{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:22:41Z","timestamp":1760059361412,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T00:00:00Z","timestamp":1749168000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Equipment Advance Research Grant Program Fund","award":["6141C08"],"award-info":[{"award-number":["6141C08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetrical bearing raceway led to the axial sliding of rolling elements, which is a crucial factor in shortening the operational lifespan. This study addresses this limitation through three-step advancements: first, a parametric equation for logarithmic spiral raceways is developed by analyzing their asymmetric geometric features; second, based on the geometrical model, we systematically investigate the parameters of the logarithmic spiral that affects the bearing performance metrics; and finally, a novel fatigue life prediction framework that integrates static mechanical analysis with raceway parameters establishes the theoretical foundation for optimizing the raceway parameters. The results of the model analysis show that the error of the maximum contact stress verified by the finite element method is less than 8.3%, which verifies the model\u2019s accuracy. Increasing the contact angle \u03b1 of the outer ring from 82 to 85 can increase fatigue life by 15.6 times while increasing the initial polar radius O of the inner ring from 7.8 mm to 8.1 mm will cause fatigue life to drop by 86.9%. The orthogonal experiment shows that the contact angle \u03b1 of the outer ring has the most significant influence on the service life, and the optimal parameter combination (clearance \u03b4 of 0.02 mm, inner race and outer race strike angles \u03b1 of 85\u00b0, an inner race initial polar radius ro of 7.8 mm, and an outer race initial polar radius ro of 7.9 mm) achieves a 60.7% fatigue life increase. The findings provide theoretical support and parameter guidance for the optimal bearing design with logarithmic spiral raceways.<\/jats:p>","DOI":"10.3390\/sym17060889","type":"journal-article","created":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T03:52:28Z","timestamp":1749181948000},"page":"889","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Influence of Geometric Parameters on Contact Mechanics and Fatigue Life in Logarithmic Spiral Raceway Bearings"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiaofeng","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Pen-Tung Sah Institute of Micro-Nano Science and Technology, Xiamen University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuidian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Industrial Technology Research Institute, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinghua","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, Xiamen University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Xu","sequence":"additional","affiliation":[{"name":"Tranf Technology Co., Ltd., Xiamen 361115, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.renene.2018.04.033","article-title":"A prediction method for the real-time remaining useful life of wind turbine bearings based on the Wiener process","volume":"127","author":"Hu","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"106278","DOI":"10.1016\/j.triboint.2020.106278","article-title":"Roller bearing under high loaded oscillations: Life evolution and accommodation mechanisms","volume":"147","author":"Cavacece","year":"2020","journal-title":"Tribol. Int."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"108312","DOI":"10.1016\/j.triboint.2023.108312","article-title":"Bearings for aerospace applications","volume":"181","author":"Rejith","year":"2023","journal-title":"Tribol. Int."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"107222","DOI":"10.1016\/j.ymssp.2020.107222","article-title":"Kinematic characteristics and fault feature frequency of flexible thin-wall ellipse bearing","volume":"149","author":"Zhao","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.mechmachtheory.2006.02.004","article-title":"Optimum design of rolling element bearings using genetic algorithms","volume":"42","author":"Rao","year":"2007","journal-title":"Mech. Mach. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.mechmachtheory.2013.10.001","article-title":"Optimization of needle roller bearing design using novel hybrid methods","volume":"72","author":"Waghole","year":"2014","journal-title":"Mech. Mach. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"233","DOI":"10.4028\/www.scientific.net\/AMR.44-46.233","article-title":"Radial Clearance is key factor Affecting Roller Bearing Life Prediction in Tri-cone Bit","volume":"44","author":"Bu","year":"2008","journal-title":"Adv. Mater. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1051\/meca\/2015032","article-title":"Optimal design of paired tapered roller bearings under centred radial and axial static loads","volume":"16","author":"Dragoni","year":"2015","journal-title":"Mech. Ind."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.mechmachtheory.2016.06.006","article-title":"Design optimization of an angular contact ball bearing for the main shaft of a grinder","volume":"104","author":"Kim","year":"2016","journal-title":"Mech. Mach. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"104851","DOI":"10.1016\/j.mechmachtheory.2022.104851","article-title":"A dynamic approach for evaluating the moment rigidity and rotation precision of a bearing-planetary frame rotor system used in RV reduce","volume":"173","author":"Xie","year":"2022","journal-title":"Mech. Mach. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1007\/s10010-023-00715-1","article-title":"Evaluation of friction calculation methods for rolling bearings","volume":"87","author":"Zander","year":"2023","journal-title":"Forsch. im Ingenieurwesen"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Chen, G., Zhang, W., and Ding, Y. (2022). Research on Non-Circular Raceway of Single-Row Four-Point Contact Ball Bearing Based on Life Optimization. Appl. Sci., 12.","DOI":"10.3390\/app122413027"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"109111","DOI":"10.1016\/j.ymssp.2022.109111","article-title":"A study on the dynamic contact feature of four-contact-point ball bearing","volume":"174","author":"Ma","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1002\/nme.1620120604","article-title":"Contcat stress minimization by contour design","volume":"12","author":"Haug","year":"1978","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_15","first-page":"1","article-title":"Study on Load Distribution Characteristics of Cylindrical Roller Bearings with Trilobe Raceways","volume":"9","author":"Lu","year":"2016","journal-title":"Bearing"},{"key":"ref_16","first-page":"11","article-title":"Study on vibration characteristic of trilobe raceway cylindrical roller bearing with elastic support","volume":"41","author":"Sun","year":"2017","journal-title":"J. Mech. Transm."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.cja.2017.07.001","article-title":"Cage slip characteristics of a cylindrical roller bearing with a trilobe-raceway","volume":"31","author":"Deng","year":"2018","journal-title":"Chin. J. Aeronaut."},{"key":"ref_18","first-page":"13","article-title":"Study on Processing for Non-Circular Raceway of Aerospace Trilobe Cylindrical Roller Bearings","volume":"9","author":"Zhang","year":"2019","journal-title":"Bearing"},{"key":"ref_19","first-page":"40","article-title":"Influence of Raceway Shape on Mechanical Properties of Four-Point Contact Ball Bearings","volume":"4","author":"Zhang","year":"2014","journal-title":"Bearing"},{"key":"ref_20","first-page":"1","article-title":"Contact Mechanics Studies for an Elliptical Curvature Deep Groove Ball Bearing Using Continuum Solid Modeling based on FEM Simulation Approach","volume":"13","author":"Singh","year":"2016","journal-title":"IOSR J. Mech. Civ. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"106711","DOI":"10.1016\/j.engfailanal.2022.106711","article-title":"Influence of elliptical truncation on the raceway in a four-point contact pitching bearing","volume":"141","author":"Wang","year":"2022","journal-title":"Eng. Fail. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Mukutadze, M.A., and Lagunova, E.O. (2022, January 16\u201320). Mathematical Model of Flow of Lubricant and Molten Coating with Micropolar Rheological Properties in Running Clearance of Journal Bearing with Non-circular Bearing Surface Profile, Considering Pressure Dependence of Viscosity. Proceedings of the 8th International Conference on Industrial Engineering, Sochi, Russia.","DOI":"10.1007\/978-3-031-14125-6_58"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, Q., Zhao, Y., and Wang, M. (2022). Analysis of contact stress distribution between rolling element and variable diameter raceway of cageless bearing. Appl. Sci., 12.","DOI":"10.3390\/app12125764"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"256","DOI":"10.3901\/JME.2023.21.256","article-title":"Design and Dynamic Characteristics Analysis of a Novel Cageless Ball Bearing with Pure Rolling","volume":"59","author":"Li","year":"2023","journal-title":"J. Mech. Eng."},{"key":"ref_25","first-page":"112","article-title":"Experimental Study on Oil Interruption Performance of Novel Cageless Angular Contact Ball Bearings","volume":"46","author":"Xu","year":"2022","journal-title":"J. Mech. Transm."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhao, X., Xu, S., Xu, T., Xu, Q., and Huang, K. (2024). Calculation Method and Experimental Study on Circumferential Total Clearance of Cageless Bearings. Lubricants, 12.","DOI":"10.3390\/lubricants12070238"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1115\/1.4009930","article-title":"Dynamic Capacity of Rolling Bearings","volume":"16","author":"Lundberg","year":"1949","journal-title":"J. Appl. Mech."},{"key":"ref_28","first-page":"9","article-title":"Comparative analysis on properties of 8Cr4Mo4V steel for bearing after vacuum gas quenching and isothermal salt bath quenching","volume":"47","author":"Tong","year":"2022","journal-title":"Heat Treat. Met."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/889\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:47:27Z","timestamp":1760032047000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/889"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,6]]},"references-count":28,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["sym17060889"],"URL":"https:\/\/doi.org\/10.3390\/sym17060889","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,6,6]]}}}