Study on Non-Symmetric Extrusion and Drawing

Upper bound analysis of extrusion from square billets through circular and square/rectangular dies

“…In the present modeling, the surface in Cartesian coordinates is represented by z s (x, y). The die surface [21] is derived by using linearly converging straight lines as:…”

“…Nanhai et al [22] stressed the importance of proper simulation of die land in the extrusion of shapes with flat-faced die so as to avoid the generations of geometrical defects and hence proposed a method of simulation, using finite element method, that the metal flow in extrusion and the die land can be adjusted according to the simulation results. Ajiboye and Adeyemi [23] improved on Kiuchi et al's formulations [21] to account for power losses due to ironing effect at the die land of an extrusion die with circular die opening. Their investigations involved the determinations of both experimental and theoretical effects of die land lengths on the quality of extruded products, extrusion pressures and flow patterns of coldextruded lead alloy of circular sections Avitzur [24] gave a detailed theoretical formulation which accounted for the power losses due to friction between the die land and round billets during drawing and extrusion processes to smaller rod products.…”

“…The differences between the friction coefficients calculated with and without the land were found to be appreciable and hence suggested the inclusion of die land effects in both the theoretical and experimental analyses. Kiuchi et al [21] developed an upper bound based analytical method to calculate power requirements, the extrusion pressure, the optimal die length in extruding/drawing from round, square and rectangular billets to rods, bars and wires with square, rectangular, hexagonal, L-type, T-type, H-type and flower-type cross-sections. For this generalized formulation, it also has a setback for neglecting to account for the frictional forces at the die land region.…”

Upper bound analysis for extrusion at various die land lengths and shaped profiles

“…Nanhai et al [19] stressed the importance of proper simulation of die land in the extrusion of shapes with flat-faced die so as to avoid the generations of geometrical defects and hence proposed a method of simulation, using finite element method, that the metal flow in extrusion and the die land can be adjusted according to the simulation results. Ajiboye and Adeyemi [20] based on Kiuchi et al's [18] approach extended and improved their analytical method by taking into account effects of die-entrance angles, frictional powers at punch-material and chamber material interfaces to frictional die surface to study the effects of die reductions, billet shapes, die opening's geometrical shapes, surface conditions and dimensional ratios of rectangle die openings on the extrusion pressures of forward extrusion operations. Avitzur [21] gave a detailed theoretical formulation which accounted for the power losses due to friction between the die land and round billets during drawing and extrusion processes to smaller rod products.…”

“…The differences between the friction coefficients calculated with and without the land were found to be appreciable and hence concluded that the inclusion of die land effects in both the theoretical and experimental analyses. Kiuchi et al [18] developed an upper bound based analytical method to calculate power requirements, the extrusion pressure, the optimal die length in extruding/drawing from round, square and rectangular billets to rods, bars and wires with square, rectangular, hexagonal, L-type, T-type, H-type and flower-type cross-sections. For this generalized formulation, it also has the setback for neglecting to account for the frictional forces at the die land region.…”