Engaging position of involute spur gear at any engagement teeth

The engagement position of individual gear teeth during gear transmission can be determined by analysis.In order to ensure the continuity of gear drive, the overlap of gears is greater than 1, resulting in the alternation of single-pair tooth engagement and two-pair tooth engagement.When two teeth engage, two adjacent teeth of gear 1 engage at the same time, and the pressure angle of the engagement point between the two teeth is shown in the figure.

From the nature of the involute, the pressure angle at the engagement point of the other engaged teeth on gear 1 at any time during double-tooth engagement can be obtained:

In the formula, Z1 is the number of teeth of gear 1.

According to the principle of involute, the pressure angles alpha1 and alpha2 at the engagement points of two meshing teeth satisfy the following requirements:

Where L is the center distance and alpha is the engagement angle.

By substituting the engagement point pressure angle, dynamic center distance and dynamic engagement angle of gear 1 into the formulas, the engagement point pressure angle of the engagement gear 2 at any time during single-tooth engagement can be obtained:

When the two teeth engage, the pressure angle of the other engagement point at any time on gear 2 is: