Design and control of forming parameters using finite element analysis

Successful forming of a part requires the prevention of wrinkling (buckling) and tearing of the sheet during the process. Wrinkling and buckling can be averted or delayed during processing by proper design and selection of restraining forces through flat binder force/friction conditions and/or draw bead design. Previous experimental results on steel and aluminum conical cup forming have shown that there exists an optimal constant binder force (CBF°) which provides the deepest cup without wrinkling or tearing failure for a given lubricant condition. The cup fails at a height lower than optimal by wrinkling when the constant binder force is lower than CBF°. On the other hand, cups fail by tearing at low heights when the binder forces are higher than CBF°. In this work, criteria are developed for predicting both wrinkling and tearing failure during a sheet forming simulation using the finite element method. The criteria are used to predict the experimental cup failure data over a range of binder constraints. Excellent agreement is obtained. An optimal variable binder force trajectory is then calculated using a closed-loop controller incorporated into the finite element simulation. The controller acts to monitor the onset of both wrinkling and tearing failures feeding back this information to alter the binder force level using a proportional integral controller in order to avoid failure. Using this newly defined variable binder force (VBF) trajectory, a 16% increase in failure height over that of CBF° is achieved in both simulation and experiment.