{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T02:24:37Z","timestamp":1773195877831,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T00:00:00Z","timestamp":1755907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Wuhan City Polytechnic High-level talents Foundation","award":["2024WHCPRB02"],"award-info":[{"award-number":["2024WHCPRB02"]}]},{"name":"Wuhan City Polytechnic High-level talents Foundation","award":["2025QCSH003"],"award-info":[{"award-number":["2025QCSH003"]}]},{"name":"Wuhan City Polytechnic High-level talents Foundation","award":["2024CSA082"],"award-info":[{"award-number":["2024CSA082"]}]},{"name":"Natural Science Project of Hubei Automobile After-sales Service Industry Association","award":["2024WHCPRB02"],"award-info":[{"award-number":["2024WHCPRB02"]}]},{"name":"Natural Science Project of Hubei Automobile After-sales Service Industry Association","award":["2025QCSH003"],"award-info":[{"award-number":["2025QCSH003"]}]},{"name":"Natural Science Project of Hubei Automobile After-sales Service Industry Association","award":["2024CSA082"],"award-info":[{"award-number":["2024CSA082"]}]},{"name":"Hubei Provincial Science and Technology Innovation Base (Platform) Program Project","award":["2024WHCPRB02"],"award-info":[{"award-number":["2024WHCPRB02"]}]},{"name":"Hubei Provincial Science and Technology Innovation Base (Platform) Program Project","award":["2025QCSH003"],"award-info":[{"award-number":["2025QCSH003"]}]},{"name":"Hubei Provincial Science and Technology Innovation Base (Platform) Program Project","award":["2024CSA082"],"award-info":[{"award-number":["2024CSA082"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Diaphragm springs, as critical components in commercial vehicle clutch assemblies, directly determine the clutch\u2019s working performance. The design of diaphragm springs, which possess a distinct symmetrical structure that underpins their mechanical behavior, centers on obtaining the large-end nonlinear load\u2013displacement curve\u2014a typical large deformation-induced nonlinear problem. Traditional design relies on the A-L formula, but studies show finite element analysis (FEA) yields results closer to actual measurements. This study established an FEA model of the diaphragm spring\u2019s disc spring (excluding separation fingers) and validated its correctness by comparing it with the A-L formula. Then, using FEA on models with separation fingers, it analyzed factors influencing the large-end load\u2013displacement characteristics. Leveraging the inherent symmetry of the diaphragm spring structure, particularly the symmetrical distribution of separation fingers, the analysis process efficiently captures uniform mechanical responses during deformation, while this symmetric arrangement also ensures balanced load distribution during clutch operation, a critical factor for stabilizing the load\u2013displacement curve. Results indicate the separation finger root is a key factor, with larger root holes, square holes (compared to circular ones), and more separation fingers reducing stiffness to effectively adjust the curve; in contrast, the tip and length of separation fingers have little impact, making the latter unsuitable for design adjustments.<\/jats:p>","DOI":"10.3390\/sym17091378","type":"journal-article","created":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T00:09:32Z","timestamp":1756080572000},"page":"1378","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Finite Element Simulation and Parametric Analysis of Load\u2013Displacement Characteristics of Diaphragm Springs in Commercial Vehicle Clutches"],"prefix":"10.3390","volume":"17","author":[{"given":"Ming","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Automotive Technology and Service, Wuhan City Polytechnic, Wuhan 430064, China"},{"name":"School of Automobile and Traffic Engineering, Wuhan University of Science and Technology, Wuhan 430065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5986-1524","authenticated-orcid":false,"given":"Zhen","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Automobile and Traffic Engineering, Wuhan University of Science and Technology, Wuhan 430065, China"},{"name":"School of Automotive Engineering, Hubei University of Automotive Technology, Shiyan 442002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianhui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automobile and Traffic Engineering, Wuhan University of Science and Technology, Wuhan 430065, China"},{"name":"School of Automotive Engineering, Hubei University of Automotive Technology, Shiyan 442002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pingxiang","family":"Ming","sequence":"additional","affiliation":[{"name":"School of Automotive Technology and Service, Wuhan City Polytechnic, Wuhan 430064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1796","DOI":"10.1177\/0954407016686010","article-title":"The calculation model of the friction torque on a dry clutch","volume":"231","author":"Lin","year":"2017","journal-title":"Proc. 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