Perform Fourier transform on the meshing force curve of the spur gear pair in Figure 1 to obtain the spectrum diagram of the meshing force of the spur gear pair at different rotational speeds, as shown in Figure 2.
Using the formula, it is calculated that the meshing frequencies of the gear pair at speeds of 0.56n, n, 1.5n, and 2n are 1447Hz, 2583Hz, 3875Hz, and 5166Hz, respectively. Based on the analysis of the meshing frequency and spectrum diagram of the spur gear pair, it can be seen that when the rotational speeds are n, 1.5n, and 2n, the main spectrum component of the meshing force of the spur gear pair is a one-fold meshing spectrum line, and the amplitude of the one-fold meshing spectrum line increases as the rotational speed increases. In addition, the spur gear pair has a large meshing impact at n and 2n rotational speeds, so the amplitude of the double meshing spectral line in its spectrum is relatively high. When the spur gear is at the resonance speed of 0.56n, the amplitude of the integer multiple meshing spectrum line in the meshing force spectrum of the spur gear pair is lower, but the amplitude of the 2.7 times meshing spectrum line is the highest, and its amplitude is increased by 1 to 2 times compared to the amplitude of the meshing spectrum line at other rotational speeds.
To sum up, an increase in rotational speed will cause the vibration of the spur gear pair to increase, and the meshing stability will both decrease. When the spur gear is at resonant rotational speed, the spur gear pair will experience severe meshing disengagement, and the meshing vibration of the spur gear presents a strong randomness, and the magnitude of the gear tooth meshing impact increases exponentially.