{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T16:36:03Z","timestamp":1785429363942,"version":"3.56.0"},"reference-count":52,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T00:00:00Z","timestamp":1775692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shanxi Provincial Key Research and Development Programme Project of China","award":["202402040201011"],"award-info":[{"award-number":["202402040201011"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U2568227"],"award-info":[{"award-number":["U2568227"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["U2568227"],"award-info":[{"award-number":["U2568227"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Science and Technology Research and Development Program of China National Railway Group Corporation","award":["K2021J042"],"award-info":[{"award-number":["K2021J042"]}]},{"name":"Central Universities Basic Scientific Research Business Fund","award":["2022JBQY007"],"award-info":[{"award-number":["2022JBQY007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>Resilient wheels are widely employed in metro vehicles to mitigate vibration and noise, in which rubber damping components play a critical role in load transmission and fatigue resistance. However, stress concentration and cyclic loading can significantly compromise their durability and service life. In this study, the structural optimization and fatigue life of rubber damping components in resilient wheels are systematically investigated based on finite element analysis and in-service metro operational data. A three-dimensional finite element model incorporating hyperelastic material behavior is developed to evaluate stress distributions under three representative conditions: press-fit assembly, straight-line operation, and curved-track operation. Based on the resulting stress fields, critical high-stress regions within the rubber component are identified and selected as targets for structural optimization. The Design of Experiments (DOE) methodology, integrated with the Isight 2022 optimization platform, is employed to determine the optimal geometric parameters that minimize the von Mises equivalent stress. Furthermore, a fatigue life prediction framework is established using actual metro service mileage data. Fatigue performance is assessed using Fe-safe 2022 software in conjunction with rubber fatigue crack propagation theory, and the results before and after optimization are systematically compared. This study demonstrates that stress concentrations in resilient wheel rubber damping components predominantly occur at fillet transition regions, governed by load transfer characteristics under press-fitting and service conditions. Through DOE-based structural optimization, the critical geometric parameters are effectively refined, leading to a significant reduction in stress levels in key regions. As a result, the proposed approach markedly improves fatigue performance, extending the minimum fatigue life from 1300 days to 24,322 days, thereby substantially enhancing the durability and reliability of the resilient wheel system.<\/jats:p>","DOI":"10.3390\/polym18080915","type":"journal-article","created":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T08:56:07Z","timestamp":1775724967000},"page":"915","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fatigue Life Evaluation and Structural Optimization of Rubber Damping Components in Metro Resilient Wheels"],"prefix":"10.3390","volume":"18","author":[{"given":"Qiang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical and Electronic Control Engineering, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Shanxi Taibao Sealing Technology Co., Ltd., Taiyuan 030032, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiming","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electronic Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiliang","family":"Shu","sequence":"additional","affiliation":[{"name":"School of Mechatronics and Vehicle Engineering, East China Jiaotong University, Nanchang 330199, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangxue","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electronic Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhan","family":"Deng","sequence":"additional","affiliation":[{"name":"BYD Company Limited, Shenzhen 518118, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1006\/jsvi.1999.2561","article-title":"Optimization of resilient wheels for rolling noise control","volume":"231","author":"Bouvet","year":"2000","journal-title":"J. Sound Vib."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1243\/0954409JRRT79","article-title":"Review of research into wheel\/rail rolling noise reduction","volume":"220","author":"Thompson","year":"2006","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"de Freitas, R.T., and Kaewunruen, S. (2016). Life cycle cost evaluation of noise and vibration control methods at urban railway turnouts. Environments, 3.","DOI":"10.3390\/environments3040034"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1177\/1077546310362452","article-title":"Geometry effects on the vibro-acoustic behavior of railway resilient wheels","volume":"17","author":"Cigada","year":"2011","journal-title":"J. Vib. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108529","DOI":"10.1016\/j.apacoust.2021.108529","article-title":"Study on the influence of resilient wheels on vibration and acoustic radiation characteristics of suburban railway concrete box girder bridges","volume":"187","author":"He","year":"2022","journal-title":"Appl. Acoust."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1016\/S0142-1123(02)00008-7","article-title":"A literature survey on fatigue analysis approaches for rubber","volume":"24","author":"Mars","year":"2002","journal-title":"Int. J. Fatigue"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"391","DOI":"10.5254\/1.3547831","article-title":"Factors that affect the fatigue life of rubber: A literature survey","volume":"77","author":"Mars","year":"2004","journal-title":"Rubber Chem. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1016\/j.ijfatigue.2018.10.009","article-title":"Fatigue of natural rubber under different temperatures","volume":"124","author":"Ruellan","year":"2019","journal-title":"Int. J. Fatigue"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"012079","DOI":"10.1088\/1742-6596\/2076\/1\/012079","article-title":"Research on fatigue failure mode and failure theory of rubber","volume":"2076","author":"Wang","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5011","DOI":"10.1021\/ma0495386","article-title":"Mechanism of fatigue crack growth in carbon black filled natural rubber","volume":"37","author":"Huneau","year":"2004","journal-title":"Macromolecules"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s11043-018-9398-8","article-title":"Numerical analysis of the dependence of rubber hysteresis loss and heat generation on temperature and frequency","volume":"23","author":"Zhi","year":"2019","journal-title":"Mech. Time Depend. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106313","DOI":"10.1016\/j.ijfatigue.2021.106313","article-title":"Fatigue of crystallizable rubber: Generation of a Haigh diagram over a wide range of positive load ratios","volume":"150","author":"Champy","year":"2021","journal-title":"Int. J. Fatigue"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"567","DOI":"10.5254\/1.3538274","article-title":"Application of fatigue methods based on fracture mechanics for tire compound development","volume":"63","author":"Young","year":"1990","journal-title":"Rubber Chem. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1111\/ffe.14533","article-title":"Improving Fatigue Life Prediction of Natural Rubber Using a Physics-Informed Neural Network Model","volume":"48","author":"Sun","year":"2025","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Qiu, X.W., Yin, H.S., and Xing, Q.C. (2022). Research Progress on Fatigue Life of Rubber Materials. Polymers, 14.","DOI":"10.3390\/polym14214592"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"304","DOI":"10.5254\/1.3539515","article-title":"Dynamic fatigue life of rubber","volume":"13","author":"Cadwell","year":"1940","journal-title":"Rubber Chem. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.matdes.2014.01.035","article-title":"Experiment and modeling of uniaxial tension fatigue performances for filled natural rubbers","volume":"58","author":"Shangguan","year":"2014","journal-title":"Mater. Des."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2304","DOI":"10.1016\/j.engfailanal.2009.03.008","article-title":"Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis","volume":"16","author":"Li","year":"2009","journal-title":"Eng. Fail. Anal."},{"key":"ref_19","first-page":"897","article-title":"Strain-based criterion for uniaxial fatigue life prediction for an SBR rubber: Comparative study and development","volume":"234","author":"Belkhiria","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.ijfatigue.2014.03.026","article-title":"Multiaxial fatigue life predictors for rubbers: Application of recent developments to a carbon-filled SBR","volume":"66","author":"Ayoub","year":"2014","journal-title":"Int. J. Fatigue"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.ijfatigue.2005.05.011","article-title":"Multiaxial fatigue life prediction for a natural rubber","volume":"28","author":"Saintier","year":"2006","journal-title":"Int. J. Fatigue"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1016\/j.ijfatigue.2011.01.014","article-title":"Biaxial fatigue behavior of a polychloroprene rubber","volume":"33","author":"Poisson","year":"2011","journal-title":"Int. J. Fatigue"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/S0167-6636(02)00175-8","article-title":"A damage model for the fatigue life of elastomeric materials","volume":"34","author":"Wang","year":"2002","journal-title":"Mech. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/j.proeng.2010.03.107","article-title":"Multiaxial fatigue life prediction of rubber-like materials using the continuum damage mechanics approach","volume":"2","author":"Ayoub","year":"2010","journal-title":"Procedia Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2458","DOI":"10.1016\/j.ijsolstr.2011.04.003","article-title":"A continuum damage model for the high-cycle fatigue life prediction of styrene-butadiene rubber under multiaxial loading","volume":"48","author":"Ayoub","year":"2011","journal-title":"Int. J. Solids Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1002\/app.1964.070080212","article-title":"Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber","volume":"8","author":"Lake","year":"1964","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"348","DOI":"10.5254\/1.3544847","article-title":"Mechanical fatigue limit for rubber","volume":"39","author":"Lake","year":"1966","journal-title":"Rubber Chem. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1179\/1743289810Y.0000000044","article-title":"Fatigue life prediction of bonded rubber components at elevated temperature","volume":"40","author":"Asare","year":"2011","journal-title":"Plast. Rubber Compos."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.ijnonlinmec.2012.03.001","article-title":"Energy release rate of small cracks in hyperelastic materials","volume":"47","author":"Mars","year":"2012","journal-title":"Int. J. Non Linear Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1016\/j.polymer.2013.01.019","article-title":"Elastic\u2013viscous transition in tear fracture of rubbers","volume":"54","author":"Fukahori","year":"2013","journal-title":"Polymer"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"48519","DOI":"10.1002\/app.48519","article-title":"Rubber fatigue life prediction using a random forest method and nonlinear cumulative fatigue damage model","volume":"137","author":"Liu","year":"2020","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107199","DOI":"10.1016\/j.ijfatigue.2022.107199","article-title":"Residual fatigue life prediction of natural rubber components under variable amplitude loads","volume":"165","author":"Liu","year":"2022","journal-title":"Int. J. Fatigue"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109351","DOI":"10.1016\/j.engfracmech.2023.109351","article-title":"Using hybrid physics-informed neural networks to predict lifetime under multiaxial fatigue loading","volume":"289","author":"Halamka","year":"2023","journal-title":"Eng. Fract. Mech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109242","DOI":"10.1016\/j.engfracmech.2023.109242","article-title":"Machine learning-based fatigue life prediction of metal materials: Perspectives of physics-informed and data-driven hybrid methods","volume":"284","author":"Wang","year":"2023","journal-title":"Eng. Fract. Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1177\/0954409718797734","article-title":"Longitudinal vibration of a resilient wheel under the adhesion limit","volume":"233","author":"Yang","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1002\/pamm.201610114","article-title":"Simulation of stiffness analysis of rubber material applied in resilient wheel","volume":"16","author":"Zhang","year":"2016","journal-title":"PAMM"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"012018","DOI":"10.1088\/1757-899X\/324\/1\/012018","article-title":"Considerations on the use of elastic wheels to the urban transport vehicles","volume":"324","author":"Sebesan","year":"2018","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1121\/1.394746","article-title":"Wheel\/rail rolling noise, I: Theoretical analysis","volume":"81","author":"Remington","year":"1987","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s10999-023-09655-8","article-title":"Mechanical characteristics of resilient wheels that consider structural nonlinearity and varying wheel\/rail contact point","volume":"20","author":"Chen","year":"2024","journal-title":"Int. J. Mech. Mater. Des."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1186\/s10033-019-0383-1","article-title":"Characteristics of Vibration and Sound Radiation of Metro Resilient Wheel","volume":"32","author":"Zhou","year":"2019","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3298","DOI":"10.1177\/10775463221094892","article-title":"An investigation into the effect of resilient wheel stiffness on the dynamic behaviour of a metro vehicle running along a tangent track","volume":"29","author":"Zhou","year":"2023","journal-title":"J. Vib. Control"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1177\/0954409720971383","article-title":"Dynamic behavior of resilient wheels at a rail weld joint","volume":"235","author":"Xiao","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2450002","DOI":"10.1142\/S0219455424500020","article-title":"Dynamic Behavior of Metro Train-LSB (Long-Span Bridge) System Considering Nonlinearity of Resilient Wheel","volume":"24","author":"Chen","year":"2024","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"104426","DOI":"10.1016\/j.cemconcomp.2022.104426","article-title":"Quantitative evaluation of steel corrosion induced deterioration in rubber concrete by integrating ultrasonic testing, machine learning and mesoscale simulation","volume":"128","author":"Zhang","year":"2022","journal-title":"Cem. Concr. Compos."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s42464-025-00331-4","article-title":"Artificial intelligence in the optimisation of rubber properties: Experimental validation and testing of predicted models","volume":"28","author":"Choudhury","year":"2025","journal-title":"J. Rubber Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"111475","DOI":"10.1016\/j.commatsci.2022.111475","article-title":"A virtual sample generation algorithm supporting machine learning with a small-sample dataset: A case study for rubber materials","volume":"211","author":"Shen","year":"2022","journal-title":"Comp. Mater. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"He, Z.F., Wu, Z.F., Niu, W.J., Wang, F.C., Zhong, S.J., Han, Z.Y., and Zhao, Q.X. (2024). A machine learning model for predicting the mechanical strength of cement-based materials filled with waste rubber modified by PVA. Front. Mater., 11.","DOI":"10.3389\/fmats.2024.1490006"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"6694610","DOI":"10.1155\/stc\/6694610","article-title":"Detection of Rupture Damage Degree in Laminated Rubber Bearings Using a Piezoelectric-Based Active Sensing Method and Hybrid Machine Learning Algorithms","volume":"2025","author":"Deng","year":"2025","journal-title":"Struct. Control. Health Monit."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"128044","DOI":"10.1016\/j.polymer.2025.128044","article-title":"Deep learning-based calibration method for material parameters of resilient wheel rubber components","volume":"319","author":"Zhang","year":"2025","journal-title":"Polymer"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1002\/app.1964.070080129","article-title":"Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue","volume":"8","author":"Gent","year":"1964","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_51","unstructured":"(2023). Railway Applications. Wheelsets and Bogies. Monobloc Wheels. Technical Approval Procedure Forged and Rolled Wheels (Standard No. BS EN 13979-1:2023)."},{"key":"ref_52","unstructured":"(2003). Technical Approval of Monobloc Wheels\u2014Application Document for Standard EN 13979-1 (Standard No. UIC 510-5 1.11.2023)."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/8\/915\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T09:08:05Z","timestamp":1775725685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/8\/915"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,9]]},"references-count":52,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["polym18080915"],"URL":"https:\/\/doi.org\/10.3390\/polym18080915","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,9]]}}}