Research on Thermal Error Prediction Technology of Ultra-Precision Machine Tool Spindle

Research on Thermal Error Prediction Technology of Ultra-Precision Machine Tool Spindle | 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 Research on Thermal Error Prediction Technology of Ultra-Precision Machine Tool Spindle yuqing tang, Hao ZHONG, Jun YAO, Shuai SU, Baorui DU, Jun TANG, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8877388/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Thermal error is a critical factor limiting the machining accuracy of ultra-precision CNC machine tools. Addressing the issue of weak generalization capability in pure data-driven models under uncalibrated operating conditions due to the lack of physical guidance, this paper proposes a physics-informed "LSTM-PDE" thermal error prediction model for ultra-precision motorized spindles. First, a lumped parameter thermal resistance network (LPTRN) for the motorized spindle is constructed based on heat transfer mechanisms and transformed into state-space equations. This approach achieves millisecond-level rapid calculation of the full-node temperature field, providing an efficient physical benchmark for thermal prediction. Second, a deep learning framework guided by physical priors is constructed, with a re-formulated loss function optimization strategy. By embedding the governing equations of the LPTRN into the neural network as consistency constraints, physical laws are utilized to rectify and guide model weight optimization in real-time. Furthermore, leveraging the advantages of Bi-LSTM in the dynamic compensation of nonlinear residuals, the model corrects systematic biases in traditional mechanistic models arising from rigid constraints and simplified boundary conditions. Experimental results demonstrate that the proposed coupled model effectively resolves prediction distortion under uncalibrated operating conditions. At an unlearned rotational speed of 5500 r/min, the prediction Root Mean Square Error (RMSE) is only 0.03. In the cutting verification of typical feature parts, the model reduced the Z-axis thermal drift error by 72%. This study confirms that the proposed method exhibits both high prediction accuracy and robustness, providing an effective solution for real-time thermal error compensation in ultra-precision machine tools. Ultra-precision Motorized Spindle Thermal Error Prediction Thermal Resistance Network LSTM-PDE Full Text Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 26 Feb, 2026 Reviewers invited by journal 25 Feb, 2026 Editor assigned by journal 24 Feb, 2026 First submitted to journal 23 Feb, 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-8877388","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":596674462,"identity":"e98aa618-aa25-43f0-bb60-681cd5c50728","order_by":0,"name":"yuqing 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Addressing the issue of weak generalization capability in pure data-driven models under uncalibrated operating conditions due to the lack of physical guidance, this paper proposes a physics-informed \"LSTM-PDE\" thermal error prediction model for ultra-precision motorized spindles. First, a lumped parameter thermal resistance network (LPTRN) for the motorized spindle is constructed based on heat transfer mechanisms and transformed into state-space equations. This approach achieves millisecond-level rapid calculation of the full-node temperature field, providing an efficient physical benchmark for thermal prediction. Second, a deep learning framework guided by physical priors is constructed, with a re-formulated loss function optimization strategy. By embedding the governing equations of the LPTRN into the neural network as consistency constraints, physical laws are utilized to rectify and guide model weight optimization in real-time. Furthermore, leveraging the advantages of Bi-LSTM in the dynamic compensation of nonlinear residuals, the model corrects systematic biases in traditional mechanistic models arising from rigid constraints and simplified boundary conditions. Experimental results demonstrate that the proposed coupled model effectively resolves prediction distortion under uncalibrated operating conditions. At an unlearned rotational speed of 5500 r/min, the prediction Root Mean Square Error (RMSE) is only 0.03. In the cutting verification of typical feature parts, the model reduced the Z-axis thermal drift error by 72%. This study confirms that the proposed method exhibits both high prediction accuracy and robustness, providing an effective solution for real-time thermal error compensation in ultra-precision machine tools.\u003c/p\u003e","manuscriptTitle":"Research on Thermal Error Prediction Technology of Ultra-Precision Machine Tool Spindle","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-02 12:26:55","doi":"10.21203/rs.3.rs-8877388/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-02-27T01:51:56+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-25T05:32:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-24T09:36:58+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2026-02-23T23:02:09+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"1843f874-711f-4cc5-b354-1984d0d69a68","owner":[],"postedDate":"March 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-02T12:26:55+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-02 12:26:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8877388","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8877388","identity":"rs-8877388","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}