The tooth profile of hot forging bevel gear is the basis for designing and inspecting the tooth profile of die cavity. It is obtained by considering the thermal expansion of forgings. According to whether the temperature field in the forging is uniform at the end of forging, the thermal expansion of bevel gear forgings can be divided into linear expansion and nonlinear expansion. In general, hot forgings are designed according to linear expansion.
In the case of linear expansion, the influence of thermal factors on the tooth profile parameters is linear, that is, all the length parameters of the tooth profile change according to the linear expansion rate, and the angle parameters remain unchanged. The involute shape of the tooth profile consists of the modulus m, the number of teeth Z and the pressure angle α Therefore, the tooth profile after linear expansion can be obtained by changing the module of the gear, as shown in the figure.
The midpoint line in the figure is the tooth profile of room temperature forgings, and the solid line is the tooth profile of hot forgings after linear expansion. The modulus calculation formula of gears after linear expansion is as follows:
Where
M1 – modulus of linear expansion hot forging;
M – module of forgings at room temperature, i.e. module of finished bevel gear;
ρ 1 – linear expansion coefficient of bevel gear blank
T1 – final forging temperature of bevel gear forgings.
The calculation formula of involute tooth profile with known modulus M can obtain the addendum circle radius, root circle radius and base circle radius of linear expansion hot forgings.