# Calculation method of cylindrical gear tooth profile and cutter profile

In the process of continuous tooth profile chamfering, the cylindrical gear rotates around the c-axis, the tool rolls with the cylindrical gear around the b-axis, and feeds axially in the direction parallel to the z-axis. The profile away from the chamfering thickness of the cylindrical gear end face profile is the chamfering target profile. The rake face of the tool is always in point contact with the chamfering target profile, and the cutting points of the left and right tooth profiles are arranged asymmetrically with the continuous hobbing movement of the cylindrical gear and the tool. To solve the profile of hobbing chamfering tool, it is necessary to establish the schematic diagram of the contact point between the tool and the chamfering target profile of cylindrical gear, as shown in the figure. The schematic diagram of the contact point represents the solution of the tool profile of the tooth profile on the left side of the end face of cylindrical gear.

Make an inclination through the tool axis φ The plane m of S is the xdodzd plane of the coordinate system OD xdydzd, which intersects with the xmomym plane of the coordinate system om xmymzm in the straight line L. The equation of the straight line L is:

Let the straight line L intersect with the chamfering target profile curve at point G, which is the contact point between the rake face of the tool and the chamfering target profile. According to the formula, the left tooth profile equation of the end face of the cylindrical gear is changed into the chamfering target profile equation, which changes with the rotation angle of the tool φ The change of D is combined with the formula to solve the G-point coordinates.

The obtained G-point coordinates are transformed into the chamfering tool moving coordinate system according to the formula to obtain the tool rotation angle φ d. Rotation angle of cylindrical gear φ Profile point of chamfering tool at position G.

Continue to rotate the cylindrical gear by an angle Δθ， The rotation angle of the tool according to the rolling motion relationship Δη。

Get the corresponding cylindrical gear angle φ g+ Δθ、 Tool angle φ d+ Δη Contact point G ‘point. Repeat the above calculation according to the unified step size, continuously solve a series of contact points between the tool rake face and the chamfering target profile, smoothly connect each point, obtain the edge curve of the tool left rake face, and complete the calculation of the tool left profile. The transformation between the tool right profile coordinate system and the calculation of profile points are the same as those on the left.

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