Dynamics and Vibration Analyses of Gearbox in Wind Turbine (eBook)

Acknowledgments 5
Contents 6
Abstract 9
1 Introduction 11
1.1 Requirement of Wind Turbine Gearbox 11
1.2 Dynamics of Gearbox 12
1.3 Structure Description of Gearbox in Wind Turbine 13
1.4 Modeling Methods for Dynamic and Vibration Analyses 14
1.5 Shaft Misalignment in Gearbox 15
1.6 Measurement and Analysis of Gearbox Vibration 16
1.7 Works in This Book 16
References 17
2 Torsional Dynamics of Gear-Rotor System in Wind Turbine Gearbox 18
2.1 Lumped Mass Model for Torsional Dynamics 18
2.1.1 Mechanical Schematic 18
2.1.2 Definition of DOFs 19
2.1.3 Mesh Stiffness Excitation 20
2.1.4 Transmission Error Excitation 21
2.1.5 Mesh Damping in the Planetary Train 22
2.1.6 Governing Equations 23
2.2 Torsional Dynamics of the Gearbox 28
2.3 Load Factors of Gear-Rotor System in Gearbox 28
2.3.1 Analysis of System Excitation and Damping 28
2.3.2 Load Factors of Gear-Rotor System 34
2.4 Load-Sharing Coefficients Based on Torsional Dynamics 39
2.4.1 Calculation of Load-Sharing Coefficients 40
2.4.2 Load-Sharing Structure Design 41
2.4.3 Load-Sharing Performance Effected by the Errors 44
2.5 Experimental Test of Load Balances in Gearbox 48
References 50
3 Parameter Optimization for Planetary Gear System Based on Torsional Dynamics 52
3.1 Design Variables and Objective Function 52
3.2 The Constraint Function 53
3.3 Parameter Optimization for High-Speed Transmission System with Parallel Axes 56
3.4 Distribution of Reliability 57
3.5 Example and Analysis 57
References 60
4 Influence of Unbalance and Misalignment on Load-Sharing Coefficient of Gear-Rotor System Based on Torsional Dynamics 61
4.1 Modeling Method for Dynamic Analysis of Gear-Rotor System 61
4.1.1 Shaft Element 61
4.1.2 Lumped Mass Element 62
4.1.3 Bearing Element 63
4.1.4 Gear Meshing Element 64
4.1.5 Basic Principles and Dynamics Model 70
4.2 Load-Sharing Coefficient Analyses 72
4.2.1 Load-Sharing Coefficient of Planetary Gear Trains 72
4.2.2 Influence of Unbalance on Load-Sharing Coefficient 72
4.2.3 Influence of Misalignment on Load-Sharing Coefficient 73
References 76
5 Modal Analyses Based on Whole Gearbox FE Model in Wind Turbine 78
5.1 FE Model of Transmission Chain System in Wind Turbine 78
5.2 Whole Gearbox FE Model (WG-FEM) of Wind Turbine 79
5.3 Modal Analysis of the Gearbox 80
References 82
6 Vibration Measurements of Wind Turbine Gearbox 83
6.1 Bench Tests 83
6.2 Operating Modal Tests 85
6.3 Vibrations of On-site Tests 89
6.4 Fault Diagnoses for Wind Turbine Gearbox Based on Vibration Measurements 91
References 96
7 Vibration Signal Analyses of Gearbox in Time-Domain, Frequency-Domain, and Time–Frequency Domain 97
7.1 Structure Description and Measuring Method 97
7.2 Vibration Measurements of Wind Turbine Gearbox 99
7.3 Analysis of Vibration Signals of Gearbox Based on Time Domain 99
7.4 Cross-Correlation Function Estimates of Vibration Signals 101
7.5 Spectra Analysis of Vibration Signals of the Wind Turbine Gearbox 102
7.6 Phase Analysis of Vibration Signals of Wind Turbine Gearbox 107
7.6.1 Phase Analysis Based on Analytic Signal Theory with Hilbert Transform 107
7.6.2 Results of Phase Analysis of Vibration Signals of Wind Turbine Gearbox 109
7.7 Hilbert–Huang Transform Analysis of Vibration Signals of Wind Turbine Gearbox 109
7.7.1 Basic Principle of Hilbert–Huang Transform Technique 112
7.7.2 HHT Analysis of Vibrations of Wind Turbine Gearbox 120
References 122
8 Conclusions 123
Appendix A: Codes of Factor KA 124
A.1 Main_Program.m 124
A.2 Subprogram.m 140
A.3 plantary_carrier_Stiffness.m 160
A.4 Excitation.m 160
Appendix B: Codes of Time-frequency Analysis of Vibration Signals 161
B.1 time domain waveform.m 161
B.2 fft.m 161
B.3 main_3D_FFT.m 162
Appendix C Codes of Hilbert-Huang Transform Analysis of Vibration Signals 163
emd.m 163
C.1 hhspectrum.m 165
C.2 toimage.m 166
C.3 disp_hhs.m 167