{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T08:54:15Z","timestamp":1777625655220,"version":"3.51.4"},"reference-count":54,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,2,19]],"date-time":"2022-02-19T00:00:00Z","timestamp":1645228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents the results of research and development of capacitive-based sensors of rotating shaft vibration for fault diagnostic systems of powerful turbines and hydro generators. It showed that diagnostic systems with special sensors are the key to increasing the reliability of powerful turbines and hydro generators. The application of sensors in monitoring systems was considered, and the requirements for the sensors used were analyzed. Structures of concentric capacitive-based sensors of rotating shaft vibration based on the measurement of the capacitance value from the distance to the metal surface were proposed. The design scheme was created for determining electrode dimensions of the rotating shaft vibration capacitive-based sensors with concentric electrodes, and analytical dependences were obtained. The calculation results allow the selection of optimal parameters of the active and guard electrodes. Analytical and computer simulation methods determined the response functions of the capacitive sensors. Analytical calculations and simulation results using 3D FEM were used to find the response functions of the sensors. The calculation of the characteristics of the capacitive-based sensors of rotating shaft vibration is presented. The study of the influence of fringe effects was carried out using the obtained results of the modeling and analytical calculations.<\/jats:p>","DOI":"10.3390\/s22041634","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T08:34:47Z","timestamp":1645432487000},"page":"1634","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Calculation of Capacitive-Based Sensors of Rotating Shaft Vibration for Fault Diagnostic Systems of Powerful Generators"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3303-471X","authenticated-orcid":false,"given":"Ievgen","family":"Zaitsev","sequence":"first","affiliation":[{"name":"Department of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment\u2019s, Institute of Electrodynamics of NAS of Ukraine, Peremohy Str., 56, 03057 Kyiv, Ukraine"},{"name":"Department of Applied Information Systems, Faculty of Information Technology, Taras Shevchenko Nation University of Kiev, Volodymyrska Str., 64\/13, 01601 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9961-1703","authenticated-orcid":false,"given":"Victoriia","family":"Bereznychenko","sequence":"additional","affiliation":[{"name":"Department of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment\u2019s, Institute of Electrodynamics of NAS of Ukraine, Peremohy Str., 56, 03057 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1086-457X","authenticated-orcid":false,"given":"Mohit","family":"Bajaj","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, National Institute of Technology Delhi, Delhi 110040, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ibrahim B. M.","family":"Taha","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7520-2286","authenticated-orcid":false,"given":"Youcef","family":"Belkhier","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo Namesti 13, 121 35 Praha, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3974-0554","authenticated-orcid":false,"given":"Vladyslav","family":"Titko","sequence":"additional","affiliation":[{"name":"Department of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment\u2019s, Institute of Electrodynamics of NAS of Ukraine, Peremohy Str., 56, 03057 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9505-5386","authenticated-orcid":false,"given":"Salah","family":"Kamel","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering, Aswan University, Aswan 81542, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,19]]},"reference":[{"key":"ref_1","unstructured":"Alekseev, B.A. (2002). 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