In order to design and control the cold lubricated extrusion of complicated helical sections through curved dies an effective method of die construction and related theoretical analysis is important from the practical viewpoint. An analytic method is proposed for representation of the die surface in helical extrusion of generalized sections. The design method includes the smooth transition of metal flow both at the entrance and exit resulting in less redundant work and more uniform deformation. The die surface is generated by employing the external conformal mapping by which the surface contours are obtained analytically and continuously. Using the concept of effective die profile and bounding function for geometrical control a smooth die surface is constructed by introducing an interpolation function. A kinematically admissible velocity field is derived based on the incompressibility condition and velocity boundary conditions. The upper-bound extrusion pressure is then found from the derived velocity field for three-dimensional extrusion of arbitrarily-shaped helical sections.
For computation and related experiment helical sections such as helical elliptic section, helical clover section and helical trocoidal gear are chosen. As working material aluminum alloy A12024 is employed for the experiment. The effect of process parameters such as area reduction, die length, sectional shape complexity and frictional condition, etc. on extrusion power has been studied. By using the proposed method of die suface construction three types of dies (helical elliptic, helical clover and helical trocoidal gear) have been designed and manufactured by the CAD/CAM system on the basis of optimal theoretical results, when area reduction and die length remain fixed. In order to verify the proposed theory experiments have been carried out with full-annealed aluminum alloy billets and with the manufactured dies for helical extrusion of chosen sections. The theoretical predictions in extrusion load have been shown to be effective in designing the helical extrusion process. The smooth geometrical transition both at the entrance and exit is proven to be beneficial for improvement of surface finish and deformation characteristics. The present method of die construction and theoretical analysis would contribute to a more effective design and manufacture of complicated extruded products by helical extrusion.