{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T23:38:53Z","timestamp":1780357133589,"version":"3.54.1"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T00:00:00Z","timestamp":1690934400000},"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":["52105083"],"award-info":[{"award-number":["52105083"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52175071"],"award-info":[{"award-number":["52175071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52205115"],"award-info":[{"award-number":["52205115"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["J2019-I-0008-0008"],"award-info":[{"award-number":["J2019-I-0008-0008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["HKCX2020-02-016"],"award-info":[{"award-number":["HKCX2020-02-016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"major projects of aero-engines and gas turbines","award":["52105083"],"award-info":[{"award-number":["52105083"]}]},{"name":"major projects of aero-engines and gas turbines","award":["52175071"],"award-info":[{"award-number":["52175071"]}]},{"name":"major projects of aero-engines and gas turbines","award":["52205115"],"award-info":[{"award-number":["52205115"]}]},{"name":"major projects of aero-engines and gas turbines","award":["J2019-I-0008-0008"],"award-info":[{"award-number":["J2019-I-0008-0008"]}]},{"name":"major projects of aero-engines and gas turbines","award":["HKCX2020-02-016"],"award-info":[{"award-number":["HKCX2020-02-016"]}]},{"name":"Innovation Centre for Advanced Aviation Power","award":["52105083"],"award-info":[{"award-number":["52105083"]}]},{"name":"Innovation Centre for Advanced Aviation Power","award":["52175071"],"award-info":[{"award-number":["52175071"]}]},{"name":"Innovation Centre for Advanced Aviation Power","award":["52205115"],"award-info":[{"award-number":["52205115"]}]},{"name":"Innovation Centre for Advanced Aviation Power","award":["J2019-I-0008-0008"],"award-info":[{"award-number":["J2019-I-0008-0008"]}]},{"name":"Innovation Centre for Advanced Aviation Power","award":["HKCX2020-02-016"],"award-info":[{"award-number":["HKCX2020-02-016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The performance of gear systems is closely related to the meshing parameters and sliding friction. However, the time-varying characteristics of meshing parameters caused by transverse vibration are usually not regarded and the sliding friction has always been ignored in previous studies. Therefore, the influence of the transverse vibration on meshing parameters and sliding friction have not been considered. In view of this, a nonlinear dynamic model for a spur gear system is proposed. The dynamic meshing parameters (pressure angle, backlash, etc.) and the effects of the variations of these parameters on the dynamic mesh force (DMF) and sliding friction are emphasized. The differential equations of motion are derived by the Lagrange method and solved by the Runge\u2013Kutta method. Then, the input speed and friction coefficient are used as control parameters to compare the dynamic responses of the new and previous models. The results show that the meshing parameters and sliding friction are affected by transverse vibration, leading to distinctive nonlinear dynamic responses. This paper can provide a basis for further research and give a better understanding of system vibration control.<\/jats:p>","DOI":"10.3390\/sym15081530","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T11:04:38Z","timestamp":1690974278000},"page":"1530","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Nonlinear Dynamic Modeling and Analysis for a Spur Gear System with Dynamic Meshing Parameters and Sliding Friction"],"prefix":"10.3390","volume":"15","author":[{"given":"Hao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dayi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"},{"name":"Beijing Key Laboratory of Aero-Engine Structure and Strength, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaicheng","family":"Liu","sequence":"additional","affiliation":[{"name":"Beijing Aerospace Propulsion Institute, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianjun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Lab of Advance Measurement and Test Technology for Aviation Propulsion System, Shenyang Aerospace University, Shenyang 110136, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yifu","family":"Long","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, Y., Ye, H., Yang, L., and Tian, A. 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