Training of artificial neural networks with reduced-order models for the prediction of thermal errors on machine tools | 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 Training of artificial neural networks with reduced-order models for the prediction of thermal errors on machine tools Christian Naumann, Tharun Suresh Kumar, Julia Vettermann, Alexander Geist, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4744195/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 5 You are reading this latest preprint version Abstract Thermal errors are among the most significant factors affecting the positioning accuracy of a machine tool. This paper demonstrates the advantages of combining reduced-order model (ROM) finite element method (FEM) simulations with data-driven error prediction algorithms, such as artificial neural networks (ANN) or characteristic diagrams. First, the thermal behavior of a five-axis milling machine (DMU 80 eVo) was modelled in ANSYS, after experimental determination of the relevant thermal boundary conditions. The FE model was then validated with measurements taken from the machine tool with movements of all five axes under different operating conditions, such as dry air-cutting, air-cutting with coolant and stand-by. The validated thermo-elastic FE model can then be used for training prediction algorithms (ANN, char. diagrams) for online thermal error compensation. The use of ROMs overcomes the long computation times of the high-dimensional simulation models by reducing them to equivalent low-dimensional models enabling much faster thermo-elastic simulations while preserving a specified result accuracy. An ANSYS ACT extension was utilized to export the FE model data in the form of an input-output system, which is required for the application of the model order reduction (MOR) techniques. This inclusion of MOR tremendously speeds up the process of generating training data for the prediction algorithms. ANN based prediction algorithms trained by the ROM simulation data are finally validated with simulated independent thermal test scenarios. artificial neural network (ANN) model order reduction (MOR) FEM simulation thermal error prediction machine tool precision Full Text Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Major Revisions Needed 04 Sep, 2024 Reviewers agreed at journal 20 Jul, 2024 Reviewers invited by journal 19 Jul, 2024 Editor assigned by journal 17 Jul, 2024 First submitted to journal 15 Jul, 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. We do this by developing innovative software and high quality services for the global research community. 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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-4744195","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":329264884,"identity":"3d2a2f05-9e65-436c-9dcf-a01282b8873d","order_by":0,"name":"Christian Naumann","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-6162-080X","institution":"Fraunhofer-Institut fur Werkzeugmaschinen und Umformtechnik IWU","correspondingAuthor":true,"prefix":"","firstName":"Christian","middleName":"","lastName":"Naumann","suffix":""},{"id":329264885,"identity":"838aaac6-b770-4bb3-b29d-081c9f4923df","order_by":1,"name":"Tharun Suresh Kumar","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Tharun","middleName":"Suresh","lastName":"Kumar","suffix":""},{"id":329264886,"identity":"9dbbcd25-35b2-4067-b364-b40388ac01f5","order_by":2,"name":"Julia Vettermann","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Julia","middleName":"","lastName":"Vettermann","suffix":""},{"id":329264887,"identity":"5e4b253d-31da-4c30-9750-e40647efe3f8","order_by":3,"name":"Alexander Geist","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Alexander","middleName":"","lastName":"Geist","suffix":""},{"id":329264888,"identity":"2abc7459-d2b7-43db-9c44-0c9b369ff6f3","order_by":4,"name":"Jens Saak","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jens","middleName":"","lastName":"Saak","suffix":""},{"id":329264889,"identity":"49d7a72b-687f-442e-96e7-b7a2f9db6691","order_by":5,"name":"Peter Benner","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"","lastName":"Benner","suffix":""},{"id":329264890,"identity":"9a558905-ff38-481b-b6b8-e33e898a853c","order_by":6,"name":"Steffen Ihlenfeldt","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Steffen","middleName":"","lastName":"Ihlenfeldt","suffix":""}],"badges":[],"createdAt":"2024-07-15 16:15:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4744195/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4744195/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":62420753,"identity":"00111648-8968-4a77-8000-ca8fec7568c4","added_by":"auto","created_at":"2024-08-14 03:41:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4048782,"visible":true,"origin":"","legend":"","description":"","filename":"morannarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4744195/v1_covered_06c9ccaa-1090-435a-86eb-ee884f3ce070.pdf"}],"financialInterests":"","formattedTitle":"Training of artificial neural networks with reduced-order models for the prediction of thermal errors on machine tools","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"
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