Meshing stiffness of spur gear pair with spalling fault

It is assumed that the spalling fault shape of spur gear driving tooth surface is matrix (as shown in Fig. 1), where the spalling length is as, the spalling width is BS, and the spalling depth is HS. Then, according to the energy method, the analytical formula for calculating the tooth surface spalling meshing stiffness is derived.

The calculation formula of bending deformation energy UB is:

The calculation formula of shear deformation energy us is:

The calculation formula of radial compression deformation energy UA is:

Where, G and E are shear modulus and elastic modulus of spur gear material. The calculation formulas of cross-sectional area as and inertia moment is are as follows:

The bending stiffness, shear stiffness and radial compression stiffness of the spalling spur gear pair are calculated by equations (1) to (5), and the meshing stiffness km is formed. The calculation method of the shape change stiffness KF of the base body can be referred to, and the calculation method of the Hertz contact stiffness KH and the meshing transmission meshing stiffness KT of the spur gear pair can be referred to.

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