Absolute transmission error: A simple new tool for assessing gear wear

Abstract

Gear transmission error (TE) has become a promising diagnostic tool due to the fact that, compared with vibration responses, it is much less affected by the transfer path from the source to the measurement, and it can be measured conveniently using shaft encoders installed on the input and output of a gear stage. It is also the direct cause of vibration and noise in gears, and it is directly linked to deviations from the perfect involute tooth profile. In the literature, TE-based gear diagnostics has revolved around the analysis of changes in the gearmesh waveform, such as its amplitude or shape, which contains information about the tooth profile and deflection under load. However, if there is a bulk removal of material from the tooth surface due to wear, appearing as a mean effect across all teeth, this would in theory manifest itself as a DC shift in the transmission error, but it would not be observed in a conventional TE signal, even though it is essentially the most crucial measurement that describes wear severity. This is because the initial phases of the encoder signals used to obtain conventional TE measurements are arbitrary, and consequently the mean of TE signals is usually set to zero since it does not represent any physical quantity. Therefore, to be able to measure the effect of average wear depth on TE (mean TE), the TE signals recorded at different wear stages must somehow be rephased so as to align them to have the same fixed-reference starting point before they can be compared. This paper proposes a novel approach to conduct this rephasing of encoder signals (or even once-per-rev tachometer signals) to have the same reference within a hunting tooth period (HTP), defined as the fundamental period where the meshing of all different tooth pairs has been encountered. This rephasing enables the determination of the DC shift in the transmission error relative to a reference measurement, typically from an unworn gearset. In the case of multi-pulse-per-rev encoder signals, this DC component can be combined with the conventional TE to obtain the ‘absolute transmission error’, which indicates not just deviations from an involute profile, but also the average wear depth for all teeth in the gear set. The proposed technique is validated using encoder and tachometer measurements from a dry gear wear experiment and is found to be very robust in assessing the severity (average depth) of gear wear.