{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T15:54:31Z","timestamp":1774540471084,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T00:00:00Z","timestamp":1568160000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2018YFB1700905"],"award-info":[{"award-number":["2018YFB1700905"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Position error-compensation control in the servo system of computerized numerical control (CNC) machine tools relies on accurate prediction of dynamic tracking errors of the machine tool feed system. In this paper, in order to accurately predict dynamic tracking errors, a hybrid modeling method is proposed and a dynamic model of the ball screw feed system is developed. Firstly, according to the law of conservation of energy, a complete multi-domain system analytical model of a ball screw feed system was established based on energy flow. In order to overcome the uncertainties of the analytical model, then the data-driven model based on the back propagation (BP) neural network was established and trained using experimental data. Finally, the data-driven model was coupled with the multi-domain analytical model and the hybrid model was developed. The model was verified by experiment at different velocities and the results show that the prediction accuracy of the hybrid model reaches high levels. The hybrid modeling method combines the advantages of analytical modeling and data-driven modeling methods, and can significantly improve the feed system\u2019s modeling accuracy. The research results of this paper are of great significance to improve the compensation control accuracy of CNC machine tools.<\/jats:p>","DOI":"10.3390\/sym11091156","type":"journal-article","created":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T11:26:34Z","timestamp":1568201194000},"page":"1156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Hybrid Multi-Domain Analytical and Data-Driven Modeling for Feed Systems in Machine Tools"],"prefix":"10.3390","volume":"11","author":[{"given":"Zaiwu","family":"Mei","sequence":"first","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianwan","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ting","family":"Pi","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zaidao","family":"Mei","sequence":"additional","affiliation":[{"name":"Department of EECS, Syracuse University, Snow City, NY 13244, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.cirp.2011.05.010","article-title":"Machine tool feed drives","volume":"60","author":"Altintas","year":"2011","journal-title":"CIRP Ann."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1177\/0954405414534641","article-title":"Dynamic modeling and analysis of the high-speed ball screw feed system","volume":"229","author":"Zhang","year":"2015","journal-title":"Proc. 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