Vehicle gearbox noise and vibration :b measurement, signal analysis, signal processing, and noise reduction measures

261 Pages·2014·18.805 MB·English

by  Tůma, Jiří

AUTOMOTIVE SERIES
VEHICLE
GEARBOX NOISE
AND VIBRATION
MEASUREMENT,
SIGNAL ANALYSIS,
SIGNAL PROCESSING
AND NOISE REDUCTION
MEASURES
JIRˇÍ TU˚MA

VEHICLE GEARBOX
NOISE AND VIBRATION
Automotive Series
SeriesEditor:ThomasKurfess
VehicleGearboxNoiseand Tu˚ma January2014
Vibration:Measurement,Signal
Analysis,SignalProcessingand
NoiseReductionMeasures
Modelling,SimulationandControlof Tanelli,CornoandSavaresi March2014
Two-WheeledVehicles
ModelingandControlofEnginesand ErikssonandNielsen February2014
Drivelines
AdvancedCompositeMaterialsfor Elmarakbi December2013
AutomotiveApplications:Structural
IntegrityandCrashworthiness
GuidetoLoadAnalysisforDurability JohannessonandSpeckert November2013
inVehicleEngineering
VEHICLE GEARBOX
NOISE AND VIBRATION
MEASUREMENT, SIGNAL ANALYSIS,
SIGNAL PROCESSING AND NOISE
REDUCTION MEASURES
Jirˇ´ıTu˚ma
VSˇBTechnicalUniversityofOstrava,CzechRepublic
Thiseditionfirstpublished2014
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Tuma,Jiri(Engineer)
Vehiclegearboxnoiseandvibration/byJiriTuma.
1onlineresource.
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ISBN978-1-118-79761-7(ePub)–ISBN978-1-118-79762-4(AdobePDF)–
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TL262
629.2′440288–dc23
2013051076
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-1-118-35941-9
Setin10/12ptTimesbyAptaraInc.,NewDelhi,India
1 2014
ToMagda,Lucie,PeterandEva
Tothememory ofmyparentsandbrother

Contents
SeriesPreface xi
Preface xiii
Acknowledgements xv
1 Introduction 1
1.1 DescriptionoftheTATRATruckPowertrainSystem 2
1.2 TestStands 3
References 5
2 ToolsforGearboxNoiseandVibrationFrequencyAnalysis 7
2.1 TheoryofDigitisationofAnalogueSignals 7
2.1.1 TypesofSignals 7
2.1.2 NormalDistribution 10
2.1.3 MeanValueandStandardDeviation(RMS)ofaGeneralSignal 10
2.1.4 Covariance 11
2.1.5 MeanValueandStandardDeviation(RMS)ofaSinusoidalSignal 12
2.1.6 DigitalisationofSignals 12
2.1.7 Signal-to-NoiseRatio 14
2.1.8 SamplingasaMapping 15
2.2 Nyquist-ShannonSamplingTheorem 16
2.2.1 AntialiasingFilter 18
2.2.2 SoundandVibrationMeasuringChain 20
2.3 SignalAnalysisBasedonFourierTransform 21
2.3.1 TimeandFrequencyDomain 21
2.3.2 FourierSeriesforPeriodicFunctions 22
2.3.3 FourierTransformoftheContinuous-TimeFunctions 24
2.3.4 Short-TimeFourierTransform 26
2.3.5 FourierTransformoftheDiscrete-TimeFunctions 27
2.3.6 InverseFourierTransformoftheDiscrete-TimeFunctions 28
2.3.7 DFTofaConstantandaCosineSignal 30
2.3.8 PhasorsasaToolforModellingHarmonicSignals 32
2.3.9 ExampleofDFTCalculation 34
2.3.10 TimeandFrequencyScales 35
viii Contents
2.3.11 SpectralUnitofAutospectrum 36
2.3.12 Cross-Spectrum 37
2.3.13 CalculationoftheInverseDiscreteFourierTransform 39
2.3.14 FastFourierTransform 39
2.3.15 TimeWindow 40
2.3.16 CalculationoftheSignalPower 43
2.3.17 FrequencyWeighting 46
2.3.18 AnalysisofRandomSignalswiththeUseofAveraginginthe
FrequencyDomain 48
2.4 ZoomFFT 52
2.4.1 Real-TimeZoom 53
2.4.2 Non-DestructiveZoom 54
2.5 FiltrationintheFrequencyDomain 55
2.5.1 Filtering 56
2.5.2 IntegrationandCalculationofDerivatives 57
2.6 AveragePoweroftheSignal 59
References 60
3 GearboxFrequencySpectrum 61
3.1 SourceofGearboxNoiseandVibration 61
3.2 SpectrumSignature 65
3.3 LowHarmonicsoftheShaftSpeed 66
3.4 HarmonicsoftheFundamentalToothmeshingFrequencyandtheirSidebands 67
3.5 SubharmonicComponents 70
3.5.1 HuntingToothFrequency 70
3.5.2 EffectoftheOilFilmInstabilityinJournalBearings 71
3.6 Ghost(orStrange)Components 71
3.7 GearRattle 72
3.8 PeriodicityinSignalsMeasuredonaPlanetaryGearbox 73
3.9 SpectrumComponentsOriginatingfromFaultsinRollingElementBearings 76
3.9.1 CalculationsforBearingDefectFrequencies 76
3.9.2 EnvelopeFrequencyAnalysis 82
References 83
4 HarmonicsandSidebands 85
4.1 Harmonics 85
4.2 Sidebands 87
4.2.1 AmplitudeModulation 88
4.2.2 PhaseModulation 89
4.2.3 MixedModulation 96
4.3 AnalyticSignal 97
4.3.1 DefinitionofHilbertTransform 99
4.3.2 CalculationofHilbertTransformofSampledSignals 101
4.3.3 DemodulationoftheModulatedHarmonicSignal 104
4.3.4 UnwrappingPhase 105