Bearing fault diagnosis under unknown time-varying rotational speed conditions via multiple time-frequency curve extraction

Abstract Under normal operating conditions, bearings often run under time-varying rotational speed conditions. Under such circumstances, the bearing vibrational signal is non-stationary, which renders ineffective the techniques used for bearing fault diagnosis under constant running conditions. One of the conventional methods of bearing fault diagnosis under time-varying speed conditions is resampling the non-stationary signal to a stationary signal via order tracking with the measured variable speed. With the resampled signal, the methods available for constant condition cases are thus applicable. However, the accuracy of the order tracking is often inadequate and the time-varying speed is sometimes not measurable. Thus, resampling-free methods are of interest for bearing fault diagnosis under time-varying rotational speed for use without tachometers. With the development of time-frequency analysis, the time-varying fault character manifests as curves in the time-frequency domain. By extracting the Instantaneous Fault Characteristic Frequency (IFCF) from the Time-Frequency Representation (TFR) and converting the IFCF, its harmonics, and the Instantaneous Shaft Rotational Frequency (ISRF) into straight lines, the bearing fault can be detected and diagnosed without resampling. However, so far, the extraction of the IFCF for bearing fault diagnosis is mostly based on the assumption that at each moment the IFCF has the highest amplitude in the TFR, which is not always true. Hence, a more reliable T-F curve extraction approach should be investigated. Moreover, if the T-F curves including the IFCF, its harmonic, and the ISRF can be all extracted from the TFR directly, no extra processing is needed for fault diagnosis. Therefore, this paper proposes an algorithm for multiple T-F curve extraction from the TFR based on a fast path optimization which is more reliable for T-F curve extraction. Then, a new procedure for bearing fault diagnosis under unknown time-varying speed conditions is developed based on the proposed algorithm and a new fault diagnosis strategy. The average curve-to-curve ratios are utilized to describe the relationship of the extracted curves and fault diagnosis can then be achieved by comparing the ratios to the fault characteristic coefficients. The effectiveness of the proposed method is validated by simulated and experimental signals.