Estimation of Optimal Blank Holder Force Trajectories in Segmented Binders Using an ARMA Model

Sheet metal forming is one of the most important and frequently used manufacturing processes in industry today. One of the key parameters affecting the forming process is the blank holder force (BHF). In the past, researchers have demonstrated the advantages of varying the blank holder force during the forming process, that is, the two primary modes of failure in sheet metal forming (wrinkling and tearing) are avoided. This gives rise to improved formability, higher accuracy and better part consistency. In recent years, researchers have also shown increasing interest in forming processes where the blank holder force is varied spatially with the help of segmented binders or flexible binders. In this paper, we have combined the above two aspects and used a robust method to determine the blank holder force trajectories for a non-circular part using segmented binders. The proposed strategy is verified by implementing it into a finite element simulation. Binder force is treated as a system input. The displacement of the binder is used as a measure of the tendency to wrinkle, and is therefore treated as a system output. The parameters of the system are continuously identified and updated using a deterministic Auto-Regressive Moving-Average model (ARMA). The model is then used to control the binder displacement to a prescribed value by adjusting the system input, i.e., the binder force. In this manner, individual binder force profiles for each of the segmented binders are obtained. Due to the generic nature of the ARMA model, the strategy proposed in this paper can be applied to a variety of forming problems, making it a robust approach.