Adaptive determination of fundamental frequency for direct time-domain averaging

Time-domain averaging (TDA), as an effective signal processing technique for periodic signal enhancement has been widely used for fault detection of gearboxes and bearings. TDA normally requires a tachometer signal to provide an accurate estimation of fundamental frequency. However, tachometer is unavailable or difficult to use in many applications. In this paper, an adaptive fundamental-frequency determination method without tachometer signal is proposed. Firstly, the effect of fundamental-frequency estimation error on direct TDA is investigated, and it indicates that minor error of estimation can cause severe deterioration in curve of attenuation coefficient. Secondly, harmonic-to-noise ratio (HNR) is proposed to evaluate the result of direct TDA for a given fundamental frequency, and it is utilized to optimize the fundamental frequency from a number of candidates. Finally, average waveform is obtained by implementing direct TDA with the optimized fundamental frequency. Examples of gear faults are given to verify the proposed method. The derived fundamental frequency is accurate, and average waveforms indicate the presence of gear faults successfully.