Abstract: Considering the excessive extrusion force and non-uniform deformation in the forming process of aluminum alloy flat-plate with flow-guide die, the boundary condition of transitional surface between flat extrusion container cavity and the inlet of shape metal is established based on the stream function method. According to conformal mapping theory of complex function, forward and reverse solution procedure of Schwarz-Christoffel transformation is analyzed. For handling the problem of mapping accuracy, the convex-concave expansion technology for Taylor series expansion is adopted. Further, the mapping function from the simply connected region of flat-plate to the unit circle is acquired, and based on this, the mathematical representation of transitional surface is established. Finally, the streamlined 3D model of transitional surface is obtained by using CAD software.

Key words: Conformal mapping, Flat-plate shape, Schwarz-Christoffel transformation, Streamlined, Transitional surface