7.6.1 Phase Analysis Based on Analytic Signal Theory with Hilbert Transform.

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Acknowledgments; Contents; Abstract; 1 Introduction; 1.1 Requirement of Wind Turbine Gearbox; 1.2 Dynamics of Gearbox; 1.3 Structure Description of Gearbox in Wind Turbine; 1.4 Modeling Methods for Dynamic and Vibration Analyses; 1.5 Shaft Misalignment in Gearbox; 1.6 Measurement and Analysis of Gearbox Vibration; 1.7 Works in This Book; References; 2 Torsional Dynamics of Gear-Rotor System in Wind Turbine Gearbox; 2.1 Lumped Mass Model for Torsional Dynamics; 2.1.1 Mechanical Schematic; 2.1.2 Definition of DOFs; 2.1.3 Mesh Stiffness Excitation; 2.1.4 Transmission Error Excitation.

2.1.5 Mesh Damping in the Planetary Train2.1.6 Governing Equations; 2.2 Torsional Dynamics of the Gearbox; 2.3 Load Factors of Gear-Rotor System in Gearbox; 2.3.1 Analysis of System Excitation and Damping; 2.3.2 Load Factors of Gear-Rotor System; 2.4 Load-Sharing Coefficients Based on Torsional Dynamics; 2.4.1 Calculation of Load-Sharing Coefficients; 2.4.2 Load-Sharing Structure Design; 2.4.3 Load-Sharing Performance Effected by the Errors; 2.5 Experimental Test of Load Balances in Gearbox; References; 3 Parameter Optimization for Planetary Gear System Based on Torsional Dynamics.

3.1 Design Variables and Objective Function3.2 The Constraint Function; 3.3 Parameter Optimization for High-Speed Transmission System with Parallel Axes; 3.4 Distribution of Reliability; 3.5 Example and Analysis; References; 4 Influence of Unbalance and Misalignment on Load-Sharing Coefficient of Gear-Rotor System Based on Torsional Dynamics; 4.1 Modeling Method for Dynamic Analysis of Gear-Rotor System; 4.1.1 Shaft Element; 4.1.2 Lumped Mass Element; 4.1.3 Bearing Element; 4.1.4 Gear Meshing Element; 4.1.5 Basic Principles and Dynamics Model; 4.2 Load-Sharing Coefficient Analyses.

4.2.1 Load-Sharing Coefficient of Planetary Gear Trains4.2.2 Influence of Unbalance on Load-Sharing Coefficient; 4.2.3 Influence of Misalignment on Load-Sharing Coefficient; References; 5 Modal Analyses Based on Whole Gearbox FE Model in Wind Turbine; 5.1 FE Model of Transmission Chain System in Wind Turbine; 5.2 Whole Gearbox FE Model (WG-FEM) of Wind Turbine; 5.3 Modal Analysis of the Gearbox; References; 6 Vibration Measurements of Wind Turbine Gearbox; 6.1 Bench Tests; 6.2 Operating Modal Tests; 6.3 Vibrations of On-site Tests.

6.4 Fault Diagnoses for Wind Turbine Gearbox Based on Vibration MeasurementsReferences; 7 Vibration Signal Analyses of Gearbox in Time-Domain, Frequency-Domain, and Time-Frequency Domain; 7.1 Structure Description and Measuring Method; 7.2 Vibration Measurements of Wind Turbine Gearbox; 7.3 Analysis of Vibration Signals of Gearbox Based on Time Domain; 7.4 Cross-Correlation Function Estimates of Vibration Signals; 7.5 Spectra Analysis of Vibration Signals of the Wind Turbine Gearbox; 7.6 Phase Analysis of Vibration Signals of Wind Turbine Gearbox.

This book explores the dynamics and vibration properties of gearboxes, with a focus on geared rotor systems. It discusses mechanical theories, finite-element based simulations, experimental measurements and vibration signal processing techniques. It introduces the vibration-resonance calculation method for the geared rotor system in wind turbines and load sharing of the planetary gear train, and offers a method for calculating the vibrations of geared rotor systems under either internal excitations from gear sets or external loads transferred from wind loads. It also defines and elaborates on parameter optimization for planetary gear systems based on the torsional dynamics of wind-turbine geared rotor systems. Moreover, it describes experimental measurements of vibrations on the wind-turbine gearbox performed on the test rig and on site, and analyzes the vibration signals of different testing points, showing them in both time and frequency domains. Lastly, it lists the gear coupling frequencies and fault characteristic frequencies from the vibrations of the gearbox housing. The technologies and results presented are valuable resources for use in dynamic design, vibration prediction and analysis of gearboxes and geared rotor systems in wind turbines as well as many other machines.