Abstract
The cold forming process becomes necessary in ship hull panel production when certain physical properties cannot be altered. To achieve precise cold forming results for doubly curved hull plates using reconfigurable dies, this paper introduces springback ratio (SR) matrices and SR feature values as descriptors and compensatory measures for springback. The feasibility and validity of the SR matrix and SR feature value are confirmed through an examination of springback outcomes from nine single-curvature plates, as documented in existing literature. Theoretical deductions highlighted a substantial contrast between sail-type and saddle-type plates. Subsequently, 14 metal doubly curved plate forming experiments are introduced employing reconfigurable dies. Upon comparing the springback results of sail-type and saddle-type plates described by SR feature values, it becomes evident that saddle-type plates exhibit significantly less springback than sail-type plates. In response, a novel springback compensation algorithm is proposed based on SR matrices. This algorithm is compared with an existing method, and the results demonstrate its superior performance in springback compensation.
Similar content being viewed by others
References
Zhang F, He K, Wei B, Huang B (2023) Multi-point incremental bending of doubly curved high strength steel sheet under minimum strain energy loading path. Int J Adv Manuf Technol 127(3):1797–1809. https://doi.org/10.1007/s00170-023-11643-3
Pandre S, Morchhale A, Kotkunde N, Kurra S (2021) Processing of DP590 steel using single point incremental forming for automotive applications. Mater Manuf Process 36(14):1658–1666. https://doi.org/10.1080/10426914.2021.1942903
Liu C, Li M, Qu E (2022) Springback prediction and compensation method for anisotropy sheet in multi-point forming. Proc Inst Mech Eng Part C: J Mech Eng Sci 236(1):511–524. https://doi.org/10.1177/09544062211034195
Liao J, Xue X, Zhou C, Barlat F, Gracio J (2013) A semi-analytic model to predict and compensate springback in the 3D stretch bending process. Steel Res Int 85(4):697–709. https://doi.org/10.1002/srin.201300216
Li MZ, Cai ZY, Sui Z, Yan QG (2002) Multi-point forming technology for sheet metal. J Mater Process Technol 129(1):333–338. https://doi.org/10.1016/S0924-0136(02)00685-4
Zhang Q-F, Cai Z-Y, Zhang Y, Li M-Z (2013) Springback compensation method for doubly curved plate in multi-point forming. Mater Design 47:377–385. https://doi.org/10.1016/j.matdes.2012.12.005
Cai Y, Hu Y, Xiong J, Wang C (2020) Dimpling suppression by chamfered rotatable cubic punch in reconfigurable die forming. J Wuhan Univ Technol-Mater Sci Ed 35(2):407–410. https://doi.org/10.1007/s11595-020-2271-z
Liu B, Villavicencio R, Guedes Soares C (2018) Experimental and numerical analysis of residual stresses and strains induced during cold bending of thick steel plates. Mar Struct 57:121–132. https://doi.org/10.1016/j.marstruc.2017.10.005
Yu TX, Johnson W, Stronge WJ (1984) Stamping rectangular plates into doubly-curved dies. Proc Inst Mech Eng Part C: J Mech Eng Sci 198(2):109–125. https://doi.org/10.1243/pime_proc_1984_198_096_02
Johnson W, Yu TX (1981) On springback after the pure bending of beams and plates of elastic work-hardening materials—III. Int J Mech Sci 23(11):687–695. https://doi.org/10.1016/0020-7403(81)90022-9
Xue P, Yu TX, Chu E (2001) An energy approach for predicting springback of metal sheets after double-curvature forming, Part II: Unequal double-curvature forming. Int J Mech Sci 43(8):1915–1924. https://doi.org/10.1016/S0020-7403(01)00004-2
Xue P, Yu TX, Chu E (2001) An energy approach for predicting springback of metal sheets after double-curvature forming, Part I: axisymmetric stamping. Int J Mech Sci 43(8):1893–1914. https://doi.org/10.1016/S0020-7403(01)00003-0
Jiang L, Tao X, Lin Y, Wang Z, Zhang S, Li H, He Y (2022) Influence of base level of the roll flower pattern on the roll forming quality of the hat-shaped section. Int J Modern Phys B 36(12n13). https://doi.org/10.1142/s0217979222400641
Zhao H, Wei B, Shao Z, Xie X, Jiang L, Xiang P (2023) Assessment of train running safety on railway bridges based on velocity-related indices under random near-fault ground motions. Structures 57:105244. https://doi.org/10.1016/j.istruc.2023.105244
Zhao H, Wei B, Jiang L, Xiang P, Zhang X, Ma H, Xu S, Wang L, Wu H, Xie X (2023) A velocity-related running safety assessment index in seismic design for railway bridge. Mech Syst Signal Pr 198:110305. https://doi.org/10.1016/j.ymssp.2023.110305
Jiang K, Hou Y, Lin J, Min J (2018) A springback energy based method of springback prediction for complex automotive parts. IOP Conf Series: Mater Sci Eng 418(1):012104. https://doi.org/10.1088/1757-899X/418/1/012104
Yang XA, Ruan F (2011) A die design method for springback compensation based on displacement adjustment. Int J Mech Sci 53(5):399–406. https://doi.org/10.1016/j.ijmecsci.2011.03.002
Asnafi N (2001) On springback of double-curved autobody panels. Int J Mech Sci 43(1):5–37. https://doi.org/10.1016/S0020-7403(99)00101-0
Cai Z-Y, Lan Y-W, Li M-Z, Hu Z-Q, Wang M (2012) Continuous sheet metal forming for doubly curved surface parts. Int J Precis Eng 13(11):1997–2003. https://doi.org/10.1007/s12541-012-0263-4
Cai Z-Y, Li M-Z, Chen X-D (2006) Digitized die forming system for sheet metal and springback minimizing technique. Int J Adv Manuf Technol 28(11):1089–1096. https://doi.org/10.1007/s00170-004-2459-y
Calladine CR (1983) Theory of shell structures. Cambridge University Press
Hill R (1998) The mathematical theory of plasticity, vol 11. Oxford University Press
Stronge WJ, Yu T (2012) Dynamic models for structural plasticity. Springer Science & Business Media. https://doi.org/10.1007/978-1-4471-0397-4
Zhu L, Liang Q, Yu TX, Yuan P, Hu Y (2019) Experimental and theoretical study of constant curvature multi-square punch forming process of strips under follower load. Int J Mech Sci 156:462–473. https://doi.org/10.1016/j.ijmecsci.2019.04.008
Cai Z-Y, Wang S-H, Li M-Z (2007) Numerical investigation of multi-point forming process for sheet metal: wrinkling, dimpling and springback. Int J Adv Manuf Technol 37(9-10):927–936. https://doi.org/10.1007/s00170-007-1045-5
Funding
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51779200 and 51379167).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethics approval
Not applicable.
Consent to participate
Not applicable.
Consent for publication
Not applicable
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhao, H., Shi, F. & Hu, Y. Springback ratio matrix-based description and compensation for precision forming of doubly curved plates using reconfigurable dies. Int J Adv Manuf Technol 130, 5853–5867 (2024). https://doi.org/10.1007/s00170-023-12933-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-023-12933-6