An envelope analysis based on the resonance modes of the mechanical system for the bearing defect diagnosis

In this paper, an envelope estimation algorithm based on the resonance modes of the mechanical system is proposed and the exponential decay frequency of the envelope signal could be further estimated to be a quantified index for the bearing defect diagnosis. According to the vibration spectrum of the bearing system, the resonance frequencies in the range of its corresponding resonance modes could be initially designated and further revised. Under the assumption of stepwise functions for the envelope signals, the vibration signal could be decomposed into the sinusoidal function bases with fundamental frequencies at the corresponding resonance frequencies. Thus, the envelope signals could be retrieved by estimating the stepwise functions. In addition, the reconstructed signal with noise rejection could be derived from the envelope signals. According to the envelope signals, the exponential decay frequency is estimated to be the diagnosis index of the bearing running condition. In the simulated and experimental studies, it is found that the envelope estimation algorithm could be effectively applied in the signal processing for the bearing vibrations. In addition, the envelope spectra also show good consistency between the proposed method and the high-frequency resonance technique. Finally, it is shown that the exponential decay frequency could successfully be the quantified index for the bearing defect diagnosis.