Mathematical Model of Non-Generated Straight Bevel Gears Based on a Four-Axis CNC Machine

Mathematical Model of Non-Generated Straight Bevel Gears Based on a Four-Axis CNC Machine | 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 Mathematical Model of Non-Generated Straight Bevel Gears Based on a Four-Axis CNC Machine yi-pei shih, Guang-Yu Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3920871/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Apr, 2024 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted 5 You are reading this latest preprint version Abstract High-precision straight bevel gears (SBGs) are commonly manufactured using the generating method, which requires specialized equipment such as a dedicated or five-axis CNC machine for mass production. While the existing forming process can also be applied to produce SBGs, which offers a more cost-effective solution with a four-axis CNC machine, it results in inferior gear contact performance. This paper introduces a novel forming (non-generating) method. The goal is to enhance the gear contact performance. First, the tool profile of the pinion is computed based on the ring gear’s conjugate tooth surface. Subsequently, a sensitivity analysis on the tooth surface, considering four-axis motion coefficients, facilitates the calculation of correction amounts for tooth cutting motion. This process determines the pinion’s tooth surface, optimizing the contact performance by ensuring it contacts the ring gears precisely at a point. Ease-off and tooth contact analyses are utilized to evaluate the contact performance of the designed gear pair. Furthermore, VERICUT software is employed for cutting simulation to validate the NC machining codes. After this, a cutting experiment is conducted to verify the correctness of our mathematical model. Straight bevel gears forming method non-generating four-axis CNC machine VERICUT Full Text Cite Share Download PDF Status: Published Journal Publication published 27 Apr, 2024 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Editorial decision: Minor Revisions Needed 03 Apr, 2024 Reviewers agreed at journal 12 Feb, 2024 Reviewers invited by journal 05 Feb, 2024 Editor assigned by journal 04 Feb, 2024 First submitted to journal 02 Feb, 2024 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-3920871","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271369750,"identity":"8bf135d1-f775-45eb-a8d0-ec7a85ee028b","order_by":0,"name":"yi-pei shih","email":"data:image/png;base64,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","orcid":"","institution":"National Taiwan University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"yi-pei","middleName":"","lastName":"shih","suffix":""},{"id":271369751,"identity":"08f8d56b-1b8f-483e-9990-687e32396614","order_by":1,"name":"Guang-Yu Chen","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Guang-Yu","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2024-02-02 12:37:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3920871/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3920871/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-024-13663-z","type":"published","date":"2024-04-28T00:11:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":55471882,"identity":"1e609537-3cd8-4271-b31e-474f785dfd76","added_by":"auto","created_at":"2024-04-29 00:11:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1505437,"visible":true,"origin":"","legend":"","description":"","filename":"Paper17v18.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3920871/v1_covered_b65e2b11-7e2e-47a8-890b-05753b595b9d.pdf"}],"financialInterests":"","formattedTitle":"Mathematical Model of Non-Generated Straight Bevel Gears Based on a Four-Axis CNC Machine","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Straight bevel gears, forming method, non-generating, four-axis CNC machine, VERICUT","lastPublishedDoi":"10.21203/rs.3.rs-3920871/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3920871/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHigh-precision straight bevel gears (SBGs) are commonly manufactured using the generating method, which requires specialized equipment such as a dedicated or five-axis CNC machine for mass production. While the existing forming process can also be applied to produce SBGs, which offers a more cost-effective solution with a four-axis CNC machine, it results in inferior gear contact performance. This paper introduces a novel forming (non-generating) method. The goal is to enhance the gear contact performance. First, the tool profile of the pinion is computed based on the ring gear\u0026rsquo;s conjugate tooth surface. Subsequently, a sensitivity analysis on the tooth surface, considering four-axis motion coefficients, facilitates the calculation of correction amounts for tooth cutting motion. This process determines the pinion\u0026rsquo;s tooth surface, optimizing the contact performance by ensuring it contacts the ring gears precisely at a point. Ease-off and tooth contact analyses are utilized to evaluate the contact performance of the designed gear pair. Furthermore, VERICUT software is employed for cutting simulation to validate the NC machining codes. 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