Dynamics and Vibration Analyses of Gearbox in Wind Turbine

168 Pages·2017·22.01 MB·English

by  Qingkai Han

Qingkai Han
Jing Wei
Qingpeng Han
Hao Zhang
Dynamics
and Vibration
Analyses of
Gearbox in
Wind Turbine
Dynamics and Vibration Analyses of Gearbox
in Wind Turbine
Qingkai Han Jing Wei Qingpeng Han
(cid:129) (cid:129)
Hao Zhang
Dynamics and Vibration
Analyses of Gearbox
in Wind Turbine
123
QingkaiHan Qingpeng Han
Collaborative Innovation Center of Major ShanghaiUniversity of Electric Power
MachineManufacturing in Liaoning Shanghai
DalianUniversity ofTechnology China
Dalian
China Hao Zhang
Collaborative Innovation Center of Major
Jing Wei MachineManufacturing in Liaoning
TheState KeyLaboratory of Mechanical DalianUniversity ofTechnology
Transmissions Dalian
ChongqingUniversity China
Chongqing
China
ISBN978-981-10-2746-8 ISBN978-981-10-2747-5 (eBook)
DOI 10.1007/978-981-10-2747-5
LibraryofCongressControlNumber:2016953209
©SpringerNatureSingaporePteLtd.2017
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Acknowledgments
This book is financially supported by Collaborative Innovation Center of Major
Machine Manufacturing in Liaoning, National Basic Research Programs of China
(Nos 2012CB026000-05, 2013CB035402-2), and Natural Science Foundations of
China (Grant Nos 51175070, 11472068).
v
Contents
1 Introduction.... .... .... ..... .... .... .... .... .... ..... .... 1
1.1 Requirement of Wind Turbine Gearbox .... .... .... ..... .... 1
1.2 Dynamics of Gearbox. ..... .... .... .... .... .... ..... .... 2
1.3 Structure Description of Gearbox in Wind Turbine ... ..... .... 3
1.4 Modeling Methods for Dynamic and Vibration Analyses.... .... 4
1.5 Shaft Misalignment in Gearbox .. .... .... .... .... ..... .... 5
1.6 Measurement and Analysis of Gearbox Vibration. .... ..... .... 6
1.7 Works in This Book.. ..... .... .... .... .... .... ..... .... 6
References.. .... .... .... ..... .... .... .... .... .... ..... .... 7
2 Torsional Dynamics of Gear-Rotor System in Wind Turbine
Gearbox... .... .... .... ..... .... .... .... .... .... ..... .... 9
2.1 Lumped Mass Model for Torsional Dynamics ... .... ..... .... 9
2.1.1 Mechanical Schematic.... .... .... .... .... ..... .... 9
2.1.2 Definition of DOFs.. .... .... .... .... .... ..... .... 10
2.1.3 Mesh Stiffness Excitation . .... .... .... .... ..... .... 11
2.1.4 Transmission Error Excitation.. .... .... .... ..... .... 12
2.1.5 Mesh Damping in the Planetary Train.... .... ..... .... 13
2.1.6 Governing Equations. .... .... .... .... .... ..... .... 14
2.2 Torsional Dynamics of the Gearbox... .... .... .... ..... .... 19
2.3 Load Factors of Gear-Rotor System in Gearbox.. .... ..... .... 19
2.3.1 Analysis of System Excitation and Damping .. ..... .... 19
2.3.2 Load Factors of Gear-Rotor System . .... .... ..... .... 25
2.4 Load-Sharing Coefficients Based on Torsional Dynamics.... .... 30
2.4.1 Calculation of Load-Sharing Coefficients . .... ..... .... 31
2.4.2 Load-Sharing Structure Design. .... .... .... ..... .... 32
2.4.3 Load-Sharing Performance Effected by the Errors.... .... 35
2.5 Experimental Test of Load Balances in Gearbox . .... ..... .... 39
References.. .... .... .... ..... .... .... .... .... .... ..... .... 41
vii
viii Contents
3 Parameter Optimization for Planetary Gear System Based
on Torsional Dynamics... ..... .... .... .... .... .... ..... .... 43
3.1 Design Variables and Objective Function... .... .... ..... .... 43
3.2 The Constraint Function.... .... .... .... .... .... ..... .... 44
3.3 Parameter Optimization for High-Speed Transmission
System with Parallel Axes .. .... .... .... .... .... ..... .... 47
3.4 Distribution of Reliability... .... .... .... .... .... ..... .... 48
3.5 Example and Analysis ..... .... .... .... .... .... ..... .... 48
References.. .... .... .... ..... .... .... .... .... .... ..... .... 51
4 Influence of Unbalance and Misalignment on Load-Sharing
Coefficient of Gear-Rotor System Based on Torsional
Dynamics.. .... .... .... ..... .... .... .... .... .... ..... .... 53
4.1 Modeling Method for Dynamic Analysis of Gear-Rotor
System .... .... .... ..... .... .... .... .... .... ..... .... 53
4.1.1 Shaft Element. ..... .... .... .... .... .... ..... .... 53
4.1.2 Lumped Mass Element ... .... .... .... .... ..... .... 54
4.1.3 Bearing Element.... .... .... .... .... .... ..... .... 55
4.1.4 Gear Meshing Element ... .... .... .... .... ..... .... 56
4.1.5 Basic Principles and Dynamics Model ... .... ..... .... 62
4.2 Load-Sharing Coefficient Analyses.... .... .... .... ..... .... 64
4.2.1 Load-Sharing Coefficient of Planetary Gear Trains... .... 64
4.2.2 Influence of Unbalance on Load-Sharing Coefficient . .... 64
4.2.3 Influence of Misalignment on Load-Sharing
Coefficient.... ..... .... .... .... .... .... ..... .... 65
References.. .... .... .... ..... .... .... .... .... .... ..... .... 68
5 Modal Analyses Based on Whole Gearbox FE Model
in Wind Turbine.... .... ..... .... .... .... .... .... ..... .... 71
5.1 FE Model of Transmission Chain System in Wind Turbine.. .... 71
5.2 Whole Gearbox FE Model (WG-FEM) of Wind Turbine.... .... 72
5.3 Modal Analysis of the Gearbox .. .... .... .... .... ..... .... 73
References.. .... .... .... ..... .... .... .... .... .... ..... .... 75
6 Vibration Measurements of Wind Turbine Gearbox .... ..... .... 77
6.1 Bench Tests .... .... ..... .... .... .... .... .... ..... .... 77
6.2 Operating Modal Tests..... .... .... .... .... .... ..... .... 79
6.3 Vibrations of On-site Tests.. .... .... .... .... .... ..... .... 83
6.4 Fault Diagnoses for Wind Turbine Gearbox Based
on Vibration Measurements . .... .... .... .... .... ..... .... 85
References.. .... .... .... ..... .... .... .... .... .... ..... .... 90
7 Vibration Signal Analyses of Gearbox in Time-Domain,
Frequency-Domain, and Time–Frequency Domain.. .... ..... .... 91
7.1 Structure Description and Measuring Method.... .... ..... .... 91
7.2 Vibration Measurements of Wind Turbine Gearbox... ..... .... 93
Contents ix
7.3 Analysis of Vibration Signals of Gearbox Based
on Time Domain .... ..... .... .... .... .... .... ..... .... 93
7.4 Cross-Correlation Function Estimates of Vibration Signals... .... 95
7.5 Spectra Analysis of Vibration Signals of the Wind Turbine
Gearbox ... .... .... ..... .... .... .... .... .... ..... .... 96
7.6 Phase Analysis of Vibration Signals of Wind Turbine
Gearbox ... .... .... ..... .... .... .... .... .... ..... .... 101
7.6.1 Phase Analysis Based on Analytic Signal Theory
with Hilbert Transform... .... .... .... .... ..... .... 101
7.6.2 Results of Phase Analysis of Vibration Signals
of Wind Turbine Gearbox. .... .... .... .... ..... .... 103
7.7 Hilbert–Huang Transform Analysis of Vibration Signals
of Wind Turbine Gearbox .. .... .... .... .... .... ..... .... 103
7.7.1 Basic Principle of Hilbert–Huang Transform
Technique.... ..... .... .... .... .... .... ..... .... 106
7.7.2 HHT Analysis of Vibrations of Wind Turbine
Gearbox . .... ..... .... .... .... .... .... ..... .... 114
References.. .... .... .... ..... .... .... .... .... .... ..... .... 116
8 Conclusions .... .... .... ..... .... .... .... .... .... ..... .... 117
Appendix A: Codes of Factor KA .. .... .... .... .... .... ..... .... 119
Appendix B: Codes of Time-frequency Analysis
of Vibration Signals .. .... .... .... .... .... ..... .... 157
Appendix C: Codes of Hilbert-Huang Transform Analysis
of Vibration Signals .. .... .... .... .... .... ..... .... 159
Abstract
Gearbox is the core part of a wind turbine which realizes the transmission and
energytransferfromwindbladestoelectricgenerator.Thedynamicsandvibration
properties of the gearbox especially of its geared rotor systems prominently
determinetheefficiencyandoperating quality,eventhewhole-lifeexpectationand
reliability of the machine set. In this book, the dynamic analyses and vibration
behaviors are investigated for the gearboxes which are popularly used to modern
wind turbines by using mechanics theories, finite element-based simulations,
experimental measurements, and vibration signal processing techniques.
Firstly,thebackgroundandmainideasofthebookaredescribed.Secondly,the
torsional dynamic model and vibration resonances are achieved based on the
lumpedmassmodelofthegearedrotorsystem,whichiscomposedoftwostagesof
planetarygeartrainsandoneparallelgearpair.Furthermore,theloadsharingofthe
planetarygeartrainbasedonthegiventorsionmodelispresentedwithconsidering
time-varying mesh stiffness, tooth backlash, fixing error, and manufacturing error
ofthegearsandcarrier.Also,themeasuredstrainsatthegeartoothrootsareusedto
confirmthatload-sharinganalysesoftheplanetarygeartrainareacceptable.Based
on the model, the vibrations of both the geared rotor systems and the gearbox
housings are calculated under either the internal excitations coming from gear sets
or external loads transferring from wind loads.
Next, the parameter optimization for planetary gear system is defined and pro-
cessedbasedonthetorsionaldynamicsofthegearedrotorsystemofwindturbine.
The fault-induced vibrations of the geared rotor system are simulated, which
involves the popularly occurring fault of support misalignment of the rotor. The
rotor-misaligned fault-induced vibrations are of importance in practical manufac-
turingerrorcontrolandassemblyprocessingoptimization,evenhelpfulinoperating
condition monitoring and fault diagnosis.
And then, the whole gearbox finite element model (WG-FEM) is built, and its
natural frequencies and modes of the gearbox system (including shells and geared
rotors)arecalculated.Experimentalmeasurementsofvibrationsonthewindturbine
gearboxareperformedonthetestrigandon-site.Thevibrationsignalsofdifferent
testingpointsareanalyzedintimeandfrequencydomainstoexploretheunderlying
xi
xii Abstract
complicated behaviors. Some technologies of Hilbert–Huang transform-based
analyses are also achieved in the vibration signal processing.
At last, the gear coupling frequencies and fault characteristic frequencies are
obtained from the vibrations of the gearbox housing.
In summary, the technologies and results of this work provide some good ref-
erences for dynamic design and vibration prediction and analysis for gearbox and
its geared rotor system of wind turbine, even for many other machines.
(cid:1) (cid:1)
Keywords Gearbox in wind turbine Geared rotor system Model of torsional
(cid:1) (cid:1) (cid:1)
dynamics Parameteroptimization Loadsharingofplanetarygear train Whole
(cid:1) (cid:1) (cid:1)
gearboxfiniteelementmodel Wholegearboxmodes Vibrationsignalprocessing
Vibrationfault diagnosis