{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:54:06Z","timestamp":1787028846214,"version":"build-2736575974"},"reference-count":41,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T00:00:00Z","timestamp":1718841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundations of China","doi-asserted-by":"publisher","award":["52205047"],"award-info":[{"award-number":["52205047"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundations of China","doi-asserted-by":"publisher","award":["52175037"],"award-info":[{"award-number":["52175037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The spline teeth fracture of separator plates in wet multi-plate clutches compromises driving safety and the vehicle\u2019s lifespan. Tooth fracture is mainly caused by stress concentration at the tooth root and uneven circumferential load distribution. This paper considers parameters such as torque, teeth count, tooth profile, and misalignment errors, establishing the corresponding finite element (FE) model to analyze the impact of the above-mentioned parameters on the strength of the separator plates. Analysis under even and biased load circumstances demonstrated that an optimum tooth count and profile can significantly increase the strength of the separator plates, offering advice for the optimized design of wet multi-plate clutch separator plates.<\/jats:p>","DOI":"10.3390\/ma17123039","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T11:42:03Z","timestamp":1718883723000},"page":"3039","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Study on Spline Stress of Separator Plates in a Wet Multi-Plate Clutch"],"prefix":"10.3390","volume":"17","author":[{"given":"Biao","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaobo","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changsong","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0231-4997","authenticated-orcid":false,"given":"Liang","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qin","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weichen","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107096","DOI":"10.1016\/j.triboint.2021.107096","article-title":"Study on the Groove Area Effects on the Friction-Wear Properties of a Cu-Based Wet Clutch","volume":"163","author":"Yu","year":"2021","journal-title":"Tribol. Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"106169","DOI":"10.1016\/j.triboint.2020.106169","article-title":"Variation Mechanism of the Friction Torque in a Cu-Based Wet Clutch Affected by Operating Parameters","volume":"147","author":"Yu","year":"2020","journal-title":"Tribol. Int."},{"key":"ref_3","first-page":"775","article-title":"Analysis and Verification on Friction Discs Buckling in Multi-Disc Clutch","volume":"39","author":"Li","year":"2017","journal-title":"Automot. Eng."},{"key":"ref_4","unstructured":"Kou, T. (2021). Investigation on Eccentric Load and Fretting Wear of Involute Spline in Friction Clutch. [Master\u2019s Dissertation, Harbin Engineering University]."},{"key":"ref_5","unstructured":"Yu, L. (2021). Friction Difference Characteristics of the Sliding Interfaces of Friction Components in Wet Shift Clutches. [Doctoral Dissertation, Beijing Institute of Technology]."},{"key":"ref_6","unstructured":"Zheng, L. (2022). Dynamic Disengaging Characteristics and Influencing Factors of Wet Multi-Disc Shift Clutches Friction Difference Characteristics of the Sliding Interfaces of Friction Components in Wet Shift Clutches. [Doctoral Dissertation, Beijing Institute of Technology]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1007\/s11668-013-9719-9","article-title":"Failure Investigation of Spline-Shaft of an Under Slung Crane","volume":"13","author":"Sinha","year":"2013","journal-title":"J. Fail. Anal. Prev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1243\/0309324011514647","article-title":"Macroscopic Fretting Variables in a Splined Coupling under Combined Torque and Axial Load","volume":"36","author":"Leen","year":"2001","journal-title":"J. Strain Anal. Eng. Des."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1243\/030932402320950161","article-title":"An Investigation of the Fatigue and Fretting Performance of a Representative Aero-Engine Spline Coupling","volume":"37","author":"Leen","year":"2002","journal-title":"J. Strain Anal. Eng. Des."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1016\/j.wear.2006.11.017","article-title":"The Application of Fretting Wear Modelling to a Spline Coupling","volume":"262","author":"Ding","year":"2007","journal-title":"Wear"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1038\/s41598-023-27615-2","article-title":"Contact Analysis and Strength Calculations of Involute Spline Couplings","volume":"13","author":"Li","year":"2023","journal-title":"Sci. Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0261-3069(00)00094-7","article-title":"Load Distribution and Pitch Errors in a Spline Coupling","volume":"22","author":"Tjernberg","year":"2001","journal-title":"Mater. Des."},{"key":"ref_13","first-page":"90","article-title":"Strength Analysis of Involute Spline of Aeroengine","volume":"4","author":"Chen","year":"2009","journal-title":"Mech. Eng. Autom."},{"key":"ref_14","first-page":"6","article-title":"Load Distribution and Stress Analysis of Tooth Alignment and Profile at Spline Connection in Shields","volume":"48","author":"Wei","year":"2017","journal-title":"Constr. Mach. Equip."},{"key":"ref_15","first-page":"551","article-title":"Stress Sources and Critical Stress Combinations for Splined Shaft","volume":"104","author":"Volfson","year":"1982","journal-title":"J. Mech. Des."},{"key":"ref_16","first-page":"23","article-title":"Irregularity of Load Distribution along a Spline Coupling","volume":"49","author":"Tatur","year":"1969","journal-title":"Russ. Eng. J.-USSR"},{"key":"ref_17","first-page":"134","article-title":"Contact Analysis of Involute Spline Joint Based on FEM","volume":"38","author":"Wang","year":"2014","journal-title":"J. Mech. Transm."},{"key":"ref_18","unstructured":"Wang, C. (2021). Research on Contact and Wear Characteristics of Aviation Spline. [Master\u2019s Dissertation, Dalian University of Technology]."},{"key":"ref_19","first-page":"229","article-title":"Failure Analysis and Improvement Measures for Spline Shaft of Sun Wheel of Shearer","volume":"36","author":"Li","year":"2015","journal-title":"Coal Mine Mach."},{"key":"ref_20","first-page":"104","article-title":"Analysis on Fretting Wear of Gear Clutch in a Hybrid Transmission","volume":"47","author":"Hua","year":"2022","journal-title":"Automob. Appl. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/S1350-6307(00)00027-3","article-title":"Load Distribution in the Axial Direction in a Spline Coupling","volume":"8","author":"Tjernberg","year":"2001","journal-title":"Eng. Fail. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1109\/TASE.2009.2033033","article-title":"Variation Analysis of Tooth Engagement and Loads in Involute Splines","volume":"7","author":"Chase","year":"2010","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1006\/jsvi.2000.3246","article-title":"A Spline Joint Formulation for Drive Train Torsional Dynamic Models","volume":"241","author":"Kahraman","year":"2001","journal-title":"J. Sound Vib."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.mechmachtheory.2014.02.002","article-title":"A Semi-Analytical Load Distribution Model for Side-Fit Involute Splines","volume":"76","author":"Hong","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"032601","DOI":"10.1115\/1.4029282","article-title":"Effects of Tooth Indexing Errors on Load Distribution and Tooth Load Sharing of Splines Under Combined Loading Conditions","volume":"137","author":"Hong","year":"2015","journal-title":"J. Mech. Des."},{"key":"ref_26","first-page":"41","article-title":"Influence of Gear Loads on Spline Couplings","volume":"3","author":"Wink","year":"2014","journal-title":"Power Transm. Eng."},{"key":"ref_27","first-page":"111","article-title":"Dynamic Meshing Force Analysis of Aviation Involute Spline Pair Considering Tooth Profile","volume":"19","author":"Huo","year":"2019","journal-title":"Sci. Technol. Eng."},{"key":"ref_28","first-page":"110","article-title":"Research of Misaligned Load Distribution of Involute Spline Pair based on Finite Element Method","volume":"40","author":"Tan","year":"2016","journal-title":"J. Mech. Transm."},{"key":"ref_29","first-page":"51","article-title":"Analysis of Axial Load of Aviation Floating Involute Spline Pair","volume":"4","author":"Jia","year":"2021","journal-title":"Mag. Equip. Mach."},{"key":"ref_30","first-page":"694","article-title":"Design Method and Its Misaligned Contact Characteristic of Aviation Crowned Spline","volume":"37","author":"Zhao","year":"2022","journal-title":"J. Aerosp. Power"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"105104","DOI":"10.1016\/j.mechmachtheory.2022.105104","article-title":"Load Distribution and Tooth Root Stress of Highly Crowned Spherical Gear Couplings Working at High Misalignment Angles","volume":"179","author":"Arana","year":"2023","journal-title":"Mech. Mach. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.mechmachtheory.2015.11.015","article-title":"Theoretical and Experimental Study on Gear-Coupling Contact and Loads Considering Misalignment, Torque, and Friction Influences","volume":"98","author":"Guo","year":"2016","journal-title":"Mech. Mach. Theory"},{"key":"ref_33","unstructured":"Chen, Y. (2015). Research on Friction and Wear Characteristic of Aviation Involute Spline Couplings under Axis Deviation and Bending Stress. [Master\u2019s Dissertation, Nanjing University of Aeronautics and Astronautics]."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"032059","DOI":"10.1088\/1757-899X\/1043\/3\/032059","article-title":"Optimization of Spline Bearing Capacity Considering the Influence of Assembly Sequence","volume":"1043","author":"Zhao","year":"2021","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_35","unstructured":"Xue, X. (2017). Investigation on Mechanism and Prediction Method of Fretting Wear in Aero-Engine Involute Spline Coupling. [Doctoral Dissertation, Northwestern Polytechnical University]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1504\/IJCAT.2002.000288","article-title":"Misalignment Loads in Splined Gear Couplings","volume":"15","author":"Elkholy","year":"2002","journal-title":"Int. J. Comput. Appl. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2195","DOI":"10.1177\/0954406212471916","article-title":"Load Distribution in Spline Coupling Teeth with Parallel Offset Misalignment","volume":"227","author":"Mura","year":"2013","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_38","first-page":"20","article-title":"Analysis of Friction Thermal Load of Internal Spline in Wet Clutch","volume":"39","author":"Yu","year":"2014","journal-title":"Lubr. Eng."},{"key":"ref_39","first-page":"26","article-title":"Thermo-Mechanical Coupling Analysis of Dual-Steel-Disc of Wet Multi-Disk Clutch","volume":"34","author":"Yang","year":"2011","journal-title":"J. Chongging Univ."},{"key":"ref_40","unstructured":"Cao, F. (2013). Study on the Characteristic of Wet Multi-Disk Clutch Engagement Process. [Master\u2019s Dissertation, Central South University]."},{"key":"ref_41","unstructured":"(2015). Alloy Structure Steels (Standard No. GB\/T 3077-2015)."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/12\/3039\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:01:59Z","timestamp":1760108519000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/12\/3039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,20]]},"references-count":41,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["ma17123039"],"URL":"https:\/\/doi.org\/10.3390\/ma17123039","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,20]]}}}