Joint amplitude and frequency demodulation analysis based on local mean decomposition for fault diagnosis of planetary gearboxes

• The characteristics of envelope spectrum and instantaneous frequency spectrum are summarized.
• A joint amplitude and frequency demodulation method is proposed.
• The theoretical derivations are validated experimentally.

The vibration signals of faulty planetary gearboxes have complicated spectral structures due to the amplitude modulation and frequency modulation (AMFM) nature of gear damage induced vibration and the additional multiplicative amplitude modulation (AM) effect caused by the time-varying vibration transfer paths (for local gear damage case) and the passing planets (for distributed gear damage case). The spectral complexity leads to the difficulty in fault diagnosis of planetary gearboxes. Observing that both the amplitude envelope and the instantaneous frequency of planetary gearbox vibration signals are associated with the characteristic frequency of the faulty gear, a joint amplitude and frequency demodulation method is proposed for fault diagnosis of planetary gearboxes. In order to satisfy the mono-component requirement by instantaneous frequency estimation, a signal is firstly decomposed into product functions (PF) using the local mean decomposition (LMD) method. Then, the earliest extracted PF that has an instantaneous frequency fluctuating around the gear meshing frequency or its harmonics is chosen for further analysis, because it contains most of the information about the gear fault. The amplitude demodulation analysis can be accomplished through Fourier transforming the amplitude envelope of the chosen PF. For the frequency demodulation analysis, Fourier transform is applied to the estimated instantaneous frequency of the chosen PF to reveal its fluctuating frequency, thus obtaining the spectrum of the instantaneous frequency. By joint application of the amplitude and frequency demodulation methods, planetary gearbox faults can be diagnosed by matching the dominant peaks in the envelope spectrum and the spectrum of instantaneous frequency with the theoretical characteristic frequencies of faulty gears. The performance of the proposed method is illustrated by simulated signal analysis, and is validated by experimental signal analysis of a lab planetary gearbox with intentionally created pitting and naturally developed wear.