{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T19:54:07Z","timestamp":1775591647085,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T00:00:00Z","timestamp":1664323200000},"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":["51975576"],"award-info":[{"award-number":["51975576"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["WDZC*******0305"],"award-info":[{"award-number":["WDZC*******0305"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["WDZC*******0301"],"award-info":[{"award-number":["WDZC*******0301"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Defense Industrial Technology Development Program","award":["51975576"],"award-info":[{"award-number":["51975576"]}]},{"name":"Defense Industrial Technology Development Program","award":["WDZC*******0305"],"award-info":[{"award-number":["WDZC*******0305"]}]},{"name":"Defense Industrial Technology Development Program","award":["WDZC*******0301"],"award-info":[{"award-number":["WDZC*******0301"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Induction motors are complex energy conversion systems across the domains of dynamics, electricity, and magnetism. Most existing models mainly consider unidirectional coupling, such as the effect of dynamics on electromagnetic properties, or the effect of unbalanced magnetic pull on dynamics, while in practice it should be a bidirectional coupling effect. The bidirectionally coupled electromagnetic-dynamics model is beneficial to the analysis of induction motor fault mechanisms and characteristics. This paper proposes a coupled electromagnetic-dynamic modeling method that introduces unbalanced magnetic pull. By using the rotor velocity, air gap length, and unbalanced magnetic pull as the coupling parameters, the coupled simulation of the dynamic and electromagnetic models can be effectively realized. Simulation results for bearing faults show that the introduction of magnetic pull induces a more complex dynamic behavior of the rotor, which in turn leads to modulation in the vibration spectrum. The fault characteristics can be found in the frequency domain of the vibration and current signals. Through the comparison between simulation and experimental results, the effectiveness of the coupled modeling approach and the frequency domain characteristics caused by the unbalanced magnetic pull are verified. The proposed model can help to obtain a variety of information that is difficult to measure in reality and can also serve as a technical basis for further research on nonlinear characteristics and chaos in induction motors.<\/jats:p>","DOI":"10.3390\/e24101386","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T20:58:47Z","timestamp":1664398727000},"page":"1386","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Coupled Electromagnetic-Dynamic Modeling and Bearing Fault Characteristics of Induction Motors considering Unbalanced Magnetic Pull"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3987-2263","authenticated-orcid":false,"given":"Liangyuan","family":"Huang","sequence":"first","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"},{"name":"Laboratory of Science and Technology on Integrated Logistics Support, NUDT, Changsha 410073, China"}]},{"given":"Guoji","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"},{"name":"Laboratory of Science and Technology on Integrated Logistics Support, NUDT, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0258-528X","authenticated-orcid":false,"given":"Niaoqing","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"},{"name":"Laboratory of Science and Technology on Integrated Logistics Support, NUDT, Changsha 410073, China"}]},{"given":"Ling","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"},{"name":"Laboratory of Science and Technology on Integrated Logistics Support, NUDT, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3430-557X","authenticated-orcid":false,"given":"Yi","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"},{"name":"Laboratory of Science and Technology on Integrated Logistics Support, NUDT, Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"(1985). Report of Large Motor Reliability Survey of Industrial and Commercial Installations, Part I. IEEE Trans. Ind. Appl., IA-21, 853\u2013864.","DOI":"10.1109\/TIA.1985.349532"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"(1985). Report of Large Motor Reliability Survey of Industrial and Commercial Installations, Part II. IEEE Trans. Ind. Appl., IA-21, 865\u2013872.","DOI":"10.1109\/TIA.1985.349533"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"(1987). Report of Large Motor Reliability Survey of Industrial and Commercial Installations: Part 3. IEEE Trans. Ind. Appl., IA-23, 153\u2013158.","DOI":"10.1109\/TIA.1987.4504880"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/TEC.1986.4765668","article-title":"Assessment of the Reliability of Motors in Utility Applications\u2014Updated","volume":"EC-1","author":"Albrecht","year":"1986","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4165","DOI":"10.1109\/TIM.2019.2948414","article-title":"Performance Prediction Using High-Order Differential Mathematical Morphology Gradient Spectrum Entropy and Extreme Learning Machine","volume":"69","author":"Zhao","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106602","DOI":"10.1016\/j.ymssp.2019.106602","article-title":"A new data-driven transferable remaining useful life prediction approach for bearing under different working conditions","volume":"139","author":"Zhu","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cui, H., Guan, Y., Chen, H., and Deng, W. (2021). A Novel Advancing Signal Processing Method Based on Coupled Multi-Stable Stochastic Resonance for Fault Detection. Appl. Sci., 11.","DOI":"10.3390\/app11125385"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.isatra.2021.03.042","article-title":"A new dynamic model and transfer learning based intelligent fault diagnosis framework for rolling element bearings race faults: Solving the small sample problem","volume":"121","author":"Dong","year":"2021","journal-title":"ISA Trans."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1186\/s10033-022-00725-0","article-title":"Establishment of Dynamic Model for Axle Box Bearing of High-Speed Trains Under Variable Speed Conditions","volume":"35","author":"Liu","year":"2022","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Randall, R.B. The Use of Simulation Models to Generate Data Corresponding to Faults in Machines. Proceedings of the 8th International Conference on Reliability, Maintainability and Safety(ICRMS 2009), Chengdu, China.","DOI":"10.1109\/ICRMS.2009.5269971"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1109\/T-AIEE.1918.4765577","article-title":"Critical review of the bibliography on unbalanced magnetic pull in dynamo-electric machines","volume":"37","author":"Gray","year":"1918","journal-title":"Trans. Am. Inst. Electr. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/T-AIEE.1900.4764152","article-title":"On the mechanical forces in dynamos caused by magnetic attraction","volume":"17","author":"Behrend","year":"1900","journal-title":"Trans. Am. Inst. Electr. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1049\/ip-epa:19960284","article-title":"Calculation and measurement of unbalanced magnetic pull in cage induction motors with eccentric rotors. Part 2: Experimental investigation","volume":"143","author":"Dorrell","year":"1996","journal-title":"IEE Proc.-Electr. Power Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1049\/ip-epa:19960155","article-title":"Calculation and measurement of unbalanced magnetic pull in cage induction motors with eccentric rotors. Part 1: Analytical model","volume":"143","author":"Smith","year":"1996","journal-title":"IEE Proc.-Electr. Power Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dorrell, D.G. (2009, January 20\u201324). Sources and characteristics of unbalanced magnetic pull in 3-phase cage induction motors with axial-varying rotor eccentricity. Proceedings of the 2009 IEEE Energy Conversion Congress and Exposition, San Jose, CA, USA.","DOI":"10.1109\/ECCE.2009.5316545"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1006\/jsvi.2001.4088","article-title":"The unbalanced magnetic pull and its effects on vibration in a three-phase generator with eccentric rotor","volume":"254","author":"Guo","year":"2002","journal-title":"J. Sound Vib."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s11071-014-1887-y","article-title":"Nonlinear vibration for PMSM used in HEV considering mechanical and magnetic coupling effects","volume":"80","author":"Chen","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.jsv.2016.01.045","article-title":"Unstable force analysis for induction motor eccentricity","volume":"370","author":"Han","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, A., Bai, Y., Yang, B., and Li, H. (2018). Analysis of Nonlinear Vibration in Permanent Magnet Synchronous Motors under Unbalanced Magnetic Pull. Appl. Sci., 8.","DOI":"10.3390\/app8010113"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s00419-006-0017-9","article-title":"Non-Linear Dynamics of a Rotor-Bearing-Seal System","volume":"76","author":"Cheng","year":"2006","journal-title":"Arch. Appl. Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"106322","DOI":"10.1016\/j.ymssp.2019.106322","article-title":"A general dynamic model coupled with EFEM and DBM of rolling bearing-rotor system","volume":"134","author":"Li","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109640","DOI":"10.1016\/j.chaos.2020.109640","article-title":"Fractional-order modeling and nonlinear dynamic analyses of the rotor-bearing-seal system","volume":"133","author":"Yan","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.jsv.2016.12.031","article-title":"Angular-based modeling of induction motors for monitoring","volume":"395","author":"Fourati","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.ymssp.2019.06.010","article-title":"Stator current model for detecting rolling bearing faults in induction motors using magnetic equivalent circuits","volume":"131","author":"Han","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_26","first-page":"216","article-title":"Vibration Characteristics Analysis of EMU Traction Motor Rotor Under Eccentric Faults","volume":"38","author":"Zhou","year":"2021","journal-title":"Eng. Mech."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1109\/28.475697","article-title":"Motor bearing damage detection using stator current monitoring","volume":"31","author":"Schoen","year":"1995","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1109\/TIE.2008.917108","article-title":"Models for Bearing Damage Detection in Induction Motors Using Stator Current Monitoring","volume":"55","author":"Blodt","year":"2008","journal-title":"IEEE Trans. Ind. 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