A simple and fast guideline for generating enhanced/squared envelope spectra from spectral coherence for bearing fault diagnosis

Rolling element bearings are widely used in machines to support rotating shafts and their health conditions degrade over time due to harsh working conditions. Once a fault occurs on the surface of either an inner race or an outer race, impacts caused by rollers striking the fault surface excite resonant frequencies of a machine and then repetitive transients are observed in vibration signals collected from the casing of the machine. Spectral correlation and its normalized version, spectral coherence, are a function of spectral frequency and cyclic frequency, and they are able to simultaneously display resonant frequency bands and bearing fault frequencies. Moreover, it has been proved that integrating spectral correlation over an informative spectral frequency band is related to a squared envelope spectrum which is more conveniently used to detect bearing fault frequencies than the direct inspection of the bi-spectra map of spectral correlation/spectral coherence. Therefore, generating enhanced/squared envelope spectra from spectral correlation/spectral coherence is an important step for the use of spectral correlation/spectral coherence for bearing fault diagnosis. However, in the past years, determining informative spectral frequency bands for generating enhanced/squared envelope spectra from spectral correlation/spectral coherence mainly depends on expertise and careful observations from spectral correlation/spectral coherence. In the case of weak bearing fault frequencies and strong interruptions from other cyclic frequencies, it is not easy for users to determine an informative spectral frequency band for generating an enhanced/squared envelope spectrum from spectral correlation/spectral coherence for bearing fault diagnosis. To solve this problem, a simple and fast guideline is proposed in this paper. Laboratorial bearing fault data and industrial railway axle bearing fault data are used to illustrate how the proposed guideline works. Results showed that the proposed guideline is effective in determining informative spectral frequency bands for generating enhanced/squared envelope spectra from spectral coherence for bearing fault diagnosis. Comparisons with the fast Kurtogram and an enhanced squared envelope spectrum generated from integrating spectral coherence over the whole spectral frequency band are conducted to highlight the superiority of the proposed guideline.