A coupled stream function-finite element analysis for wire drawing processes

Abstract

A numerical approach has been developed based on the stream function technique and the finite element analysis to predict required power and temperature rise in wire drawing processes. An admissible velocity field is first proposed using a stream function and then power consumption in the wire drawing is optimized to achieve sensible and unique deformation geometry. In addition, the finite element method together with axi-symmetric Petrov–Galerkin algorithm is coupled with the deformation model to assess the temperature distribution in both the deforming wire and the die during the process. The work hardening effects are also considered in the model both in the deformation zone and on the velocity discontinuity surfaces. The model can estimate the effects of various process parameters such as drawing velocity and die geometry. In order to evaluate the results of the model, the predictions are compared with the established models including force equilibrium as a lower-bound approach and an upper-bound solution based on the spherical velocity field.