# Time varying meshing stiffness of tractor planetary gears

In order to ensure the continuous operation, the meshing process of gears is actually the alternating meshing of single pair of teeth and multiple pairs of teeth, so the meshing stiffness changes periodically. The results are as follows:

1.Meshing stiffness of faulty gear in single pair meshing gear system

Assuming that the change of meshing stiffness of each tooth in the gear pair is the same, the Fourier expression of meshing stiffness of the gear pair under normal meshing state is as follows:

Where, ω m is the meshing frequency.

Assuming that the number of teeth of a gear in a single pair of meshing gear system is Z, one of the teeth is broken, and the peak value of meshing stiffness at the broken tooth is the same as that of the normal tooth, the Fourier expression of meshing stiffness at the broken tooth is as follows:

Where, ω f is the meshing frequency of the fault gear.

2.Meshing stiffness of planetary gear failure in planetary gear drive

In the traditional design of planetary gear, two planetary gears mesh with the inner gear of fixed ring gear at the same time, and there are two groups of vibration with the same meshing frequency, corresponding to four groups of meshing stiffness.

Assuming that the physical and geometric parameters of each planetary gear are exactly the same and the load is uniform, the failure degree of a planetary gear is λ. Based on the meshing stiffness expression of single pair of teeth, the dimensionless expression of each group of meshing stiffness can be obtained. 