Analytical vibration signal model and signature analysis in resonance region for planetary gearbox fault diagnosis

Abstract

Complex components and multi-modulations characterize planetary gearbox vibration signals. As the vibration signals become time-varying under nonstationary conditions, it is difficult to extract fault features around meshing frequency harmonics, since they are all dependent on speed, and change under time-varying speed conditions. To address this issue, we turn to the resonance region and exploit the time-invariability of resonance frequency and the sideband symmetry around resonance frequency for planetary gearbox fault diagnosis under both constant and time-varying speed conditions. Gear fault generates impulses and thereby excites resonance of the planetary gearbox and even the measurement system. As such, gear fault information can be explored in the resonance region. To thoroughly understand gear fault vibration features in resonance region, the vibration signal is modeled as an amplitude modulation and frequency modulation (AM-FM) process, considering the multi-modulations due to gear fault, time-varying vibration transmission path, and time-varying angle between mesh line of action and measurement axis of vibration sensor. Furthermore, explicit time-varying Fourier spectra under nonstationary conditions are derived. Sideband symmetry features around resonance frequency can be utilized to detect gear fault. This is a major progress and contribution in contrast to reported researches that focus on meshing frequency or its harmonics only. Resonance frequency identification is the key to gear fault feature extraction in resonance region. An on-line resonance frequency identification method under time-varying speeds is proposed by exploiting the nature of resonance independence of running conditions. To effectively pinpoint the time-varying sidebands in the time-frequency domain, the iterative generalized demodulation (IGD) method is used to achieve high time-frequency resolution and to avoid both outer and inner interferences at the same time. The theoretical derivations and proposed method are validated through numerical simulation and lab experiments. Gear fault features are extracted in the resonance region of the planetary gearbox and the accelerometer under time-varying speed conditions.