A stochastic model for simulation and diagnostics of rolling element bearings with localized faults

This paper addresses the stochastic modeling of the vibration signal produced by localized faults in rolling element bearings and its use for diagnostic purposes. The aim is essentially to provide a better understanding of the recognized "envelope analysis" technique as classically used in the diagnostics of rolling element bearings, and incidentally give theoretical proofs for the specific features of envelope spectra as obtained from experimental data. The proposed model may also prove useful for simulation purposes. First, the excitation force generated by a defect is modeled as a random point process and its spectral signature is derived analytically. Then its transmission through the bearing is investigated in detail in order to find the spectral characteristics of the resulting vibration signal. The analysis finally gives sound justification for "squared" envelope analysis and the type of spectral indicators that should be used with it.