A numerical method of optimizing the stretch forming process for the production of panels
Keywords:elasticity, plasticity, stretch-forming, variational principles, finite element method, damage, discrete optimal control problem, dynamic programming method
We analyze the stretch-forming technology using a press to manufacture the double-curvature shells. The automated shaping of parts requires the development of a control program and an electronic model of a punch. The quality of the part obtained depends on the accuracy of the calculated and manufactured tools that specify the anticipated shape of the panel and on the deformation path of the sheet. Under the condition of a given tooling, an optimal control problem is formulated to find the best trajectory of movement of the clamps in the equipment. Some criteria for deformation optimization processes are introduced to ensure a minimum damage and maximum residual deformations. The calculation of the criteria is performed with the aid of modeling and analyzing the panel nonlinear deformation with contact constraints by the finite element method. The problems of inelastic deformation are solved by the finite element method. A discrete optimal control problem is formulated and solved by the methods of dynamic programming. The algorithms are implemented using the MSC.Marc package and allow us to calculate the optimal parameters of the stretch-forming press in serial and parallel modes. The obtained numerical results show the efficiency of parallel implementations on a cluster of computers.
- M. V. Molod, “Control of a Shell-Forming Process Using the NC-Machining Technique,” Vestn. Voronezh Gos. Tekh. Univ. 7 (12), 62-64 (2011).
- S. V. Belykh, A. A. Krivenok, V. V. Mironenko, and V. A. Mishagin, “Stretch Die Position Determination in Fet-Type Sheet Stretch Press Workspace during Preproduction Engineering,” Vestn. Irkutsk Gos. Tekh. Univ., No. 12, 36-40 (2013).
- V. A. Miheev, F. V. Grechnikov, S. G. Dementyev, et al., “Simulation of Kinematic Scheme Serial of Shells Stretch-Forming Double-Convex Form on Stretch-Forming Press FEKD,” Izv. Samara Nauch. Tsentra Ross. Akad. Nauk 16 (6), 172-179 (2014).
- V. A. Miheev, Y. S. Klochkov, A. A. Kuzina, et al., “The Choice of the Kinematic Forming Scheme by Stretch Forming of Contour Shells of Complex Spatial Shape,” Vestn. Samara Gos. Aerokosm. Univ., No. 5, 239-245 (2012).
- A. V. Kolesnikov, V. V. Mironenko, A. A. Cheslavskaya, and A. K. Shmakov, “Optimization of Technological Processes of Manufacturing Parts from Sheets by Virtual Technological Simulation Tools,” Vestn. Irkutsk Gos. Tekh. Univ., No. 12, 73-77 (2013).
- R. F. Krupskiy, A. A. Krivenok, A. V. Stankevich, et al., “Modeling Motion Kinematics of FET Stretch Forming Press Working Elements,” Vestn. Irkutsk Gos. Tekh. Univ., No. 9, 40-44 (2014).
- V. V. Mironenko, A. A. Cheslavskaya, and S. V. Belykh, “Simulation of Stretch-Forming of Airborne Vehicle Skin with Regard to the Effects Arising in the Zones of the Workpiece Blank Clamping by Jaws,” Uchen. Zap. Komsomolsk-on-Amur Gos. Tekh. Univ. 1 (2), 13-18 (2014).
- J. Peng, W. Li, J. Han, et al., “Kinetic Locus Design for Longitudinal Stretch Forming of Aircraft Skin Components,” Int. J. Adv. Manuf. Technol. 86 (9-12), 3571-3582 (2016).
- S. Kurukuri, A. Miroux, H. Wisselink, and T. van den Boogaard, “Simulation of Stretch Forming with Intermediate Heat Treatments of Aircraft Skins,” Int. J. Mater. Form. 4 (2), 129-140 (2011).
- K. S. Bormotin and Win Aung, “Method of Solving the Inverse Problem in the Process of Panel Stretch-Forming,” Vestn. Chuvash Gos. Univ., Ser. Mekh., No. 3, 48-58 (2018).
- K. S. Bormotin, “A Method for Solving Inverse Problems of Inelastic Deformation of Thin-Walled Panels,” Vychisl. Metody Programm. 18, 359-370 (2017).
- V. P. Radchenko and M. N. Saushkin, Creep and Relaxation of Residual Stresses in Hardened Structures (Mashinostroenie-1, Moscow, 2005) [in Russian].
- P. Wriggers, Computational Contact Mechanics (Springer, Heidelberg, 2006).
- S. N. Korobeinikov, Nonlinear Deformation of Solids (Izd. Ross. Akad. Nauk, Novosibirsk, 2000) [in Russian].
- K.-J. Bathe, Finite Element Procedures (Prentice Hall, Upper Saddle River, 1982).
- Marc 2016, Vol. A: Theory and User Information, MSC.Software Corporation.
http://www.mscsoftware.com/product/marc . Cited September 30, 2019.
- F. P. Vasil’ev, Methods of Optimization (Faktorial Press, Moscow, 2002) [in Russian].
- N. N. Moiseev, Elements of the Theory of Optimal Systems (Nauka, Moscow, 1975) [in Russian].
- K. S. Bormotin and Win Aung, “A Method of Dynamic Programming in the Problems of Optimal Panel Deformation in the Creep Mode,” Vychisl. Metody Programm. 19, 470-478 (2018).