A new surface modelling method and its application in tool shape design for finite element simulation of metal forming

In this paper, a new surface modelling method has been developed to represent the shape of an extrusion-forming die. Once the end cross sections (at the entry and exist) of a die are specified, the tool surface generated by this method is able to both interpolate the two section curves and vary over the length of the die smoothly. The surface shape can be easily modified by either adjusting the shape parameters or the tangential boundary conditions without affecting the shape of the entry and exist cross sections. Moreover, the surface shape along the die axis can be made either linear or non-linear at the user’s will. The finite element simulation of the extrusion forming of hot metals from a round billet to a square bar is carried out. It is clear from the simulation that the non-linearly converging dies obtained with the developed method can both reduce the deformation resistance and significantly improve the product quality compared with the linearly converging dies.