Fault diagnosis of a gearbox based on the analysis of a fractional energy gathering band

To extract the weak fault feature of the accelerating process from a gearbox, a fractional energy gathering band time–frequency aggregated spectrum (FETFAS) is proposed to achieve a fast time–frequency analysis of a large signal and to highlight target components. The best order of the fractional Fourier transform (FRFT) is determined according to the rotating speed signal and transmission ratio. The vibration signal from the accelerating process of a gearbox is processed using the best order FRFT. The energy gathering band (EGB) is determined from the modulus spectrum of the FRFT. Then, the result of the FRFT within the EGB is analyzed using time–frequency analysis, and the energy from this result is aggregated to form the FETFAS. The experimental results show that the method to determine the best order of the FRFT from the rotating speed signal is fast and accurate. The time–frequency analysis of the FRFT’s results in the EGB requires less computation and has a high resolution. The FETFAS has the ability to focus and zoom and is able to highlight the target components and restrain noise. Therefore, the FETFAS is an effective method to extract weak fault feature from the signal of gearbox’s accelerating process.