Doctoral Dissertations

Title

Die shapes to minimize distortion during 3D extrusion

January 2002

Keywords

Engineering, Mechanical|Engineering, Metallurgy

Ph.D.

Abstract

The objective of the present investigation is to determine extrusion die shapes, which minimize distortion during axisymmetric and 3D extrusion. An axisymmetric upper bound model with a flexible die shape is developed in a spherical coordinate system. The flexible streamlined die shape is described by a Legendre polynomial series, where the higher order coefficients are selected based upon optimization. Four criteria to minimize distortion are used in the upper bound model to determine optimal die shapes. Analysis of the optimal die shapes with FEM confirms two robust criteria: average effective strain and volumetric effective strain rate deviation. ^ When average effective strain is minimized with the axisymmetric upper bound model, die shapes are obtained which minimize the average effective strain in the extrudate, but do not minimize distortion. When volumetric effective strain rate deviation is minimized with the upper bound model, die shapes are obtained which minimize the deviation of the effective strain rate distribution in the deformation zone. Such a die is called a controlled strain rate die. The axisymmetric results show that minimizing the volumetric effective strain rate deviation produces controlled strain rate die shapes, which form product with minimum distortion. ^ The axisymmetric upper bound model in spherical coordinates is extended to the 3D extrusion from round to square and round to rectangle and is used to obtain die shapes which produce minimum distortion in the extrudate by minimizing the volumetric effective strain rate deviation. The 3D streamlined die shape is characterized by a Legendre polynomial series where the higher order coefficients are either constants or functions of the rotational coordinate, ϕ. FEM is used to compare the average distortion along the rectangle symmetry planes for two optimal die shapes. ^ When the optimal die shape is described by the Legendre coefficients as function of ϕ, the difference in the average distortion between the symmetry planes decreases. Such a die shape causes material in the deformation zone to speed up or slow down, creating a more uniform distortion distribution in the finished product. ^

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