{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T10:27:43Z","timestamp":1779359263024,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,14]],"date-time":"2020-03-14T00:00:00Z","timestamp":1584144000000},"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":["51279020"],"award-info":[{"award-number":["51279020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Fault size estimation is of great importance to bearing performance degradation assessment and life prediction. Until now, fault size estimation has generally been based on acoustic emission signals or vibration signals; an approach based on current signals has not yet been mentioned. In the present research, an approximate estimation approach based on current is introduced. The proposed approach is easy to implement for existing inverter-driven induction motors without complicated calculations and additional sensors, immune to external disturbances, and suitable for harsh conditions. Firstly, a feature transmission route from spall, to Hertzian forces, and then to friction torque is simulated based on a spall model and dynamic model of the bearing. Based on simulated results, the relation between spall size and the multiple characteristic vibration frequencies in friction torque is revealed. Secondly, the multiple characteristic vibration frequencies modulated in the current is investigated. Analysis results show that those frequencies modulated in the current are independent of each other, without spectrum overlap. Thirdly, to address the issue of which fault features modulated in the current are very weak, a fault-feature-highlighting approach based on reduced voltage frequency ratio is proposed. Finally, experimental tests were conducted. The obtained results validate that the proposed approach is feasible and effective for spall size estimation.<\/jats:p>","DOI":"10.3390\/s20061631","type":"journal-article","created":{"date-parts":[[2020,3,18]],"date-time":"2020-03-18T08:13:27Z","timestamp":1584519207000},"page":"1631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An Approximate Estimation Approach of Fault Size for Spalled Ball Bearing in Induction Motor by Tracking Multiple Vibration Frequencies in Current"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6446-8831","authenticated-orcid":false,"given":"Chidong","family":"Qiu","sequence":"first","affiliation":[{"name":"College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9764-6673","authenticated-orcid":false,"given":"Xinbo","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5344-4903","authenticated-orcid":false,"given":"Changqing","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6452-7707","authenticated-orcid":false,"given":"Xiang","family":"Qiu","sequence":"additional","affiliation":[{"name":"College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengyu","family":"Xue","sequence":"additional","affiliation":[{"name":"College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1109\/TIE.2015.2509913","article-title":"Motor bearing fault detection using spectral kurtosis-based feature extraction coupled with k-nearest neighbor distance analysis","volume":"63","author":"Tian","year":"2016","journal-title":"IEEE Trans. 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