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{{#Wiki_filter: | {{#Wiki_filter:BBCBROWNBQVERIRotorsorLargeSteamTurbinesPublication No.CH-T060053E RotorsforLargeSteamTurbinesA.HohnAstheunitcapacityofsteamturbosets Increases, sotoodoesthesfseoftherotor,andhencealsothestressesappliedtoit.Thevariousdesignsofrotorarediscussed andresultsofstresscalculations given.Rotormaterials areconsidered briefly,followedbycommentonthefuturedevelopment ofrotordesignforlargesteamturbines. | ||
dandsincecrt=-(rrtr)+(2r'o'l'2cos(3~<<)/I+3<<2rt~rr'Z8(3+.b. | RotorConfigurations Thedesignscurrenttodayarerestricted totheformsshowninFig.l:-Diagramashowstworotors,eachproducedfromasingleforging.-Shrinking discsontoacentralshai?whichtransmits thetorquegivesrisetothecomposite construction ofdiagramb.-Indiagramc,separatediscshavebeenweldedtogethertoformadrum.typerotor[I],Eachconfiguration hasitsownadvantages anddisad-vantagesasregardsproduction ofthe'teel, heattreatment, machining andtesting,butthesewillnotbedealtwithspecifically here.Distinctive differences inthematterofstressesareconsidered inthefollowing | ||
higherloadingthanthesoliddisc. | 'twosectlolls. | ||
Fig.S-VonMlscs' | StaticsofRotorsundertheInfluence ofSpeed,DiscGeometryandTemperature TheDiscundertheinfluence ofRotationintroduction Steamturbinestodayareremarkable particularly fortheirsize:unitcapacities ofmorethanl000MWarenowtobefoundbothinconventional powerstationswithfossil-fuelled boilersandalsoinnuclearpowerplant.Foranumberofreasons,unitcapacities willriseevenfurtherinfuture,anditwouldbcpremature atthemomenttospeakofanylimit.Machinesofthissizerepresent asubstantial financial commitment andinthceventoffailurecauseseriousdisruption ofthepowersupplytobothdomesticandindustrial users.Itistherefore under-standable thatthemanufacturer ofsuchmachinesdoesasmuchasthelateststateofthetechnology willallowinordertoensurethattheselargemachinesarereliableinservice.Thisarticleisconcerned withtheheartofthemachine,therotor,andreference ismadetothevariousrotordesignsandthedifiercnces betweenthem.Fulltreatment ofthesubjectwouldhavetoincludethcstaticbehaviour insteady-state operation andundertransient conditions, andalsothedynamicsoftherotorundertheinfluence oftheflowofsteam.This,however,wouldgobeyondthcscopeofanarticle,andtherefore themainfocusofattention hereisonsteady-state operation whichatalleventsconstitutes thebasisofthemechanical design,andonwhichallotherphenomena arcsuperimpose* | ||
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$ | Csticot(3-.')o~Ci~a8Disregarding anyexternaltensionforthctimebeing,thecurvesofradialandtangential stressarefoundtobeasfollowsfor:a.asoliddisc:t.~'(3+v)(..8(2)Alldesigners ofturbomachines usethcrotatingdiscinoncformorthcotherasabasiccomponent oftherotor.Thefollowing remarksontherotatingdisc,whicharcofanelementary natureandcanbepursuedfurtherin(2,3,4]forexample,aretherefore applicable toall,withaccounttakenoftheboundaryconditions particular toaspecificdesign.Iftheequilibrium offorcesintheradialdirection istakenonarotatingdiscelementofconstantthickness, al-lowanceismadefortherelationship betweenradialandtangential expansion inthcdiscandHooke'slawforbiaxialstressisintroduced, weobtainthediflerential equationofthe'rotating discintermsofa<withthegeneralsolution: | ||
2,0l,gesax,SetsasarSoirl.g1,2Vgl.oO,gheal.I/1(l+-"+(-,"j',600,20.40,6rtPsFig.lz- | dandsincecrt=-(rrtr)+(2r'o'l'2cos(3~<<)/I+3<<2rt~rr'Z8(3+.b.aperforated disc:(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.Toillustrate moreclearlythemutualinfiuences ofradialandtangential stress,Fig.2alsoincludesthedimensionless comparative stressSvonthcassumption ofconstantworkofdeformation, thus:;-y;*+;*-;., | ||
utldSv~8clv(2rs'o'3+2)FromFig.2wccandrawafirstconclusion: | |||
Inordertoshowequations (2)to(5)ingeneralformtheyaremadedimensionless withthestressprevailing attheForthesamedimension (rs),thesamematerial((2)andthcsamespeed(co),theperforated discwillexhibitaFig.I-Dlirerent typesofrotorconstruction Fig.2-Dimensionless radial,tangential andcombinedstressesol'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.Ameasureofthisisthemeantangential stress.Thisresultalsoremainsessentially unchanged whentheadditional loadscausedbybladetension,steampressureandshrinkage aresuperimposed ontherotational StreSseS.Theconsiderations presented sofararesuFIcient fordetermining therotational stressesinthecaseofasoliddisc.Fortheperforated andshrunk-on discofFig.lb,however,deformation alsohastobetakenintoaccount,owingtothediFerentstiffness ofthecentralshaftandthedisc.Onlythencanoncdefinetherequireddegreeofshrinkage, whichinturnhasaninfiuence onthechoiceofmaterial. | |||
Deformation Affecting thePerforated DiscHerewecanagainstartfromEq.(I)anddetermine theintegration constants C<andCtappropriate totheboundaryconditions. | |||
Withthcaidofthccalcuhted stressesitispossibletodetermine theradialexpansion, andhencealsothcradialdisplacement UforanyradiusofthecentralshaAoroftheshrunk-on disc.Ofparticular interestaretherelativedisplacements UtofshaAanddiscatthepointofattachment withradiusr1.Thcresultofconsidering deformation inthiswaycanbcreadfromthcTable.Thus,anyexpansion ofdiscorshaAisproportion-altotheforces.artandarswhichcauseit.Thereisasquare-law relationship betweentheexpansion androta-tionru.Hereitmustbcnotedthatfordifferent speedsthcexternaltensionarsalsovariesasthesquareofthespeed.Theshrunkwnbodyhastosatisfythefollowing condi-tions:atthepointofcontactbetweendiscandshaAatradiusrtthesumofdisc,expansion andshaltcompres-sionmustequalthedegreeofshrinkage du,i.e.rtw-rtsUtw+UtsWiththisitisnowpossibletoconstruct a"springdiagram"oftheshrunkjoint(Fig.3),andwithinthistherelativedegreeofshrinkage hrjrcanbcdetermined foragivengeometry(rt,r1)andadesiredshrinkage forceo<t.Thcshrinkage forceischoseninthelightofthetwofollowing points:-Expansion ofthediscduetorotationmayonlybelargeenoughto<<nsurethatapositivefixingismaintained whenrunatoverspeed (normally l2xoperating speed),i.e.thediscmustnotcomeloose.Publications bymanufacturers ofthistypeofconstruction indicatethattheliAwFspeed(zero-shrinkage) liesapproximatefy 35%abovethenormaloperating speed[5).-Itmustalsobeascertained whether,atnormaloperat-ingspeed,thcshrunk-on discisf'ullycapableoftrans-ferringthcbhdetorquetothccentralshaft.Generally | |||
: speaking, thisrequirement isalwaysmetiftheoverspeed condition issatisfied. | |||
Ourconsiderations regarding theshrunkwndisccanthusbcsummarized asfollows:Atstandstill thediscisstretched becauseitwasundersize whenfittedon-theshaft,andtheshaAiscompressed bythcshrinkage. | |||
Owingto'tsownrotationandthetensileforceexertedbythebladesthediscexpandsmorethanthecentralshaft.Theshrinkage forceisthusreduced.Aresidualdegreeofshrinkage mustberetainedwhentherotorisrunatovcrspeed. | |||
Expansion ofshaftanddiscShrinkagforceRotationExternaltensionNON>I~8)B)COmruii(tt1)er1icu'(I | |||
-r)riJuan,4aDiscriix(I-r)+-(I+r)r11I'iiX[-(S+r)+(I-rtrli Figurc3showstheserelauonships forstandstill (co=0),operating speed(co),overspeed (co~co')andliftofspeed(co'I35co)foradiscofuniformwidthwitharadiusratioofrr/ri~3.Inthisdiagramthcelasticity properties ofthediscandthccentralshafthavebeendetermined inaccordance withtheTable.Ontheabscissathcpointoforiginisthedesireddegreeofshrinkage | |||
(&/ri)o,whichisselectedaccording totheresidualshrinkage (ordinate) desiredattheoverspeed condition. | |||
Theindividual com-ponentsofthediscandshaftexpansion duetorotationandexternaltensionorehavealsobeentakenfromtheTable.Inordertoestablish theorderofmagnitude ofthecompressive forcesoriinvolved, andalsotheresidualshrinkage, thediagramwascompiledusingrealistic conditions suchasoccurinthecaseofI.p.rotorsforhalf-speedsteamturbines: | |||
n1500rev/min,equivalent toco=157s-',overspeed co'12co;bladetensionerisbeingtakenas8kgf/mrnaatthenormaloperating speed.Theresidualshrinkage foranyspeedscanbeobtaineddirectlyfromFig.3bymeansofthcfollowing conversion fromthestationary shrinkage diagram.Thebasicprin-ciplesofthisareexplained in[6].octE2,$~IO32,0I,OO,SI2Uisps34IUswrIUsripgWehave:(9)Sincetheresidualshrinkage duatoperating speedcoisgivenbyco~0(10)fortheresidualshrinkage weobtainI-co~cu'II)Fig.3-Shrinkage diagramforshrunkendiscsunderdlirereni operating eondiiions ThusitcanbeseenfromFig.3thatanextremely largedegreeofshrinkage (415x10-')isnecessary toachievealift-offspeedofco'I35co,takingintoaccountthebladetension.IffortheexampleinFig.3ithadbeenstipulated thatliiboffistooccurat135%ofoperating speedwithoutallowance fortheexternaltensionetre(i.e.withoutblad-ing),thiswouldresultinthestandstill shrinkage diagramshownbythebrokenlineinFig.3,withastandstill shrinkage of26x10-s.Inthiscase,however,thebladedrotorwouldloseitsresidualshrinkage evenatsmalloverspeeds (9%inthisinstance), | |||
owingtothebladetension,andsomemeanssuchaskeyswouldbeneededtopreventthediscfromslipping. | |||
Thereserveofspeeduptoliftwifmentioned hereisdetermined bythcresidualshrinkage obtainedwithEq.(11).influence ofDiscGeometryTheabovestatements areofafundamental natureandaidone'sunderstanding whencomparing dificrent designs.Butinpracticetheshrunk-on discisnotofconstantwidth.Thediscmeridianwilltherefore beshapedinsomeway,itwillbeformedtoyieldadiscofuniformstrengthortheperforated discwillbegivenahyperbolic meridiansimilartoy=c/rn,inordertomakethebestpossibleuscofthematerial. | |||
Thisthenresultsinamoregentledisccharacteristic thanshowninFig.3,andhenceinareduction ofthenecessary shrinkage force.Buthere,too,averytightshrinkfitwillstillbeneededforagreatvarietyofdiscmeridianshapes,whichisonereasonwhyhighlytemperedmaterials arechosenforthediscs.Thereareanumberofmethods(e.g.[2])forcalculating thestressinadiscofanytechnically feasiblecontour.Themethodoffiniteelementshasrecentlycometobeusedforthispurpose,evengoingtotheextentofnotonlydetermining thestressconditions intheindividual parts(discs)oftherotor,butalsoofconsidering therotorasanentityandtakingintoaccounttheinteractions be-tweenneighbouring partsofthediscs.Averygoodoverallinvestigation oftherotorisalwayspossiblewiththemethodoffiniteelements, thefundamentals ofwhichcanbcfounddescribed in[6].Detailedinvestigations, FISA-Grid forcnlcttlctinsttretics RInttnllnnI.p.rotorhythe5nhedctncntmethodl3~tol2CIC'4/>"inInjfuenee ofTemperature Undernormaloperating conditions therotorsoflargesteamturbinesarcingeneralexposedtoasteady-state temperature field:afterstart-upandsettlingdowntonormalloadanisothermal distribution becomesestab-lishedintherespective rotorswhichvariesonlyslightlyinresponsetomoderateloadfluctuations. | |||
Aknowledge oftheisothermdistribution intherotorisnecessary fortworeasons:-first,oncneedstoknowthelocaltemperature inordertocomparethclocalstresspresentwiththecharacteristic ofthcmaterial(e.g.long-time strength) validatthislocaltemperature, | |||
-second,theisothermal condition givesrisetoastressfieldwhichitmaybeimportant tocalculate forthetotalloadingonthcrotor.Thismisesthequestionofhowonedetermines theisothermdistribution intherotor.Basically thisisaproblemofthermalconduction P]inarotationally symmetrical bodydescribed bytheFourierequation-~arhTaTar(12)suchasintheslotsofbladefixings,needmorerefinedcalculation appliedoveraveryfinegrid,whiletheaidof.photoelastic techniques mustbcenlistedforassessing thesurfacestressinthcgrooves.Inthismanneronecanaccountforallthestresscomponents involved. | |||
wherea'tr(l3)-Thcisotherms intherotorarefoundwiththeaidofanelectrical analoguemodel,inwhichcasethcrotational symmetryoftherotorisaccounted forbyselecting suitableresistances (perforations) onthetwMimensional model.Theconduction ofanelectrical currentthroughabodyisdescribed bytheequationaU-~-hUatc(l4)andisthusanalogous totheheatconduction equation(l2).Here,Uistheappliedvoltage,Ctheelectrical capacitance andxthcelectrical conductivity ofthcmaterial. | |||
LinesofequalvoltageU,orequalpotential, arcananalogueoftheisotherms T~constant. | |||
-Anotherpossiblewayofdetermining thctemperature distribution intherotoristosolvetheheatconduction equationbynumerical methods.Thispossibility hasgainedgreatlyinsignificance inrecentyearswith.theuscBeforesettingaboutsolvingthisequationonemustknowtheboundaryconditions, e.g.surfacetemperature, heatsuppliedandremoved.Inpractice, therotorgeometrydoesnotfollowasimpleshapeandthetemperature distribution atthesurfaceiscomplex,owingthecoolingeKectofthestcam.Con-sequently, onecannotexpectacompletesolutiontotheheatconduction equation. | |||
Therearenevertheless twopractical waysofsolvingthisproblem: | |||
Fig.S-VonMlscs'combined ttrcssMdofthatoUdIp.rotorshownlaFig.taValues20to47it//mm~.-.~20.~3timmi100020'-''II4740offiniteelementsforcalculating stress.Onehasthcadvantage thattheresultsofcalculating temperature inthiswaylieonthesamelatticeasthesubsequent stresscalculation, andthuscanbeusedasadirectinputforcomputing thetermalstress.Finally,asregardsdetermining theisotherms itmustbesaidthatwithoutthcsubsequent stresscalculation itwillalwaysbefragmentary andyieldonlymoderately usefulinformation. | |||
Practical ResultsofStressCalculations Rorarlonal StressesinDig@rentLPRotorDesignsThediscussion intheprevioussectiononstresscalcula-tioninrotorsofdifferent constructions isnowillustrated belowwiththeaidofafewpractical examples. | |||
Figure4showsthcgridimposedonaI.p.rotorfordetermining themechanical stressesbythefiniteelementmethod.AllthebasicdesignsdepictedinFig.Iwerccalculated inasimilarmanner.Whencomputing thestresses, thespeedandbladetensionwerekeptconstantforalltypesofrotor.Shape,dimen-sions,speedandbladetensioncorrespond tovalues'oundinpractice. | |||
Figure5illustrates thccomparative stressfieldforaI.p.rotormachinedfromthesolidasshowninFig.Ia.Herethecomparative stresshasbeentakenasaccording tovonMiscs:av~~(ar-at)'+(at-az)+'(ar-ar).'arr'15) | |||
Itwillbeseenthatowingtotheabruptchangeofcross-sectionfromthecentralshahportiontothcdisc,stressconcentrations ashighas31kgf/mmeoccur.Stresscon-centrations ofthiskindarealwaystobefoundwhentheforcefieldisdisturbed asaresultofchangesincross-section.Fig.5alsoshowsthestresslevelatthcinnerbore,witharadiusratioofrt/rs~015.At47kgf/mm thestresshercreachesaveryhighvalue,althoughitisstillalwaysbelowthatofshrunkendiscs.Resultsofcalculating thestressesinshrunk-on discsarcshowninFig.6.Owingtothelargercentralborefortheshaftamuchhigherstressof68kgf/mm'sfoundhere,other-wisetheconditions arethesameasinFig.5.Atthetransition fromthcslimpartofthedisctothebroadoutershoulderonecanagainseeastressconcentration inthecornerofthedivergence, attaining localvaluesof70to80kgf/mmeandcausedchieflybydisruption oftheradialstresspattern.Atechnique oftenusedinthepastwastosecuretheshrunk-on discswithextrakeys.Thisinevitably givesrisetostressconcentrations inthekeywaywhichinthemostfavourable casehaveastressconcentration factorofaboutthree.Whatthismeanswiththehighbasicstresslevelofaperforated disciseasytoappreciate: | |||
fromthcstartaplasticzonewillformroundtheslotwhich,ifthcproperties ofthematerialarelessthanideal,canleadtocrackingandhencetofailureofthediscwhenitisrotating. | |||
Sufficient instances ofthishaveunfortunately occurredinthepast[9,IO).Inordertomeetthestandards, ofreliability requiredinpowerstations, there-fore,itisessential thatnokeysofanykindshouldbcprovidedasanextrameansofsecuringthediscs.Asalreadyexplained inconnection withFig.2,thcsoliddiscwillshowthemostfavourable stresscharacteristics. | |||
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$IJltj41jSLlSIAltjFigure7illustrates thecombinedstr<<ssdistribution (aAervonMises)inaweldeddrumrotorofatypefoundinmachinesofover1000MW.Tlieboundaryconditions-outsidediameterandbladntension-arecomparable withthedesignsshowninFig.5and6,thespeedbeingtakenas1800rcv/mininallthecasesshown.Itwillbcnoticedthatwitharotorofthiskind,whichiscomposedofsoliddiscs,thcgreateststressisroughlybetween40%(Fig.5)and60%(Fig.6)lowerthanforrotorsmachinedfromthesolidorforshrunkendiscs.Thisfactwillagainbeimportant whenconsidering thechoiceofmaterialandthcburstingspeed.HPandIPRotors,Including Temperature sectsFigurc8showstheisotherms inaweldedh.p.rotorunderconditions offullload.Hereonccanseethccharactcris-ticfeatureofsteady-state operation thattheisotherms runalmostperpendicular tothcaxisofrotation, andonthebasisoftheisothermdistribution onecanpredictthatthethermalstrcsscswillbeverysmallcomparedtothe.stressescausedbyrotation. | |||
Inthisexampletheyinfactamounttoonlysome5to10%ofthemechanical stresses. | |||
Incontrasttothecoldlow-pressure section,thcmechani-caldesignofrotorsexposedtohightemperatures in-cludestheirbehaviour inrelationtotime.Becauseofcreepphenomena, whichwillbediscussed inmoredetailinthenextsection,thematerialagesinthecourseoftime.Thisageingprocessisafunctionofthematerial, temperature andstress,aswellastime,andtherefore inordertoassessthesuitability ofadesignonemustknowalltheseparameters, i.e.-thebehaviour ofthematerialasafunctionofloading,temperature | |||
: andtime, Fig.7-CombinedstressIIelaweldeddrumrotorasshowninFig.IcValues20to28ltgf/mme. | |||
I20I/+2gI0002026-thcisothermdistribution intherotor,and-thestressesintherotor.Anexampleofadetailedstudyofahigh-pressure bladefixingisshowninFig.9.Usingphotoelastic techniques, theedgestressesinthelateralgroovesaredetermined underdiFerentloadsandaddedassupplementary in-formation totheresultsofarefinedstresscalculation (Fig.9).Inthisway,togetherwithallowance forthebehaviour ofthematerialandstringent production quali-tycontrol,itispossibletoguarantee theperformance oftherotorovermanyyears.TheRotorIVlaterial High-Pressure andIntermediate-Pressure RotorsTherotorsofmodernlargesteamturbinesare,alloffcrriticmaterial. | |||
Thisisrelatedtothefactthatforconventional planttheworldoverthelivesteamtempera-turehasbecomeestablished at538'C.Withthismaterialonecanexpectgoodlong-time properties, nosoftening, littlecreep,uniformheattreatment, adequatelong-term ductility, lownotchsensitivity andgoodresistance toscale.Nuclearpowerstationsatpresentdonotraiseanyproblemsoftemperature becausetheturbinesrunonsaturated steam,andeventhehigh-temperature reactorsforlargepowerstationswillnotexceedthelivesteamtemperature ofconventional plant,atleastinthenearfuture.Figurcl0showstwotypicalrotorsteels[11]usedforh.p.andi.p.turbines. | |||
Toallowinternationally consistent comparisons, thelong-time rupturevaluesforl00000hoursaretakenasabasisformechanical designpur-poses.Thefollowing remarkssurveybrieflythebehaviour ofrotormaterials underthcinfluence oftemperature, stressandtime.Ifatestbarissubjected toaloadattandatthcsametimeatemperature Te,itwillintimeundergoplasticelonga-tion(creep)andfinallybreak.Forthesameloadingthebarwillfailearlierwithahighertesttemperature Tt)Tethanwithalowertemperature. | |||
Fig.g-Isothermdistribution inaweldedh.p.rotor450$005I0'C460'00I10 IItiIafig.9-Combinedstressesinthegroovesofh.p.bladeAxing'theAguradenotethevonMiscscombmcdstressmltgtimms. | |||
rI3500'C505C5IOCslsCThecreepprocessisillustrated inFig.Il.Wecandistinguish threemainphasesofcreep;primary(I),secondary (II)andtertiary(III),inwhichthebarrapidlyreachesbreakingpoint.Allhigh.pressure andinterme-diate.pressure rotorsoperatewithinthesecondary phase,andthedesignerhastomakesurethathisdesignhasanadequatereservewithrespecttothetertiarystage.Inthesecondary phasetherateofcreepi~de/dtisconstant, whichinpracticemakesiteasiertoassesstherotorafteralongperiodinservice.Everytimetheturbineisinspected, specially providedcontroldiameters aremeasuredandtheresultscomparedwithmeasurements ofpreviousyears.Here,'however, accountmustbctakenofthefactthatthccreepratewithinadiscvarieswidelyfrominsidetooutsideowingtovariations inthestress.-I.ong-time tionofsteels24fig.loeomposifnptUrecnrvcsCrMov55andeeainhgrtmmsandchemicalLo~~pressure Rotors2lCrMov5II70605040pelt'02520IO9g1654IO2ICrMoV5lloooiso.24CrMoV55io'O<<ho~J~Whereasforhigh-temperature conditions thenumberofdiHcrentrotormaterials usedbythevariousmanufac-turersislimited,theselection ofmaterials forlow-pressurerotorsismuchwider.Thisisnotallthatremarkable whenoneremembers thevarietyofl.p.rotordesigns,becausethematerialisprincipally matchedtothedill'erent stressconditions oftheindividual typesofconstruction. | |||
Furthermore, becausetheserotorsareessentially cool,thefactorsgoverning thechoiceof'material willonlybetheyieldpoint,ultimatestrength, elasticlimitandnotchtoughness. | |||
Hereitisassumedthattherotoroperatesintheupperpartofthenotch-toughness range,i.e.thcfractureappearance transition temperature isbelowthcoperating temperature. | |||
: Recently, andnottheleastofthcreasonsbeingseveralcasesofexplosive failureofsolidandshrunkMisc rotors,whichalsoextendedtonuclearstations[IOJ,therehasbeenatendencytobasethechoiceofmaterialonadditional criteriainordertoavoidsuchinstances ofbrittlefracture. | |||
Forthis,therotorisconsidered fromthestandpoint offracturemechanics, theaimbeingtoarriveatappropriate valuesofcrackresistance andrateofI05propagation forsubcritical crackgrowthWithoutgoingintothefundamentals offracturemechanics | |||
-thesubjectIO rt)rort)ro//rtrconst.0/dl)do/zroIOltNIfig.1I-CreepcurvesfordifFerent temperatures andloads(schematic) failureofallcontrolandsafetysystems.Inthishypothet-icalsituation, rejection oftheelectrical loadwouldcausetherotorspeedtorunaway,possiblyresulting inex-plosivefailure.Ourownstudieshaveshownthath.p.andi.p.rotorshaveamuchhigherburstingspeedthanI.p.rotors.Thereasonforthisisthatthehighandintermediate-pressure rotorsstretchradiallylessthanthelow-pressure rotors,andwhilethematerialcharacteristic governing burstingistheyieldpoint,h.p.andi.p.rotorsaregenerally designedtowithstand long-time failure.Sincethevalueforlong-timefailureisonlyafractionofthecorresponding yieldpoint.depending onthetemperature, theserotorshavealargerreservewithrespecttotheburstingspeedthandoI.p.rotors.Inordertostudythebehaviour ofdiFerentdiscdesignsinrelationtotheburstingspeedwcagainusethediscofuniformwidthasastartingpoint.Grammelhasshown[14)thatthemeantangential stressinthediscissuitableasameasureoftheresistance toexplosive failure.Themeantangential stresstrtMisgivenbyrscrtdr(16)istreatedin(12)and[13),forexample-itshouldbementioned thatthisaspectofmechanics wasoriginally evolvedforhigh-strength, relatively brittlematerials. | |||
However,itisonlysuitablefordescribing acrackwhichalreadyexists,andtakesnoaccountoftheactualforma-tionofthecrack.Atthesametimeitshouldnotbeforgotten thatturbinerotorsconsistofductilematerials whichhavetheability,ifneedbe,tofiowlocallyanddispersestresspeaks,thuspreventing cracksfromform-ing,oratleastgreatlydelayingtheironset.Itcan,ofcourse,happenthatthereissomejustification f'rexamining arotorfromafracturemechanics view-point.Thiswillalwaysbesoif,becauseofthehighlevelofdiscstresses, onehastoresorttohigh-strength materials orwhen,asinthecaseofsolidlow-pressure rotors,thelargedimensions, makeitverydifficult todetectfaultsinsidetheforging.Itmaythenbeofadvantage toassumeafaultofacertainsizeinacertainpositionandchecktoseewhattheconsequences mightbeinthecourseoftime.crtÃ-fsrtandcanbewrittenindimensionless formasfollows:n8trtdrgrestos(3+t)StMfs-rt(17)(18)'heratioofthcburstingspeedsofperforated disctosoliddiscisthendescribed byFortrtwethenuseEq.(3)forasoliddiscandEq.(5)foraperforated disc.Ifwenowwritetheratioofthemean,tangential stressStwr,oftheperforated disctothemeantangential stressStlvofthesoliddisc,wehaveBurstingSpeed<BRLirBRVI+-+(19)Inrecentyears,andinitially attherequestoftheUSAtomicEnergyCommission, manufacturers oflargetur-binesfornuclearpowerplanthavehadtoanalysetheextentofdamagetotheturbosetintheeventoftotalEquations (18)and(19)areshowngraphically iriFig.I?Asexamination willquicklyshow,forrt(rs~Itheywillofcourseprovidetheburstingspeedratioforthethinring. | |||
2,0l,gesax,SetsasarSoirl.g1,2Vgl.oO,gheal.I/1(l+-"+(-,"j',600,20.40,6rtPsFig.lz-Ratiosofmeantangential stressandberatingspeedlorperforated andsoliddiscsFigure13showsinqualitative termsthebehaviour oftwodiff'erent I.p.rotorconstructions atelevatedspeed.Forthesamesize.bladetensionandoperating speed,thctangential stressforthedrumrotorwillfollowcurveI.Thesameappliestothediscrotor,butatthcborediameterchosenthisrotorshowsastressroughlydoublethatofthcdrumrotor.Intheelasticregionthereisproportionality betweenthestressandthesquareofthespeed.IfthespeedisraisedrelativetothenormalspeedbyafactorofI4,forexample,thestressesincreasebyafactorof196(curve2).Theinnerportionofthcper-forateddiscisthenalreadybeyondtheyieldpoint,andthecorresponding zonerelaxes.Owingtoplasticdeformation, therefore, theelasticcurve2giveswaytocurve2'ndthcpartsofthediscwhicharestillelasticarcthussubjected toadditional, stress.According towhathasbeensaid.sofar,ameasureofthercscrvewithrespecttofractureistheratioofthe.yieldpointtothemeantangential stress,i.e.essentially. | |||
theareainFig.13contained betweencurvesIandtheyieldpoint.Therootofthisarearatiorepresents the.relationship oftheburstingspeedofthctwodesignsshowninFig.13.Ifonewishestocompensate thedisadvantage ofthelowerfracturespeedofaperforated discbyusingmorehighlytemperedmaterial, theincrease-inyieltIpointrequiredforaperforated disccanalsobe.foundwithEq.(18)(Fig.12).Itcanbcseenthatwiththeradiusratiosoccurring inpracticeitisdifficult toachieveaperforated discofsuchaqualitythatitisequivalent toasoliddiscasregardsitsburstingspeed.Thiswouldmeanhigh-strength materialhastobeused,withtheconsequent higherriskofbrittlefracture. | |||
Fig.ls-Behaviour oftteotypesofI.p.rotorat<<leratedspeed~tdidi2ldldiPaOutlookAsmentioned earlier,theunitcapacityoflargesteamturbosets willcontinuetoriscinthcforeseeable future,andhence.influencc thedemandsmadeoftherotors.Adecisive, andtosolneextentlimiting, factoroverthepastdecadewasthefinalstage,whichifthevacuumwasgoodhadtohandleenormousflowvolumes.Allmanufacturers ofsteamturbinestherefore carefully developed longerfinalbladesandintroduced thesetothemarket.Butlongerbladesalsomeansalargerrotordiameter, accom-paniedbyhighercentrifugal loadingsonbothbladesandrotor.Tokeepstressesbelowthelimit,thespeedofthemachineswashalved.Thetechnique employedintheUSAwastorunthchighandintermediate-prcssure sectionsatthcfullspeedof3600rev/min,andcombinethelow-pressure unitswitha4-polegenerator onasecondshaftstringrunningat1800rev/min.Europelateradoptedtheideaofthehalf-speed machine,althoughin12 single-shaft formandonlyfornuclearplant.Byhalvingthespeedinthisway.andatthesametimedoubling, thesize,thestressesinfull-speed andhalf-speed machineswerekeptthesame,butthecorresponding exhaustareaofthefinalbladesincreased fourfold. | |||
Afeatureofrecentyearshasbeenagrowingworldwide shortageofcoolingwater[15].Intheindustrialized countries, andtheseifonlybecauseoftheir.powerdistribution networksarethepotential buyersoflargemachines. | |||
itisbecomingnolongerpossibletouscfreshwaterforcoolingpurposes. | |||
Futurelargepowerstationswilltherefore beequippedmainlywithwetordrycoolingtowers.whichmeanstheturbinevacuumwillberclativcly poorandthesteamexhaustvolumecorrespondingly smaller.ItmaythuswellbethatthefinalbladelengthsandI.p.rotordimensions customary todaywillbeade-quateforsometimetocome,withoutbeingtiedtohalf-speedI.p.sectionsbecauseofthcstresses, evenwithlargecapacities. | |||
Itislikelythatlargemachinesfornuclearpowerstations, withpoorvacuum,willalsobebuiltforfullspeedandstillbeabletocopewiththcstressesinthebladesandrotor.Thepossibility ofmakingtheI.p.rotorrelatively smallalsoimprovesthechancesofthesolid-rotor designtosomedegree.Greatadvancesinforgingtechnology havebeenmadeoverthepastfewyears,andthishasincreased confidence intheuseofforgedone-piece shafts.Finishedweightsofover200thavebeenachievedtodate.Theserotorsrequireaningotweighingmorcthan400tandwiththeassociated riskscanbeproducedonlyinJapanandtheUnitedStates.Itisimprobable thatthesteel-workswillcontemplate afurtherincreaseinrotorsize.withthecorrespondingly heavyinvestment neededtodealwithlargeringots,becausethemarketfortheselargeforgingsistoorestricted. | |||
Theconceptofthelargeone-piecerotorcantherefore beextrapolated intothefuturetoonlyalimitedextent.Thcsituation isslightlydifferent forthehigh-pressure section.Ontheassumption thatfuturenuclearpowerstationswillalsooperatewithsteamconditions suchasarefoundtodayinconventional plant(I50to250bar,538'C),theverysizeoftheI.p.rotorcouldpresentastressproblem.Overcoming thiscanbeapproached intwodifferent ways:thematerialandthedesign.Thereisnolikelihood inthenearfutureoffindingadifferent materialforh.p.rotorswhichhassubstantially betterlong-term properties anddoesnotforfeittheadvantages ofthelowalloysteelsusedatpresent.Muchmoreprobableisthatstressesintheh.p.rotorcanbekeptincheckthroughsuitabledesign:thelargesteamturbinetodayisquiteclearlyfollowing thcpathtakenmanyyearsagobythegasturbinetowardscoolingtherotorbymeansofsteam.ThedesignerthushasathisSymbolsF.=Modulusofelasticity L=Perforated discS<---Dimensionless radialstressSi=Dimensionless tangential stressSist=-Dimensionless meantangential stressSv~Dimensionless equivalent voltageT=Tempcraturc U=Radialdisplacement V=Soliddisca=Thermalconductivity c=Specificheatofrotormaterialnnn=.Burstingspeedr=Considered discradiusri=Innerradiusofperforated discri--Outerradiusofdischr=Degreeofshrinkage du-~Relativedegreeofshrinkage tir~Timee<--Radialexpansion | |||
=Tangential expansion | |||
=Conductivity ofrotormaterial~Transverse contraction ratio=Specificmassofdiscmateriale<=Radialstresse<i=Shrinkage forcee~=.Bladetensionappliedatradiusrs(ri%std!COOPyp4Tangential stress=Meantangential stressovermeridional areaofblade=Axialstressesinrotor=Angularvelocityofrotation=Overspeed | |||
=Lift-offspeedIndicesWS0=Centralshaft=Disc=Standstill disposaladesignconceptsufficientl flcxibletoallowhimanadequatemarginofsafetyindesigning rotorsforthehigh-pressure sectionasunitcapacities continuetorisc.13 Bibliography | |||
[I]A.LNhyrSomeadvantages ofweldingturbinerotors.Weld.J.June1968.[2]C.B.Bienzeno, R.Grammel:Technische Dynamik,vol.II,Springer1953.[3]W.Traupel:Thermische Turbomaschinen, vol.Il,Springer1960.[4]K.Lofter:DieBcrechnung vonrotierenden ScheibenundSchalen.Springer1961.[5]A.Bald:Besonderheiten grosserNassdampAurbo-sgtze.Mitt.Vereinig. | |||
Grosskesselbesitzer S21972(4).[6]0.C.Zleriklewlczr Thefiniteelementmethodinstruc-turalandcontinuum mechanics. | |||
McGraw-Hill, London1967.[7]B.BaulerDieMathematik desNaturforschers undIngenieurs, vol.IV.Hitzel1952.[S]H.Lelpholz: | |||
Festigkeitslehre furdenKonstrukteur. | |||
Springer1969.[9]H.D.EnunerrInvestigation oflargeturbinespindlefailure.ASMEPaper55-A17?[IO]D.Calderonr StcamturbinefailureatHinkleyPoint.Proc.Inst.mech.Engrs186.[II]StghtefQrgrQssereSchmiedestQcke (GQtevorschrift). | |||
Stahl-Eisen-Werkstoffblatt 550-S7.[12]K.Hecke/:EinfQhrung indietechnische Anwendung derBruchmechanik. | |||
Hanser1970.[13]D.Radaj:Grundlegendc Beziehungen derlincar-elastischen Bruchmechanik. | |||
Schweissen u.Schneidcn 231971(IO).[14]R.Grammel:DieErklarung desProblemsderhohenSprengfestigkeit umlaufender Scheiben. | |||
Ingenieur-Archiv 161947(I).[IS]H.Flohn,D.Hensehler, H.Schuller: | |||
"DerWasser-haushaltderErde.Aus:MenschundUmwelt.Tech.Rdsch.641972(47).14 | |||
SICBROWNBOVERIBBCBrown,Boveri5Company,Ltd.CH-5401Baden/ | SICBROWNBOVERIBBCBrown,Boveri5Company,Ltd.CH-5401Baden/Switzerland printedInswiuorlsnd (74e41000.0)Casahcation Na01010}} | ||
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BBCBROWNBQVERIRotorsorLargeSteamTurbinesPublication No.CH-T060053E RotorsforLargeSteamTurbinesA.HohnAstheunitcapacityofsteamturbosets Increases, sotoodoesthesfseoftherotor,andhencealsothestressesappliedtoit.Thevariousdesignsofrotorarediscussed andresultsofstresscalculations given.Rotormaterials areconsidered briefly,followedbycommentonthefuturedevelopment ofrotordesignforlargesteamturbines.
RotorConfigurations Thedesignscurrenttodayarerestricted totheformsshowninFig.l:-Diagramashowstworotors,eachproducedfromasingleforging.-Shrinking discsontoacentralshai?whichtransmits thetorquegivesrisetothecomposite construction ofdiagramb.-Indiagramc,separatediscshavebeenweldedtogethertoformadrum.typerotor[I],Eachconfiguration hasitsownadvantages anddisad-vantagesasregardsproduction ofthe'teel, heattreatment, machining andtesting,butthesewillnotbedealtwithspecifically here.Distinctive differences inthematterofstressesareconsidered inthefollowing
'twosectlolls.
StaticsofRotorsundertheInfluence ofSpeed,DiscGeometryandTemperature TheDiscundertheinfluence ofRotationintroduction Steamturbinestodayareremarkable particularly fortheirsize:unitcapacities ofmorethanl000MWarenowtobefoundbothinconventional powerstationswithfossil-fuelled boilersandalsoinnuclearpowerplant.Foranumberofreasons,unitcapacities willriseevenfurtherinfuture,anditwouldbcpremature atthemomenttospeakofanylimit.Machinesofthissizerepresent asubstantial financial commitment andinthceventoffailurecauseseriousdisruption ofthepowersupplytobothdomesticandindustrial users.Itistherefore under-standable thatthemanufacturer ofsuchmachinesdoesasmuchasthelateststateofthetechnology willallowinordertoensurethattheselargemachinesarereliableinservice.Thisarticleisconcerned withtheheartofthemachine,therotor,andreference ismadetothevariousrotordesignsandthedifiercnces betweenthem.Fulltreatment ofthesubjectwouldhavetoincludethcstaticbehaviour insteady-state operation andundertransient conditions, andalsothedynamicsoftherotorundertheinfluence oftheflowofsteam.This,however,wouldgobeyondthcscopeofanarticle,andtherefore themainfocusofattention hereisonsteady-state operation whichatalleventsconstitutes thebasisofthemechanical design,andonwhichallotherphenomena arcsuperimpose*
Csticot(3-.')o~Ci~a8Disregarding anyexternaltensionforthctimebeing,thecurvesofradialandtangential stressarefoundtobeasfollowsfor:a.asoliddisc:t.~'(3+v)(..8(2)Alldesigners ofturbomachines usethcrotatingdiscinoncformorthcotherasabasiccomponent oftherotor.Thefollowing remarksontherotatingdisc,whicharcofanelementary natureandcanbepursuedfurtherin(2,3,4]forexample,aretherefore applicable toall,withaccounttakenoftheboundaryconditions particular toaspecificdesign.Iftheequilibrium offorcesintheradialdirection istakenonarotatingdiscelementofconstantthickness, al-lowanceismadefortherelationship betweenradialandtangential expansion inthcdiscandHooke'slawforbiaxialstressisintroduced, weobtainthediflerential equationofthe'rotating discintermsofa<withthegeneralsolution:
dandsincecrt=-(rrtr)+(2r'o'l'2cos(3~<<)/I+3<<2rt~rr'Z8(3+.b.aperforated disc:(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.Toillustrate moreclearlythemutualinfiuences ofradialandtangential stress,Fig.2alsoincludesthedimensionless comparative stressSvonthcassumption ofconstantworkofdeformation, thus:;-y;*+;*-;.,
utldSv~8clv(2rs'o'3+2)FromFig.2wccandrawafirstconclusion:
Inordertoshowequations (2)to(5)ingeneralformtheyaremadedimensionless withthestressprevailing attheForthesamedimension (rs),thesamematerial((2)andthcsamespeed(co),theperforated discwillexhibitaFig.I-Dlirerent typesofrotorconstruction Fig.2-Dimensionless radial,tangential andcombinedstressesol'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.Ameasureofthisisthemeantangential stress.Thisresultalsoremainsessentially unchanged whentheadditional loadscausedbybladetension,steampressureandshrinkage aresuperimposed ontherotational StreSseS.Theconsiderations presented sofararesuFIcient fordetermining therotational stressesinthecaseofasoliddisc.Fortheperforated andshrunk-on discofFig.lb,however,deformation alsohastobetakenintoaccount,owingtothediFerentstiffness ofthecentralshaftandthedisc.Onlythencanoncdefinetherequireddegreeofshrinkage, whichinturnhasaninfiuence onthechoiceofmaterial.
Deformation Affecting thePerforated DiscHerewecanagainstartfromEq.(I)anddetermine theintegration constants C<andCtappropriate totheboundaryconditions.
Withthcaidofthccalcuhted stressesitispossibletodetermine theradialexpansion, andhencealsothcradialdisplacement UforanyradiusofthecentralshaAoroftheshrunk-on disc.Ofparticular interestaretherelativedisplacements UtofshaAanddiscatthepointofattachment withradiusr1.Thcresultofconsidering deformation inthiswaycanbcreadfromthcTable.Thus,anyexpansion ofdiscorshaAisproportion-altotheforces.artandarswhichcauseit.Thereisasquare-law relationship betweentheexpansion androta-tionru.Hereitmustbcnotedthatfordifferent speedsthcexternaltensionarsalsovariesasthesquareofthespeed.Theshrunkwnbodyhastosatisfythefollowing condi-tions:atthepointofcontactbetweendiscandshaAatradiusrtthesumofdisc,expansion andshaltcompres-sionmustequalthedegreeofshrinkage du,i.e.rtw-rtsUtw+UtsWiththisitisnowpossibletoconstruct a"springdiagram"oftheshrunkjoint(Fig.3),andwithinthistherelativedegreeofshrinkage hrjrcanbcdetermined foragivengeometry(rt,r1)andadesiredshrinkage forceo<t.Thcshrinkage forceischoseninthelightofthetwofollowing points:-Expansion ofthediscduetorotationmayonlybelargeenoughto<<nsurethatapositivefixingismaintained whenrunatoverspeed (normally l2xoperating speed),i.e.thediscmustnotcomeloose.Publications bymanufacturers ofthistypeofconstruction indicatethattheliAwFspeed(zero-shrinkage) liesapproximatefy 35%abovethenormaloperating speed[5).-Itmustalsobeascertained whether,atnormaloperat-ingspeed,thcshrunk-on discisf'ullycapableoftrans-ferringthcbhdetorquetothccentralshaft.Generally
- speaking, thisrequirement isalwaysmetiftheoverspeed condition issatisfied.
Ourconsiderations regarding theshrunkwndisccanthusbcsummarized asfollows:Atstandstill thediscisstretched becauseitwasundersize whenfittedon-theshaft,andtheshaAiscompressed bythcshrinkage.
Owingto'tsownrotationandthetensileforceexertedbythebladesthediscexpandsmorethanthecentralshaft.Theshrinkage forceisthusreduced.Aresidualdegreeofshrinkage mustberetainedwhentherotorisrunatovcrspeed.
Expansion ofshaftanddiscShrinkagforceRotationExternaltensionNON>I~8)B)COmruii(tt1)er1icu'(I
-r)riJuan,4aDiscriix(I-r)+-(I+r)r11I'iiX[-(S+r)+(I-rtrli Figurc3showstheserelauonships forstandstill (co=0),operating speed(co),overspeed (co~co')andliftofspeed(co'I35co)foradiscofuniformwidthwitharadiusratioofrr/ri~3.Inthisdiagramthcelasticity properties ofthediscandthccentralshafthavebeendetermined inaccordance withtheTable.Ontheabscissathcpointoforiginisthedesireddegreeofshrinkage
(&/ri)o,whichisselectedaccording totheresidualshrinkage (ordinate) desiredattheoverspeed condition.
Theindividual com-ponentsofthediscandshaftexpansion duetorotationandexternaltensionorehavealsobeentakenfromtheTable.Inordertoestablish theorderofmagnitude ofthecompressive forcesoriinvolved, andalsotheresidualshrinkage, thediagramwascompiledusingrealistic conditions suchasoccurinthecaseofI.p.rotorsforhalf-speedsteamturbines:
n1500rev/min,equivalent toco=157s-',overspeed co'12co;bladetensionerisbeingtakenas8kgf/mrnaatthenormaloperating speed.Theresidualshrinkage foranyspeedscanbeobtaineddirectlyfromFig.3bymeansofthcfollowing conversion fromthestationary shrinkage diagram.Thebasicprin-ciplesofthisareexplained in[6].octE2,$~IO32,0I,OO,SI2Uisps34IUswrIUsripgWehave:(9)Sincetheresidualshrinkage duatoperating speedcoisgivenbyco~0(10)fortheresidualshrinkage weobtainI-co~cu'II)Fig.3-Shrinkage diagramforshrunkendiscsunderdlirereni operating eondiiions ThusitcanbeseenfromFig.3thatanextremely largedegreeofshrinkage (415x10-')isnecessary toachievealift-offspeedofco'I35co,takingintoaccountthebladetension.IffortheexampleinFig.3ithadbeenstipulated thatliiboffistooccurat135%ofoperating speedwithoutallowance fortheexternaltensionetre(i.e.withoutblad-ing),thiswouldresultinthestandstill shrinkage diagramshownbythebrokenlineinFig.3,withastandstill shrinkage of26x10-s.Inthiscase,however,thebladedrotorwouldloseitsresidualshrinkage evenatsmalloverspeeds (9%inthisinstance),
owingtothebladetension,andsomemeanssuchaskeyswouldbeneededtopreventthediscfromslipping.
Thereserveofspeeduptoliftwifmentioned hereisdetermined bythcresidualshrinkage obtainedwithEq.(11).influence ofDiscGeometryTheabovestatements areofafundamental natureandaidone'sunderstanding whencomparing dificrent designs.Butinpracticetheshrunk-on discisnotofconstantwidth.Thediscmeridianwilltherefore beshapedinsomeway,itwillbeformedtoyieldadiscofuniformstrengthortheperforated discwillbegivenahyperbolic meridiansimilartoy=c/rn,inordertomakethebestpossibleuscofthematerial.
Thisthenresultsinamoregentledisccharacteristic thanshowninFig.3,andhenceinareduction ofthenecessary shrinkage force.Buthere,too,averytightshrinkfitwillstillbeneededforagreatvarietyofdiscmeridianshapes,whichisonereasonwhyhighlytemperedmaterials arechosenforthediscs.Thereareanumberofmethods(e.g.[2])forcalculating thestressinadiscofanytechnically feasiblecontour.Themethodoffiniteelementshasrecentlycometobeusedforthispurpose,evengoingtotheextentofnotonlydetermining thestressconditions intheindividual parts(discs)oftherotor,butalsoofconsidering therotorasanentityandtakingintoaccounttheinteractions be-tweenneighbouring partsofthediscs.Averygoodoverallinvestigation oftherotorisalwayspossiblewiththemethodoffiniteelements, thefundamentals ofwhichcanbcfounddescribed in[6].Detailedinvestigations, FISA-Grid forcnlcttlctinsttretics RInttnllnnI.p.rotorhythe5nhedctncntmethodl3~tol2CIC'4/>"inInjfuenee ofTemperature Undernormaloperating conditions therotorsoflargesteamturbinesarcingeneralexposedtoasteady-state temperature field:afterstart-upandsettlingdowntonormalloadanisothermal distribution becomesestab-lishedintherespective rotorswhichvariesonlyslightlyinresponsetomoderateloadfluctuations.
Aknowledge oftheisothermdistribution intherotorisnecessary fortworeasons:-first,oncneedstoknowthelocaltemperature inordertocomparethclocalstresspresentwiththecharacteristic ofthcmaterial(e.g.long-time strength) validatthislocaltemperature,
-second,theisothermal condition givesrisetoastressfieldwhichitmaybeimportant tocalculate forthetotalloadingonthcrotor.Thismisesthequestionofhowonedetermines theisothermdistribution intherotor.Basically thisisaproblemofthermalconduction P]inarotationally symmetrical bodydescribed bytheFourierequation-~arhTaTar(12)suchasintheslotsofbladefixings,needmorerefinedcalculation appliedoveraveryfinegrid,whiletheaidof.photoelastic techniques mustbcenlistedforassessing thesurfacestressinthcgrooves.Inthismanneronecanaccountforallthestresscomponents involved.
wherea'tr(l3)-Thcisotherms intherotorarefoundwiththeaidofanelectrical analoguemodel,inwhichcasethcrotational symmetryoftherotorisaccounted forbyselecting suitableresistances (perforations) onthetwMimensional model.Theconduction ofanelectrical currentthroughabodyisdescribed bytheequationaU-~-hUatc(l4)andisthusanalogous totheheatconduction equation(l2).Here,Uistheappliedvoltage,Ctheelectrical capacitance andxthcelectrical conductivity ofthcmaterial.
LinesofequalvoltageU,orequalpotential, arcananalogueoftheisotherms T~constant.
-Anotherpossiblewayofdetermining thctemperature distribution intherotoristosolvetheheatconduction equationbynumerical methods.Thispossibility hasgainedgreatlyinsignificance inrecentyearswith.theuscBeforesettingaboutsolvingthisequationonemustknowtheboundaryconditions, e.g.surfacetemperature, heatsuppliedandremoved.Inpractice, therotorgeometrydoesnotfollowasimpleshapeandthetemperature distribution atthesurfaceiscomplex,owingthecoolingeKectofthestcam.Con-sequently, onecannotexpectacompletesolutiontotheheatconduction equation.
Therearenevertheless twopractical waysofsolvingthisproblem:
Fig.S-VonMlscs'combined ttrcssMdofthatoUdIp.rotorshownlaFig.taValues20to47it//mm~.-.~20.~3timmi100020'-II4740offiniteelementsforcalculating stress.Onehasthcadvantage thattheresultsofcalculating temperature inthiswaylieonthesamelatticeasthesubsequent stresscalculation, andthuscanbeusedasadirectinputforcomputing thetermalstress.Finally,asregardsdetermining theisotherms itmustbesaidthatwithoutthcsubsequent stresscalculation itwillalwaysbefragmentary andyieldonlymoderately usefulinformation.
Practical ResultsofStressCalculations Rorarlonal StressesinDig@rentLPRotorDesignsThediscussion intheprevioussectiononstresscalcula-tioninrotorsofdifferent constructions isnowillustrated belowwiththeaidofafewpractical examples.
Figure4showsthcgridimposedonaI.p.rotorfordetermining themechanical stressesbythefiniteelementmethod.AllthebasicdesignsdepictedinFig.Iwerccalculated inasimilarmanner.Whencomputing thestresses, thespeedandbladetensionwerekeptconstantforalltypesofrotor.Shape,dimen-sions,speedandbladetensioncorrespond tovalues'oundinpractice.
Figure5illustrates thccomparative stressfieldforaI.p.rotormachinedfromthesolidasshowninFig.Ia.Herethecomparative stresshasbeentakenasaccording tovonMiscs:av~~(ar-at)'+(at-az)+'(ar-ar).'arr'15)
Itwillbeseenthatowingtotheabruptchangeofcross-sectionfromthecentralshahportiontothcdisc,stressconcentrations ashighas31kgf/mmeoccur.Stresscon-centrations ofthiskindarealwaystobefoundwhentheforcefieldisdisturbed asaresultofchangesincross-section.Fig.5alsoshowsthestresslevelatthcinnerbore,witharadiusratioofrt/rs~015.At47kgf/mm thestresshercreachesaveryhighvalue,althoughitisstillalwaysbelowthatofshrunkendiscs.Resultsofcalculating thestressesinshrunk-on discsarcshowninFig.6.Owingtothelargercentralborefortheshaftamuchhigherstressof68kgf/mm'sfoundhere,other-wisetheconditions arethesameasinFig.5.Atthetransition fromthcslimpartofthedisctothebroadoutershoulderonecanagainseeastressconcentration inthecornerofthedivergence, attaining localvaluesof70to80kgf/mmeandcausedchieflybydisruption oftheradialstresspattern.Atechnique oftenusedinthepastwastosecuretheshrunk-on discswithextrakeys.Thisinevitably givesrisetostressconcentrations inthekeywaywhichinthemostfavourable casehaveastressconcentration factorofaboutthree.Whatthismeanswiththehighbasicstresslevelofaperforated disciseasytoappreciate:
fromthcstartaplasticzonewillformroundtheslotwhich,ifthcproperties ofthematerialarelessthanideal,canleadtocrackingandhencetofailureofthediscwhenitisrotating.
Sufficient instances ofthishaveunfortunately occurredinthepast[9,IO).Inordertomeetthestandards, ofreliability requiredinpowerstations, there-fore,itisessential thatnokeysofanykindshouldbcprovidedasanextrameansofsecuringthediscs.Asalreadyexplained inconnection withFig.2,thcsoliddiscwillshowthemostfavourable stresscharacteristics.
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$IJltj41jSLlSIAltjFigure7illustrates thecombinedstr<<ssdistribution (aAervonMises)inaweldeddrumrotorofatypefoundinmachinesofover1000MW.Tlieboundaryconditions-outsidediameterandbladntension-arecomparable withthedesignsshowninFig.5and6,thespeedbeingtakenas1800rcv/mininallthecasesshown.Itwillbcnoticedthatwitharotorofthiskind,whichiscomposedofsoliddiscs,thcgreateststressisroughlybetween40%(Fig.5)and60%(Fig.6)lowerthanforrotorsmachinedfromthesolidorforshrunkendiscs.Thisfactwillagainbeimportant whenconsidering thechoiceofmaterialandthcburstingspeed.HPandIPRotors,Including Temperature sectsFigurc8showstheisotherms inaweldedh.p.rotorunderconditions offullload.Hereonccanseethccharactcris-ticfeatureofsteady-state operation thattheisotherms runalmostperpendicular tothcaxisofrotation, andonthebasisoftheisothermdistribution onecanpredictthatthethermalstrcsscswillbeverysmallcomparedtothe.stressescausedbyrotation.
Inthisexampletheyinfactamounttoonlysome5to10%ofthemechanical stresses.
Incontrasttothecoldlow-pressure section,thcmechani-caldesignofrotorsexposedtohightemperatures in-cludestheirbehaviour inrelationtotime.Becauseofcreepphenomena, whichwillbediscussed inmoredetailinthenextsection,thematerialagesinthecourseoftime.Thisageingprocessisafunctionofthematerial, temperature andstress,aswellastime,andtherefore inordertoassessthesuitability ofadesignonemustknowalltheseparameters, i.e.-thebehaviour ofthematerialasafunctionofloading,temperature
- andtime, Fig.7-CombinedstressIIelaweldeddrumrotorasshowninFig.IcValues20to28ltgf/mme.
I20I/+2gI0002026-thcisothermdistribution intherotor,and-thestressesintherotor.Anexampleofadetailedstudyofahigh-pressure bladefixingisshowninFig.9.Usingphotoelastic techniques, theedgestressesinthelateralgroovesaredetermined underdiFerentloadsandaddedassupplementary in-formation totheresultsofarefinedstresscalculation (Fig.9).Inthisway,togetherwithallowance forthebehaviour ofthematerialandstringent production quali-tycontrol,itispossibletoguarantee theperformance oftherotorovermanyyears.TheRotorIVlaterial High-Pressure andIntermediate-Pressure RotorsTherotorsofmodernlargesteamturbinesare,alloffcrriticmaterial.
Thisisrelatedtothefactthatforconventional planttheworldoverthelivesteamtempera-turehasbecomeestablished at538'C.Withthismaterialonecanexpectgoodlong-time properties, nosoftening, littlecreep,uniformheattreatment, adequatelong-term ductility, lownotchsensitivity andgoodresistance toscale.Nuclearpowerstationsatpresentdonotraiseanyproblemsoftemperature becausetheturbinesrunonsaturated steam,andeventhehigh-temperature reactorsforlargepowerstationswillnotexceedthelivesteamtemperature ofconventional plant,atleastinthenearfuture.Figurcl0showstwotypicalrotorsteels[11]usedforh.p.andi.p.turbines.
Toallowinternationally consistent comparisons, thelong-time rupturevaluesforl00000hoursaretakenasabasisformechanical designpur-poses.Thefollowing remarkssurveybrieflythebehaviour ofrotormaterials underthcinfluence oftemperature, stressandtime.Ifatestbarissubjected toaloadattandatthcsametimeatemperature Te,itwillintimeundergoplasticelonga-tion(creep)andfinallybreak.Forthesameloadingthebarwillfailearlierwithahighertesttemperature Tt)Tethanwithalowertemperature.
Fig.g-Isothermdistribution inaweldedh.p.rotor450$005I0'C460'00I10 IItiIafig.9-Combinedstressesinthegroovesofh.p.bladeAxing'theAguradenotethevonMiscscombmcdstressmltgtimms.
rI3500'C505C5IOCslsCThecreepprocessisillustrated inFig.Il.Wecandistinguish threemainphasesofcreep;primary(I),secondary (II)andtertiary(III),inwhichthebarrapidlyreachesbreakingpoint.Allhigh.pressure andinterme-diate.pressure rotorsoperatewithinthesecondary phase,andthedesignerhastomakesurethathisdesignhasanadequatereservewithrespecttothetertiarystage.Inthesecondary phasetherateofcreepi~de/dtisconstant, whichinpracticemakesiteasiertoassesstherotorafteralongperiodinservice.Everytimetheturbineisinspected, specially providedcontroldiameters aremeasuredandtheresultscomparedwithmeasurements ofpreviousyears.Here,'however, accountmustbctakenofthefactthatthccreepratewithinadiscvarieswidelyfrominsidetooutsideowingtovariations inthestress.-I.ong-time tionofsteels24fig.loeomposifnptUrecnrvcsCrMov55andeeainhgrtmmsandchemicalLo~~pressure Rotors2lCrMov5II70605040pelt'02520IO9g1654IO2ICrMoV5lloooiso.24CrMoV55io'O<<ho~J~Whereasforhigh-temperature conditions thenumberofdiHcrentrotormaterials usedbythevariousmanufac-turersislimited,theselection ofmaterials forlow-pressurerotorsismuchwider.Thisisnotallthatremarkable whenoneremembers thevarietyofl.p.rotordesigns,becausethematerialisprincipally matchedtothedill'erent stressconditions oftheindividual typesofconstruction.
Furthermore, becausetheserotorsareessentially cool,thefactorsgoverning thechoiceof'material willonlybetheyieldpoint,ultimatestrength, elasticlimitandnotchtoughness.
Hereitisassumedthattherotoroperatesintheupperpartofthenotch-toughness range,i.e.thcfractureappearance transition temperature isbelowthcoperating temperature.
- Recently, andnottheleastofthcreasonsbeingseveralcasesofexplosive failureofsolidandshrunkMisc rotors,whichalsoextendedtonuclearstations[IOJ,therehasbeenatendencytobasethechoiceofmaterialonadditional criteriainordertoavoidsuchinstances ofbrittlefracture.
Forthis,therotorisconsidered fromthestandpoint offracturemechanics, theaimbeingtoarriveatappropriate valuesofcrackresistance andrateofI05propagation forsubcritical crackgrowthWithoutgoingintothefundamentals offracturemechanics
-thesubjectIO rt)rort)ro//rtrconst.0/dl)do/zroIOltNIfig.1I-CreepcurvesfordifFerent temperatures andloads(schematic) failureofallcontrolandsafetysystems.Inthishypothet-icalsituation, rejection oftheelectrical loadwouldcausetherotorspeedtorunaway,possiblyresulting inex-plosivefailure.Ourownstudieshaveshownthath.p.andi.p.rotorshaveamuchhigherburstingspeedthanI.p.rotors.Thereasonforthisisthatthehighandintermediate-pressure rotorsstretchradiallylessthanthelow-pressure rotors,andwhilethematerialcharacteristic governing burstingistheyieldpoint,h.p.andi.p.rotorsaregenerally designedtowithstand long-time failure.Sincethevalueforlong-timefailureisonlyafractionofthecorresponding yieldpoint.depending onthetemperature, theserotorshavealargerreservewithrespecttotheburstingspeedthandoI.p.rotors.Inordertostudythebehaviour ofdiFerentdiscdesignsinrelationtotheburstingspeedwcagainusethediscofuniformwidthasastartingpoint.Grammelhasshown[14)thatthemeantangential stressinthediscissuitableasameasureoftheresistance toexplosive failure.Themeantangential stresstrtMisgivenbyrscrtdr(16)istreatedin(12)and[13),forexample-itshouldbementioned thatthisaspectofmechanics wasoriginally evolvedforhigh-strength, relatively brittlematerials.
However,itisonlysuitablefordescribing acrackwhichalreadyexists,andtakesnoaccountoftheactualforma-tionofthecrack.Atthesametimeitshouldnotbeforgotten thatturbinerotorsconsistofductilematerials whichhavetheability,ifneedbe,tofiowlocallyanddispersestresspeaks,thuspreventing cracksfromform-ing,oratleastgreatlydelayingtheironset.Itcan,ofcourse,happenthatthereissomejustification f'rexamining arotorfromafracturemechanics view-point.Thiswillalwaysbesoif,becauseofthehighlevelofdiscstresses, onehastoresorttohigh-strength materials orwhen,asinthecaseofsolidlow-pressure rotors,thelargedimensions, makeitverydifficult todetectfaultsinsidetheforging.Itmaythenbeofadvantage toassumeafaultofacertainsizeinacertainpositionandchecktoseewhattheconsequences mightbeinthecourseoftime.crtÃ-fsrtandcanbewrittenindimensionless formasfollows:n8trtdrgrestos(3+t)StMfs-rt(17)(18)'heratioofthcburstingspeedsofperforated disctosoliddiscisthendescribed byFortrtwethenuseEq.(3)forasoliddiscandEq.(5)foraperforated disc.Ifwenowwritetheratioofthemean,tangential stressStwr,oftheperforated disctothemeantangential stressStlvofthesoliddisc,wehaveBurstingSpeed<BRLirBRVI+-+(19)Inrecentyears,andinitially attherequestoftheUSAtomicEnergyCommission, manufacturers oflargetur-binesfornuclearpowerplanthavehadtoanalysetheextentofdamagetotheturbosetintheeventoftotalEquations (18)and(19)areshowngraphically iriFig.I?Asexamination willquicklyshow,forrt(rs~Itheywillofcourseprovidetheburstingspeedratioforthethinring.
2,0l,gesax,SetsasarSoirl.g1,2Vgl.oO,gheal.I/1(l+-"+(-,"j',600,20.40,6rtPsFig.lz-Ratiosofmeantangential stressandberatingspeedlorperforated andsoliddiscsFigure13showsinqualitative termsthebehaviour oftwodiff'erent I.p.rotorconstructions atelevatedspeed.Forthesamesize.bladetensionandoperating speed,thctangential stressforthedrumrotorwillfollowcurveI.Thesameappliestothediscrotor,butatthcborediameterchosenthisrotorshowsastressroughlydoublethatofthcdrumrotor.Intheelasticregionthereisproportionality betweenthestressandthesquareofthespeed.IfthespeedisraisedrelativetothenormalspeedbyafactorofI4,forexample,thestressesincreasebyafactorof196(curve2).Theinnerportionofthcper-forateddiscisthenalreadybeyondtheyieldpoint,andthecorresponding zonerelaxes.Owingtoplasticdeformation, therefore, theelasticcurve2giveswaytocurve2'ndthcpartsofthediscwhicharestillelasticarcthussubjected toadditional, stress.According towhathasbeensaid.sofar,ameasureofthercscrvewithrespecttofractureistheratioofthe.yieldpointtothemeantangential stress,i.e.essentially.
theareainFig.13contained betweencurvesIandtheyieldpoint.Therootofthisarearatiorepresents the.relationship oftheburstingspeedofthctwodesignsshowninFig.13.Ifonewishestocompensate thedisadvantage ofthelowerfracturespeedofaperforated discbyusingmorehighlytemperedmaterial, theincrease-inyieltIpointrequiredforaperforated disccanalsobe.foundwithEq.(18)(Fig.12).Itcanbcseenthatwiththeradiusratiosoccurring inpracticeitisdifficult toachieveaperforated discofsuchaqualitythatitisequivalent toasoliddiscasregardsitsburstingspeed.Thiswouldmeanhigh-strength materialhastobeused,withtheconsequent higherriskofbrittlefracture.
Fig.ls-Behaviour oftteotypesofI.p.rotorat<<leratedspeed~tdidi2ldldiPaOutlookAsmentioned earlier,theunitcapacityoflargesteamturbosets willcontinuetoriscinthcforeseeable future,andhence.influencc thedemandsmadeoftherotors.Adecisive, andtosolneextentlimiting, factoroverthepastdecadewasthefinalstage,whichifthevacuumwasgoodhadtohandleenormousflowvolumes.Allmanufacturers ofsteamturbinestherefore carefully developed longerfinalbladesandintroduced thesetothemarket.Butlongerbladesalsomeansalargerrotordiameter, accom-paniedbyhighercentrifugal loadingsonbothbladesandrotor.Tokeepstressesbelowthelimit,thespeedofthemachineswashalved.Thetechnique employedintheUSAwastorunthchighandintermediate-prcssure sectionsatthcfullspeedof3600rev/min,andcombinethelow-pressure unitswitha4-polegenerator onasecondshaftstringrunningat1800rev/min.Europelateradoptedtheideaofthehalf-speed machine,althoughin12 single-shaft formandonlyfornuclearplant.Byhalvingthespeedinthisway.andatthesametimedoubling, thesize,thestressesinfull-speed andhalf-speed machineswerekeptthesame,butthecorresponding exhaustareaofthefinalbladesincreased fourfold.
Afeatureofrecentyearshasbeenagrowingworldwide shortageofcoolingwater[15].Intheindustrialized countries, andtheseifonlybecauseoftheir.powerdistribution networksarethepotential buyersoflargemachines.
itisbecomingnolongerpossibletouscfreshwaterforcoolingpurposes.
Futurelargepowerstationswilltherefore beequippedmainlywithwetordrycoolingtowers.whichmeanstheturbinevacuumwillberclativcly poorandthesteamexhaustvolumecorrespondingly smaller.ItmaythuswellbethatthefinalbladelengthsandI.p.rotordimensions customary todaywillbeade-quateforsometimetocome,withoutbeingtiedtohalf-speedI.p.sectionsbecauseofthcstresses, evenwithlargecapacities.
Itislikelythatlargemachinesfornuclearpowerstations, withpoorvacuum,willalsobebuiltforfullspeedandstillbeabletocopewiththcstressesinthebladesandrotor.Thepossibility ofmakingtheI.p.rotorrelatively smallalsoimprovesthechancesofthesolid-rotor designtosomedegree.Greatadvancesinforgingtechnology havebeenmadeoverthepastfewyears,andthishasincreased confidence intheuseofforgedone-piece shafts.Finishedweightsofover200thavebeenachievedtodate.Theserotorsrequireaningotweighingmorcthan400tandwiththeassociated riskscanbeproducedonlyinJapanandtheUnitedStates.Itisimprobable thatthesteel-workswillcontemplate afurtherincreaseinrotorsize.withthecorrespondingly heavyinvestment neededtodealwithlargeringots,becausethemarketfortheselargeforgingsistoorestricted.
Theconceptofthelargeone-piecerotorcantherefore beextrapolated intothefuturetoonlyalimitedextent.Thcsituation isslightlydifferent forthehigh-pressure section.Ontheassumption thatfuturenuclearpowerstationswillalsooperatewithsteamconditions suchasarefoundtodayinconventional plant(I50to250bar,538'C),theverysizeoftheI.p.rotorcouldpresentastressproblem.Overcoming thiscanbeapproached intwodifferent ways:thematerialandthedesign.Thereisnolikelihood inthenearfutureoffindingadifferent materialforh.p.rotorswhichhassubstantially betterlong-term properties anddoesnotforfeittheadvantages ofthelowalloysteelsusedatpresent.Muchmoreprobableisthatstressesintheh.p.rotorcanbekeptincheckthroughsuitabledesign:thelargesteamturbinetodayisquiteclearlyfollowing thcpathtakenmanyyearsagobythegasturbinetowardscoolingtherotorbymeansofsteam.ThedesignerthushasathisSymbolsF.=Modulusofelasticity L=Perforated discS<---Dimensionless radialstressSi=Dimensionless tangential stressSist=-Dimensionless meantangential stressSv~Dimensionless equivalent voltageT=Tempcraturc U=Radialdisplacement V=Soliddisca=Thermalconductivity c=Specificheatofrotormaterialnnn=.Burstingspeedr=Considered discradiusri=Innerradiusofperforated discri--Outerradiusofdischr=Degreeofshrinkage du-~Relativedegreeofshrinkage tir~Timee<--Radialexpansion
=Tangential expansion
=Conductivity ofrotormaterial~Transverse contraction ratio=Specificmassofdiscmateriale<=Radialstresse<i=Shrinkage forcee~=.Bladetensionappliedatradiusrs(ri%std!COOPyp4Tangential stress=Meantangential stressovermeridional areaofblade=Axialstressesinrotor=Angularvelocityofrotation=Overspeed
=Lift-offspeedIndicesWS0=Centralshaft=Disc=Standstill disposaladesignconceptsufficientl flcxibletoallowhimanadequatemarginofsafetyindesigning rotorsforthehigh-pressure sectionasunitcapacities continuetorisc.13 Bibliography
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SICBROWNBOVERIBBCBrown,Boveri5Company,Ltd.CH-5401Baden/Switzerland printedInswiuorlsnd (74e41000.0)Casahcation Na01010