Planetary Gearbox Fault diagnosis via Joint Amplitude and Frequency Demodulation Analysis Based on Variational Mode Decomposition

Planetary gearbox vibration signals have strong modulation features due to the amplitude modulation and frequency modulation (AM-FM) effect of gear faults, as well as the amplitude modulation (AM) effect of time-varying vibration transfer paths, on gear meshing vibrations. This results in an involute sidebands structure in Fourier spectrum, possibly misleading fault diagnosis. The modulating frequency of both amplitude modulation (AM) and frequency modulation (FM) parts is closely related to the gear fault characteristic frequency. This inspires the idea of joint amplitude and frequency demodulation analysis, thus addressing the complex sidebands issue inherent in Fourier spectrum. Demodulation analysis requires mono-component signals for accurate estimation of instantaneous frequency, and proper selection of an AM-FM component sensitive to gear fault. To this end, we firstly decompose the complex signal into intrinsic mode functions (IMFs) via variational mode decomposition (VMD), by exploiting its capability in decomposing complex modulated signal into constituent AM-FM components. For effective application of VMD in complex planetary gearbox signal analysis, we propose a method to determine a key parameter in VMD, i.e. the number of IMFs to be separated. For accurate instantaneous frequency estimation, we decompose IMFs via empirical AM-FM decomposition, to remove the influence of AM on instantaneous frequency estimation. Then, we select the sensitive IMF that contains the main gear fault information for further demodulation analysis. In order to properly select the sensitive IMF, we propose a criterion based on the gear vibration characteristics and the VMD properties. Finally, we obtain the amplitude and frequency demodulated spectra by applying Fourier transform to the amplitude envelope and instantaneous frequency of the selected sensitive IMF. According to the characteristics exhibited in the demodulated spectra, we can detect planetary gearbox fault. The proposed method is illustrated via a numerical simulated planetary gearbox vibration signal, and is further validated using lab experimental vibration signals of a planetary gearbox. Faults on all the three types of gear (sun, planet and ring) are successfully identified.