2-Process controller design for sheet metal forming.pdf

Proceedings of the American Control Conference San Diego, Cahfornla June 1999 Process Controller Design for Sheet Metal Forming Cheng-Wei Hsu and A. Galip Ulsoy Mechanical Engineering and Applied Mechanics University of Michigan Ann Arbor, MI 48109-2125, USA Mahmoud Y. Demeri Ford Research Laboratories Ford Motor Company Dearbom, MI 48121, USA Abstract In-process adjustment of the blank holder force can lead to higher formability and accuracy, and better part consistency. There are many studies on the application of process con- trol to sheet metal forming. However, process controller de- sign has not been thoroughly addressed, and is studied in this paper. A constant gain proportional plus integral (PI) con- troller with approximate inverse dynamics will be presented to achieve small tracking error regardless of model uncer- tainty and disturbances. 1 Introduction Sheet metal stamping is an important manufacturing process because of its high speed and low cost for mass production. Figure 1 shows a schematic of a simplified stamping process. Holder Figure 1 : Schematic of a stamping process The basic components are a punch, and a set of blank holders which may include drawbeads. The punch draws the blank to form the shape while the blank holder holds the blank to control the flow of metal into the die cavity. Some process variables are also shown: Fp is the punch force, Fb is the blank holder force, and F, is the restraining force within the blank. The good quality (i.e., no tearing, no wrinkling, and high di- mensional accuracy) of stamped parts is critical in avoiding problems in assembly and in the final product performance. Consistency (i.e., dimensional variations between parts) in the stamping process also significantly affects subsequent assem- bly in mass production. New challenges emerge from the use of new materials. For example, lightweight materials (e.g., aluminum) are essential for reduction of car weight to achieve high fuel economy. However, aluminum has reduced forma- bility and produces more springback l, 21. The control of flow of material into the die cavity is crucial to good part quality and consistency. Previous research showed that variable blank holder force during forming improves ma- terial formability 3, 41, reduces springback l, 2, 51, and achieves part consistency 1,2. One strategy (i.e process control) for the application of variable blank holder force is shown in Fig. 2 l, 21. Figure 2 : Process control of sheet metal forming In this strategy, a measurable process variable (e.g., punch force) is controlled by following a predetermined (e.g., punch force-displacement) trajectory through manipulating the blank holder force. A similar approach has also been re- ported 5,6,7. Recent work on process control in sheet metal forming led to the following conclusions 8: 1. Consistency of part quality can be improved through 2. Better part quality can be achieved through selection of It is important to realize that a badly designed process con- troller cannot ensure good tracking performance, and, in turn, cannot guarantee good part quality and consistency. Clearly, the process controller plays an important role in the feedback control system and needs further investigation. Issues of process controller design for sheet metal forming have not been properly addressed, especially, from a control point of view. Modeling sheet metal forming for process con- troller design has been investigated 9. Hsu et al. lo re- cently proposed a first-order non-linear dynamic model for u- channel forming which can capture the main characteristics of the process dynamics observed during experiments. Propor- tional plus integral (PI) control has been used for sheet metal forming and controller parameters were typically determined by trial and error ll. The disadvantage of PI control is that high controller gains can achieve good tracking performance but cannot maintain good stability robustness while low controller gains can main- tain good stability robustness but cannot achieve good track- ing performance. Since sheet metal forming is a highly non- linear process, it is difficult to tune a PI controller to stabilize the closed-loop system with good tracking performance. Hsu the tracking property of feedback control. the reference punch force trajectory. 0-7803-4990-6/99 $10.00 0 1999 AACC 192 et al. 8 investigated constant gain PI control with feedfor- ward action (PIF). Although PIF control worked well under dry condition, it generated a huge peak in the blank holder force under lubricated condition. The purpose of this investigation is to systematically develop a process controller for sheet metal forming to stabilize the closed-loop system with good tracking performance. A con- stant gain PI process controller with approximate inverse dy- namics for sheet metal forming will be proposed. The first- order non-linear dynamic model for u-channel forming lo will be explored to obtain the approximate inverse dynamics, which is related to tracking performance. The constant gain PI control will be designed to ensure the tracking performance regardless of disturbance and model uncertainty. Numerical simulation results will demonstrate the capabilities of the pro- posed controller. 2 Systematic Process Controller Design A schematic of the constant gain PI controller with inverse dynamics is shown in Fig. 3. The block “Plant” refers Plant Figure 3: Schematic of the constant gain PI controller with inverse to the real stamping process or its process model. Fpd is the reference punch force trajectory, Fb is the blank holder force applied to the plant, and Fp is the punch force generated by the plant. A systematic development of the proposed controller requires the following steps: 1. Model sheet metal forming (i.e., “Plant”) for process controller design. 2. Design the process controller (i.e., “Inverse Dynamics” and “PI”). 3. Adjust and test the performance of the process con- troller through simulation. 4. Adjust and verify the performance of the process con- troller through experiment. Adjustment and verification of the performance of the process controller will not be presented in this paper. 2.1 Modeling of Sheet Metal Forming The process model for u-channel forming can be represented by the following first-order non-linear dynamic model 8, 101: dynamics. where F P C oI(Fb) = 1.3537- 1.8511 X 10-2*Fb (3) Z ( f i ) = 1.5689+5.6906 X lo-*- therefore, it cannot maintain its performance when disturbance or model uncertainty appears. The feed- back control (i.e., the constant P I controller) is designed to maintain the tracking performance regardless of disturbance or model uncertainty. Although the tracking errors in Figs. 9(c) and 1O(c) are larger than the tracking error in Fig. 8(c), they decay asymptotically. Therefore, the tracking perfor- mance can be maintained through the constant P I controller regardless of disturbance or model uncertainty. 5 Summary and Conclusions A constant gain P I controller with approximate inverse dy- namics is systematically designed based on the first-order non-linear dynamics. The proposed controller has a feedfor- ward loop (i.e., the approximate inverse dynamics) and a feed- back loop (i.e., the constant gain P I control). The feedforward loop determines the tracking performance while the feedback loop relates to disturbance rejection and robustness to model uncertainty. Simulation shows that the proposed controller can track the reference regardless of disturbance and model uncertainty. Future work will include experimental imple- mentation and validation of the proposed controller. Acknowledgements The authors gratefully acknowledge the technical and finan- cial support provided by the Ford Motor Company. References 1 3 Adamson, A. M., 1995, “Closed-Loop Dimensional Control in Sheet Metal Forming via the Blank Restraining Force”, M.S. thesis, University of Michigan, Ann Arbor, MI. 2 Adamson, A., Ulsoy, A. G., and Demeri, M., 1996, “Dimensional Control in Sheet Metal Forming via Active Binder Force Adjustment,” SME Transactions, Vol. 24, pp. 3 Ahmetoglu, M., Broek, T. R., Kinzel, G., and Altan, T., 1995, “Control of Blank Holder Force to Eliminate Wrinkling and Fracture in Deep-Drawing Rectangular P a r t s , ” CIRP An- 4 Jalkh, P., Cao, J., Hardt, D., and Boyce, M. C., 1993, “Optimal Forming of Aluminum 2008-T4 Conical Cups Us- ing Force Trajectory Control,” SAE Technical Paper No. 930286. 5 Sunseri, M., Kara!illis, A. P . , Cao, J., and Boyce, M. C., 1994, “Methods to Obtain Net Shape in Aluminum Sheet Forming Using Active Binder Force Control,” AMD-Vol. 194, Mechanics in Materials Processing and Manufacturing, 6 Hardt, D. E. and Fenn, R. C., 1993, “Real-Time Con- trol of Sheet Stability during Forming,” Transactions of the ASME, Jorunal of Engineering for Industry, Vol. 115, pp. 7 Siegert, K., Wagner, S., and Ziegler, M., 1996, “Closed Loop Binder Force System,” SAE