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Research Papers

A Generalized Velocity Field for Plane Strain Extrusion Through Arbitrarily Curved Dies

[+] Author and Article Information
H. Haghighat, P. Amjadian

Mechanical Engineering Department,  Razi University, Kermanshan, 67149-67346 Iran

J. Manuf. Sci. Eng 133(4), 041006 (Jul 20, 2011) (7 pages) doi:10.1115/1.4004407 History: Received January 13, 2011; Revised May 24, 2011; Published July 20, 2011; Online July 20, 2011

In this paper, plane strain extrusion through arbitrarily curved dies is investigated analytically, numerically, and experimentally. Two kinematically admissible velocity fields based on assuming proportional angles, angular velocity field, and proportional distances from the midline in the deformation zone, sine velocity field, are developed for use in upper bound models. The relative average extrusion pressures for the two velocity fields are compared to each other and also with the velocity field of a reference for extrusion through a curved die. The results demonstrate that the angular velocity field is the best. Then, by using the developed analytical model, optimum die lengths which minimize the extrusion loads are determined for a streamlined die and also for a wedge shaped die. The corresponding results for those two die shapes are also determined by using the finite element code and by doing some experiments and are compared with upper bound results. These comparisons show a good agreement.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of half-section of plane strain extrusion to show the derivation of the velocity field

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Figure 2

Sketch of plane strain extrusion through a curved die and its deformation zones in Cartesian coordinate system [22]

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Figure 3

Relative extrusion pressures for extrusion through a Yang and Han die shape using the angle and sine velocity fields: (a) for to/tf=1.54 and mf=0.2, (b) for to/tf=2.5 and mf=0.2, (c) for to/tf=2.5 and mf=0.5

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Figure 4

Comparison between upper bound results for Yang and Han die shape and the wedge shaped die for to/tf=1.54 and mf=0.3

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Figure 5

Initial strips and extruded samples for: (a) wedge shaped die and (b) Yang and Han die shape

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Figure 6

Experimental load-displacement curves of the two dies

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Figure 7

(a) The finite element mesh and (b) the deformed mesh

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Figure 8

Comparison of analytical, FEM, and experimental extrusion pressure-displacement curves for: (a) wedge shaped die and (b) Yang and Han die shape

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