{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T18:10:58Z","timestamp":1789150258939,"version":"build-2803163510"},"reference-count":30,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T00:00:00Z","timestamp":1789084800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003995","name":"Anhui Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["2308085QE166"],"award-info":[{"award-number":["2308085QE166"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100006248","name":"Anhui University of Technology","doi-asserted-by":"publisher","award":["QD202326"],"award-info":[{"award-number":["QD202326"]}],"id":[{"id":"10.13039\/501100006248","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91960109"],"award-info":[{"award-number":["91960109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006248","name":"Anhui University of Technology","doi-asserted-by":"publisher","award":["S202510360355"],"award-info":[{"award-number":["S202510360355"]}],"id":[{"id":"10.13039\/501100006248","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>Non-uniform residual preload in bolt groups can reduce the assembly accuracy and interface-load uniformity of aerospace curvic-coupling structures. This study investigates residual-preload redistribution in a ten-bolt curvic-coupling assembly under different tightening strategies and initial preload levels. An equally sized shaft disk is used as a flat-interface reference structure to isolate the influence of contact-interface morphology from other geometric and material factors. Finite-element simulations are combined with an elastic-interaction framework to compare single-step, two-step, and three-step tightening paths. The results show that the periodic tooth-to-tooth interface of the curvic coupling changes local contact stiffness and load-transfer paths, thereby markedly amplifying bolt-to-bolt residual-preload differences compared with the shaft disk. Although the curvic-coupling structure does not change the basic role of tightening sequence in shaping the relative distribution pattern, it increases the sensitivity of residual preload to loading path and staged tightening. Among the investigated strategies, sequential tightening is not recommended, whereas the dual-axis crisscross strategy provides better preload uniformity. For high-precision assembly, the three-step dual-axis crisscross path of 40%\u201380%\u2013100% provides the best overall uniformity under the present working conditions. The study clarifies why conclusions obtained from conventional flat-interface bolted joints cannot be directly transferred to curvic couplings and provides process-level guidance for tightening-path design in high-precision curvic-coupling assembly.<\/jats:p>","DOI":"10.1371\/journal.pone.0357915","type":"journal-article","created":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T17:44:02Z","timestamp":1789148642000},"page":"e0357915","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["A study on a tightening method for optimizing bolt preload distribution in high-precision assembly of curvic couplings for aerospace applications"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-0180-1023","authenticated-orcid":true,"given":"Jun","family":"Lin","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Anhui University of Technology","place":["Ma\u2019anshan, Anhui, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,9,11]]},"reference":[{"key":"pone.0357915.ref001","doi-asserted-by":"crossref","first-page":"7580","DOI":"10.1177\/09544062251344520","article-title":"Theoretical prediction model for residual preload of annular homogeneous multi-bolt group considering bolted joint stiffness and elastic interaction","volume":"239","author":"W Pan","year":"2025","journal-title":"Proc Inst Mech Eng C J Mech Eng Sci"},{"key":"pone.0357915.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"},{"issue":"2","key":"pone.0357915.ref003","doi-asserted-by":"crossref","first-page":"212","DOI":"10.3390\/machines11020212","article-title":"Failure of Threaded Connections: A Literature Review","volume":"11","author":"D Croccolo","year":"2023","journal-title":"Machines"},{"key":"pone.0357915.ref004","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.ijpvp.2018.06.012","article-title":"Analytical evaluation of elastic interaction in bolted flange joints","volume":"165","author":"L Zhu","year":"2018","journal-title":"International Journal of Pressure Vessels and Piping"},{"key":"pone.0357915.ref005","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.ijmecsci.2018.01.023","article-title":"Effect of axial preload on durability of aerospace fastened joints","volume":"137","author":"T Benhaddou","year":"2018","journal-title":"Int J Mech Sci"},{"issue":"1","key":"pone.0357915.ref006","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1111\/j.1460-2695.2010.01493.x","article-title":"Fatigue behaviour of double lap riveted joints assembled with and without interfay sealant","volume":"34","author":"L Boni","year":"2010","journal-title":"Fatigue & Fracture of Engineering Materials & Structures"},{"key":"pone.0357915.ref007","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1016\/j.ijfatigue.2009.03.017","article-title":"Ultrasonic detection of fretting fatigue damage at bolt joints of aluminum alloy plates","volume":"31","author":"S Wagle","year":"2009","journal-title":"International Journal of Fatigue"},{"key":"pone.0357915.ref008","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/j.engfailanal.2007.04.009","article-title":"Experimental and numerical investigation of the effect of clamping force on the fatigue behaviour of bolted plates","volume":"15","author":"TN Chakherlou","year":"2008","journal-title":"Eng Fail Anal"},{"key":"pone.0357915.ref009","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1007\/s40430-025-05391-6","article-title":"The preload prediction model of single- and multi-step preload of the casing connection system is obtained by using the elastic interaction theory of bolt group","volume":"47","author":"W Pan","year":"2025","journal-title":"J Braz Soc Mech Sci Eng"},{"key":"pone.0357915.ref010","first-page":"63","article-title":"Finite element analysis of bolted rabbet joint structure under dispersed pre-tightening force","volume":"61","author":"F Chen","year":"2018","journal-title":"Aeronaut Manuf Technol"},{"key":"pone.0357915.ref011","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.engfailanal.2010.09.015","article-title":"Failure analysis of bolted joints: Effect of friction coefficients in torque\u2013preloading relationship","volume":"18","author":"D Croccolo","year":"2011","journal-title":"Eng Fail Anal"},{"key":"pone.0357915.ref012","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.ijmecsci.2017.05.032","article-title":"Analysis of elastic interaction stiffness and its effect on bolt preloading","volume":"130","author":"YQ Wang","year":"2017","journal-title":"Int J Mech Sci"},{"key":"pone.0357915.ref013","doi-asserted-by":"crossref","first-page":"104054","DOI":"10.1016\/j.ijpvp.2020.104054","article-title":"Study of bolt load scatter due to tightening sequence","volume":"182","author":"I Coria","year":"2020","journal-title":"International Journal of Pressure Vessels and Piping"},{"key":"pone.0357915.ref014","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.ijpvp.2016.02.022","article-title":"Optimized bolt tightening strategies for gasketed flanged pipe joints of different sizes","author":"M Abid","year":"2016","journal-title":"International Journal of Pressure Vessels and Piping"},{"issue":"4","key":"pone.0357915.ref015","article-title":"Elastic Interaction in Bolted Flange Joints: An Analytical Model to Predict and Optimize Bolt Load","volume":"140","author":"L Zhu","year":"2018","journal-title":"Journal of Pressure Vessel Technology"},{"key":"pone.0357915.ref016","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1108\/EC-03-2021-0131","article-title":"Topological sensitivity analysis with respect to a small idealized bolt","volume":"39","author":"L Rakotondrainibe","year":"2022","journal-title":"Eng Comput"},{"key":"pone.0357915.ref017","doi-asserted-by":"crossref","first-page":"109626","DOI":"10.1016\/j.ymssp.2022.109626","article-title":"Combination resonances of rotor systems with asymmetric residual preloads in bolted joints","volume":"183","author":"J Hong","year":"2023","journal-title":"Mechanical Systems and Signal Processing"},{"key":"pone.0357915.ref018","doi-asserted-by":"crossref","first-page":"108433","DOI":"10.1016\/j.ymssp.2021.108433","article-title":"Nonlinear effects of bolted flange connections in aeroengine casing assemblies","volume":"166","author":"S-E Mir-Haidari","year":"2022","journal-title":"Mechanical Systems and Signal Processing"},{"key":"pone.0357915.ref019","doi-asserted-by":"crossref","first-page":"105538","DOI":"10.1016\/j.ijmecsci.2020.105538","article-title":"The investigation of viscoelastic mechanical behaviors of bolted GLARE joints: modeling and experiments","volume":"175","author":"P Xu","year":"2020","journal-title":"Int J Mech Sci"},{"key":"pone.0357915.ref020","doi-asserted-by":"crossref","first-page":"106663","DOI":"10.1016\/j.jcsr.2021.106663","article-title":"Nonlinear interaction effect on main cable clamp bolts tightening in suspension bridge","volume":"182","author":"R Miao","year":"2021","journal-title":"Journal of Constructional Steel Research"},{"key":"pone.0357915.ref021","unstructured":"Liu E, Zhang M, Dong J, Li Z, Tong J, Zheng J. Study on contact stress distribution at curvic couplings fitting surface under pretightening force. In: Proceedings of the International Conference on Intelligent Vehicles and Mechanical Engineering (IVME 2026), 2026."},{"issue":"9","key":"pone.0357915.ref022","doi-asserted-by":"crossref","first-page":"1815","DOI":"10.1243\/09544062JMES1853","article-title":"Stress distribution and contact status analysis of a bolted rotor with curvic couplings","volume":"224","author":"SX Yuan","year":"2010","journal-title":"Proc Inst Mech Eng C J Mech Eng Sci"},{"issue":"19","key":"pone.0357915.ref023","doi-asserted-by":"crossref","first-page":"4231","DOI":"10.1177\/0954406220974051","article-title":"Modelling and stress analysis for double-row curvic couplings","volume":"235","author":"D Zhang","year":"2021","journal-title":"Proc Inst Mech Eng C J Mech Eng Sci"},{"key":"pone.0357915.ref024","doi-asserted-by":"crossref","first-page":"109984","DOI":"10.1016\/j.triboint.2024.109984","article-title":"Nonlinear modeling and vibration response analysis of rod fastening rotor-bearing system with curvic coupling","volume":"199","author":"C Wang","year":"2024","journal-title":"Tribol Int"},{"key":"pone.0357915.ref025","doi-asserted-by":"crossref","first-page":"115721","DOI":"10.1016\/j.apm.2024.115721","article-title":"Analytical model of curvic coupling and application in nonlinear vibration analysis of a squeeze film damper - rolling bearing - rotor system","volume":"137","author":"J He","year":"2025","journal-title":"Appl Math Model"},{"issue":"4","key":"pone.0357915.ref026","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1115\/1.2929252","article-title":"An Improved Flange Bolt-Up Procedure Using Experimentally Determined Elastic Interaction Coefficients","volume":"114","author":"GD Bibel","year":"1992","journal-title":"Journal of Pressure Vessel Technology"},{"key":"pone.0357915.ref027","first-page":"95","article-title":"Study on the elastic interaction of bolt group of engine disk-shaft connected structure","volume":"34","author":"J Chen","year":"2018","journal-title":"Mach Des Res"},{"key":"pone.0357915.ref028","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1108\/EC-12-2022-0731","article-title":"General prediction model of residual pretightening force of bolt group with one-step and multi-step pretightening and analysis of influencing factors from the perspective of elastic interaction","volume":"40","author":"W Pan","year":"2023","journal-title":"Eng Comput"},{"key":"pone.0357915.ref029","volume-title":"ASME PCC-1-2019: Guidelines for Pressure Boundary Bolted Flange Joint Assembly","author":"A S M E","year":"2019"},{"issue":"1","key":"pone.0357915.ref030","doi-asserted-by":"crossref","first-page":"2","DOI":"10.3390\/buildings15010002","article-title":"A New Single-Step Bolt Tightening Method for Multi-Bolt Flange Structures","volume":"15","author":"J Zhong","year":"2024","journal-title":"Buildings"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0357915","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T17:44:11Z","timestamp":1789148651000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0357915"}},"subtitle":[],"editor":[{"given":"Mohit","family":"Kumar","sequence":"first","affiliation":[{"name":"King Mongkut\u2019s University of Technology North Bangkok","place":["THAILAND"]}],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,9,11]]},"references-count":30,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9,11]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0357915","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,11]]}}}