{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:54:41Z","timestamp":1785412481300,"version":"3.56.0"},"reference-count":22,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T00:00:00Z","timestamp":1779840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52275505"],"award-info":[{"award-number":["52275505"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["52275505"],"award-info":[{"award-number":["52275505"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the increasing complexity of operating conditions and the trend toward structural compactness in generators, the unbalanced electromagnetic force induced by air-gap eccentricity has become a critical factor affecting rotor dynamic behavior and operational reliability. To address the strong coupling and modeling challenges among the electromagnetic field, mechanical force field, and lubrication flow field under eccentric conditions, this study proposes a multi-physics coupled modeling approach that integrates electromagnetic, structural, and fluid dynamic interactions. Based on the spatial pose characteristics of the rotor under eccentric conditions, a three-dimensional mathematical model of the air-gap length is established, and an analytical expression for the lubricating oil film thickness distribution is derived. This framework enables the coupled solution of unbalanced electromagnetic force, hydrodynamic oil film supporting force, and rotor dynamic response. A 60 kW-rated diesel generator was selected as the research object for both numerical simulations and experimental investigations. The numerical results indicate that when the load power increases from 0 kW to 60 kW, the displacement amplitude of the rotor in the y-direction increases by approximately 155%, demonstrating a significant enhancement of transverse vibration intensity under increasing unbalanced electromagnetic excitation. Comparison between experimental and numerical results shows good agreement in both variation trends and amplitude levels, with a maximum relative error of 4.07%, thereby validating the accuracy and reliability of the proposed electromagnetic\u2013structural\u2013fluid coupled model for predicting rotor dynamic response in generators.<\/jats:p>","DOI":"10.3390\/s26113392","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T12:31:56Z","timestamp":1779885116000},"page":"3392","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigation of Generator Rotor Dynamic Characteristics Under Unbalanced Electromagnetic Forces"],"prefix":"10.3390","volume":"26","author":[{"given":"Jiashun","family":"Dai","sequence":"first","affiliation":[{"name":"School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3620-1659","authenticated-orcid":false,"given":"Hong","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yukuo","family":"Guo","sequence":"additional","affiliation":[{"name":"China Merchants Heavy Industry (Jiangsu) Co., Ltd., Nantong 226100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangnuo","family":"Mei","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"ref_1","first-page":"578","article-title":"Vibration analysis of electric motors considering rotating rotor structure using flexible multibody dynamics\u2013electromagnetic\u2013structural vibration coupled analysis","volume":"10","author":"Cho","year":"2023","journal-title":"J. Comput. Des. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1177\/14680874251316038","article-title":"An electromechanical coupling model for performance enhancement in diesel generator sets","volume":"26","author":"Tao","year":"2025","journal-title":"Int. J. Engine Res."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wu, W., Pang, J., Liu, X., Zhao, W., Lu, Z., Yan, D., Zhou, L., and Wang, Z. (2023). Effect of unbalanced magnetic pull of generator rotor on the dynamic characteristics of a pump\u2013turbine rotor system. Water, 15.","DOI":"10.3390\/w15061120"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, J., Zhang, J., Huang, X., Chen, G., Wang, Z., and You, C. (2023). Effect of generator rotor radial deviation on the unbalanced magnetic pull of 1000 MW hydro-generator unit. Processes, 11.","DOI":"10.3390\/pr11030899"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"109807","DOI":"10.1016\/j.ymssp.2022.109807","article-title":"Dynamic characteristics analysis of asynchronous motorized spindle considering combined unbalanced magnetic pull and nonlinear bearing restoring force effects","volume":"185","author":"Hao","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhuang, K., Huang, S., Fu, X., and Chen, L. (2022). Nonlinear hydraulic vibration modeling and dynamic analysis of hydro-turbine generator unit with multiple faults. Energies, 15.","DOI":"10.3390\/en15093386"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5284815","DOI":"10.1155\/2016\/5284815","article-title":"Impact of different static air-gap eccentricity forms on rotor UMP of turbogenerator","volume":"2016","author":"He","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"8859","DOI":"10.15282\/ijame.18.2.2021.02.0679","article-title":"Study on lubrication efficiency and friction power loss of engine based on a hybrid hydrodynamic model","volume":"18","author":"Jiao","year":"2021","journal-title":"Int. J. Automot. Mech. Eng."},{"key":"ref_9","first-page":"623","article-title":"Effect of the unbalanced magnetic pull force and oil-film force on nonlinearity of a dual-rotor bearing system","volume":"236","author":"Ma","year":"2022","journal-title":"Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.aej.2024.06.088","article-title":"A comprehensive study on electromagnetic torque and rotor UMP based on an improved 3D static air-gap eccentricity model","volume":"105","author":"Xu","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_11","first-page":"8206104","article-title":"Magnetic field calculation in axial flux permanent magnet motor with rotor eccentricity","volume":"58","author":"Guo","year":"2022","journal-title":"IEEE Trans. Magn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1049\/elp2.12033","article-title":"Diagnosis and detection of dynamic eccentricity fault for permanent magnet transverse flux generator","volume":"15","author":"Pourmoosa","year":"2021","journal-title":"IET Electr. Power Appl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ma, T., Deng, Z., Liu, W., and Hou, M. (2024). A numerical method to determine the radial electromagnetic force of the switched reluctance motor under air gap eccentricity. Machines, 12.","DOI":"10.3390\/machines12110823"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1007\/s00202-024-02316-9","article-title":"Analysis of dynamic electromagnetic stress in synchronous reluctance motor accounting for rotor eccentric","volume":"106","author":"Tao","year":"2024","journal-title":"Electr. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"257","DOI":"10.11648\/j.ajam.20200805.13","article-title":"Numerical solution of elastohydrodynamic lubrication for sliding\/rolling bearing for non-Newtonian lubricant","volume":"8","author":"Samuel","year":"2020","journal-title":"Am. J. Appl. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"012044","DOI":"10.1088\/1742-6596\/1939\/1\/012044","article-title":"Numerical analysis based on oil film characteristics of sliding bearing","volume":"1939","author":"Deng","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wu, Y., Yang, L., Xu, T., and Wu, W. (2020). Thermo-elasto-hydrodynamic characteristics analysis of journal microbearing lubricated with rarefied gas. Micromachines, 11.","DOI":"10.3390\/mi11110955"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhang, D., Wei, H., and Gu, C. (2025). Sensitivity of texture evolution and performance to eccentricity, misalignment, and oil supply in journal bearings with the circumferential oil groove: An adjoint-based optimization study. Lubricants, 13.","DOI":"10.3390\/lubricants13110479"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"031802","DOI":"10.1115\/1.4048164","article-title":"Tilting pad journal bearing misalignment effect on thermally induced synchronous instability (Morton effect)","volume":"143","author":"Shin","year":"2021","journal-title":"J. Tribol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.triboint.2018.09.011","article-title":"Dynamic coefficients and stability analysis of finite-length journal bearings considering approximate analytical solutions of the Reynolds equation","volume":"130","author":"Dyk","year":"2019","journal-title":"Tribol. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"26871","DOI":"10.1038\/s41598-024-78242-4","article-title":"Nonlinear transient analysis of water lubricated bearing in the turbulent regime","volume":"14","author":"Mallya","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Song, L., Yuan, G., Zhang, H., Ding, Y., and Cheng, K. (2022). Non-linear dynamic analysis on hybrid air bearing-rotor system under ultra-high speed condition. Materials, 15.","DOI":"10.3390\/ma15020675"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/11\/3392\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T12:43:33Z","timestamp":1779885813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/11\/3392"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,27]]},"references-count":22,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["s26113392"],"URL":"https:\/\/doi.org\/10.3390\/s26113392","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,27]]}}}