An envelope detection method based on the first-vibration-mode of bearing vibration

In this paper, the resonance frequency in the first-vibration-mode of mechanical system is studied and applied in the envelope detection for the bearing vibration. The vibration signal of a bearing system is a typical vibration with amplitude modulation. Under the assumption of a stepwise function for the envelope signal, the modulated signal could be decomposed into a sinusoidal function basis at the first-vibration-mode resonance frequency. According to the vibration spectrum, the first-vibration-mode resonance frequency could be initially designated. By applying a recursive estimation algorithm, the resonance frequency could be derived more precisely. Thus, the envelope signal could be retrieved by estimating the coefficients of the function basis with the linear least squares analysis. In addition, the vibration signal with noise rejection could be directly reconstructed from the envelope signal. According to the experimental study, the envelope detection method for the first-vibration-mode resonance frequency could be effectively applied in the signal processing for the bearing defect diagnosis.