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Modeling of the stamping process of box-type forging

A new mathematical model for manufacturing rectangular of box-type forgings is proposed. Along the outer contour of the forging there are walls with thickness comparable to the thickness of the bottom part of the forging. To calculate the power parameters of the technological process under study, the authors use the theory of flow in a relatively thin plastic layer as described by A. A. Ilyushin. A thickness-averaged two-dimensional mathematical model of the plastic layer spreading process is described by nonlinear partial differential equations of the first order with respect to the contact pressure and the flow velocity components. For a metal that is in a flat deformed state, the condition of complete plasticity is assumed, under which the tangent stresses in the layer are small in comparison with normal stresses and they can be ignored, and two normal stresses in the cross section can be considered equal in the first approximation. The third normal stress is equal to the contact pressure of the layer on the tool. In this case, it is sufficient to set a single boundary condition on the border of the regions.