StressWaves in a Stamping Tool

Analytic Treatment of a One-dimensional Model

Abstract

A simple one-dimensional model for a stamping process is set up, taking into account the compliance of the workpiece. Two kinds of boundary conditions are considered at the end where the impact takes place. The one dimensional wave equation, describing the displacement of the cross-sections of the tool with non-trivial boundary conditions is solved by means of the Laplace transformation. The technique used for the inverse transformation back into the time domain allows for a closed-form representation and efficient numerical evaluation of the solution. The result is finally discussed with regard to the influence of the compliance of the workpiece on the loading of the tool. Restricting the discussion to a special limit case, we can show that the results agree with those found in the literature.