The sensor-perceived vibration signals of multistage wind turbine gearboxes have more complex frequency features than that of single-stage gearboxes since there are more meshing vibration sources and more complicated transmission paths inside them, which lead to difficulties in condition monitoring and fault diagnosis. Aiming to understand the vibration frequency features of multistage wind turbine gearboxes, a mathematical vibration model of healthy wind turbine gearboxes is developed and the spectral structure of the model is deduced by adopting Fourier series analysis. In the vibration model, the time-varying transmission paths from all the meshing vibration sources to the fixed sensor are considered, and the equivalent transmission path functions of the time-varying transmission paths are proposed for the first time. The theoretical derivations are validated by both simulations and engineering tests using two cases of 2.0MW industrial wind turbine gearboxes. The findings in this work are not only applicable to the gearboxes studied in this paper, but also to other similar multistage gearboxes, which can provide a priori spectral structure for the multistage gearbox to assist its condition monitoring and fault diagnosis.

多级风电机组齿轮箱的传感器感知振动信号比单级齿轮箱具有更复杂的频率特征，因为其内部啮合振动源更多，传递路径更复杂，导致状态监测和故障诊断困难。为了解多级风电机组齿轮箱的振动频率特征，建立了健康风电机组齿轮箱的振动数学模型，并采用傅立叶级数分析推导了模型的谱结构。在振动模型中，考虑了所有啮合振动源到固定传感器的时变传递路径，首次提出了时变传递路径的等效传递路径函数。理论推导通过使用两个 2.0MW 工业风力涡轮机齿轮箱的模拟和工程测试得到验证。这项工作的发现不仅适用于本文研究的齿轮箱，也适用于其他类似的多级齿轮箱，可以为多级齿轮箱提供先验谱结构，辅助其状态监测和故障诊断。