A new angle-domain cepstral method for generalised gear diagnostics under constant and variable speed operation. (1st October 2022) - Randall, R.B.; Smith, W.A.; Borghesani, P.; Peng, Z.
Highlights: ACCL technique produces a gear vibration spectrum that is periodic with the gearmesh frequency. Result can be made independent of machine speed and speed variation. Mark's analysis means that this finds approximate transmission error (TE) faults by removing transfer function effects. Using only the log amplitude spectrum gives an improved ALR (average log ratio) severity indicator for each gear. Combining the periodic amplitude spectrum with the response phase spectrum gives averaged (order tracked) time signals similar to TE. Removing gearmesh harmonics and close sidebands gives improved residual signals. Abstract: This paper proposes a gear diagnostic method denoted as the angle cepstrum comb liftering (ACCL) method. It uses comb liftering in the cepstrum of the order tracked acceleration signal to select all rahmonics of the gearmesh quefrency of a particular meshing gear pair. When converted to the equivalent log spectrum, it thus contains only the harmonics of both gear speeds, and in particular the gearmesh harmonics. The spectrum could thus be adjusted to be periodic at the gearmesh frequency. This implies that the technique not only removes dynamic transfer function effects, independently of speed, but also the (purely static) "mesh transfer functions" (MTFs), defined in Mark's classic papers on gear vibrations, to give a forcing function very closely related to the combined elemental transmission error (TE) components, both geometric and due to elastic deflections. The paper first develops the method, including the theoretical basis for the removal of the transfer functions, and important practical considerations. The method is then applied to several sets of data corresponding to a range of different faults in gear pairs, including tooth root cracks, and pitting due to surface failure. It was found that Mark's ALR (average log ratio) method, applied to the cepstrally edited signal, was a natural and appropriate way to evaluate the results, and track fault development. By combining the modified amplitude spectrum with the response phase spectrum, the newly proposed method also allows extraction of angular-domain waveforms similar to the classic TSA (time synchronous average) for each gear, and also the residual signal obtained by removing gearmesh harmonics and one or two pairs of sidebands around them. These are however "closer to the source", without resonant response effects, and thus not dependent on the operating conditions. The newly proposed approach was found to give similar results for different speeds, and even speed variations up to ±20%, making it a very powerful generalised diagnostic tool. When combined with the original ALR approach, the method is particularly effective for local faults, such as tooth root cracks and presumably large localised spalls, but also for uniformly distributed pitting. In the latter case, it was possible to find parameters that correlate well with indicators of pitting severity, as measured from direct observations of the tooth surface topography. One gear diagnostic technique excluded by this approach is that based on resonant responses to sharp impacts (similar to bearing fault diagnosis), which has been found in some cases to give earlier warning of incipient cracks, for which a different approach would be required. Another is uniform abrasive wear of profiles, but this can often be easily diagnosed by changes in gearmesh harmonics and close sidebands, for which the proposed approach might also be found useful.