Mathematical model and numerical simulation for the extrusion of polygonal sections from round billets through polynomial streamlined dies

الملخص EN

Despite increasing demand for the application of three-dimensional extrusion of various shaped sections through continuous dies, so far little work has been done by general analytical and numerical analyses to predict the total extrusion pressure for the extrusion of polygonal sections from round billets through polynomial streamlined dies.

For effective die design, efficient design method and the related method of theoretical analysis are required for extrusion of complicated sections.

A systematic method for the die surface representation using blending function and trigonometric relationships is proposed in which smooth transitions of the die contour from the die entrance to the die exit are obtained.

The upper bound extrusion pressure is obtained by derived a general velocity and strain rate felids.

The effects of area reduction, the optimum die length, the shape of streamline function and frictional conditions are also discussed in relation to the relative extrusion pressure.

Another advantage of the present work is that it could easily be applied to the extrusion of many different shapes just by defining the entry and exit sections functions and putting them into the general formulations.

The results obtained in this work were compared with the theoretical results of other workers and found to be in highly compatible.

The extrusion process is also simulated using the finite element code, ANSYS (V 14.0) in order to assist the mathematical solution and to show the stress and strain distributions for the products when the strain hardening effect taking into the account.