{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:55:04Z","timestamp":1762325704713,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:00:00Z","timestamp":1692662400000},"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":["52105087","52205087","2023A04J0280","2022SDKYA019"],"award-info":[{"award-number":["52105087","52205087","2023A04J0280","2022SDKYA019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangzhou Science and Technology Program Projects","award":["52105087","52205087","2023A04J0280","2022SDKYA019"],"award-info":[{"award-number":["52105087","52205087","2023A04J0280","2022SDKYA019"]}]},{"name":"Special Talents for Scientific Research Projects of Guangdong Polytechnic Normal University","award":["52105087","52205087","2023A04J0280","2022SDKYA019"],"award-info":[{"award-number":["52105087","52205087","2023A04J0280","2022SDKYA019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The vibration modulation of the localized faults of sun gears is complicated because of the structure and motion features of planetary gearboxes. It is challenging to completely determine the vibration modulation mechanism. To address this issue, the influences of fluctuations in speed on the factors that affect vibration like the transfer path function, time-varying projection function, and meshing force were studied. Improved vibration amplitude and frequency modulation models were then established by combining the factors affecting vibration considering the speed fluctuations caused by the localized faults of sun gears. Regarding the features of vibration modulation of localized faults of sun gears, we concluded that both fault feature frequency and carrier rotational frequency modulate the harmonics of the meshing frequency, which form two groups of modulation sidebands. In addition, the harmonics of the fault feature frequency over the whole frequency range are modulated by the rotational frequency of the carrier, which is more dominant in the resonance domain. The experimental results of localized faults of sun gears strongly agree with those deduced using the proposed models. This research contributes an effective frequency indicator that can be used to confirm the condition of planetary gearboxes.<\/jats:p>","DOI":"10.3390\/sym15091621","type":"journal-article","created":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T07:25:24Z","timestamp":1692775524000},"page":"1621","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improved Vibration Signal Models of Localized Faults of Sun Gears to Predict Modulation"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiaoqing","family":"Yang","sequence":"first","affiliation":[{"name":"School of Automobile and Transportation Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Yang","sequence":"additional","affiliation":[{"name":"Product Planning & Automotive New Technology Research Institude, BYD Automobile Industry Company Limited, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5787-329X","authenticated-orcid":false,"given":"Qiang","family":"Zeng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Canyi","family":"Du","sequence":"additional","affiliation":[{"name":"School of Automobile and Transportation Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangkun","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Automobile and Transportation Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feifei","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Automobile and Transportation Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6100-7332","authenticated-orcid":false,"given":"Zhuyun","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1982","DOI":"10.1109\/TCYB.2022.3195355","article-title":"Multi-source Weighted Deep Transfer Network for Open-set Fault Diagnosis of Rotary Machinery","volume":"53","author":"Chen","year":"2022","journal-title":"IEEE Trans. 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