Vertical Curve Analysis of Extruding Die Cavity and Conformal Mapping

With the help of numerical analysis of trigonometric interpolation and Conformal Mapping theory, the conformal mapping function could be set up to translate the non-circle cross-section region of special-shaped products into unit dish region, over numerical finite interpolation points between even and odd. Thus, forming of products extrusion could be turned into two-dimension problem, and plastic stream function could be deduced as well, whilst, mathematical model of die cavity surface was determined based on different kinds of vertical curve. By Upper-bound Principle, both vertical curves of die cavity and its parameters were optimized. Furthermore, taking ellipse-shaped products as an instance, the calculation and analysis were carried out.