History of Rotating Machinery Dynamics

380 Pages·2011·7.72 MB·English

by  J. S. Rao (auth.)

History of Rotating Machinery Dynamics
HISTORY OF MECHANISM AND MACHINE SCIENCE
Volume20
SeriesEditor
MARCOCECCARELLI
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J.S. Rao
History of Rotating
Machinery Dynamics
ABC
J.S.Rao
AltairEngineering
ChiefScienceOfficer
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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
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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