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We proposed a relationship model between the exit velocity distribution and the shape of the extrusion profile. To verify the model, we designed multiple-extrusion ram differential extrusion and used the Arbitrary Lagrangian-Eulerian (ALE) method to simulate the natural bending deformation of the sheet metal. The die experimental test used a self-bending extrusion die for sheet metal was designed via a spline curve with inclination as the contour of the deflector chamber. The results showed that the standard arc profile was extruded when the exit velocity was linear, and the relative error between the predicted radius of curvature and the ALE simulation result was controlled within 5%. The relative error between the predicted value and the actual experimental result was 9.9%. Thus, this study can provide a reference for the design of self-bending extrusion dies.

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