3D modeling of unconstrained tools used in hot forging

Abstract : Unconstrained tools are frequently used in complex forging processes. Their motion is caused by the flow of the workpiece and is a priori unknown. In hot forging the behavior of the part can be described by a viscoplastic, incompressible flow. Applying the virtual work principle to the system (workpiece + tools) the coupled equations determine the velocity/pressure field in the part and the six degrees of freedom of the rigid motion of unconstrained tools. These equations can be numerically solved using a finite element discretization of the velocity/pressure field. The resulting non-linear equations are simultaneously computed by a Newton type linearization and a preconditioned conjugate residual type iterative solver. Applications show the convergence of the solver for the coupled problem and the additional computational cost due the unconstrained tools.