Upper bound analysis of wire drawing through a twin parabolic die

Abstract

According to the demand of stream function, a twin parabolic die as a streamline for wire drawing was designed and its kinematically admissible velocity field was then developed. Using the specific energy rate of MY (mean yield) criterion, the mathematical expression of internal deformation energy rate is obtained. Through surface integral of the proposed velocity field, the friction energy rate is also determined. Based on upper bound method, an analytical solution of drawing force is ultimately obtained. The effect of percentage reduction and die semi-angle on the drawing force are discussed. Comparison shows that the calculated drawing forces of the proposed die closely match its numerical drawing forces, and are the lowest compared with those based on conical die, hyperbolic die and elliptic die.