The analytical determination of friction for flow through conical converging dies

The effects of friction upon the intermediate and final distorted grids for wire drawing and/or extrusion were analytically studied for an assumed triangular velocity field. An upper-bound solution for the process was used. This solution predicted that the shape of the final and intermediate distorted grids were functions of the process geometry and of friction. Initially, combinations of reduction and semi-cone angle (α) were found for which the triangular velocity field was energetically preferred over an existing spherical velocity field. The analytical final distorted grids were then compared to experimentally obtained final distorted grids to determine the experimental friction. This was done by plotting calibration curves for distortion where friction served as the parameter and by comparing the actual distortion with the family of calibration curves.