In the process of gear meshing, the time-varying meshing stiffness is mainly related to the meshing force and deformation of gear teeth, but also affected by the deformation of the wheel body. Sainso et al. Considered that the actual gear body is an elastic ring, and combined with Muskhelishvili method, the influence of the deformation of gear matrix on the time-varying meshing stiffness of gear is derived by using elastic ring theory. The expression formula of the deformation of the gear body caused by the meshing force of the gear is shown in the formula. The parameters μ F and SF in the expression are shown in the figure respectively. The polynomials of L *, m *, p *, Q * are calculated as follows, and the coefficients in the formula are shown in the following formula.

Where:

Rint — hub radius,

RF — root circle radius;

RB — radius of base circle.

The expression of elastic stiffness of gear matrix is as follows