{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:43:18Z","timestamp":1792791798765,"version":"4.5.0"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T00:00:00Z","timestamp":1761868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"crossref","award":["BK20250700"],"award-info":[{"award-number":["BK20250700"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This study systematically analyzes the dynamic behavior of bearing tilt-misalignment coupling faults in rotary joints and establishes a high-fidelity nonlinear dynamic model for a dual-support bearing\u2013rotor system. By integrating Hertzian contact theory, the nonlinear contact forces induced by the tilt of the inner\/outer rings and axial misalignment are considered, and expressions for bearing forces incorporating time-varying stiffness and radial clearance are derived. The system\u2019s vibration response is solved using the Newmark-\u03b2 numerical integration method. This study reveals the influence of tilt angle and misalignment magnitude on contact forces, vibration patterns, and fault characteristic frequencies, demonstrating that the system exhibits multi-frequency harmonic characteristics under misalignment conditions, with vibration amplitudes increasing nonlinearly with the degree of misalignment. Furthermore, dynamic models for single-point faults (inner\/outer ring) and composite faults are constructed, and Gaussian filtering technology is employed to simulate defect surface roughness, analyzing the modulation effects of faults on spectral characteristics. Experimental validation confirms that the theoretical model effectively captures actual vibration features, providing a theoretical foundation for health monitoring and intelligent diagnosis of rotary joints.<\/jats:p>","DOI":"10.3390\/e27111123","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:15:14Z","timestamp":1762175714000},"page":"1123","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamic Modeling and Analysis of Rotary Joints with Coupled Bearing Tilt-Misalignment Faults"],"prefix":"10.3390","volume":"27","author":[{"given":"Jun","family":"Lu","sequence":"first","affiliation":[{"name":"Jiangsu NARI Power Electric Co., Ltd., Nanjing 211106, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zixiang","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Ji","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yichao","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xueyang","family":"Miao","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6986-6943","authenticated-orcid":false,"given":"Xiaoan","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3648-648X","authenticated-orcid":false,"given":"Qinghua","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liu, Q., Li, Q., Qian, H., Wang, Y., and Jiang, D. (2024). Diagnosis of rotor faults through generative adversarial networks enhanced by embedded wavelet scattering transforms. Nondestruct. Test. Eval., 1\u201318.","DOI":"10.1080\/10589759.2024.2440818"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"081202","DOI":"10.1115\/1.4053262","article-title":"Vibration analysis of deep groove ball bearing using finite element analysis and dimension analysis","volume":"144","author":"Salunkhe","year":"2022","journal-title":"J. Tribol."},{"key":"ref_3","first-page":"448","article-title":"Dynamic analysis of flexible rotor-ball bearings system with unbalance-misalignment-rubbing coupling faults","volume":"105","author":"Zhang","year":"2012","journal-title":"Appl. Mech. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"104178","DOI":"10.1016\/j.mechmachtheory.2020.104178","article-title":"Effect of angular misalignment of inner ring on the contact characteristics and stiffness coefficients of duplex angular contact ball bearings","volume":"157","author":"Xu","year":"2021","journal-title":"Mech. Mach. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"105960","DOI":"10.1016\/j.triboint.2019.105960","article-title":"Internal loads and contact pressure distributions on the main shaft bearing in a modern gearless wind turbine","volume":"141","author":"Zheng","year":"2020","journal-title":"Tribol. Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/j.ijmecsci.2018.04.056","article-title":"Mechanical behavior of double-row tapered roller bearing under combined external loads and angular misalignment","volume":"142","author":"Yang","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_7","first-page":"1393","article-title":"Bearing wear analysis in multi-bearing spindle system","volume":"43","author":"Zhang","year":"2022","journal-title":"J. Mech. Strength"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"121201","DOI":"10.1115\/1.4054435","article-title":"Contact characteristics analysis of deep groove ball bearings under combined angular misalignments and external loads","volume":"144","author":"Xu","year":"2022","journal-title":"J. Tribol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1177\/1350650120948292","article-title":"Influence of angular misalignment on the tribological performance of high-speed micro ball bearings considering full multibody interactions","volume":"235","author":"Wen","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part J J. Eng. Tribol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/j.apm.2020.12.041","article-title":"Mechanical characteristics and nonlinear dynamic response analysis of rotor-bearing-coupling system","volume":"93","author":"Cheng","year":"2021","journal-title":"Appl. Math. Model."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103916","DOI":"10.1016\/j.mechmachtheory.2020.103916","article-title":"Vibration responses of rotating elastic coupling with dynamic spatial misalignment","volume":"151","author":"Wu","year":"2020","journal-title":"Mech. Mach. Theory"},{"key":"ref_12","first-page":"172","article-title":"Influence of misalignment on nonlinear dynamic characteristics for matched bearings-rotor system","volume":"228","author":"Yi","year":"2014","journal-title":"Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3391","DOI":"10.1007\/s11071-022-07451-1","article-title":"Dynamic characteristics of ball bearing-coupling-rotor system with angular misalignment fault","volume":"108","author":"Wang","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104366","DOI":"10.1016\/j.mechmachtheory.2021.104366","article-title":"Effect of dynamic misalignment on the vibration response, trajectory followed and defect-depth achieved by the rolling-elements in a double-row spherical rolling-element bearing","volume":"162","author":"Parmar","year":"2021","journal-title":"Mech. Mach. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"012014","DOI":"10.1088\/1757-899X\/1081\/1\/012014","article-title":"Effect of ball bearing misalignment on dynamic characteristics of rotor system","volume":"Volume 1081","author":"Wen","year":"2021","journal-title":"IOP Conference Series: Materials Science and Engineering"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4176430","DOI":"10.1155\/2020\/4176430","article-title":"Research on meshing stiffness and vibration response of pitting fault gears with different degrees","volume":"2020","author":"Liu","year":"2020","journal-title":"Int. J. Rotating Mach."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"153","DOI":"10.5755\/j01.mech.26.2.23270","article-title":"Solution of spur gear meshing stiffness and analysis of degradation characteristics","volume":"26","author":"Dong","year":"2020","journal-title":"Mechanics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107936","DOI":"10.1016\/j.measurement.2020.107936","article-title":"A novel method for gear crack fault diagnosis using improved analytical-FE and strain measurement","volume":"163","author":"Wu","year":"2020","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"00368504211035604","DOI":"10.1177\/00368504211035604","article-title":"Dynamic characteristics analysis of planetary gear system with internal and external excitation under turbulent wind load","volume":"104","author":"Yang","year":"2021","journal-title":"Sci. Prog."},{"key":"ref_20","first-page":"89","article-title":"Analysis and Modeling of Dynamic Performance of Planetary Gears with Complex Broken Tooth Fault","volume":"43","author":"Jia","year":"2023","journal-title":"Noise Vib. Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1016\/j.engfailanal.2005.07.020","article-title":"Fatigue failure of a helical gear in a gearbox","volume":"13","author":"Asi","year":"2006","journal-title":"Eng. Fail. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"108961","DOI":"10.1016\/j.engfailanal.2024.108961","article-title":"Effect of tooth surface pitting on dynamic characteristics under mixed lubrication","volume":"167","author":"Zhao","year":"2025","journal-title":"Eng. Fail. Anal."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.ymssp.2017.11.046","article-title":"Chatter detection in milling process based on VMD and energy entropy","volume":"105","author":"Liu","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"200081","DOI":"10.1016\/j.sasc.2024.200081","article-title":"A vibration signal processing method based on SE-PSO-VMD for ultrasonic machining","volume":"6","author":"Chen","year":"2024","journal-title":"Syst. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"847","DOI":"10.5194\/ms-12-847-2021","article-title":"Dynamic modeling and vibration analysis of a cracked 3K-II planetary gear set for fault detection","volume":"12","author":"Sang","year":"2021","journal-title":"Mech. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6015","DOI":"10.1007\/s11071-024-09323-2","article-title":"Research on the time-varying mesh stiffness and dynamic characteristics of steel\u2013POM gear pair with off-line meshing","volume":"112","author":"Xiong","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"103786","DOI":"10.1016\/j.mechmachtheory.2020.103786","article-title":"Vibration response and fault characteristics analysis of gear based on time-varying mesh stiffness","volume":"148","author":"Meng","year":"2020","journal-title":"Mech. Mach. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"105162","DOI":"10.1016\/j.engfailanal.2020.105162","article-title":"Fault feature analysis of planetary gear set influenced by cracked gear tooth and pass effect of the planet gears","volume":"121","author":"Han","year":"2021","journal-title":"Eng. Fail. Anal."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"108736","DOI":"10.1016\/j.ymssp.2021.108736","article-title":"Effects of three types of bearing misalignments on dynamic characteristics of planetary gear set-rotor system","volume":"169","author":"Wang","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.measurement.2014.10.031","article-title":"Detection and monitoring of coupling misalignment in rotors using torque measurements","volume":"61","author":"Reddy","year":"2015","journal-title":"Measurement"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5077366","DOI":"10.1155\/2021\/5077366","article-title":"Fault dynamic modeling and characteristic parameter simulation of rolling bearing with inner ring local defects","volume":"2021","author":"Zhang","year":"2021","journal-title":"Shock Vib."},{"key":"ref_32","first-page":"3526311","article-title":"Multi-domain class-imbalance generalization with fault relationship-induced augmentation for intelligent fault diagnosis","volume":"73","author":"Zhao","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1123\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T05:41:50Z","timestamp":1762234910000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,31]]},"references-count":32,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["e27111123"],"URL":"https:\/\/doi.org\/10.3390\/e27111123","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,31]]}}}