Guide to load analysis for durability in vehicle engineering

458 Pages·2014·15.438 MB·English

by  Par Johannesson, Michael Speckert

GUIDE TO LOAD
ANALYSIS FOR
DURABILITY IN
VEHICLE ENGINEERING

GUIDE TO LOAD
ANALYSIS FOR
DURABILITY IN
VEHICLE ENGINEERING
Editors
P. Johannesson
SPTechnicalResearchInstituteofSweden,Sweden
M. Speckert
FraunhoferInstituteforIndustrialMathematics(ITWM),Germany
Thiseditionfirstpublished2014byJohnWiley&Sons,Ltd
©2014Fraunhofer-ChalmersResearchCentreforIndustrialMathematics
Registeredoffice
JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom
Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyfor
permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com.
Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththe
Copyright,DesignsandPatentsAct1988.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,in
anyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedby
theUKCopyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe
availableinelectronicbooks.
Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnames
andproductnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheir
respectiveowners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook.
LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsin
preparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessof
thecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessfora
particularpurpose.Itissoldontheunderstandingthatthepublisherisnotengagedinrenderingprofessional
servicesandneitherthepublishernortheauthorshallbeliablefordamagesarisingherefrom.Ifprofessional
adviceorotherexpertassistanceisrequired,theservicesofacompetentprofessionalshouldbesought
LibraryofCongressCataloging-in-PublicationData
Guidetoloadanalysisfordurabilityinvehicleengineering/editors,ParJohannesson,MichaelSpeckert;
contributors,KlausDressler,SaraLoren,JacquesdeMare,NikolausRuf,IgorRychlik,AnjaStreitand
ThomasSvensson–Firstedition.
1onlineresource.–(Automotiveseries;1)
Includesbibliographicalreferencesandindex.
DescriptionbasedonprintversionrecordandCIPdataprovidedbypublisher;resourcenotviewed.
ISBN978-1-118-70049-5(AdobePDF)–ISBN978-1-118-70050-1(ePub)–ISBN978-1-118-64831-5
(hardback)1.Trucks–Dynamics.2.Finiteelementmethod.3.Trucks–Designandconstruction.
I.Johannesson,Par,editorofcompilation.II.Speckert,Michael,editorofcompilation.
TL230
629.2(cid:2)31–dc23
2013025948
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-1-118-64831-5
Typesetin10/12ptTimesbyLaserwordsPrivateLimited,Chennai,India
1 2014
Contents
About the Editors xiii
Contributors xv
Series Editor’s Preface xvii
Preface xix
Acknowledgements xxi
Part I OVERVIEW
1 Introduction 3
1.1 Durability in Vehicle Engineering 4
1.2 Reliability, Variation and Robustness 6
1.3 Load Description for Trucks 7
1.4 Why Is Load Analysis Important? 9
1.5 The Structure of the Book 10
2 Loads for Durability 15
2.1 Fatigue and Load Analysis 15
2.1.1 ConstantAmplitudeLoad 15
2.1.2 BlockLoad 16
2.1.3 VariableAmplitudeLoadingandRainflowCycles 16
2.1.4 RainflowMatrix,LevelCrossingsandLoadSpectrum 18
2.1.5 OtherKindsofFatigue 20
2.2 Loads in View of Fatigue Design 23
2.2.1 FatigueLife:CumulativeDamage 23
2.2.2 FatigueLimit:MaximumLoad 23
2.2.3 SuddenFailures:MaximumLoad 24
2.2.4 SafetyCriticalComponents 24
2.2.5 DesignConceptsinAerospaceApplications 24
vi Contents
2.3 Loads in View of System Response 25
2.4 Loads in View of Variability 27
2.4.1 DifferentTypesofVariability 27
2.4.2 LoadsinDifferentEnvironments 28
2.5 Summary 29
Part II METHODS FOR LOAD ANALYSIS
3 Basics of Load Analysis 33
3.1 Amplitude-based Methods 35
3.1.1 FromOuterLoadstoLocalLoads 36
3.1.2 Pre-processingofLoadSignals 37
3.1.3 RainflowCycleCounting 40
3.1.4 Range-pairCounting 49
3.1.5 MarkovCounting 51
3.1.6 RangeCounting 53
3.1.7 LevelCrossingCounting 55
3.1.8 IntervalCrossingCounting 56
3.1.9 IrregularityFactor 56
3.1.10 PeakValueCounting 56
3.1.11 ExamplesComparingCountingMethods 56
3.1.12 PseudoDamageandEquivalentLoads 60
3.1.13 MethodsforRotatingComponents 67
3.1.14 RecommendationsandWork-flow 70
3.2 Frequency-based Methods 72
3.2.1 ThePSDFunctionandthePeriodogram 73
3.2.2 EstimatingtheSpectrumBasedonthePeriodogram 74
3.2.3 SpectrogramorWaterfallDiagram 79
3.2.4 Frequency-basedSystemAnalysis 79
3.2.5 ExtremeResponseandFatigueDamageSpectrum 85
3.2.6 WaveletAnalysis 86
3.2.7 RelationBetweenAmplitudeandFrequency-basedMethods 87
3.2.8 MoreExamplesandSummary 87
3.3 Multi-input Loads 91
3.3.1 FromOuterLoadstoLocalLoads 92
3.3.2 TheRPMethod 94
3.3.3 PlottingPseudoDamageandExamples 95
3.3.4 EquivalentMulti-inputLoads 99
3.3.5 PhasePlotsandCorrelationMatricesforMulti-inputLoads 101
3.3.6 Multi-inputTimeatLevelCounting 104
3.3.7 BiaxialityPlots 104
3.3.8 TheWang-BrownMulti-axialCycleCountingMethod 105
3.4 Summary 105
Contents vii
4 Load Editing and Generation of Time Signals 107
4.1 Introduction 107
4.1.1 EssentialLoadProperties 108
4.1.2 CriteriaforEquivalence 108
4.2 Data Inspections and Corrections 110
4.2.1 ExamplesandInspectionofData 110
4.2.2 DetectionandCorrection 112
4.3 Load Editing in the Time Domain 115
4.3.1 Amplitude-basedEditingofTimeSignals 115
4.3.2 Frequency-basedEditingofTimeSignals 126
4.3.3 Amplitude-basedEditingwithFrequencyConstraints 136
4.3.4 EditingofTimeSignals:Summary 138
4.4 Load Editing in the Rainflow Domain 139
4.4.1 Re-scaling 139
4.4.2 Superposition 141
4.4.3 ExtrapolationonLengthorTestDuration 143
4.4.4 ExtrapolationtoExtremeUsage 150
4.4.5 LoadEditingfor1DCountingResults 154
4.4.6 Summary,HintsandRecommendations 154
4.5 Generation of Time Signals 156
4.5.1 Amplitude-orCycle-basedGenerationofTimeSignals 156
4.5.2 Frequency-basedGenerationofTimeSignals 163
4.6 Summary 167
5 Response of Mechanical Systems 169
5.1 General Description of Mechanical Systems 169
5.1.1 MultibodyModels 170
5.1.2 FiniteElementModels 172
5.2 Multibody Simulation (MBS) for Durability Applications or: from System
Loads to Component Loads 173
5.2.1 AnIllustrativeExample 173
5.2.2 SomeGeneralModellingAspects 175
5.2.3 FlexibleBodiesinMultibodySimulation 178
5.2.4 SimulatingtheSuspensionModel 181
5.3 Finite Element Models (FEM) for Durability Applications or: from
Component Loads to Local Stress-strain Histories 186
5.3.1 LinearStaticLoadCasesandQuasi-staticSuperposition 188
5.3.2 LinearDynamicProblemsandModalSuperposition 189
5.3.3 FromtheDisplacementSolutiontoLocalStressesandStrains 192
5.3.4 SummaryofLocalStress-strainHistoryCalculation 192
5.4 Invariant System Loads 193
5.4.1 DigitalRoadandTyreModels 194
5.4.2 BackCalculationofInvariantSubstituteLoads 196
5.4.3 AnExample 199
5.5 Summary 200
viii Contents
6 Models for Random Loads 203
6.1 Introduction 203
6.2 Basics on Random Processes 206
6.2.1 SomeAveragePropertiesofRandomProcesses∗ 207
6.3 Statistical Approach to Estimate Load Severity 209
6.3.1 TheExtrapolationMethod 210
6.3.2 FittingRange-pairsDistribution 210
6.3.3 Semi-parametricApproach 213
6.4 The Monte Carlo Method 215
6.5 Expected Damage for Gaussian Loads 218
6.5.1 StationaryGaussianLoads 219
6.5.2 Non-stationaryGaussianLoadswithConstantMean∗ 223
6.6 Non-Gaussian Loads: the Role of Upcrossing Intensity 224
6.6.1 Bendat’sNarrowBandApproximation 224
6.6.2 GeneralizationofBendat’sApproach∗ 225
6.6.3 LaplaceProcesses 228
6.7 The Coefficient of Variation for Damage 230
6.7.1 SplittingtheMeasuredSignalintoParts 230
6.7.2 ShortSignals 231
6.7.3 GaussianLoads 232
6.7.4 CompoundPoissonProcesses:RoadswithPotHoles 233
6.8 Markov Loads 235
6.8.1 MarkovChains∗ 240
6.8.2 DiscreteMarkovLoads–Definition 242
6.8.3 MarkovChainsofTurningPoints 243
6.8.4 SwitchingMarkovChainLoads 244
6.8.5 ApproximationofExpectedDamageforGaussianLoads 247
6.8.6 IntensityofIntervalUpcrossingsforMarkovLoads∗ 248
6.9 Summary 249
7 Load Variation and Reliability 253
7.1 Modelling of Variability in Loads 253
7.1.1 TheSourcesofLoadVariability:StatisticalPopulations 254
7.1.2 ControlledorUncontrolledVariation 255
7.1.3 ModelErrors 255
7.2 Reliability Assessment 256
7.2.1 TheStatisticalModelComplexity 256
7.2.2 ThePhysicalModelComplexity 257
7.3 The Full Probabilistic Model 258
7.3.1 MonteCarloSimulations 259
7.3.2 AccuracyoftheFullProbabilisticApproach 263
7.4 The First-Moment Method 263
7.5 The Second-Moment Method 264
7.5.1 TheGaussApproximationFormula 264
7.6 The Fatigue Load-Strength Model 265
7.6.1 TheFatigueLoadandStrengthVariables 265