End face profile of cylindrical gear

The profile of hobbing chamfering tool and the profile of the end face of the processed cylindrical gear are no longer conjugate tooth profiles, so the analytical method based on the meshing principle of cylindrical gear can not be used to solve the tool profile.

According to the chamfering requirements of cylindrical gear tooth profile, the complete chamfering tooth profile includes two parts: involute and tooth root arc (as shown in the figure, take the left tooth profile as an example).

(1) Left tooth profile involute RL of cylindrical gear:

Where: A is the development angle, Rb is the radius of the base circle, δ Is the initial deflection angle.

(2) For the tooth root arc of cylindrical gear, select the arc radius RC, and determine that the center is at the starting point of involute according to the initial spread angle as, then the center coordinates of left profile arc (XC, YC):

On the basis of determining the coordinates of the center of the circle, the basic equation RCL of the tooth root arc of the left tooth profile is established:

Due to the symmetrical arrangement of the end tooth profile of cylindrical gear, the involute and tooth root arc equations of the right tooth profile will not be repeated.

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