Bearing signal models and their effect on bearing diagnostics

•A generalised bearing signal model is proposed and analytically studied.•The physical effects of cage clearance (jitter) and slip are distinguished.•The effects of jitter on CS1/CS2 content and slip on pseudo-CS are quantified.•Time and frequency domain rules for estimating slip and jitter are proposed.•Derivations for outer race faults are confirmed with numerical and experimental evidence. Signal models of rolling-element bearings have been a fundamental tool for the development and justification of new bearing signal processing techniques. A cyclostationary model proposed twenty years ago is still the most common reference for physically-justified bearing diagnostics. Surprisingly, a pseudo-cyclostationary bearing model proposed just a few years later has been almost entirely neglected. Moreover, the validity of the two models has not been tested against actual bearing signals, and there is limited knowledge about the quantitative effect of their parameters. This paper therefore aims at discussing the physical motivations of the two models, developing a single generalised model which includes the properties of both, and assessing the impact of key model parameters, corresponding to physical properties of the bearing, on the signal in the time and frequency domains. This work’s main novelties are analytical and include an assessment of truly- vs pseudo-cyclostationarity in rolling element bearing signals and of the relative importance of first- and second-order (pseudo-) cyclostationary fault symptoms. The first aspect sheds light on the spectral spread of bearing fault harmonics in both the spectrum and envelope-spectrum, while the second provides useful information for the selection of the best diagnostic indicator. Application of the model is illustrated on test-rig data using a bearing with an outer race fault.