The vibration response of gear pair with root crack is shown in Fig. 1: there are three abrupt peaks in the time domain diagram, and the sudden change of peak value increases with the increase of crack depth. The time interval between the two adjacent abrupt peaks is 0.0333s, which corresponds to the frequency of input shaft (i.e. the rotation frequency of driving wheel) f1 = 30Hz.

Fig. 2 is the frequency domain diagram of the displacement of the driving wheel with root cracks of different depths in the 𝑦 direction. By observing and comparing the three pictures, it can be found that when the crack depth is 1 mm, the main frequency components are the meshing frequency fm of the gear pair and its frequency doubling frequency 2fm, 3fm, etc., and there is a very weak side band between the frequency doubling; when the crack depth is 2 mm In addition to the meshing frequency⻕⻕m and its multiple frequency, the side band between the multiple frequency is more obvious than that when the crack depth is 1 mm; when the crack depth is 3 mm, the side band of gear meshing frequency with⻕m and its double frequency is very obvious. Through the above analysis, it can be found that the influence of root crack fault on the vibration response of gear pair will become more and more obvious with the increase of crack depth. By observing the distribution range and amplitude of side band in frequency domain diagram, the fault degree of root crack can be identified, which provides theoretical support for fault diagnosis of gear pair.