History of Rotating Machinery Dynamics HISTORY OF MECHANISM AND MACHINE SCIENCE Volume20 SeriesEditor MARCOCECCARELLI AimsandScopeoftheSeries This bookseries aims to establish a well defined forumfor Monographsand Pro- ceedings on the History of Mechanism and Machine Science (MMS). The series publishesworksthatgiveanoverviewofthehistoricaldevelopments,fromtheear- liesttimesuptoandincludingtherecentpast,ofMMSinallitstechnicalaspects. This technical approach is an essential characteristic of the series. By discussing technicaldetailsandformulationsandevenreformulatingthoseintermsofmodern formalismsthepossibilityiscreatednotonlytotrackthehistoricaltechnicaldevel- opmentsbutalso to use pastexperiencesin technicalteachingandresearchtoday. In order to do so, the emphasis must be on technical aspects rather than a purely historicalfocus,althoughthelatterhasitsplacetoo. Furthermore,the series will considerthe republicationof out-of-printolder works withEnglishtranslationandcomments. Thebookseriesisintendedtocollecttechnicalviewsonhistoricaldevelopmentsof thebroadfieldofMMSinauniqueframethatcanbeseeninitstotalityasanEncy- clopaediaoftheHistoryofMMSbutwiththeadditionalpurposeofarchivingand teachingtheHistoryofMMS.Thereforethebookseriesisintendednotonlyforre- searchersoftheHistoryofEngineeringbutalsoforprofessionalsandstudentswho are interested in obtaininga clear perspectiveof the past for their futuretechnical works.Thebookswillbewritteningeneralbyengineersbutnotonlyforengineers. Prospectiveauthorsandeditorscancontacttheserieseditor,ProfessorM.Ceccarelli, aboutfuturepublicationswithintheseriesat: LARM:LaboratoryofRoboticsandMechatronics DiMSAT–UniversityofCassino ViaDiBiasio43,03043Cassino(Fr) Italy E-mail:[email protected] Forothertitlespublishedinthisseries,goto www.springencom/series/748l J.S. Rao History of Rotating Machinery Dynamics ABC J.S.Rao AltairEngineering ChiefScienceOfficer OuterRingRoad 560103Bangalore India E-mail:[email protected] ISBN978-94-007-1164-8 e-ISBN978-94-007-1165-5 DOI10.1007/978-94-007-1165-5 (cid:2)c SpringerScience+BusinessMediaB.V.2011 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthemate- rialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting, reproduction onmicrofilmor inanyother way, andstorage indatabanks. Dupli- cationofthispublicationorpartsthereof ispermittedonlyunder theprovisions oftheGerman CopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalways beobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoes notimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Everyefforthasbeenmadetocontactthecopyrightholdersofthefigureswhichhavebeenrepro- ducedfromothersources.Anyonewithacopyrightclaimwhohasnotbeenproperlycreditedis requestedtocontactthepublishers,sothatdueacknowledgementmaybemade. Typesetting:Datasuppliedbytheauthors CoverDesign:ScientificPublishingServicesPvt.Ltd.,Chennai,India Printedonacid-freepaper 987654321 springer.com Dedicatedtothememoryofmyparents JammiChikkaRao JammiRamanamma Contents Foreword.......................................................... xi Preface............................................................ xv Acknowledgements ................................................. xix 1 BeginningsoftheWheel ........................................ 1 References......................................................... 4 2 SciencebeforetheMedievalPeriod............................... 5 References......................................................... 7 3 WaterWheels.................................................. 9 References......................................................... 12 4 WindMills .................................................... 13 References......................................................... 14 5 RenaissanceandScientificRevolution ............................ 15 References......................................................... 20 6 RenaissanceEngineers.......................................... 23 References......................................................... 30 7 IndustrialRevolution........................................... 31 References......................................................... 34 vii viii Contents 8 Turbomachines ................................................ 35 References......................................................... 42 9 FundamentalsofElasticity ...................................... 45 References......................................................... 46 10 EnergyMethods ............................................... 49 10.1 Euler–LagrangeEquations................................... 50 10.2 LagrangeMethod .......................................... 55 10.3 Rayleigh’sEnergyApproach................................. 56 10.4 RitzMethod............................................... 58 10.5 LagrangeMethodforVibrationProblems ...................... 61 10.6 GalerkinMethod ........................................... 63 10.7 Hamilton’sPrinciple ....................................... 66 10.8 ComplementaryVirtualWork ................................ 78 10.9 Hellinger–ReissnerVariationalPrinciple ....................... 81 10.10Hu–WashizuPrinciple ...................................... 87 10.11DifferentTheoriesofTorsionofRods ......................... 90 10.11.1Coulomb(1784)ElementaryTheory,seeTimoshenko andGoodier[42]forCircularRods ..................... 90 10.11.2St. Venant (1853)Theory, see Todhunter [43] and TimoshenkoandGoodier[42]forCircularRods .......... 90 10.11.3Love’s(1944)Theory................................. 91 10.11.4Timoshenko(1945)–Gere’s(1954)Theory.............. 91 10.11.5Reissner(1952)andLo–Goulard’s(1955)Theory ........ 92 10.11.6Barr’s(1962)Theory ................................. 93 10.11.7RefinedTheorybyRao(1974) ......................... 93 References......................................................... 97 11 20thCenturyGraphicalandNumericalMethods .................. 99 11.1 Stodola–Viannello(Rayleigh’sMaximumEnergy)Methodin GraphicalForm ............................................ 99 11.2 Stodola–ViannelloIterativeMethodinTabularForm .............101 11.3 Dunkerley’sMethod ........................................104 11.4 ProofoftheDunkerleyFormulabyBlaess[1]...................104 11.5 Hahn’sProofUsingMatrixAlgebra[3] ........................105 11.6 HolzerMethodforTorsionalVibration.........................107 11.7 TheMyklestadMethod[7,8].................................108 11.8 Prohl’sMethod[9] .........................................112 References.........................................................114 Contents ix 12 MatrixMethods................................................115 12.1 TorsionalVibrationSystems .................................118 12.2 Far-CoupledSystems .......................................121 12.3 Gräffe’sMethodofSuccessiveApproximations .................122 12.4 MatrixIterationMethod.....................................124 12.5 MethodofPriebs[10].......................................127 12.6 TheHolzerMethod(CloseCoupledSystems)inTransferMatrix Form .....................................................131 12.7 Myklestad–Thomson(1949,1953)–ProhlMethodsinTransfer MatrixFormforFar-CoupledSystems.........................133 12.8 ABriefNoteonComputersandEvolution......................136 References.........................................................138 13 FiniteElementMethods.........................................141 13.1 BeamFiniteElement .......................................143 13.2 TocherTriangularPlateElement(1962)........................147 13.3 ShellElement..............................................154 13.4 InterfaceDampingthroughFiniteElementAnalysis .............163 13.5 IllustrationofTurbomachineBladeAnalysisusingCommercial Codes ....................................................176 References.........................................................183 14 RotorDynamicsMethods .......................................185 14.1 DeLavalModel............................................186 14.2 JeffcottRotorAnalysis......................................188 14.3 FluidFilmBearings ........................................190 14.4 OilFilmInstabilities........................................198 14.5 QualityFactor .............................................204 14.6 GyroscopicEffects .........................................207 14.7 InternalFriction,Hysteresis..................................212 14.8 ShaftswithGravityandVariableElasticity .....................218 14.9 Misalignment..............................................226 14.10BowedRotors .............................................230 14.11VariableInertia ............................................233 14.12SealsandInstabilities .......................................236 14.13SteamWhirl...............................................240 14.14CrackedShafts.............................................242 References.........................................................248 15 TransferMatrixMethods .......................................253 15.1 TorsionalVibrationduetoShortCircuitofGenerators............253 15.2 TransferMatrixMethodforLateralVibrationsofRotors..........258 15.3 TwinSpoolRotorAnalysis ..................................262