The rolling bearings often suffer from compound fault in practice. Compared with single fault, compound fault contains multiple fault features that are coupled together and make it difficult to detect and extract all fault features by traditional methods such as Hilbert envelope demodulation, wavelet transform and empirical node decomposition (EMD). In order to realize the compound fault diagnosis of rolling bearings and improve the diagnostic accuracy, we developed negentropy spectrum decomposition (NSD), which is based on fast empirical wavelet transform (FEWT) and spectral negentropy, with cyclic extraction as the extraction method. The infogram is constructed by FEWT combined with spectral negentropy to select the best band center and bandwidth for band-pass filtering. The filtered signal is used as a new measured signal, and the fast empirical wavelet transform combined with spectral negentropy is used to filter the new measured signal again. This operation is repeated to achieve cyclic extraction, until the signal no longer contains obvious fault features. After obtaining the envelope of all extracted components, compound fault diagnosis of rolling bearings can be realized. The analysis of the simulation signal and the experimental signal shows that the method can realize the compound fault diagnosis of rolling bearings, which verifies the feasibility and effectiveness of the method. The method proposed in this paper can detect and extract all the fault features of compound fault completely, and it is more reliable for the diagnosis of compound fault. Therefore, the method has practical significance in rolling bearing compound fault diagnosis.

Planetary gears are widely used in automobiles, helicopters, heavy machinery, etc., due to the high speed reductions in compact spaces; however, the gear fault and early damage induced by the vibration of planetary gears remains a key concern. The time-varying parameters have a vital influence on dynamic performance and reliability of the gearbox. An analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness, and then the dynamical model of the planetary gears with time-varying parameters is established. The natural characteristics of the transmission system are calculated, and the dynamic responses of transmission components, as well as dynamic meshing force of each pair of gear are investigated based on varying internal excitations induced by time-varying parameters and tooth root crack. The effects of gear tooth root crack size on the planetary gear dynamics are simulated, and the mapping rules between damage degree and gear dynamics are revealed. In order to verify the theoretical model and simulation results, the planetary gear test rig was built by assembling faulty and healthy gear separately. The failure mechanism and dynamic characteristics of the planetary gears with tooth root crack are clarified by comparing the analytical results and experimental data.

Singular spectrum decomposition (SSD) is a new adaptive signal processing method for nonlinear and non-stationary signals. By constructing a trajectory matrix and adaptively selecting the embedding dimensions, the method divides non-stationary signals into several single-component signals successively from high frequency to low frequency. However, in the process of component reconstruction, bandwidth estimation and determining sizable trends by building a Gaussian function superposition spectral model are extremely complicated. Moreover, the parameter setting requires too much manual intervention and lacks theoretical support. Hence, aimed at nonlinear and non-stationary vibration signals of rolling bearings, a novel method of fault feature extraction based on the order statistic filter (OSF) for fast SSD (FSSD) is proposed. The FSSD method adopts the envelope method of OSFs to divide the spectrum and determine the sizable trend to improve the process. The proposed method is applied to bearing fault diagnosis. The analysis results of simulation signals and bearing experimental signals show that the new method can decompose signals quickly, effectively and accurately, and the mode mixing and time-consuming problems are refined.