关键词: 行星齿轮箱, 无键相阶次跟踪, 变分模态分解, 故障诊断, 非线性短时傅里叶变换（NLSTFT）

Abstract: Aiming at the problems that vibration signal frequencies of planetary gearboxs were fuzzy and interfered by strong noises under variable speed conditions，a fault diagnosis method was proposed based on NLSTFT non-bonding phase order tracking and variational modal decomposition. Firstly，NLSTFT was used to precisely estimate instantaneous frequency of vibration signals，and then transformed into the instantaneous phase curves through integral operation. A smooth angular domain signal was obtained by signal resampling. Secondly，NCOGS（non-convex overlapping group shrinkage） algorithm was used to de-noise the angular domain signals，and VMD（variational mode decomposition） algorithm was used to perform modal decomposition of the angular domain signals. Finally，the fault diagnosis was realized through the demodulation analysis of the envelope spectrum of each modal component signal. The experimental results show that the new method may effectively promote the performances of fault diagnosis under variable speed conditions，which has the high computational efficiency and strong noise robustness.

Key words: planetary gearbox, non-bonding phase order tracking, variational mode decomposition(VMD), fault diagnosis, non-liner short-time Fourier transform（NLSTFT）