Establishment of stiffness equation of helical gear under spalling fault

The tooth spalling model is shown in Figure 1, where SH is the depth of tooth spalling, SL is the length of tooth spalling, SW is the width of tooth spalling, and l is the component of contact line length in the direction of tooth width. The establishment is shown in Figure 2 In this model, the radius of the base circle is larger than the radius of the tooth root circle. Considering the deformation between the base circle and the tooth root circle, the transition curve between the base circle and the tooth root circle is replaced by a straight line Some parameters in Fig. 2 are shown in the following equation.

Among them:

Z — number of teeth of gear teeth;

α n — normal pressure angle;

RB — base circle radius of gear;

RR — root radius of gear;

X — the distance from any point to the tooth root circle;

D — the distance between the meshing point of gear teeth and the tooth root circle;

D1 — distance from base circle to tooth root circle;

α 2 — the half tooth angle corresponding to the base circle;

α 3 — the half tooth angle corresponding to the tooth root circle.

Bending stiffness of spur gear with quadrilateral spalling

The expressions of KB, radial compressive stiffness Ka, Hertz contact stiffness KH and shear stiffness KS are as follows: