During cold precision forging of helical gears, the die experiences high forming pressure resulting in elastic deformation of the die, a main factor affecting dimensional accuracy of a formed gear. The divided flow method in material plastic deformation is an effective way to reduce the forming force and the die pressure during cold precision forging of helical gears. In this study, by utilizing the flow-relief-hole method, a billet design with different initial diameters of the relief-hole is developed to improve the dimensional accuracy of cold forging gears. Three-dimensional Finite Element (FE) models are established to simulate the plastic deformation process of billet during cold precision forging of a helical gear and to determine the forming force acting on the die. Further models of die stress analysis are developed to examine the die elastic deformation and distribution of the displacement. Effects of the relief-hole diameters on die elastic deformation are studied. The results show that the elastic deformation of the die is different in the addendum, dedendum, and involute parts of forging gear using different relief-hole diameters. The die elastic deformation increases firstly and then decreases when the relief-hole diameter increases. The tooth portions are of larger elastic deformation and the peak value locates in the addendum. It shows the importance of optimizing the relief-hole diameter to minimize the dimensional inaccuracy of forging gears caused by the die elastic deformation.
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