Angle⧹⧹time cyclostationarity for the analysis of rolling element bearing vibrations

• Bearing diagnostic in nonstationary regime is a challenging task.
• The cyclostationary assumption of the emitted vibrations is jeopardized.
• Bearing vibrations are angle⧹⧹time cyclostationary on average.
• The order⧹⧹frequency spectral correlation is an efficient diagnostic tool.
• The optimality of the angle⧹⧹time approach is demonstrated on real bearing signals.

In speed-varying conditions, the assumption of cyclostationarity of rolling-element bearing vibrations is jeopardized. The emitted signal comprises an interaction between (i) time-dependent components related to the system dynamics (e.g. transfer function) and (ii) angle-dependent mechanisms related to the system kinematics (e.g. impact, load modulations…). This necessarily implies the inadequacy of classical cyclostationary tools no matter a temporal or angular vision is adopted. This consequently calls for an angle⧹⧹time approach which preserves—via the angle variable—the cyclic evolution of the signal while maintaining—via the time variable—a temporal description of the system dynamics. The first object of this paper is to analytically characterize bearing fault vibrations and explore its angle⧹⧹time cyclostationary property. The second object is to experimentally validate these results on real-world vibration signals and demonstrate the optimality of the angle–time approach over classical approaches for rolling element bearing diagnosis.