Modeling and experimental study of cutting forces of a variable pitch ball-end cutter in five-axis milling

Modeling and experimental study of cutting forces of a variable pitch ball-end cutter in five-axis milling | 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 Article Modeling and experimental study of cutting forces of a variable pitch ball-end cutter in five-axis milling Weijun Tian, Jinhua Zhou, Junxue Ren, Yizhuo Wang, Zerui Bai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7593342/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted 3 You are reading this latest preprint version Abstract This study develops a cutting force prediction model for variable-pitch ball-nose cutters used in multi-axis milling. It starts by defining the five-axis machining coordinate system and creating a geometric model of the cutter. Then, using micro-element cutting force theory, the study establishes a cutting force model specific to ball-nose milling.To simplify the complexity from dynamic tool orientations, the research proposes a practical method. It projects the engagement region onto a plane that is perpendicular to the tool axis. This approach accurately defines the boundary curve. After calculating the engagement region with a fixed tool axis, a rotation transformation matrix is applied. This helps determine the engagement domain in the tool coordinate system for any tool orientation.The study also finds the instantaneous entry and exit angles for each element. It does this by identifying intersection points between the infinitesimal projection circle and the engagement domain boundary, along with the lines connecting their centers.Lastly, the research introduces a method for identifying milling force coefficients based on the average milling force per tooth cycle. Through systematic milling experiments, these coefficients are calibrated. The results indicate that the predicted milling forces closely match the measured ones, with a maximum root mean square error of 6.74%. This validates the model's effectiveness for variable-pitch ball-nose cutters. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 28 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Accepted 19 Jan, 2026 Submission checks completed at journal 13 Jan, 2026 First submitted to journal 13 Jan, 2026 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7593342","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":574827486,"identity":"1e7be0f2-912f-4698-830f-e5d3b9ff0551","order_by":0,"name":"Weijun 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milling","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7593342/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7593342/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study develops a cutting force prediction model for variable-pitch ball-nose cutters used in multi-axis milling. It starts by defining the five-axis machining coordinate system and creating a geometric model of the cutter. Then, using micro-element cutting force theory, the study establishes a cutting force model specific to ball-nose milling.To simplify the complexity from dynamic tool orientations, the research proposes a practical method. It projects the engagement region onto a plane that is perpendicular to the tool axis. This approach accurately defines the boundary curve. After calculating the engagement region with a fixed tool axis, a rotation transformation matrix is applied. This helps determine the engagement domain in the tool coordinate system for any tool orientation.The study also finds the instantaneous entry and exit angles for each element. It does this by identifying intersection points between the infinitesimal projection circle and the engagement domain boundary, along with the lines connecting their centers.Lastly, the research introduces a method for identifying milling force coefficients based on the average milling force per tooth cycle. Through systematic milling experiments, these coefficients are calibrated. The results indicate that the predicted milling forces closely match the measured ones, with a maximum root mean square error of 6.74%. This validates the model's effectiveness for variable-pitch ball-nose cutters.\u003c/p\u003e","manuscriptTitle":"Modeling and experimental study of cutting forces of a variable pitch ball-end cutter in five-axis milling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-16 04:56:04","doi":"10.21203/rs.3.rs-7593342/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2026-01-19T07:23:35+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-13T14:42:12+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-01-13T08:26:14+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"79874bd8-a6e1-46a2-adcb-59bf85048560","owner":[],"postedDate":"January 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-02-02T16:06:16+00:00","versionOfRecord":{"articleIdentity":"rs-7593342","link":"https://doi.org/10.1038/s41598-026-36982-5","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-01-28 15:58:19","publishedOnDateReadable":"January 28th, 2026"},"versionCreatedAt":"2026-01-16 04:56:04","video":"","vorDoi":"10.1038/s41598-026-36982-5","vorDoiUrl":"https://doi.org/10.1038/s41598-026-36982-5","workflowStages":[]},"version":"v1","identity":"rs-7593342","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7593342","identity":"rs-7593342","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}