Filtering based on FRFT for extracting fault orders of sun gears in a variable speed planetary gear system

ObjectiveIn order to better extract the weak fault characteristics of variable-speed planetary gear trains in the noise environment, a method was proposed to determine the optimal order of fractional Fourier transform (FRFT） based on the speed signal and obtain the gear fault order under variable-speed conditions through the bandpass filtering.MethodsFirstly, the gear meshing frequency was calculated according to the rotational speed signal of the input shaft of the planetary gear train and the gear parameters of the system, and then the optimal FRFT order of the meshing frequency was determined by the least square fitting method. On this basis, the bandpass filtering centered on the peak value of the fractional domain was carried out, and the envelope order was analyzed at the same time, so that the envelope order related to the gear fault was obtained. The test was carried out for the second-stage sun gear root crack fault of a planetary gear reducer.ResultsThe results show that it is feasible to determine the optimal order of FRFT based on the speed signal, and the noise and other components can be effectively separated. The maximum relative error between the test results and the theoretical values is 3.4％, which occurs at the low speed and low load.