{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:17:57Z","timestamp":1760235477725,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,25]],"date-time":"2021-08-25T00:00:00Z","timestamp":1629849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2019YFB2004400"],"award-info":[{"award-number":["2019YFB2004400"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Industry and Information Technology of China","award":["not applicable"],"award-info":[{"award-number":["not applicable"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Planetary gearboxes are the key components of large equipment, such as wind turbines, shield machines, etc. The operating state of the planetary gearbox is related to the safety of the equipment as a whole, and its feature extraction technology is essential. In assessing the problem of the non-stationarity of the current signal under variable speed conditions and the difficulty of evaluating the operating state of the planetary gearbox under a tacholess condition, a three-phase current, variable-speed tacholess envelope order analysis method is proposed. Firstly, a tacholess rotation speed estimation is completed by extracting the trend term of the instantaneous frequency of the asynchronous motor\u2019s three-phase currents. The motor slip rate is assumed to be constant. Then, the envelope order analysis signal is obtained by re-sampling in the angular domain. Finally, the features of the envelope order signal are extracted, and a linear discriminant analysis (LDA) algorithm is used to fuse multiple indexes to generate a comprehensive feature reflecting the operating status of the planetary gearbox. The results of the simulation analysis and experimental verification show that the proposed method is effective in evaluating the operating state of the planetary gearbox under variable speed conditions. Compared with the traditional time\u2013frequency ridge extraction method, the tacholess speed estimation method can improve the instantaneous speed estimation accuracy. The comprehensive index of envelope order completes the planetary gearbox state identification process, and a 95% classification accuracy rate is achieved.<\/jats:p>","DOI":"10.3390\/s21175714","type":"journal-article","created":{"date-parts":[[2021,8,25]],"date-time":"2021-08-25T23:25:50Z","timestamp":1629933950000},"page":"5714","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Three-Phase Current Tacholess Envelope Order Analysis Method for Feature Extraction of Planetary Gearbox under Variable Speed Conditions"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2165-7525","authenticated-orcid":false,"given":"Xun","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghua","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiachen","family":"Kuang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Suo","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sicong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umair","family":"Khalique","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1352","DOI":"10.1016\/j.ymssp.2008.07.019","article-title":"Application of spectral kurtosis for detection of a tooth crack in the planetary gear of a wind turbine","volume":"23","author":"Barszcz","year":"2009","journal-title":"Mech. 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