# Dynamic meshing stiffness of involute spur gear transmission system

It can be seen from the analysis that the dynamic boundary conditions α B (T) and the dynamic boundary conditions α 2 (T) in the modification area change with the change of the center distance, while α 1 and α 2 (T) change with the change of the modification length. There are many combinations of size relations among α B (T), α 1 and α 2 (T) under different modification length and center distance.

Under different dynamic boundary conditions, there may be five cases in the meshing position of the gear

1. The meshing point is in the single tooth meshing area;
2. The meshing point is in the double tooth meshing area;
3. The meshing point is in the modification area of the gear;
4. The meshing point is in the modification area of the gear;
5. The meshing point is in the same modification area of the two teeth.

The meshing stiffness of single pair of gears and the meshing stiffness of the gear in the modification area are calculated by the analytical method. In the above five cases, the meshing stiffness of the gear changes dynamically with the change of the meshing position. The expressions are as follows:

In the formula, it is the pressure angle of the actual meshing point at any time, and the state of tooth surface and tooth back are shown in the formula respectively.

The meshing stiffness of a single pair of teeth at any time can be expressed as:

Among them, the deformation of the tooth itself and the additional deformation of the wheel body are functions of the gear engagement position.

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