Upper bound analysis of forging penetration in a radial forging process

• A theoretical model based on transformations for geometry and velocity is proposed.
• Forging penetration depth is defined from the distribution of deforming regions.
• Effects of radial reduction and die angle on the forging penetration are studied.

A theoretical model based on upper bound approach is proposed to study forging penetration in a radial forging process. Using the transformations for both the geometric coordinate system and the velocity field, the parabolic discontinuity boundaries in axisymmetric problem are mapped into straight lines in the transformed field. As a result, the present model is simplified and its implementation is analogous to the rigid block upper bound approach in plane strain problem. In order to quantify the penetration of plastic deformation, forging penetration depth is introduced and defined as the radial distance from the outside surface of the workpiece to the intersection point of the assumed plastic and rigid regions. This model is verified by comparing the predicted forging load with published experimental data, and by comparing the predicted forging penetration depth with that of the finite element simulation. Finally the effects of process parameters such as the radial reduction rate and the inlet angle of hammer on the forging penetration are investigated.

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