Dynamics of Machinery: Theory and Applications

554 Pages·2010·9.17 MB·English

by  Hans Dresig

Dynamics of Machinery
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·
Hans Dresig Franz Holzweißig
Dynamics of Machinery
Theory and Applications
Translated by Dr. Wolf Grosskopf and
Assoc. Prof. Dr.-Ing. Sven Esche
with CD-ROM
123
Univ.-Prof.Dr.-Ing.habil.HansDresig
Mittelstr.1
D-09244LichtenauOTAuerswalde
Germany
[email protected]
Homepage:http://www.dresig.de
Univ.-Prof.Dr.-Ing.habil.FranzHolzweißig
KaitzerStr.66
D-01187Dresden
Germany
Translators
Dr.WolfGrosskopf(Northridge)
[email protected]
Assoc.Prof.Dr.-Ing.SvenEsche
(StevensInstituteofTechnology)
[email protected]
ISBN978-3-540-89939-6 e-ISBN978-3-540-89940-2
DOI10.1007/978-3-540-89940-2
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2010929624
(cid:2)c Springer-VerlagBerlinHeidelberg2010
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Preface to the English Edition
Thistextbook,thetranslationofthenintheditionoftheGermanbook“Maschinen-
dynamik”(publishedinitsfirsteditioninGermanyandAustriain1979),discusses
disciplinesthatinmanycountriesarepresentedseparatelyinlecturestitled“Theory
ofMechanismsandMachines”(TMM)and“Vibrations”or“TheoryofVibrations”.
The basic idea by my distinguished colleague, Prof. Holzweissig, was to combine
these disciplines into the “Dynamics of Machinery”. We worked out this concept
together in the first three editions, relying on our experience gained in our collab-
orations with engineers here in Saxony. Since he became a professor emeritus in
1993,Ihaveconstantlyupdatedthebooksinceits4theditionandhaveaddedmore
exercisesandsections.
Thistextbookisbasedonthefour-semesterlectureserieson“EngineeringMe-
chanics”andconfrontsstudentsdirectlywithdynamicproblemsoftheirfield.Dy-
namics of machinery is viewed both as a typical field for the mathematical mod-
eling of technological processes and as a branch of mechanical engineering that
addressesdynamicproblemsofpowermachines(reciprocatingenginesandturbo-
machines), processing machines (printing machines, textile machines, packaging
machines),hoistsandconveyors,agriculturalmachinesandvehicles,aswellasin-
dustrialplants.
Thebookcomprisesrelativelyindependentchaptersthatdiscusstypicalissuesof
thedynamicsofmechineryfromthepointofviewofmechanicalengineers.Chapter
6 gives a general overview of linear oscillators and includes methods discussed in
Chaps.3,4and5.Wewerefullyawareandacceptedsomeoverlapandrepetitions,
making many cross-references among sections. Chapter 7 discusses nonlinear and
self-excitedoscillators,forwhichcalculationsarebecomingmoreandmorerelevant
topracticalapplication.Chapter8stilldoesnotcontainanyequations,buttherules
compiled there are important for engineering practice. We included a new chapter
“on interrelations with system dynamics and mechatronics” to enhance the under-
standingoftheseadjacentdisciplines.Thischapterpreparesthereadersforamore
general approach to solving problems of the dynamics of machinery by including
sensorsandactuators.
V
VI PrefacetotheEnglishEdition
The60problemswithsolutionsaremeanttohelpingraspingandconsolidating
thesubjectstaught.AnewfeatureofthiseditionistheenclosedCD-ROM,which
does not only contain the student version of the SimulationX(cid:2)R software, but also
programpartsthatwereusedforsolvingtheexamplesgiveninthebooksothatthe
readerscanworkwiththemthemselves.
The book was not only written for students, but also for practicing engineers.
The examples from many fields of mechanical engineering and the specification
of parameter values, as well as references to guidelines and regulations, underline
this.Wehaveconsideredthewayinwhichengineersthinkbydiscussingestimation
methods,roughcalculationsandminimalmodels,andbyexplainingmanyinstruc-
tivedynamiceffects(gyroscopiceffect,resonance,absorption,self-synchronization,
...)thatarerelevantforthedesignofmachinesthatoperateunderahighdynamic
load.Thefastdevelopmentofhardwareandsoftwareentailedthatnowadaysthere
issoftwareavailableforalmosteveryprobleminthedynamicsofmachinery.While
computersalwaysprovidesomenumbersanddiagrams,theengineerisstillrespon-
siblefortheresults.Itremainstheengineer’sjobtoprovidetherespectivecalcula-
tionmodels,toassesstheapplicabilityofasoftwareproduct,tochecktheresultofa
simulation,andtohavesomeideaoftheresulttobeexpectedbeforethecalculation
starts.
Since the current development shows a trend towards refined modeling, we
pointed out three aspects: the training of physical understanding, the utilization of
modalanalysisincludingsensitivityanalysis,andtheapplicationofcomputer-aided
methods. We stress the fact that the goal of calculations is not only to arrive at a
numericalresult,buttoachieveabetterunderstandingofthedynamicbehaviorof
realobjectsandtobeabletotakedesignmeasuresthatarebasedinphysicaltheory.
I would like to thank many specialists for their suggestions and tips, in partic-
ular my former coworkers at the professorship of Dynamics of Machinery of the
Chemnitz University of Technology and my colleagues at ITI GmbH Dresden, in
particular Dipl.-Ing. Uwe Schreiber, who helped me work out practical examples.
ThewholebookhasbeentranslatedbyDr.WolfGrosskopf(Northridge).Iwasvery
pleasedthatmyformerstudent,Prof.Dr.-Ing.SvenEsche(StevensInstituteofTech-
nology),agreedtoproof-readthemanuscriptandtoreviewtheterminology.Iamin
particulargratefulforthis.Iwouldliketogivespecialpraisetothecommittedwork
ofDipl.-Ing.AndreasAbelwhopreparedthefinalmanuscriptandtherebytookinto
accountallmymanyextrawishes,sothatthemanuscriptcouldbesubmittedtothe
publisherreadyforprinting.
Auerswalde,inMay2010 HansDresig
Contents
PurposeandStructureoftheDynamicsofMachinery .................. 1
1 ModelGenerationandParameterIdentification ................... 5
1.1 ClassificationofCalculationModels .......................... 5
1.1.1 GeneralPrinciples ................................... 5
1.1.2 Examples........................................... 10
1.2 DeterminationofMassParameters ............................ 14
1.2.1 Overview........................................... 14
1.2.2 MassandPositionoftheCenterofGravity............... 15
1.2.3 MomentofInertiaaboutanAxis ....................... 17
1.2.4 MomentofInertiaTensor ............................. 21
1.3 SpringCharacteristics....................................... 25
1.3.1 GeneralContext ..................................... 25
1.3.2 MachineElements,Sub-Assemblies .................... 29
1.3.3 RubberSprings...................................... 36
1.3.4 ProblemsP1.1toP1.3 ................................ 38
1.3.5 SolutionsS1.1toS1.3 ................................ 40
1.4 DampingCharacteristics..................................... 42
1.4.1 GeneralContext ..................................... 42
1.4.2 Methods for Determining Characteristic Damping
Parameters.......................................... 47
1.4.3 EmpiricalDampingValues ............................ 51
1.5 CharacteristicExcitationParameters........................... 55
1.5.1 PeriodicExcitation................................... 55
1.5.2 TransientExcitation.................................. 56
1.5.3 ProblemsP1.4toP1.6 ................................ 62
1.5.4 SolutionsS1.4toS1.6 ................................ 63
2 DynamicsofRigidMachines .................................... 67
2.1 Introduction ............................................... 67
2.2 KinematicsofaRigidBody.................................. 68
VII
VIII Contents
2.2.1 CoordinateTransformations ........................... 68
2.2.2 KinematicParameters ................................ 73
2.2.3 KinematicsoftheGimbal-MountedGyroscope ........... 75
2.2.4 ProblemsP2.1andP2.2............................... 76
2.2.5 SolutionsS2.1andS2.2............................... 78
2.3 KineticsoftheRigidBody................................... 82
2.3.1 KineticEnergyandMomentofInertiaTensor ............ 82
2.3.2 PrinciplesofLinearMomentumandofAngularMomentum 87
2.3.3 KineticsofEdgeMills................................ 90
2.3.4 ProblemsP2.3andP2.4............................... 93
2.3.5 SolutionsS2.3andS2.4............................... 95
2.4 KineticsofMultibodySystems ...............................100
2.4.1 MechanismswithMultipleDrives ......................100
2.4.2 PlanarMechanisms ..................................112
2.4.3 StatesofMotionofaRigidMachine ....................122
2.4.4 SolutionoftheEquationsofMotion ....................124
2.4.5 Example:PressDrive.................................129
2.4.6 ProblemsP2.5toP2.8 ................................133
2.4.7 SolutionsS2.5toS2.8 ................................136
2.5 JointForcesandFoundationLoading ..........................141
2.5.1 GeneralPerspective ..................................141
2.5.2 CalculatingJointForces ..............................142
2.5.3 CalculationoftheForcesActingontotheFrame ..........145
2.5.4 JointForcesintheLinkageofaProcessingMachine.......148
2.5.5 ProblemsP2.9andP2.10..............................150
2.5.6 SolutionsS2.9andS2.10..............................151
2.6 MethodsofMassBalancing..................................153
2.6.1 Objective...........................................153
2.6.2 CounterbalancingofRigidRotors ......................153
2.6.3 MassBalancingofPlanarMechanisms ..................160
2.6.4 ProblemsP2.11toP2.14 ..............................167
2.6.5 SolutionsS2.11toS2.14 ..............................170
3 FoundationandVibrationIsolation ..............................177
3.1 IntroductoryRemarks.......................................177
3.2 FoundationLoadingforPeriodicExcitation ....................181
3.2.1 MinimalModelswithOneDegreeofFreedom............181
3.2.2 BlockFoundations ...................................191
3.2.3 FoundationswithTwoDegreesofFreedom–Vibration
Absorption..........................................200
3.2.4 Example:VibrationsofanEngine-GeneratorSystem ......204
3.2.5 ProblemsP3.1toP3.3 ................................206
3.2.6 SolutionstoProblemsS3.1toS3.3 .....................208
3.3 FoundationsunderImpactLoading............................211
3.3.1 ModelingForgingHammers...........................211
Contents IX
3.3.2 CalculationModelwithTwoDegreesofFreedom .........213
3.3.3 ProblemsP3.4toP3.6 ................................216
3.3.4 SolutionsS3.4toS3.6 ................................218
4 TorsionalOscillatorsandLongitudinalOscillators .................223
4.1 Introduction ...............................................223
4.2 FreeVibrationsofTorsionalOscillators ........................229
4.2.1 ModelswithTwoDegreesofFreedom ..................229
4.2.2 OscillatorChainswithMultipleDegreesofFreedom ......234
4.2.3 EvaluationofNaturalFrequenciesandModeShapes ......238
4.2.4 Examples...........................................242
4.2.5 ProblemsP4.1toP4.3 ................................251
4.2.6 SolutionsS4.1toS4.3 ................................253
4.3 ForcedVibrationsofDiscreteTorsionalOscillators ..............259
4.3.1 PeriodicExcitation...................................259
4.3.2 Examples...........................................263
4.3.3 TransientExcitation..................................272
4.3.4 ProblemsP4.4toP4.6 ................................278
4.3.5 SolutionsS4.4toS4.6 ................................280
4.4 AbsorbersandDampersinDriveSystems ......................283
4.4.1 Introduction.........................................283
4.4.2 DesignofanUndampedAbsorber ......................284
4.4.3 DesignofaSpring-ConstrainedDamper.................286
4.4.4 DesignofaSpringlessDamper.........................289
4.4.5 Examples...........................................291
4.5 Parameter-ExcitedVibrationsbyGearMechanismswithVarying
TransmissionRatio .........................................295
4.5.1 ProblemFormulation/EquationofMotion................295
4.5.2 SolutionoftheEquationofMotion,StabilityBehavior.....297
4.5.3 Examples...........................................299
4.5.4 ProblemsP4.7andP4.8...............................306
4.5.5 SolutionsS4.7andS4.8...............................308
5 BendingOscillators ............................................311
5.1 ProblemDevelopment ......................................311
5.2 Fundamentals..............................................312
5.2.1 Self-CenteringinaSymmetricalRotor ..................312
5.2.2 PassingthroughtheResonancePoint....................315
5.2.3 RotatingShaftwithDisk(GyroscopicEffect).............316
5.2.4 BendingOscillatorswithaFiniteNumberofDegreesof
Freedom............................................326
5.2.5 Examples...........................................328
5.2.6 ProblemsP5.1toP5.3 ................................335
5.2.7 SolutionsS5.1toS5.3 ................................336
5.3 BeamwithDistributedMass .................................338