Plastic mechanical analysis of drawing force based on a twin elliptical die

Abstract

According to the stream function requirement, a twin elliptical die for rod or wire drawing is designed, and the subsequent plastic mechanical analysis is carried out. In terms of the volume constant condition, a kinematically admissible velocity field describing the drawing process is constructed. Based on the velocity field, the analytical expression of internal plastic deformation energy rate accounting for the non-zero shear strain rate is obtained by using the mean value theorem of integral. Then, the analytical expression of friction energy rate is also derived by the mean value theorem of integral. Ultimately, the analytical expression of the drawing force is obtained based on the upper bound method. It is found that there exists the optimal die semi-angle which depends on the relative reduction and friction factor. The analytical drawing force based on the twin elliptical die is validated by the corresponding simulated results, and a very agreement is found since the relative errors between them are less than 9.2%.