Aanlysis of three-dimensional extrusion of sections

Abstract

Various sections have been manufactured with better productivity by extrusion in preference to other processes. Improved strength and better surface finish of sections require lubricated cold extrusion through continuous dies rather than conventional hot extrusion through square dies. To achieve the sound die design, some efficient design method and related theoretical analysis are required for the extrusion of practical sections. To date, no general and systematic approach has been attempted for the generalized three-dimensional extrusion of arbitrarily-shaped sections, either through continuous dies or through square dies, except for models of limited scope. In this study, the following four basic types of three-dimensional extrusion of sections are studied: (i) Three-dimensional extrusion of arbitrarily-shaped sections from similar billets through curved dies when geometrical similarity of cross-section is maintained during extrusion (ii) Three-dimensional extrusion of helical shapes from round billets when axis of cross-section rotates during extrusion (iii) Generalized three-dimensional extrusion of arbitrarily-shaped sections from round billets through continuous dies (iv) Square die extrusion of sections as a three-dimensional extrusion. Kinematically admissible velocity fields for these types of extrusion are derived to formulate upper-bound solutions under the following basic assumptios : (i) Elastic-plastic boundaries are flat planes perpendicular to the axial direction (ii) Distribution of axial velocity at each cross-section is uniform in the plastically deforming region. Conformal transformation or special transformation of a unit circle onto a section is utilized in the derivation. Computations are carried out for various sections with respect to diverse process variables. In the generalized three-dimensional extrusion of sections through continuous dies, a practical method of die design to minimize the extrusion power is proposed from the ...