The precision forged bevel gear tooth surface can be directly applied without machining. It requires that the precision forged gear tooth surface has high dimensional accuracy, so the tooth shape design plays a very important role in the precision forging of bevel gear. There are two main difficulties in the tooth profile design of bevel gears formed by “one fire two forging” process: one is that the involute tooth profile curve is composed of multiple curve segments, so it is difficult to accurately describe the curve; Second, there are many factors that affect the tooth shape design. The tooth shape of forgings, die cavities and electrodes are not completely consistent, which makes it difficult to ensure the accuracy of tooth shape design.

Therefore, the tooth profile design of bevel gear precision forging is studied. Taking the basic parameters of involute tooth profile as independent variables, the involute tooth profile curve equation is established, which can accurately describe the involute tooth profile. The relationship among the basic parameters of forging, die cavity and electrode tooth profile is deduced, and the accurate quantitative relationship between them is established. The design method is convenient and reliable, which can ensure the accuracy of tooth profile design.
The involute tooth profile curve equation with the basic tooth profile parameters of the bevel gear as independent variables is given. Using the curve command in the three-dimensional modeling software, the involute tooth profile diagram of the bevel gear can be drawn conveniently and accurately; Various factors affecting the tooth shape design of bevel gear formed by “one fire two forging” process are analyzed, and the quantitative relationship between the basic tooth shape parameters of finished bevel gear, forged bevel gear, die cavity and electrode bevel gear is established; A new tooth profile design model for non-linear expansion hot forgings is proposed and its curve equation is given.