthediscs.Averygoodoverallinvestigationoftherotorisalwayspossiblewiththemethodoffiniteelements,thefundamentalsofwhichcanbcfounddescribedin[6].Detailedinvestigations, FISA-GridforcnlcttlctinsttreticsRInttnllnnI.p.rotorhythe5nhedctncntmethodl3~tol2CIC'4/>"inInjfueneeofTemperatureUndernormaloperatingconditionstherotorsoflargesteamturbinesarcingeneralexposedtoasteady-statetemperaturefield:afterstart-upandsettlingdowntonormalloadanisothermaldistributionbecomesestab-lishedintherespectiverotorswhichvariesonlyslightlyinresponsetomoderateloadfluctuations.Aknowledgeoftheisothermdistributionintherotorisnecessaryfortworeasons:-first,oncneedstoknowthelocaltemperatureinordertocomparethclocalstresspresentwiththecharacteristicofthcmaterial(e.g.long-timestrength)validatthislocaltemperature,-second,theisothermalconditiongivesrisetoastressfieldwhichitmaybeimportanttocalculateforthetotalloadingonthcrotor.Thismisesthequestionofhowonedeterminestheisothermdistributionintherotor.BasicallythisisaproblemofthermalconductionP]inarotationallysymmetricalbodydescribedbytheFourierequation-~arhTaTar(12)suchasintheslotsofbladefixings,needmorerefinedcalculationappliedoveraveryfinegrid,whiletheaidof.photoelastictechniquesmustbcenlistedforassessingthesurfacestressinthcgrooves.Inthismanneronecanaccountforallthestresscomponentsinvolved.wherea'tr(l3)-Thcisothermsintherotorarefoundwiththeaidofanelectricalanaloguemodel,inwhichcasethcrotationalsymmetryoftherotorisaccountedforbyselectingsuitableresistances(perforations)onthetwMimensionalmodel.TheconductionofanelectricalcurrentthroughabodyisdescribedbytheequationaU-~-hUatc(l4)andisthusanalogoustotheheatconductionequation(l2).Here,Uistheappliedvoltage,Ctheelectricalcapacitanceandxthcelectricalconductivityofthcmaterial.LinesofequalvoltageU,orequalpotential,arcananalogueoftheisothermsT~constant.-Anotherpossiblewayofdeterminingthctemperaturedistributionintherotoristosolvetheheatconductionequationbynumericalmethods.Thispossibilityhasgainedgreatlyinsignificanceinrecentyearswith.theuscBeforesettingaboutsolvingthisequationonemustknowtheboundaryconditions,e.g.surfacetemperature,heatsuppliedandremoved.Inpractice,therotorgeometrydoesnotfollowasimpleshapeandthetemperaturedistributionatthesurfaceiscomplex,owingthecoolingeKectofthestcam.Con-sequently,onecannotexpectacompletesolutiontotheheatconductionequation.Thereareneverthelesstwopracticalwaysofsolvingthisproblem:
Fig.S-VonMlscs'combinedttrcssMdofthatoUdIp.rotorshownlaFig.taValues20to47it//mm~.-.~20.~3timmi100020'-II4740offiniteelementsforcalculatingstress.Onehasthcadvantagethattheresultsofcalculatingtemperatureinthiswaylieonthesamelatticeasthesubsequentstresscalculation,andthuscanbeusedasadirectinputforcomputingthetermalstress.Finally,asregardsdeterminingtheisothermsitmustbesaidthatwithoutthcsubsequentstresscalculationitwillalwaysbefragmentaryandyieldonlymoderatelyusefulinformation.PracticalResultsofStressCalculationsRorarlonalStressesinDig@rentLPRotorDesignsThediscussionintheprevioussectiononstresscalcula-tioninrotorsofdifferentconstructionsisnowillustratedbelowwiththeaidofafewpracticalexamples.Figure4showsthcgridimposedonaI.p.rotorfordeterminingthemechanicalstressesbythefiniteelementmethod.AllthebasicdesignsdepictedinFig.Iwerccalculatedinasimilarmanner.Whencomputingthestresses,thespeedandbladetensionwerekeptconstantforalltypesofrotor.Shape,dimen-sions,speedandbladetensioncorrespondtovalues'oundinpractice.Figure5illustratesthccomparativestressfieldforaI.p.rotormachinedfromthesolidasshowninFig.Ia.HerethecomparativestresshasbeentakenasaccordingtovonMiscs:av~~(ar-at)'+(at-az)+'(ar-ar).'arr'15)Itwillbeseenthatowingtotheabruptchangeofcross-sectionfromthecentralshahportiontothcdisc,stressconcentrationsashighas31kgf/mmeoccur.Stresscon-centrationsofthiskindarealwaystobefoundwhentheforcefieldisdisturbedasaresultofchangesincross-section.Fig.5alsoshowsthestresslevelatthcinnerbore,witharadiusratioofrt/rs~015.At47kgf/mmthestresshercreachesaveryhighvalue,althoughitisstillalwaysbelowthatofshrunkendiscs.Resultsofcalculatingthestressesinshrunk-ondiscsarcshowninFig.6.Owingtothelargercentralborefortheshaftamuchhigherstressof68kgf/mm'sfoundhere,other-wisetheconditionsarethesameasinFig.5.Atthetransitionfromthcslimpartofthedisctothebroadoutershoulderonecanagainseeastressconcentrationinthecornerofthedivergence,attaininglocalvaluesof70to80kgf/mmeandcausedchieflybydisruptionoftheradialstresspattern.Atechniqueoftenusedinthepastwastosecuretheshrunk-ondiscswithextrakeys.Thisinevitablygivesrisetostressconcentrationsinthekeywaywhichinthemostfavourablecasehaveastressconcentrationfactorofaboutthree.Whatthismeanswiththehighbasicstresslevelofaperforateddisciseasytoappreciate:fromthcstartaplasticzonewillformroundtheslotwhich,ifthcpropertiesofthematerialarelessthanideal,canleadtocrackingandhencetofailureofthediscwhenitisrotating.Sufficientinstancesofthishaveunfortunatelyoccurredinthepast[9,IO).Inordertomeetthestandards,ofreliabilityrequiredinpowerstations,there-fore,itisessentialthatnokeysofanykindshouldbcprovidedasanextrameansofsecuringthediscs.AsalreadyexplainedinconnectionwithFig.2,thcsoliddiscwillshowthemostfavourablestresscharacteristics.
0-44554415h4)1)l5RS.6-CorobipedStretttiddofaLp.discrotorotshowalaFia.lb,Ia)$Sf/a)a)j~ISO5)545454555$)4)0)4)5~Il1545)XO4$I)SX~1)I)I)tJ)tjll,)ll,l44Jl444oD5)4$JltD4)jlIP4)Pl5P44444,44)J41J4IJ<<L))tj))J))D)tj~lIP)tj)tj)tpr)Lt)45)SJ5)J)tD))J)tj4)j4)J~tj4)j41JltJ$4)$4740.l5)Jllj4L)~)p47J41JSal5)4stjIOJIcj4)J4)j4L)4L441j44J4474L)4)J4$441P4)Jl)j$4J5)D5)j44$$1j5L14L44L4)tpi5Stp4454SJ$IJltj41jSLlSIAltjFigure7illustratesthecombinedstr<<ssdistribution(aAervonMises)inaweldeddrumrotorofatypefoundinmachinesofover1000MW.Tlieboundaryconditions-outsidediameterandbladntension-arecomparablewiththedesignsshowninFig.5and6,thespeedbeingtakenas1800rcv/mininallthecasesshown.Itwillbcnoticedthatwitharotorofthiskind,whichiscomposedofsoliddiscs,thcgreateststressisroughlybetween40%(Fig.5)and60%(Fig.6)lowerthanforrotorsmachinedfromthesolidorforshrunkendiscs.Thisfactwillagainbeimportantwhenconsideringthechoiceofmaterialandthcburstingspeed.HPandIPRotors,IncludingTemperaturesectsFigurc8showstheisothermsinaweldedh.p.rotorunderconditionsoffullload.Hereonccanseethccharactcris-ticfeatureofsteady-stateoperationthattheisothermsrunalmostperpendiculartothcaxisofrotation,andonthebasisoftheisothermdistributiononecanpredictthatthethermalstrcsscswillbeverysmallcomparedtothe.stressescausedbyrotation.Inthisexampletheyinfactamounttoonlysome5to10%ofthemechanicalstresses.Incontrasttothecoldlow-pressuresection,thcmechani-caldesignofrotorsexposedtohightemperaturesin-cludestheirbehaviourinrelationtotime.Becauseofcreepphenomena,whichwillbediscussedinmoredetailinthenextsection,thematerialagesinthecourseoftime.Thisageingprocessisafunctionofthematerial,temperatureandstress,aswellastime,andthereforeinordertoassessthesuitabilityofadesignonemustknowalltheseparameters,i.e.-thebehaviourofthematerialasafunctionofloading,temperatureandtime, Fig.7-CombinedstressIIelaweldeddrumrotorasshowninFig.IcValues20to28ltgf/mme.I20I/+2gI0002026-thcisothermdistributionintherotor,and-thestressesintherotor.Anexampleofadetailedstudyofahigh-pressurebladefixingisshowninFig.9.Usingphotoelastictechniques,theedgestressesinthelateralgroovesaredeterminedunderdiFerentloadsandaddedassupplementaryin-formationtotheresultsofarefinedstresscalculation(Fig.9).Inthisway,togetherwithallowanceforthebehaviourofthematerialandstringentproductionquali-tycontrol,itispossibletoguaranteetheperformanceoftherotorovermanyyears.TheRotorIVlaterialHigh-PressureandIntermediate-PressureRotorsTherotorsofmodernlargesteamturbinesare,alloffcrriticmaterial.Thisisrelatedtothefactthatforconventionalplanttheworldoverthelivesteamtempera-turehasbecomeestablishedat538'C.Withthismaterialonecanexpectgoodlong-timeproperties,nosoftening,littlecreep,uniformheattreatment,adequatelong-termductility,lownotchsensitivityandgoodresistancetoscale.Nuclearpowerstationsatpresentdonotraiseanyproblemsoftemperaturebecausetheturbinesrunonsaturatedsteam,andeventhehigh-temperaturereactorsforlargepowerstationswillnotexceedthelivesteamtemperatureofconventionalplant,atleastinthenearfuture.Figurcl0showstwotypicalrotorsteels[11]usedforh.p.andi.p.turbines.Toallowinternationallyconsistentcomparisons,thelong-timerupturevaluesforl00000hoursaretakenasabasisformechanicaldesignpur-poses.Thefollowingremarkssurveybrieflythebehaviourofrotormaterialsunderthcinfluenceoftemperature,stressandtime.IfatestbarissubjectedtoaloadattandatthcsametimeatemperatureTe,itwillintimeundergoplasticelonga-tion(creep)andfinallybreak.ForthesameloadingthebarwillfailearlierwithahighertesttemperatureTt)Tethanwithalowertemperature.Fig.g-Isothermdistributioninaweldedh.p.rotor450$005I0'C460'00I10 IItiIafig.9-Combinedstressesinthegroovesofh.p.bladeAxing'theAguradenotethevonMiscscombmcdstressmltgtimms.rI3500'C505C5IOCslsCThecreepprocessisillustratedinFig.Il.Wecandistinguishthreemainphasesofcreep;primary(I),secondary(II)andtertiary(III),inwhichthebarrapidlyreachesbreakingpoint.Allhigh.pressureandinterme-diate.pressurerotorsoperatewithinthesecondaryphase,andthedesignerhastomakesurethathisdesignhasanadequatereservewithrespecttothetertiarystage.Inthesecondaryphasetherateofcreepi~de/dtisconstant,whichinpracticemakesiteasiertoassesstherotorafteralongperiodinservice.Everytimetheturbineisinspected,speciallyprovidedcontroldiametersaremeasuredandtheresultscomparedwithmeasurementsofpreviousyears.Here,'however,accountmustbctakenofthefactthatthccreepratewithinadiscvarieswidelyfrominsidetooutsideowingtovariationsinthestress.-I.ong-timetionofsteels24fig.loeomposifnptUrecnrvcsCrMov55andeeainhgrtmmsandchemicalLo~~pressureRotors2lCrMov5II70605040pelt'02520IO9g1654IO2ICrMoV5lloooiso.24CrMoV55io'O<<ho~J~Whereasforhigh-temperatureconditionsthenumberofdiHcrentrotormaterialsusedbythevariousmanufac-turersislimited,theselectionofmaterialsforlow-pressurerotorsismuchwider.Thisisnotallthatremarkablewhenoneremembersthevarietyofl.p.rotordesigns,becausethematerialisprincipallymatchedtothedill'erentstressconditionsoftheindividualtypesofconstruction.Furthermore,becausetheserotorsareessentiallycool,thefactorsgoverningthechoiceof'materialwillonlybetheyieldpoint,ultimatestrength,elasticlimitandnotchtoughness.Hereitisassumedthattherotoroperatesintheupperpartofthenotch-toughnessrange,i.e.thcfractureappearancetransitiontemperatureisbelowthcoperatingtemperature.Recently,andnottheleastofthcreasonsbeingseveralcasesofexplosivefailureofsolidandshrunkMiscrotors,whichalsoextendedtonuclearstations[IOJ,therehasbeenatendencytobasethechoiceofmaterialonadditionalcriteriainordertoavoidsuchinstancesofbrittlefracture.Forthis,therotorisconsideredfromthestandpointoffracturemechanics,theaimbeingtoarriveatappropriatevaluesofcrackresistanceandrateofI05propagationforsubcriticalcrackgrowthWithoutgoingintothefundamentalsoffracturemechanics-thesubjectIO rt)rort)ro//rtrconst.0/dl)do/zroIOltNIfig.1I-CreepcurvesfordifFerenttemperaturesandloads(schematic)failureofallcontrolandsafetysystems.Inthishypothet-icalsituation,rejectionoftheelectricalloadwouldcausetherotorspeedtorunaway,possiblyresultinginex-plosivefailure.Ourownstudieshaveshownthath.p.andi.p.rotorshaveamuchhigherburstingspeedthanI.p.rotors.Thereasonforthisisthatthehighandintermediate-pressurerotorsstretchradiallylessthanthelow-pressurerotors,andwhilethematerialcharacteristicgoverningburstingistheyieldpoint,h.p.andi.p.rotorsaregenerallydesignedtowithstandlong-timefailure.Sincethevalueforlong-timefailureisonlyafractionofthecorrespondingyieldpoint.dependingonthetemperature,theserotorshavealargerreservewithrespecttotheburstingspeedthandoI.p.rotors.InordertostudythebehaviourofdiFerentdiscdesignsinrelationtotheburstingspeedwcagainusethediscofuniformwidthasastartingpoint.Grammelhasshown[14)thatthemeantangentialstressinthediscissuitableasameasureoftheresistancetoexplosivefailure.ThemeantangentialstresstrtMisgivenbyrscrtdr(16)istreatedin(12)and[13),forexample-itshouldbementionedthatthisaspectofmechanicswasoriginallyevolvedforhigh-strength,relativelybrittlematerials.However,itisonlysuitablefordescribingacrackwhichalreadyexists,andtakesnoaccountoftheactualforma-tionofthecrack.Atthesametimeitshouldnotbeforgottenthatturbinerotorsconsistofductilematerialswhichhavetheability,ifneedbe,tofiowlocallyanddispersestresspeaks,thuspreventingcracksfromform-ing,oratleastgreatlydelayingtheironset.Itcan,ofcourse,happenthatthereissomejustificationf'rexaminingarotorfromafracturemechanicsview-point.Thiswillalwaysbesoif,becauseofthehighlevelofdiscstresses,onehastoresorttohigh-strengthmaterialsorwhen,asinthecaseofsolidlow-pressurerotors,thelargedimensions,makeitverydifficulttodetectfaultsinsidetheforging.Itmaythenbeofadvantagetoassumeafaultofacertainsizeinacertainpositionandchecktoseewhattheconsequencesmightbeinthecourseoftime.crtÃ-fsrtandcanbewrittenindimensionlessformasfollows:n8trtdrgrestos(3+t)StMfs-rt(17)(18)'heratioofthcburstingspeedsofperforateddisctosoliddiscisthendescribedbyFortrtwethenuseEq.(3)forasoliddiscandEq.(5)foraperforateddisc.Ifwenowwritetheratioofthemean,tangentialstressStwr,oftheperforateddisctothemeantangentialstressStlvofthesoliddisc,wehaveBurstingSpeed<BRLirBRVI+-+(19)Inrecentyears,andinitiallyattherequestoftheUSAtomicEnergyCommission,manufacturersoflargetur-binesfornuclearpowerplanthavehadtoanalysetheextentofdamagetotheturbosetintheeventoftotalEquations(18)and(19)areshowngraphicallyiriFig.I?Asexaminationwillquicklyshow,forrt(rs~Itheywillofcourseprovidetheburstingspeedratioforthethinring.
2,0l,gesax,SetsasarSoirl.g1,2Vgl.oO,gheal.I/1(l+-"+(-,"j',600,20.40,6rtPsFig.lz-RatiosofmeantangentialstressandberatingspeedlorperforatedandsoliddiscsFigure13showsinqualitativetermsthebehaviouroftwodiff'erentI.p.rotorconstructionsatelevatedspeed.Forthesamesize.bladetensionandoperatingspeed,thctangentialstressforthedrumrotorwillfollowcurveI.Thesameappliestothediscrotor,butatthcborediameterchosenthisrotorshowsastressroughlydoublethatofthcdrumrotor.Intheelasticregionthereisproportionalitybetweenthestressandthesquareofthespeed.IfthespeedisraisedrelativetothenormalspeedbyafactorofI4,forexample,thestressesincreasebyafactorof196(curve2).Theinnerportionofthcper-forateddiscisthenalreadybeyondtheyieldpoint,andthecorrespondingzonerelaxes.Owingtoplasticdeformation,therefore,theelasticcurve2giveswaytocurve2'ndthcpartsofthediscwhicharestillelasticarcthussubjectedtoadditional,stress.Accordingtowhathasbeensaid.sofar,ameasureofthercscrvewithrespecttofractureistheratioofthe.yieldpointtothemeantangentialstress,i.e.essentially.theareainFig.13containedbetweencurvesIandtheyieldpoint.Therootofthisarearatiorepresentsthe.relationshipoftheburstingspeedofthctwodesignsshowninFig.13.Ifonewishestocompensatethedisadvantageofthelowerfracturespeedofaperforateddiscbyusingmorehighlytemperedmaterial,theincrease-inyieltIpointrequiredforaperforateddisccanalsobe.foundwithEq.(18)(Fig.12).Itcanbcseenthatwiththeradiusratiosoccurringinpracticeitisdifficulttoachieveaperforateddiscofsuchaqualitythatitisequivalenttoasoliddiscasregardsitsburstingspeed.Thiswouldmeanhigh-strengthmaterialhastobeused,withtheconsequenthigherriskofbrittlefracture.Fig.ls-BehaviouroftteotypesofI.p.rotorat<<leratedspeed~tdidi2ldldiPaOutlookAsmentionedearlier,theunitcapacityoflargesteamturbosetswillcontinuetoriscinthcforeseeablefuture,andhence.influenccthedemandsmadeoftherotors.Adecisive,andtosolneextentlimiting,factoroverthepastdecadewasthefinalstage,whichifthevacuumwasgoodhadtohandleenormousflowvolumes.Allmanufacturersofsteamturbinesthereforecarefullydevelopedlongerfinalbladesandintroducedthesetothemarket.Butlongerbladesalsomeansalargerrotordiameter,accom-paniedbyhighercentrifugalloadingsonbothbladesandrotor.Tokeepstressesbelowthelimit,thespeedofthemachineswashalved.ThetechniqueemployedintheUSAwastorunthchighandintermediate-prcssuresectionsatthcfullspeedof3600rev/min,andcombinethelow-pressureunitswitha4-polegeneratoronasecondshaftstringrunningat1800rev/min.Europelateradoptedtheideaofthehalf-speedmachine,althoughin12 single-shaftformandonlyfornuclearplant.Byhalvingthespeedinthisway.andatthesametimedoubling,thesize,thestressesinfull-speedandhalf-speedmachineswerekeptthesame,butthecorrespondingexhaustareaofthefinalbladesincreasedfourfold.Afeatureofrecentyearshasbeenagrowingworldwideshortageofcoolingwater[15].Intheindustrializedcountries,andtheseifonlybecauseoftheir.powerdistributionnetworksarethepotentialbuyersoflargemachines.itisbecomingnolongerpossibletouscfreshwaterforcoolingpurposes.Futurelargepowerstationswillthereforebeequippedmainlywithwetordrycoolingtowers.whichmeanstheturbinevacuumwillberclativclypoorandthesteamexhaustvolumecorrespondinglysmaller.ItmaythuswellbethatthefinalbladelengthsandI.p.rotordimensionscustomarytodaywillbeade-quateforsometimetocome,withoutbeingtiedtohalf-speedI.p.sectionsbecauseofthcstresses,evenwithlargecapacities.Itislikelythatlargemachinesfornuclearpowerstations,withpoorvacuum,willalsobebuiltforfullspeedandstillbeabletocopewiththcstressesinthebladesandrotor.ThepossibilityofmakingtheI.p.rotorrelativelysmallalsoimprovesthechancesofthesolid-rotordesigntosomedegree.Greatadvancesinforgingtechnologyhavebeenmadeoverthepastfewyears,andthishasincreasedconfidenceintheuseofforgedone-pieceshafts.Finishedweightsofover200thavebeenachievedtodate.Theserotorsrequireaningotweighingmorcthan400tandwiththeassociatedriskscanbeproducedonlyinJapanandtheUnitedStates.Itisimprobablethatthesteel-workswillcontemplateafurtherincreaseinrotorsize.withthecorrespondinglyheavyinvestmentneededtodealwithlargeringots,becausethemarketfortheselargeforgingsistoorestricted.Theconceptofthelargeone-piecerotorcanthereforebeextrapolatedintothefuturetoonlyalimitedextent.Thcsituationisslightlydifferentforthehigh-pressuresection.Ontheassumptionthatfuturenuclearpowerstationswillalsooperatewithsteamconditionssuchasarefoundtodayinconventionalplant(I50to250bar,538'C),theverysizeoftheI.p.rotorcouldpresentastressproblem.Overcomingthiscanbeapproachedintwodifferentways:thematerialandthedesign.Thereisnolikelihoodinthenearfutureoffindingadifferentmaterialforh.p.rotorswhichhassubstantiallybetterlong-termpropertiesanddoesnotforfeittheadvantagesofthelowalloysteelsusedatpresent.Muchmoreprobableisthatstressesintheh.p.rotorcanbekeptincheckthroughsuitabledesign:thelargesteamturbinetodayisquiteclearlyfollowingthcpathtakenmanyyearsagobythegasturbinetowardscoolingtherotorbymeansofsteam.ThedesignerthushasathisSymbolsF.=ModulusofelasticityL=PerforateddiscS<---DimensionlessradialstressSi=DimensionlesstangentialstressSist=-DimensionlessmeantangentialstressSv~DimensionlessequivalentvoltageT=TempcraturcU=RadialdisplacementV=Soliddisca=Thermalconductivityc=Specificheatofrotormaterialnnn=.Burstingspeedr=Considereddiscradiusri=Innerradiusofperforateddiscri--Outerradiusofdischr=Degreeofshrinkagedu-~Relativedegreeofshrinkagetir~Timee<--Radialexpansion=Tangentialexpansion=Conductivityofrotormaterial~Transversecontractionratio=Specificmassofdiscmateriale<=Radialstresse<i=Shrinkageforcee~=.Bladetensionappliedatradiusrs(ri%std!COOPyp4Tangentialstress=Meantangentialstressovermeridionalareaofblade=Axialstressesinrotor=Angularvelocityofrotation=Overspeed=Lift-offspeedIndicesWS0=Centralshaft=Disc=Standstilldisposaladesignconceptsufficientlflcxibletoallowhimanadequatemarginofsafetyindesigningrotorsforthehigh-pressuresectionasunitcapacitiescontinuetorisc.13 Bibliography[I]A.LNhyrSomeadvantagesofweldingturbinerotors.Weld.J.June1968.[2]C.B.Bienzeno,R.Grammel:TechnischeDynamik,vol.II,Springer1953.[3]W.Traupel:ThermischeTurbomaschinen,vol.Il,Springer1960.[4]K.Lofter:DieBcrechnungvonrotierendenScheibenundSchalen.Springer1961.[5]A.Bald:BesonderheitengrosserNassdampAurbo-sgtze.Mitt.Vereinig.GrosskesselbesitzerS21972(4).[6]0.C.ZleriklewlczrThefiniteelementmethodinstruc-turalandcontinuummechanics.McGraw-Hill,London1967.[7]B.BaulerDieMathematikdesNaturforschersundIngenieurs,vol.IV.Hitzel1952.[S]H.Lelpholz:FestigkeitslehrefurdenKonstrukteur.Springer1969.[9]H.D.EnunerrInvestigationoflargeturbinespindlefailure.ASMEPaper55-A17?[IO]D.CalderonrStcamturbinefailureatHinkleyPoint.Proc.Inst.mech.Engrs186.[II]StghtefQrgrQssereSchmiedestQcke(GQtevorschrift).Stahl-Eisen-Werkstoffblatt550-S7.[12]K.Hecke/:EinfQhrungindietechnischeAnwendungderBruchmechanik.Hanser1970.[13]D.Radaj:GrundlegendcBeziehungenderlincar-elastischenBruchmechanik.Schweissenu.Schneidcn231971(IO).[14]R.Grammel:DieErklarungdesProblemsderhohenSprengfestigkeitumlaufenderScheiben.Ingenieur-Archiv161947(I).[IS]H.Flohn,D.Hensehler,H.Schuller:"DerWasser-haushaltderErde.Aus:MenschundUmwelt.Tech.Rdsch.641972(47).14
SICBROWNBOVERIBBCBrown,Boveri5Company,Ltd.CH-5401Baden/SwitzerlandprintedInswiuorlsnd(74e41000.0)CasahcationNa01010