The dynamic boundary condition of the modification area of involute spur gear

If there is tooth profile modification, the dynamic boundary condition of the modification area should be added on the basis of the dynamic boundary condition of single and double tooth mesh. In this paper, only the modification of tooth top is considered, and the modification of tooth profile is introduced in detail.

The boundary conditions of the modification area of the external gear pair are shown in the figure. In the figure, L1 and L2 are the addendum length of gear 1 and gear 2 respectively, cmax1 and cmax2 are the maximum addendum corresponding to the addendum position of gear 1 and gear 2 respectively. α 1 is the boundary condition of gear 1 modification starting point, and α 1 corresponding to different modification length L1 is also different.

When the gear mesh enters into the modification zone of gear 2, the boundary condition α 2 of another modification zone on gear 1 can be determined by combining the formula

Where, l (T) is the dynamic center distance; α (T) is the dynamic engagement angle; α 2 is the pressure angle at the starting point of gear 2 modification, which is related to the modification length L2; Z1 is the number of teeth of gear 1.

Due to the symmetry, the dynamic boundary conditions of single tooth, double tooth and modification area are the same under the meshing condition of tooth surface and tooth back.