Finite Element Analyses of Real-Time Stability Control in Sheet Forming Processes

Sheet metal forming processes involve the plastic deformation of a sheet of material into a desired shape. In practice, the uncontrolled variation of boundary and material conditions have made the continual reproducibility of a sheet forming process a very difficult operation. Recently, real-time control schemes based on simplified models of “average” in-process stresses and/or strains have provided a repeatability of end product quality in terms of final shape, failure modes, and/or material state. The success of these control schemes have warranted a more detailed investigation into the complete physics of the deformation process. This study takes one such operation, the axisymmetric cup-forming process, and conducts an off-line detailed analysis using the finite element method in order to obtain information on the state of the material during the deformation process. In our analysis, actual closed-loop feedback control laws which have previously been applied in experiments have been numerically simulated with a novel method of modifying the boundary conditions based on current conditions. This has lead to further understanding of the role of the control law in optimizing draw failure height. Our further investigation and analysis directly incorporates the predicted localized nature of failure of this process into the feedback loop and has lead to the construction of an improved control algorithm which has the potential of dramatically increasing the failure height and which can be used in on-line control of the process. The study clearly demonstrates the utility and power of using off-line detailed analyses which incorporate closed-loop feedback laws to obtain a better understanding of the physics of the deformations which occur during processing, and thereby greatly improve upon the algorithms which are used for real time control of forming or other processing.