Time domain averaging（TDA） is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error（PCE） to different extent.Several improved TDA methods have been proposed,however they cannot completely eliminate the waveform reconstruction error caused by PCE.In order to overcome the shortcomings of conventional methods,a flexible time domain averaging（FTDA） technique is established,which adapts to the analyzed signal through adjusting each harmonic of the comb filter.In this technique,the explicit form of FTDA is first constructed by frequency domain sampling.Subsequently,chirp Z-transform（CZT） is employed in the algorithm of FTDA,which can improve the calculating efficiency significantly.Since the signal is reconstructed in the continuous time domain,there is no PCE in the FTDA.To validate the effectiveness of FTDA in the signal de-noising,interpolation and harmonic reconstruction,a simulated multi-components periodic signal that corrupted by noise is processed by FTDA.The simulation results show that the FTDA is capable of recovering the periodic components from the background noise effectively.Moreover,it can improve the signal-to-noise ratio by 7.9 dB compared with conventional ones.Experiments are also carried out on gearbox test rigs with chipped tooth and eccentricity gear,respectively.It is shown that the FTDA can identify the direction and severity of the eccentricity gear,and further enhances the amplitudes of impulses by 35%.The proposed technique not only solves the problem of PCE,but also provides a useful tool for the fault symptom extraction of rotating machinery.
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