{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T16:55:11Z","timestamp":1773939311439,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T00:00:00Z","timestamp":1624924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["E2019202132"],"award-info":[{"award-number":["E2019202132"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Research Project of Colleges and Universities of Hebei Province","award":["BJ2019049"],"award-info":[{"award-number":["BJ2019049"]}]},{"name":"Science and Technology on Space Intelligent Control Laboratory","award":["6142208200101"],"award-info":[{"award-number":["6142208200101"]}]},{"name":"Innovation Foundation Project of CAST","award":["CAST-2021-01-11"],"award-info":[{"award-number":["CAST-2021-01-11"]}]},{"name":"Tianjin Key Laboratory of Micro-Low Gravity Environment Simulation Technology Open Subjects","award":["WDZL-2020-01"],"award-info":[{"award-number":["WDZL-2020-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Internal gear mechanism is widely used in micro-nano satellites due to its compact structure and high precision transmission. However, the vibration coupling caused by the small clearance coupling is more obvious and cannot be ignored under low speed, light load and zero gravity conditions. Based on the geometric relationship between radial clearance and backlash, a coupled model between dynamic backlash and radial clearance of internal meshing gear is established. Based on the conformal contact theory, the radial collision force model of the gear shaft and shaft sleeve considering the small clearances is established. Additionally, a multi-clearance gear rotor system test device is built to measure the vibration acceleration of the internal gear rotor system by an acceleration sensor and transmitted to the industrial computer through a signal collector for data processing. Through the comparison of simulation and experiment, the accuracy of the gear dynamics model is verified. The analysis results show that, compared with the traditional model, the calculation results of the gear mechanism model considering the small clearance coupling is closer to the experimental data.<\/jats:p>","DOI":"10.3390\/e23070834","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T22:39:43Z","timestamp":1625006383000},"page":"834","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Dynamics Modeling and Experimental Investigation of Gear Mechanism with Coupled Small Clearances"],"prefix":"10.3390","volume":"23","author":[{"given":"Jianchao","family":"Han","sequence":"first","affiliation":[{"name":"Department of Astronautics Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Beijing Satellite Manufacturing Factory, Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0752-4507","authenticated-orcid":false,"given":"Lei","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Astronautics Engineering, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1896-9437","authenticated-orcid":false,"given":"Huibo","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Astronautics Engineering, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.mechmachtheory.2012.05.009","article-title":"Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance","volume":"50","author":"Xu","year":"2012","journal-title":"Mech. Mach. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.mechmachtheory.2012.02.007","article-title":"Numerical study of parametric effects on the dynamic response of planar multi-body systems with differently located frictionless revolute clearance joints","volume":"53","author":"Onesmus","year":"2012","journal-title":"Mech. Mach. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11071-009-9583-z","article-title":"Spatial rigid-multibody systems with lubricated spherical clearance joints: Modeling and simulation","volume":"60","author":"Flores","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/0022-460X(91)90564-Z","article-title":"Non-linear dynamics of a geared rotor-bearing system with multiple clearances","volume":"144","author":"Kahraman","year":"1991","journal-title":"J. Sound Vib."},{"key":"ref_5","first-page":"523","article-title":"An experimental investigation of spur gear efficiency","volume":"130","author":"Kahraman","year":"2008","journal-title":"J. Mech. Des."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1115\/1.2885194","article-title":"An experimental study of the influence of manufacturing errors on the planetary gear stresses and planet load sharing","volume":"130","author":"Ligata","year":"2008","journal-title":"J. Mech. Des."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.mechmachtheory.2013.07.006","article-title":"Experiments on the relationship between the dynamic transmission error and the dynamic stress factor of spur gear pairs","volume":"70","author":"Hotait","year":"2013","journal-title":"Mech. Mach. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.mechmachtheory.2010.10.007","article-title":"On modeling and vibration of gear drives influenced by nonlinear couplings","volume":"46","author":"Byrtus","year":"2011","journal-title":"Mech. Mach. Theory"},{"key":"ref_9","first-page":"807","article-title":"Influence of clearances and thermal effects on the dynamic behavior of Gear-Hydrodynamic journal bearing systems","volume":"135","author":"Velex","year":"2013","journal-title":"J. Vib. Acoust."},{"key":"ref_10","first-page":"1","article-title":"Bifurcation and chaos prediction in nonlinear gear systems","volume":"1","author":"Farshidianfar","year":"2014","journal-title":"Shock. Vib."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/j.ymssp.2016.08.031","article-title":"Enhanced model of gear transmission dynamics for condition monitoring applications: Effects of torque, friction and bearing clearance","volume":"85","author":"Garcia","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1850034","DOI":"10.1142\/S0218127418500347","article-title":"Jingtang Nonlinear dynamics of a multistage gear transmission system with multi-clearance","volume":"28","author":"Xiang","year":"2018","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_13","first-page":"116","article-title":"Bifurcation characteristics of bending-torsional coupled gear nonlinear vibration with multi-clearance","volume":"33","author":"Sheng","year":"2014","journal-title":"J. Vib. Shock"},{"key":"ref_14","first-page":"144","article-title":"Nonlinear dynamic analysis of a gear-rotor system with coupled multi-clearance","volume":"34","author":"Zhang","year":"2015","journal-title":"J. Vib. Shock"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.jsv.2003.11.029","article-title":"A Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: Sub-harmonic motions","volume":"279","author":"Kahraman","year":"2005","journal-title":"J. Sound Vib."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/7\/834\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:27:21Z","timestamp":1760164041000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/7\/834"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,29]]},"references-count":15,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["e23070834"],"URL":"https:\/\/doi.org\/10.3390\/e23070834","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,29]]}}}