{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T21:08:21Z","timestamp":1767647301182,"version":"3.48.0"},"reference-count":24,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>Threaded joints, particularly bolted joints, are critical components in the design and fabrication of mechanical systems due to their high strength and ease of disassembly. Their widespread application spans across structural engineering, transportation, bridge construction, and industrial machinery. The external load factor (\u03c7), which characterizes the load-sharing behavior between the bolt and the clamped components, plays a vital role in assessing joint performance and reliability. This study presents an experimental investigation into the effects of friction coefficient, surface roughness, and material hardness of the clamped plates on the external load factor in threaded joints. A second-order regression model is developed using the Box\u2013Wilson design method to quantitatively describe the influence of these parameters. The results reveal that all three factors significantly affect \u03c7, with material hardness showing the strongest influence, \u03c7 decreases as hardness increases. Surface roughness exhibits a nonlinear effect, while the friction coefficient also has a notable impact. An optimization was carried out to identify the parameter combination that meets the target external load factor of \u03c7\u2009=\u20090.2501. The optimal conditions include a friction coefficient \u03bc\u2009=\u20090.1809, surface roughness Ra\u2009=\u20093.5181 \u03bcm, and material hardness of HB\u2009=\u2009216.859. The resulting composite desirability of 0.9996 confirms the model\u2019s predictive accuracy and the high reliability of the joint under the specified conditions. These findings allow better design of reliable bolted joints in engineering applications.<\/jats:p>","DOI":"10.1371\/journal.pone.0340073","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T18:53:57Z","timestamp":1767639237000},"page":"e0340073","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Experimental investigation of the influence of friction, surface roughness and material hardness on the external load factor in threaded joints"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3849-3556","authenticated-orcid":true,"given":"Van Thuy","family":"Tran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huu Loc","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2026,1,5]]},"reference":[{"key":"pone.0340073.ref001","doi-asserted-by":"crossref","first-page":"107933","DOI":"10.1016\/j.triboint.2022.107933","article-title":"Effect of frequency on the fatigue performance of bolted joints under axial excitation","volume":"176","author":"H Li","year":"2022","journal-title":"Tribology International"},{"issue":"1","key":"pone.0340073.ref002","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1186\/s10033-024-01082-w","article-title":"Preload control method of threaded fasteners: a review","volume":"37","author":"X Yan","year":"2024","journal-title":"Chin J Mech Eng"},{"key":"pone.0340073.ref003","doi-asserted-by":"crossref","first-page":"119410","DOI":"10.1016\/j.engstruct.2024.119410","article-title":"A novel theoretical analysis on mechanical properties of bolted joints under torsional loads considering service torque","volume":"325","author":"M Zheng","year":"2025","journal-title":"Engineering Structures"},{"year":"2025","author":"JK Ramsey","key":"pone.0340073.ref004"},{"issue":"6","key":"pone.0340073.ref005","first-page":"2106","article-title":"Study on the stress evolution at threads of bolted joint under transverse loads","volume":"239","author":"C Wang","year":"2024","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science"},{"key":"pone.0340073.ref006","unstructured":"Budynas RG, Nisbett JK. Shigley\u2019s mechanical engineering design: McGraw-Hill New York; 2011."},{"volume-title":"Fundamental of machine design","year":"2016","author":"NH Loc","key":"pone.0340073.ref007"},{"key":"pone.0340073.ref008","first-page":"55","article-title":"Investigation on design and manufacturing equipment for determination of the external force coefficient of the threaded joints","volume":"28","author":"VT Tran","year":"2024","journal-title":"J Sci Technol"},{"key":"pone.0340073.ref009","doi-asserted-by":"crossref","unstructured":"Boujnah I, Afifi N, Wettstein A, Matthiesen S. 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In: 2006.","DOI":"10.1115\/IJTC2006-12090"},{"issue":"1","key":"pone.0340073.ref014","article-title":"Investigation of the effect of the surface treatment and lubrication during repeated tightening on the nut coefficient of a bolted joint using the Taguchi method","volume":"18","author":"T Alsardia","year":"2024","journal-title":"Jordan Journal of Mechanical & Industrial Engineering"},{"issue":"1","key":"pone.0340073.ref015","doi-asserted-by":"crossref","first-page":"17182","DOI":"10.1038\/s41598-025-02436-7","article-title":"Experimental study on the energy dissipation mechanism of bolted rock under dynamic loading","volume":"15","author":"PQ Qiu","year":"2025","journal-title":"Sci Rep"},{"issue":"4","key":"pone.0340073.ref016","doi-asserted-by":"crossref","first-page":"187","DOI":"10.3390\/lubricants13040187","article-title":"The Impact of Surface Roughness on the Friction and Wear Performance of GCr15 Bearing Steel","volume":"13","author":"T He","year":"2025","journal-title":"Lubricants"},{"key":"pone.0340073.ref017","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.wear.2015.10.012","article-title":"Experimental and numerical studies of bolted joints subjected to axial excitation","author":"J Liu","year":"2016","journal-title":"Wear"},{"volume-title":"Design and analysis of experiments","year":"2017","author":"DC Montgomery","key":"pone.0340073.ref018"},{"issue":"8","key":"pone.0340073.ref019","doi-asserted-by":"crossref","first-page":"1687814018797033","DOI":"10.1177\/1687814018797033","article-title":"An experimental study on the relationship between torque and preload of threaded connections","volume":"10","author":"Q Yu","year":"2018","journal-title":"Adv Mech Eng"},{"issue":"3","key":"pone.0340073.ref020","article-title":"Effect of surface parameters on anti-loosening performance of bolts for engineering machinery","volume":"28","author":"C Wang","year":"2023","journal-title":"Mat\u00e9ria (Rio J)"},{"issue":"1","key":"pone.0340073.ref021","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1186\/s43251-024-00117-5","article-title":"Experimental study on long friction-type bolted joint combined with interference fit bolt","volume":"5","author":"Y Chen","year":"2024","journal-title":"Advances in Bridge Eng"},{"key":"pone.0340073.ref022","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jsv.2019.01.050","article-title":"The effect of preload and surface roughness quality on linear joint model parameters","volume":"447","author":"H Jalali","year":"2019","journal-title":"J Sound Vibration"},{"issue":"4","key":"pone.0340073.ref023","doi-asserted-by":"crossref","first-page":"1913","DOI":"10.1007\/s12206-022-0328-y","article-title":"Methodology for evaluating the tightening torque-clamping force relationship and friction coefficients in bolted joints","volume":"36","author":"J Lee","year":"2022","journal-title":"J Mech Sci Technol"},{"issue":"9","key":"pone.0340073.ref024","first-page":"4240","article-title":"A prediction model of bolted joint loosening based on deep learning network","volume":"238","author":"Z Liu","year":"2023","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part C: J Mechanical Engineering Science"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0340073","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T18:54:05Z","timestamp":1767639245000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0340073"}},"subtitle":[],"editor":[{"given":"Giulia","family":"Pascoletti","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2026,1,5]]},"references-count":24,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,5]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0340073","relation":{},"ISSN":["1932-6203"],"issn-type":[{"type":"electronic","value":"1932-6203"}],"subject":[],"published":{"date-parts":[[2026,1,5]]}}}