Upper bound analysis of axial metal flow inhomogeneity in radial forging process

• An upper bound model considering inhomogeneous deformation mode is proposed.
• Reasonable predictions of radial load is achieved.
• The predicted neutral plane is no longer a planar cross section.
• Inhomogeneous distribution of axial flow along the radial direction is studied.

An axisymmetric upper bound method model is proposed to analyze the inhomogeneity of axial metal flow in the radial forging process from the viewpoint of end profile in the meridian plane of the workpiece. The velocity fields are newly derived using stream function approach so that they can automatically satisfy the volume constancy as well as the velocity boundary conditions on the contact surface between the hammers and the workpiece. The assumed stream function has considered the inhomogeneous deformation mode. As a result, compared to the parallel velocity fields proposed in previous studies, reasonable predictions of radial load can be achieved even though the value of radial reduction is relatively low. Besides, the axial flow inhomogeneity along the radial direction can be described by this model because the axial velocity is no longer independent of the radial position. This model is verified by comparing the predicted forging load with published experimental data. Finally, the influences of axial feed and radial reduction on the end profile in the meridian plane of the workpiece are investigated.