Nonlinear dynamic modeling and dynamic characteristics analysis of a coaxial reverse closed differential herringbone gear transmission system considering floating backlash

Nonlinear dynamic modeling and dynamic characteristics analysis of a coaxial reverse closed differential herringbone gear transmission system considering floating backlash | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Nonlinear dynamic modeling and dynamic characteristics analysis of a coaxial reverse closed differential herringbone gear transmission system considering floating backlash Hao Han, Hao Dong, Dong-bo Zhang, Yue Bi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4122378/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A nonlinear dynamic model of Bending-Torsional-Axial-Pendular (BTAP) has been developed for a Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS) with consideration of gear floating. This model takes into account factors such as gear floating backlash, tooth surface friction, gyroscopic effect, Time Varying Meshing Stiffness (TVMS), meshing damping, and dynamic meshing parameters. To investigate the impact of gear floating on the nonlinear dynamic characteristics of the system, a gear floating model was developed using the concept of gear floating. The calculations included determining gear floating backlash and TVMS with consideration for gear floating. The impact of input speed, initial backlash, gear float value, and system transmission error on the nonlinear dynamic vibration characteristics is analyzed using various diagrams including bifurcation diagram, Maximum Lyapunov Exponent (MLE), time history diagram, frequency diagram, phase diagram, and Poincaré section diagram. The research reveals that gear floating diminish the chaotic motion behavior of the system under different excitation factors, improving the system's global bifurcation characteristics. The developed BTAP coupled nonlinear dynamic model provides more accurate numerical solutions compared to models with fixed meshing parameters, making it more suitable for analyzing the system's dynamic characteristics. Analysis of the gear floating value indicates an optimal range of 0-20μm and 34-43μm for generating periodic motion, with floating values around 10-20μm showing better performance in reducing the negative effects of initial backlash and transmission error. Herringbone Gear Bending Torsional Axial Pendular Nonlinear Dynamics Gear Floating Backlash Bifurcation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4122378","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":283178382,"identity":"5e98f00c-57a1-4dfb-ac09-97e73742f5c1","order_by":0,"name":"Hao Han","email":"","orcid":"","institution":"Xi'an Technological University","correspondingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Han","suffix":""},{"id":283178383,"identity":"d1dcc48c-df4d-4e7b-afb3-ddfd686aa722","order_by":1,"name":"Hao Dong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYDCCAwwMzECKH4gZHzAYkKBFsgFIG5CshU2CKHfxHe89/LqgxkaCf3bzscofBXfkGdgPH92AT4vkmXNp1jOOpUlI3DmWdpvH4JlhA09a2g18Wgxu5JgZ87AdrmMAMm4zGBxmbJDgMSNCy7/DEvI38r8V/jA4bE+MFuPHvG2HJYAMNgYeg8OJBLVInjljxszblyZheCPNWBqoJbmNkF/4jvcYf+b5ZiMhdyP54ccffw7b9rMfPoZXCwNGdLARUA4CzB+IUDQKRsEoGAUjGQAArRhMpc9ZrpQAAAAASUVORK5CYII=","orcid":"","institution":"Xi'an Technological University","correspondingAuthor":true,"prefix":"","firstName":"Hao","middleName":"","lastName":"Dong","suffix":""},{"id":283178384,"identity":"1f89f341-c7c7-4d13-8554-f265aaf5444f","order_by":2,"name":"Dong-bo Zhang","email":"","orcid":"","institution":"Xi'an Technological University","correspondingAuthor":false,"prefix":"","firstName":"Dong-bo","middleName":"","lastName":"Zhang","suffix":""},{"id":283178385,"identity":"4e446756-66a4-4f9e-9f8c-d70a2d4336ab","order_by":3,"name":"Yue Bi","email":"","orcid":"","institution":"Xi'an Technological University","correspondingAuthor":false,"prefix":"","firstName":"Yue","middleName":"","lastName":"Bi","suffix":""}],"badges":[],"createdAt":"2024-03-18 10:33:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4122378/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4122378/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54211351,"identity":"3a0d1f00-7954-4515-bbed-3277bb35dcf1","added_by":"auto","created_at":"2024-04-06 12:13:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9001389,"visible":true,"origin":"","legend":"","description":"","filename":"Nonlineardynamicmodelinganddynamiccharacteristicsanalysisofacoaxialreversecloseddifferentialherringbonegeartransmissionsystemconsideringfloatingbacklash.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4122378/v1_covered_2c4a5696-0975-4dff-8756-f2646e327244.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear dynamic modeling and dynamic characteristics analysis of a coaxial reverse closed differential herringbone gear transmission system considering floating backlash","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Herringbone Gear, Bending Torsional Axial Pendular, Nonlinear Dynamics, Gear Floating Backlash, Bifurcation","lastPublishedDoi":"10.21203/rs.3.rs-4122378/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4122378/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA nonlinear dynamic model of Bending-Torsional-Axial-Pendular (BTAP) has been developed for a Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS) with consideration of gear floating. This model takes into account factors such as gear floating backlash, tooth surface friction, gyroscopic effect, Time Varying Meshing Stiffness (TVMS), meshing damping, and dynamic meshing parameters. To investigate the impact of gear floating on the nonlinear dynamic characteristics of the system, a gear floating model was developed using the concept of gear floating. The calculations included determining gear floating backlash and TVMS with consideration for gear floating. The impact of input speed, initial backlash, gear float value, and system transmission error on the nonlinear dynamic vibration characteristics is analyzed using various diagrams including bifurcation diagram, Maximum Lyapunov Exponent (MLE), time history diagram, frequency diagram, phase diagram, and Poincaré section diagram. The research reveals that gear floating diminish the chaotic motion behavior of the system under different excitation factors, improving the system's global bifurcation characteristics. The developed BTAP coupled nonlinear dynamic model provides more accurate numerical solutions compared to models with fixed meshing parameters, making it more suitable for analyzing the system's dynamic characteristics. Analysis of the gear floating value indicates an optimal range of 0-20μm and 34-43μm for generating periodic motion, with floating values around 10-20μm showing better performance in reducing the negative effects of initial backlash and transmission error.\u003c/p\u003e","manuscriptTitle":"Nonlinear dynamic modeling and dynamic characteristics analysis of a coaxial reverse closed differential herringbone gear transmission system considering floating backlash","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-27 17:19:08","doi":"10.21203/rs.3.rs-4122378/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8682f18c-f738-44f6-b5b6-49e1ffc95f3d","owner":[],"postedDate":"March 27th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-04-06T12:05:15+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-27 17:19:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4122378","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4122378","identity":"rs-4122378","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}