Position-independent geometric error identification and Compensation for Five-Axis Machine Tool Using Projection-Based Fitting Methods

Position-independent geometric error identification and Compensation for Five-Axis Machine Tool Using Projection-Based Fitting Methods | 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 Position-independent geometric error identification and Compensation for Five-Axis Machine Tool Using Projection-Based Fitting Methods Ting-Hua Zhang, Zheng-Wei Jian, Meng-Shiun Tsai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7507156/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 This paper proposes a Projection-Based Fitting Method (PBFM) for identifying eight positionindependent geometric errors (PIGEs), including squareness errors and linear offsets, associated with the two rotary axes of a five-axis machine tool. By using a touch probe and a precision sphere, the X, Y and Z positions of the rotary axes are measured at various angular configurations. These errors are then projected onto a 2D plane, where they form distinctive geometric patterns. By deriving error equations and fitting these projected patterns, the eight PIGEs can be effectively identified. To minimize the coupling effects among different error components, a two-stage geometric error identification process is introduced. In the first stage, squareness errors are calculated and compensated to reduce angular deviations. The second stage focuses on identifying and compensating for linear offsets, further improving the system’s overall accuracy. Compared to the conventional Least Squares Method (LSM), the proposed PBFM not only offers a more intuitive interpretation of how different errors affect the geometry of the projection patterns, but also shows greater robustness against outliers and measurement noise. Experiments were conducted on the five-axis machine tool with compensation data implemented directly to the Heidenhain controller. After compensation, the RMS errors for the A axis and C axis were reduced by over 77% and 90%, respectively. These results demonstrate that the proposed PBFM can significantly reduce geometric errors in rotary axes, confirming both the feasibility and effectiveness of the approach. Position-Independent Geometric Errors Rotary Axis Projection-Based Fitting Method Error Identification Full Text 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. 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-7507156","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":512526725,"identity":"c778efe4-f1c2-4516-a911-8943d0031005","order_by":0,"name":"Ting-Hua Zhang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Ting-Hua","middleName":"","lastName":"Zhang","suffix":""},{"id":512526726,"identity":"a033644d-e181-4209-bffe-6319db3fd913","order_by":1,"name":"Zheng-Wei Jian","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zheng-Wei","middleName":"","lastName":"Jian","suffix":""},{"id":512526727,"identity":"0fffa3ab-70b1-4fa9-901a-1b1ef037af80","order_by":2,"name":"Meng-Shiun Tsai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6UlEQVRIiWNgGAWjYNACAwkefvbmAxDOAYLKmUFabGQke44lQFQfYGBsIKyFIc3G4IaPAXFadPvPH/7wo+AwD8MNnm+PP7YxyPHdSGB/zINHi9mNZDbJHoPDPIyze7cbHGxjMJa8kcDYjF8LMxsDD1ALs8zZbRJALYkbQFpy8Gk5f5j54x+gFjaJnGcgLfWEtRxIZpDmMUjj4ZHIYQNpSTAgqOVGspm0jIENjwTPMTOJM+ckDGeeedg4+w9ehx18/PHNHwl7++PNzyQqymzk+Y4nH/g4A48WdCABxIRichSMglEwCkYBQQAAjDlREvVTz8QAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-2812-5975","institution":"National Taiwan University","correspondingAuthor":true,"prefix":"","firstName":"Meng-Shiun","middleName":"","lastName":"Tsai","suffix":""}],"badges":[],"createdAt":"2025-09-01 10:09:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7507156/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7507156/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97138571,"identity":"e31731ba-9fa1-40b6-be77-040e205131c6","added_by":"auto","created_at":"2025-12-01 09:59:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1742688,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7507156/v1_covered_85c69fc5-63dc-411e-9a95-d074a69fe4fd.pdf"}],"financialInterests":"","formattedTitle":"Position-independent geometric error identification and Compensation for Five-Axis Machine Tool Using Projection-Based Fitting Methods","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":"Position-Independent Geometric Errors, Rotary Axis, Projection-Based Fitting Method, Error Identification","lastPublishedDoi":"10.21203/rs.3.rs-7507156/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7507156/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper proposes a Projection-Based Fitting Method (PBFM) for identifying eight positionindependent geometric errors (PIGEs), including squareness errors and linear offsets, associated with the two rotary axes of a five-axis machine tool. By using a touch probe and a precision sphere, the X, Y and Z positions of the rotary axes are measured at various angular configurations. These errors are then projected onto a 2D plane, where they form distinctive geometric patterns. By deriving error equations and fitting these projected patterns, the eight PIGEs can be effectively identified. To minimize the coupling effects among different error components, a two-stage geometric error identification process is introduced. In the first stage, squareness errors are calculated and compensated to reduce angular deviations. The second stage focuses on identifying and compensating for linear offsets, further improving the system’s overall accuracy. Compared to the conventional Least Squares Method (LSM), the proposed PBFM not only offers a more intuitive interpretation of how different errors affect the geometry of the projection patterns, but also shows greater robustness against outliers and measurement noise. Experiments were conducted on the five-axis machine tool with compensation data implemented directly to the Heidenhain controller. After compensation, the RMS errors for the A axis and C axis were reduced by over 77% and 90%, respectively. These results demonstrate that the proposed PBFM can significantly reduce geometric errors in rotary axes, confirming both the feasibility and effectiveness of the approach.","manuscriptTitle":"Position-independent geometric error identification and Compensation for Five-Axis Machine Tool Using Projection-Based Fitting Methods","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-16 06:22:26","doi":"10.21203/rs.3.rs-7507156/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":"c3ab1848-f6fc-4d39-9548-1f53a9c69154","owner":[],"postedDate":"September 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-28T14:01:53+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-16 06:22:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7507156","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7507156","identity":"rs-7507156","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}