Joint envelope and frequency order spectrum analysis based on iterative generalized demodulation for planetary gearbox fault diagnosis under nonstationary conditions

Planetary gearbox vibration signals under nonstationary conditions are characterized by time-varying nature and complex multi-components, making it very difficult to extract features for fault diagnosis. Order spectrum analysis is one of the effective approaches for nonstationary signal analysis of rotating machinery. The main idea of order analysis is to map the time-varying frequency components into constant ones. Inspired by this idea, we propose a new order spectrum analysis method to exploit the unique property of iterative generalized demodulation in converting arbitrary instantaneous frequency trajectories of multi-component signals into constant frequency lines on the time-frequency plane. This new method is completely algorithm-based and tachometer/encoder-free, thus easy to implement. It does not involve equi-angular resampling commonly required by most order tracking methods and is hence free from the decimation and/or interpolation error. The proposed order analysis method can eliminate the time-variation effect of frequency and thus can effectively reveal the harmonic order constituents of nonstationary multi-component signals. However, the planetary gearbox vibration signals also lead to complex sideband orders. As such, we further propose to analyze the order spectrum of amplitude envelope. This will eliminate the complex sideband orders in the order spectrum of original signals, leading to a substantially simplified and more reliable gear characteristic frequency identification process. Nevertheless, the gear and/or planet carrier rotating frequency orders, which are irrelevant to gear fault, may still exist. To avoid possible misleading results due to such frequency orders, we also propose to analyze the order spectrum of instantaneous frequency. Theoretically, the peaks present in frequency order spectrum directly correspond to the gear characteristic frequency orders, which can be used to extract gear fault signature more explicitly. The proposed method has been illustrated via analysis of the simulated signals of planetary gearboxes, and validated using lab experimental planetary gearbox datasets, both under variable speed conditions. The analysis results have shown that the method is effective in extracting both distributed and localized gear faults under nonstationary conditions.