Optimum die surface design of general three-dimensional section extrusions by using a surface model with tension parameter

In this paper, an integrated CAD/CAM/CAE method for the optimum die surface design of three-dimensional section extrusions has been proposed. The die surface is represented by a surface model with tension parameter and, therefore, general shapes of products, such as clover, polygonal, T- and L-sections and gear splines which can be designed using only one surface model. Tension parameter is used to obtain the straight line segments when those are required to present the product section. By applying the upper-bound method and the variable metric optimization scheme, the material flow is optimized and a minimum extrusion pressure is obtained. The optimum die surface is subsequently manufactured by using CAD/CAM software and NC machining for making the EDM electrode. Extrusion tests for straight-sided gear splines were performed to obtain the extrusion load and the experimental grid deformation. The theoretical predictions of gear spline extrusion are in close agreement with the experimental results. The numerical results of clover, polygonal, T- and L-shapes are also compared with results available in the literature. The results confirm that better extrusion performance could be obtained with the die surfaces which employed the developed design method. The proposed surface model and the optimum design method can be applied to the die design for general three-dimensional section extrusions.