{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:26:41Z","timestamp":1760146001104,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:00:00Z","timestamp":1726012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12402294","KJQN202101117","KJQN202301130","cstc2021jcyj-msxmX0010"],"award-info":[{"award-number":["12402294","KJQN202101117","KJQN202301130","cstc2021jcyj-msxmX0010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["12402294","KJQN202101117","KJQN202301130","cstc2021jcyj-msxmX0010"],"award-info":[{"award-number":["12402294","KJQN202101117","KJQN202301130","cstc2021jcyj-msxmX0010"]}]},{"name":"Natural Science Foundation of Chongqing","award":["12402294","KJQN202101117","KJQN202301130","cstc2021jcyj-msxmX0010"],"award-info":[{"award-number":["12402294","KJQN202101117","KJQN202301130","cstc2021jcyj-msxmX0010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>By anchoring the lower rollers and dynamically adjusting the upper roller\u2019s downfeed of a pyramid roll bender, one can achieve the precise bending of a workpiece into a desired planar form characterized by variable curvature. To ensure the seamless processing of individual cross sections without impinging upon adjacent areas, critical roller spacings are identified through theoretical mechanics analyses. The reaction force exerted on the top roller is calculated by integrating the desired curvature into the elastoplastic constitutive equation and subsequently deriving a dynamic adjustment of the downfeed from quasi-static finite element simulations. This preliminary downfeed protocol undergoes refinement to mitigate discrepancies between the targeted and the actual curvatures. Numerical instances demonstrate that the application of roller configurations, as outlined herein, yields a product profile that closely mirrors the intended curve. This congruence can be further improved with an additional iteration; however, subsequent iterations are seen to yield negligible improvements, indicating a rapid convergence of this algorithm.<\/jats:p>","DOI":"10.3390\/axioms13090613","type":"journal-article","created":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T02:34:49Z","timestamp":1726022089000},"page":"613","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Roller Position Design in the Roll Bending Process of a Non-Uniform Curvature Profile"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9806-179X","authenticated-orcid":false,"given":"Zijun","family":"Zheng","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaru","family":"Shao","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziying","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chu","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1687814019847861","DOI":"10.1177\/1687814019847861","article-title":"Research on numerical simulation and process parameters of three-roll bending based on thickness characteristics of extra-thick plate","volume":"11","author":"Wang","year":"2019","journal-title":"Adv. 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Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.promfg.2019.06.107","article-title":"Product planning system for manufacture-oriented modeling of freeform bend tubes produced by three-roll-push-bending","volume":"34","author":"Groth","year":"2019","journal-title":"Procedia Manuf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.proeng.2014.09.160","article-title":"Deriving Position of Bending Roll in Roll Bending of Titanium Alloy Wire for Glasses Frame","volume":"81","author":"Sasaki","year":"2014","journal-title":"Procedia Eng."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/9\/613\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:53:24Z","timestamp":1760111604000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/9\/613"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,11]]},"references-count":28,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["axioms13090613"],"URL":"https:\/\/doi.org\/10.3390\/axioms13090613","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,9,11]]}}}