A Transfer Function Description of Sheet Metal Forming for Process Control

Abstract

Three-dimensional forming of sheet metal parts is typically accomplished using one or two shaped tools (dies) that impart the necessary complex curvature and induce sufficient in-plane strain for part strength and shape stability. This research proposes a method of applying closed-loop process control concepts to sheet forming in a manner that automatically converges upon the appropriate tooling design. The problem of controlling complex deformation is reduced to a system identification problem where the die-part transformation is developed as a spatial frequency domain transfer function. This transfer function is simply the ratio of the measured change in spatial frequency content of the part and the die. It is then shown that such a transfer function can be used to implement closed-loop process control via rapid die redesign. Axisymmetric forming experiments are presented that establish the appropriateness of the linear transfer function description (via a test of superposition) and demonstrate the convergence properties of the proposed control method.