{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T14:27:04Z","timestamp":1781620024264,"version":"3.54.5"},"reference-count":34,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T00:00:00Z","timestamp":1666656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation for Young Scientists of China","award":["62001079"],"award-info":[{"award-number":["62001079"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As one of the important parameters of bearing operation, temperature is a key metric to diagnose the state of service of a bearing. However, there are still some shortcomings in the study of the temperature variation law for damaged bearings. In this paper, according to the structural characteristics of bearings, the influence law of thermal-solid coupling effect on bearing structure is considered, and a novel transient temperature analysis model of damaged bearings is established. First, a quasi-static analysis of the bearing is performed to obtain the variation laws of the key parameters of the bearing under thermal expansion. Then, the load variation law of the bearing under the condition of damage is discussed, and the heat generation and heat transfer of the damaged bearing during operation are studied. Based on the thermal grid method, a transient temperature analysis model of the damaged bearing is developed. Finally, the model is tested experimentally and the influence of the rotate speed and load on the bearing temperature variation is analyzed. The results show that the established model can effectively predict the temperature variation and thermal equilibrium temperature of damaged bearings.<\/jats:p>","DOI":"10.3390\/s22218171","type":"journal-article","created":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T07:17:48Z","timestamp":1666768668000},"page":"8171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Transient Thermal Analysis Model of Damaged Bearing Considering Thermo-Solid Coupling Effect"],"prefix":"10.3390","volume":"22","author":[{"given":"Yali","family":"Sun","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, Dalian Jiaotong University; Dalian 116028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chong","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Dalian Jiaotong University; Dalian 116028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xing","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling, Dalian Jiaotong University; Dalian 116028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaodong","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling, Dalian Jiaotong University; Dalian 116028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chang","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Dalian Jiaotong University; Dalian 116028, China"},{"name":"PLA Army Academy of Artillery and Air Defense, Shenyang 110000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiyou","family":"Fei","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling, Dalian Jiaotong University; Dalian 116028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s10033-022-00789-y","article-title":"Analysis of the Temperature Characteristics of High-speed Train Bearings Based on a Dynamics Model and Thermal Network Method","volume":"35","author":"Wang","year":"2022","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jang, G., and Cho, S. (2021). Feature Space Transformation for Fault Diagnosis of Rotating Machinery under Different Working Conditions. Sensors, 21.","DOI":"10.3390\/s21041417"},{"key":"ref_3","first-page":"443","article-title":"Numerical Simulation of Rough Thrust Pad Bearing Under Thin-Film Lubrication Using Variable Mesh Density","volume":"44","author":"Kumar","year":"2018","journal-title":"Trans. Mech. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1500","DOI":"10.1108\/ILT-11-2016-0265","article-title":"Measurement and calculation of oil film thickness in a ball bearing","volume":"70","author":"Wen","year":"2018","journal-title":"Ind. Lubr. Tribol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Wang, Y., Lin, J., and Wang, D. (2022). Study on Factors Influencing Film Formation of Grease and Calculation Model for Grease Film Thickness. Lubricants, 10.","DOI":"10.3390\/lubricants10060123"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","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_7","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1016\/j.triboint.2005.11.020","article-title":"Influence of temperature distributions in EHL film on its thickness under high slip ratio conditions","volume":"40","author":"Nakahara","year":"2007","journal-title":"Tribol. Int."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1243\/JMES_JOUR_1959_001_004_02","article-title":"A Numerical Solution to the Elasto-Hydrodynamic Problem","volume":"1","author":"Dowson","year":"1959","journal-title":"J. Mech. Eng. Sci."},{"key":"ref_9","first-page":"4","article-title":"EHL Circular Contact Film Thickness Correction Factor for Shear-Thinning Fluids","volume":"130","author":"Khonsari","year":"2008","journal-title":"J. Tribol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1080\/10402009208982118","article-title":"Viscoelastic Effects in MIL-L-7808-Type Lubricant, Part II: Experimental Data Correlations","volume":"35","author":"Forster","year":"2008","journal-title":"Tribol. Trans."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1177\/1350650111398848","article-title":"Analytical model for predicting the friction coefficient in point contacts with thermal elastohydrodynamic lubrication","volume":"225","year":"2011","journal-title":"Proc. Inst. Mech. Eng. Part J J. Eng. Tribol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106059","DOI":"10.1016\/j.triboint.2019.106059","article-title":"Influences of solid and lubricant thermal conductivity on traction in an EHL circular contact","volume":"146","author":"Liu","year":"2020","journal-title":"Tribol. Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1016\/j.triboint.2015.10.010","article-title":"Low degree of freedom approach for predicting friction in elastohydrodynamically lubricated contacts","volume":"94","author":"Shirzadegan","year":"2016","journal-title":"Tribol. Int."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, Y., Cao, J., Tong, Q., An, G., Liu, R., Zhang, Y., and Yan, H. (2020). Study on the Thermal Performance and Temperature Distribution of Ball Bearings in the Traction Motor of a High-Speed EMU. Appl. Sci., 10.","DOI":"10.3390\/app10124373"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1002\/ls.1325","article-title":"Analytical model for predicting friction in line contacts","volume":"28","year":"2016","journal-title":"Lubr. Sci."},{"key":"ref_16","unstructured":"Palmgren, A. (1959). Ball and Roller Bearing Engineering, SKF Industries Inc.. [3rd ed.]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1115\/1.2899232","article-title":"A State-Space Model for Monitoring Thermally Induced Preload in Anti-Friction Spindle Bearings of High-Speed Machine Tools","volume":"116","author":"Stein","year":"1994","journal-title":"J. Dyn. Syst. Meas. Control."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s12541-015-0017-1","article-title":"A numerical approach to determine the frictional torque and temperature of an angular contact ball bearing in a spindle system","volume":"16","author":"Kim","year":"2015","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gao, P., Tang, W., Cui, Y., Wang, Y., Mo, G., and Yin, J. (2022). Theoretical and Experimental Investigation on Thermal Characteristics of Railway Double-Row Tapered Roller Bearing. Energies, 15.","DOI":"10.3390\/en15124217"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.triboint.2018.09.031","article-title":"Investigation on thermal behavior and temperature distribution of bearing inner and outer rings","volume":"130","author":"Zhou","year":"2019","journal-title":"Tribol. Int."},{"key":"ref_21","first-page":"81","article-title":"Micro-Contact EHL Friction and Heat Generation Analysis of High Speed Ball Bearings","volume":"50","author":"Mohan","year":"2016","journal-title":"Xi\u2019an Jiaotong Univ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1177\/1350650115604873","article-title":"An accurate calculation method for heat generation rate in grease-lubricated spherical roller bearings","volume":"230","author":"Ma","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part J J. Eng. Tribol."},{"key":"ref_23","first-page":"53","article-title":"An improved thermal model for machine tool bearings","volume":"47","author":"Xu","year":"2006","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_24","unstructured":"Ai, S.Y. (2015). Study on Temperature Distribution and Lubrication Performance of Rolling Bearings. [Ph.D. Thesis, Beijing Institute of Technology]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"7500","DOI":"10.1177\/09544062221075185","article-title":"Heat-flow coupling variation in double-row tapered-roller bearings during the loss of lubrication process","volume":"236","author":"Li","year":"2022","journal-title":"Proc. Inst. Mech. Engineers. Part C J. Mech. Eng. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.triboint.2017.01.035","article-title":"Thermal performances on angular contact ball bearing of high-speed spindle considering structural constraints under oil-air lubrication","volume":"109","author":"Zheng","year":"2017","journal-title":"Tribol. Int."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.triboint.2015.09.004","article-title":"Transient thermal analysis of grease-lubricated spherical roller bearings","volume":"93","author":"Fangbo","year":"2016","journal-title":"Tribol. Int."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1051\/meca\/2020083","article-title":"Thermo-dynamical modelisation of the degradation of a ball bearing in variables use conditions","volume":"21","author":"Belmiloud","year":"2020","journal-title":"Mech. Ind."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1007\/s10483-022-2893-5","article-title":"Characteristic analysis of mechanical thermal coupling model for bearing rotor system of high-speed train","volume":"43","author":"Liu","year":"2022","journal-title":"Appl. Math. Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.triboint.2015.02.011","article-title":"Temperature rise of double-row tapered roller bearings analyzed with the thermal network method","volume":"87","author":"Ai","year":"2015","journal-title":"Tribol. Int."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"17","DOI":"10.3901\/JME.2018.08.017","article-title":"Nonlinear Dynamic Behaviors Analysis of the Bearing Rotor System with Outer Ring Faults in the High-speed Train","volume":"54","author":"Liu","year":"2018","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_32","first-page":"151","article-title":"Distribution characteristics of stress and displacement of rings of cylindrical roller bearing","volume":"233","author":"Xu","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1243\/13506501JET695","article-title":"Investigations on the power losses and thermal behaviour of rolling element bearings","volume":"224","author":"Pouly","year":"2010","journal-title":"Proc. Inst. Mech. Eng. Part J J. Eng. Tribol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s12541-015-0039-8","article-title":"A study on the thermal characteristics and experiments of High-Speed spindle for machine tools","volume":"16","author":"Lee","year":"2015","journal-title":"Int. J. Precis. Eng. Manuf."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8171\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:02:26Z","timestamp":1760144546000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,25]]},"references-count":34,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22218171"],"URL":"https:\/\/doi.org\/10.3390\/s22218171","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,25]]}}}