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            <title xml:lang="en">3D modeling of unconstrained tools used in hot forging</title>
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                <title xml:lang="en">3D modeling of unconstrained tools used in hot forging</title>
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                  <date type="start">1998-06-22</date>
                  <date type="end">1998-06-25</date>
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                <editor>Huetink J, Baaijens FPT</editor>
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              <p>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.</p>
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