Due to the multiple gear-pair meshes in planetary gear train, fault features of tooth root crack are weak and complicated in vibration signals. Influenced by the time-varying transfer paths of vibration signals, the fault features of crack are further weakened, which becomes hard to diagnose. To reveal the origination of crack fault features, a lumped-parameter-model of planetary gear train is firstly built to solve the excitation forces that generate vibration signals. Gear mesh stiffness that drives the excitation forces is used to equivalently reflect the crack characteristics. Secondly, a finite-element-model of flexible housing is used to calculate the time-varying transfer functions that determine the amplitude characteristics of vibration signals. Based on the signal convolution theorem, the full-band vibration signal is deduced by the convolution of excitation forces and flexible transfer functions. Simulations and experimental tests on two typical types of planetary gear trains show good consistency at crack fault frequency features, which effectively validates the proposed models. Significant fault features locating at resonance modulation sidebands are summarized as effective indicators for crack diagnosis.

由于行星齿轮系中的多个齿轮副啮合，齿根裂纹的故障特征较弱且振动信号复杂。受振动信号时变传递路径的影响，裂纹的断裂特征进一步减弱，难以诊断。为了揭示裂纹断裂特征的起源，首先建立了集总参数模型的行星齿轮系来解决产生振动信号的激励力。驱动激振力的齿轮啮合刚度用于等效地反映裂纹特征。其次，使用柔性壳体的有限元模型来计算随时间变化的传递函数，该函数确定振动信号的振幅特性。根据信号卷积定理，通过激励力和灵活的传递函数的卷积推导出全频带振动信号。对两种典型类型的行星齿轮系的仿真和实验测试表明，在裂纹故障频率特征上具有良好的一致性，从而有效地验证了所提出的模型。总结了位于共振调制边带的重要故障特征，作为裂纹诊断的有效指标。