# Effect of discharge gap on electrode tooth profile in precision cold rotary forging of bevel gear

In EDM, there is a discharge gap between the tooth profile of concave model cavity and electrode tooth profile δ。 According to the discharge property of EDM, it is assumed that the discharge gap value is equal along the normal direction of the electrode surface, so the tooth profile size of the concave model cavity minus the discharge gap is the electrode tooth profile size at the end of EDM. Fig. 1 shows an equivalent cavity tooth profile L1 and an equivalent electrode tooth profile L2 at a pitch of L.

As shown in Fig. 1, a point A1 on L1 reduces a discharge gap boundary in its normal direction δ That is, the point A2 on L2 is obtained.

Because the points on L1 and L2 differ by the same distance in the normal direction δ， According to the properties of involute, when L1 is involute, L2 is also involute, and their base circles are equal, but Li is one earlier than L2 θ Horn. That is, the equivalent electrode tooth profile L2 can rotate counterclockwise around the coordinate origin by the equivalent die cavity tooth profile L1 θ The angle is obtained.

Let the tooth profile L1 of the equivalent concave model cavity be a standard involute, and its parameter equation is:

In the above formula, (x1, Y1) represents the coordinates of any point A1 on L1, R is the base circle radius of L1 tooth profile, and t is the parameter.

Therefore, according to the principle of graphic transformation, the rotation transformation formula is used:

By substituting the formula:

The formThe formula is the theoretical profile parameter equation of equivalent electrode tooth profile. It is not a standard involute equation, but a modified involute equation based on the involute of equivalent die cavity tooth profile. Their tooth profiles correspond to the same base circle, so their involute shapes are the same, but the involute starting point of equivalent electrode tooth profile is one later than that of equivalent cavity tooth profile θ Angle, that is, the electrode tooth profile is formed by the negative displacement of the die cavity tooth profile.

Therefore, the electrode can use the same tooth profile parameters and tools as the die cavity tooth profile, but it is necessary to change the bed and process the tooth profile with equal radial negative displacement. 