Abstract: Extraction of the rotational frequency is the key step of employing order tracking based on the time-frequency representation (TFR) in fault diagnosis of rotational mechanical machinery under varying rotational speed the assistance of a speed sensor. However, the lack of obvious and extractable rotational frequency components in the TFR of the vibration signal of the rolling bearing will block the usage of this algorithm. As such, a new equivalent rotational frequency (ERF) of IRF, the instantaneous fault characteristic frequency (IFCF), is introduced, and a corresponding estimation algorithm based on the lower fault characteristic order coefficient is proposed to estimate this ERF. A series of band-pass filters whose frequency bands can be determined by the range of rotational frequency are constructed along the frequency axis. The ERFs of all these band-pass filtered results are then extracted from the envelope time-frequency representation of the corresponding band-pass filtered results. The fault characteristic order (FCO) envelope spectrums are calculated based on the resampled version of the band-passed filtered signal using the corresponding ERF. The lower fault characteristic order coefficient which equals to the amplitude summation of the 1st, the 2nd and the 3rd fault characteristic order is finally used to determine the best filtered band and corresponding ERF. Resampling the original vibration signal with the IFCF trend can result in the resampled signal which can be used for the final diagnosis of rolling bearing under the varying rotational speed. The effectiveness of the proposed method is validated by both simulated and experimental bearing vibration signals.

Key words: varying rotational speed, equivalent rotational frequency, fault diagnosis, instantaneous fault characteristic frequency, rolling bearing, lower fault characteristic order coefficient