Dynamics and Vibration Analyses of Gearbox in Wind Turbine

Dynamics and Vibration Analyses of Gearbox in Wind Turbine
Qingkai Han , Jing Wei , Qingpeng Han , Hao Zhang
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
vii3 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
viii Contents7.3 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
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