{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T11:40:09Z","timestamp":1768477209828,"version":"3.49.0"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents a theoretical analysis of the single-pressure straightening process for large-scale pipes, addressing the challenges of inadequate straightening precision and low efficiency associated with the current practice, which heavily relies on operator expertise. The straightening process of pipes through pressure is fundamentally a symmetrical three-point bending elastic\u2013plastic deformation process. With the assumption of small deformations, the symmetric three-point bending of the pipe can be divided into two distinct deformation stages: fully elastic and elastic\u2013plastic. For each stage, calculation models are developed, yielding the deflection formulae for any point on the pipe before and after unloading under varying punch strokes. The accuracy and reliability of the theoretical models are confirmed through finite element analysis and physical simulation experiments on smaller pipes. These models enhance the accuracy of single-pressure straightening and lay the groundwork for online material performance parameter identification based on load\u2013stroke curves during the initial straightening phase. Both theoretical analysis and experimental outcomes demonstrate that the relationship between the maximum deflection after springback and the punch stroke are nearly linear, offering a practical method for developing intelligent control systems for pressure straightening.<\/jats:p>","DOI":"10.3390\/sym17010095","type":"journal-article","created":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T09:54:27Z","timestamp":1736416467000},"page":"95","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Analysis of Symmetrical Three-Point Bending and Springback Process of Pipes"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiaokang","family":"Song","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Dalian University, Dalian 116622, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Forging & Stamping Technology and Science, Yanshan University, Ministry of Education of China, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Ma","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Forging & Stamping Technology and Science, Yanshan University, Ministry of Education of China, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Dalian University, Dalian 116622, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,9]]},"reference":[{"key":"ref_1","unstructured":"American Petroleum Institute (2012). ANSI\/API Specification 5L, Specification for Line Pipe, American Petroleum Institute. [45th ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, C., Yu, G., Zhao, J., and Liu, W. (2022). Pure-Bend and Over-Bend Straightening Theory for In-Plane Curved Beams with Symmetrical Section and Straightening Mechanism Analysis. Metals, 12.","DOI":"10.3390\/met12081362"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105536","DOI":"10.1016\/j.ijmecsci.2020.105536","article-title":"Predictive model of grinding residual stress for linear guideway considering straightening history","volume":"176","author":"Ling","year":"2020","journal-title":"Int. J. Mech. Sci."},{"key":"ref_4","first-page":"456","article-title":"Simulation of the roller straightening process with respect to residual stresses and the curvature trend","volume":"768\u2013769","author":"Kaiser","year":"2014","journal-title":"Mater. Sci. Forum"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2386","DOI":"10.1007\/s11431-011-4447-4","article-title":"Springback equation of small curvature plane bending","volume":"54","author":"Zhao","year":"2011","journal-title":"Sci. China Technol. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2955","DOI":"10.1007\/s10586-018-1710-5","article-title":"Load-deflection model for T-section rail press straightening process under lateral loads","volume":"22","author":"Song","year":"2018","journal-title":"Clust. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Lu, H., Zang, Y., Zhang, X., Zhang, Y., and Li, L. (2020). A General Stroke-Based Model for the Straightening Process of D-Type Shaft. Processes, 8.","DOI":"10.3390\/pr8050528"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Lu, H., Ling, H., Lian, Y., and Ma, M. (2018). 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Steel Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1336","DOI":"10.1016\/j.cja.2013.07.039","article-title":"Springback prediction of thick-walled high-strength titanium tube bending","volume":"26","author":"Song","year":"2013","journal-title":"Chin. J. Aeronaut."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.ijplas.2006.07.003","article-title":"Study on the influence of work-hardening modeling in springback prediction","volume":"23","author":"Oliveira","year":"2007","journal-title":"Int. J. Plast."},{"key":"ref_14","first-page":"64","article-title":"Effects of Heat Treatment Process on Microstructure and Mechanical Properties of X70 Pipeline Steel","volume":"54","author":"Li","year":"2025","journal-title":"Hot Work. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.tws.2018.03.016","article-title":"Cross-sectional distortion of LSAW pipes in over-bend straightening process","volume":"129","author":"Wang","year":"2018","journal-title":"Thin-Walled Struct."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/95\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:25:55Z","timestamp":1759919155000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/95"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,9]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["sym17010095"],"URL":"https:\/\/doi.org\/10.3390\/sym17010095","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,9]]}}}