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首页> 外文期刊>International Journal of Mechanical Sciences >Axisymmetric extrusion through adaptable dies - Part 2: Comparison of velocity fields
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Axisymmetric extrusion through adaptable dies - Part 2: Comparison of velocity fields

机译：通过可适应模具进行轴对称挤压-第2部分：速度场比较

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摘要

In Part 1 of this series of papers, six kinematically admissible velocity fields, along with the power terms, were developed for use in upper bound models for arbitrarily shaped dies for axisymmetric extrusion. The three base velocity fields in the deformation zone were derived: (1) assuming proportional angles in the deformation zone, (2) assuming proportional areas in the deformation zone, or (3) assuming proportional distances from the centerline in the deformation zone. In each case the base velocity was modified by an additional term comprised of two functions, each function containing pseudo-independent parameters. One function allows extra flexibility in the radial direction, and the second function allows extra flexibility in the angular direction. In Part 2, the results obtained in upper bound models for the six velocity fields for extrusion through a spherical die are compared to one another. The velocity fields are compared based upon: (a) the base velocity field, (b) the number and distribution of pseudo-independent parameters in the flexible functions, and (c) the form of the angular flexible function. A spherical extrusion die shape is, used to evaluate and compare the three velocity fields. The results demonstrate that the sine-based velocity field is the best. Furthermore, a natural boundary condition exists which allows the shear surface associated with the streamlined portion of a die to energetically disappear. Part 3 uses the best velocity field to determine an adaptable die shape, which minimizes the extrusion pressure and compares the shape to the arbitrarily curved and streamlined die shape of Yang and Han.
机译：在该系列论文的第1部分中，开发了六个运动学上允许的速度场以及功率项，用于轴对称挤压的任意形状模具的上限模型。得出了变形区中的三个基本速度场：（1）假设变形区中的比例角，（2）假设变形区中的比例面积，或（3）假设距变形区中线的比例距离。在每种情况下，基本速度都由包含两个函数的附加项修改，每个函数包含伪独立参数。一种功能允许在径向方向上额外的柔韧性，第二种功能允许在角度方向上额外的柔韧性。在第2部分中，将通过球形模头挤出的六个速度场的上限模型中获得的结果相互比较。根据以下条件比较速度场：（a）基本速度场;（b）弹性函数中伪独立参数的数量和分布;（c）角度弹性函数的形式。球形挤压模具形状用于评估和比较三个速度场。结果表明，基于正弦的速度场是最好的。此外，存在自然边界条件，该自然边界条件允许与模具的流线型部分相关的剪切表面从能量上消失。第3部分使用最佳速度场来确定合适的模具形状，该模具形状将挤出压力降至最低，并将该形状与Yang和Han任意弯曲和流线型的模具形状进行比较。

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