On the validity of time synchronous averaging in variable speed conditions


One of the most common techniques in vibration-based machine diagnostics, particularly of gears, is time synchronous averaging (TSA), which involves averaging the corresponding points from a number of rotational periods of a given shaft. Under constant speed and load, and with a sufficient number of averages, the TSA result is a periodic signal, containing only harmonics of shaft speed. This is a natural processing tool for gear diagnostics, because the gearmesh frequency and its harmonics are retained in the average signal, while random noise and non-synchronous discrete frequency components are removed in the ‘residual’ signal, which itself is useful for studying the random signal content (e.g. for bearing diagnostics).

Under variable speed the situation is more complex. While sophisticated order tracking techniques are available to remove the resulting frequency modulation in the signal, it is difficult to remove the amplitude modulation effects associated with passage of the gearmesh harmonics through system resonances. The resulting TSA signal will not truly represent the gearmeshing signal components, but rather some sort of time average of these components, with much of the deterministic signal – the fluctuations around the mean – leaking through to the residual, reducing the effectiveness of both for subsequent diagnostic analysis.

Techniques based on cepstral filtering have recently been proposed to remove the amplitude modulation arising from transfer path effects under variable speed. It has been found, however, that even after this treatment, the obtained TSA signals are not always reliable, because with variable speed it is not only the transfer path that is time-varying but also the dominant forcing function (gearmesh), which changes as the machine accelerates and decelerates.

This paper uses measurements from a laboratory spur gearbox test rig to examine this phenomenon and to explain the limitations of time synchronous averaging under variable speed. Recommendations are given on how to obtain the most reliable TSA signal in such conditions.