On the study of applying Morlet wavelet to the Hilbert transform for the envelope detection of bearing vibrations

In this paper, the Morlet wavelet is studied to apply in the envelope analysis for the bearing vibration and, in practice, would be easier to apply in the real-time vibration analyses. The parameter designation of Morlet wavelet is proposed to filter out and demodulate one of the resonance modes of a bearing vibration, but the designation of the filtering passband would not be required. Therefore, the mode vibration and its corresponding envelope could be derived from the real part and the absolute value of the wavelet transform, respectively. In addition, the Morlet wavelet with properly designating the parameters possesses a very excellent property of fast waveform convergence and could effectively reduce the computing burden. From theoretical and experimental studies, it is shown that the designation of Morlet wavelet could be effectively applied in the envelope detection for the vibration signals and could be useful in the defect diagnosis of bearing vibrations.