{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T10:41:13Z","timestamp":1773744073902,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,18]],"date-time":"2024-01-18T00:00:00Z","timestamp":1705536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program","award":["2020YFB1713100"],"award-info":[{"award-number":["2020YFB1713100"]}]},{"name":"National Key Research and Development Program","award":["JCKY2020204B017"],"award-info":[{"award-number":["JCKY2020204B017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Thin-walled aluminum alloy parts are widely used in the aerospace field because of their favorable characteristics that cater to various applications. However, they are easily deformed during milling, leading to a low pass rate of workpieces. On the basis of on-machine measurement (OMM) and surrogate stiffness models (SSMs), we developed an iterative optimization compensation method in this study to overcome the machining deformation of thin-walled parts. In the error compensation process, the time-varying factors of workpiece stiffness and the impact of prediction model errors were considered. First, we performed machining deformation simulation and information extraction on the key nodes of the machined surface, and an SSM containing the stiffness information of discrete nodes of each cutting layer was established. Subsequently, the machining errors were monitored through intermittent OMM to suppress the adverse impact of prediction model errors. Further, an interlayer correction coefficient was introduced in the compensation process to iteratively correct the prediction model error of each node in the SSM along the depth direction, and a correction coefficient between parts was introduced to realize the iterative correction of the prediction model for the same node position between different parts. Finally, the feasibility of the proposed method was verified through multiple sets of actual machining experiments on thin-walled parts with added pads.<\/jats:p>","DOI":"10.3390\/s24020613","type":"journal-article","created":{"date-parts":[[2024,1,18]],"date-time":"2024-01-18T05:52:03Z","timestamp":1705557123000},"page":"613","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Adaptive Optimization Method for Prediction and Compensation of Thin-Walled Parts Machining Deformation Based on On-Machine Measurement"],"prefix":"10.3390","volume":"24","author":[{"given":"Long","family":"Wu","sequence":"first","affiliation":[{"name":"Digital Manufacturing Institute, Beijing Institute of Technology, Beijing 100081, China"},{"name":"School of Mechanical and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China"}]},{"given":"Aimin","family":"Wang","sequence":"additional","affiliation":[{"name":"Digital Manufacturing Institute, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Kang","family":"Wang","sequence":"additional","affiliation":[{"name":"Digital Manufacturing Institute, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Wenhao","family":"Xing","sequence":"additional","affiliation":[{"name":"Digital Manufacturing Institute, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Baode","family":"Xu","sequence":"additional","affiliation":[{"name":"Beijing Xinghang Mechanical-Electric Equipment Co., Ltd., Beijing 100074, China"}]},{"given":"Jiayu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Xinghang Mechanical-Electric Equipment Co., Ltd., Beijing 100074, China"}]},{"given":"Yuan","family":"Yu","sequence":"additional","affiliation":[{"name":"Beijing Xinghang Mechanical-Electric Equipment Co., Ltd., Beijing 100074, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1016\/j.ijmachtools.2005.06.003","article-title":"An advanced FEA based force induced error compensation strategy in milling","volume":"46","author":"Ratchev","year":"2006","journal-title":"Int. J. Mach. Tool Manuf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1579","DOI":"10.1007\/s00170-021-08291-w","article-title":"A prediction model of the cutting force-induced deformation while considering the removed material impact","volume":"119","author":"Xi","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.jmatprotec.2007.12.089","article-title":"Deformations of thin-walled plate due to static end milling force","volume":"206","author":"Tang","year":"2008","journal-title":"J. Mater. Process. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1177\/0954405420949214","article-title":"Modeling of flatness errors in end milling of thin-walled components","volume":"235","author":"Agarwal","year":"2021","journal-title":"Proc. Inst. Mech. Eng. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1177\/09544054221076987","article-title":"Machining-path mapping from free-state to clamped-state for thin-walled parts","volume":"236","author":"Ma","year":"2022","journal-title":"Proc. Inst. Mech. Eng. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.ijmachtools.2018.01.005","article-title":"Surface form error prediction in five-axis flank milling of thin-walled parts","volume":"128","author":"Li","year":"2018","journal-title":"Int. J. Mach. Tool Manuf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"117258","DOI":"10.1016\/j.jmatprotec.2021.117258","article-title":"Force-induced deformation prediction and flexible error compensation strategy in flank milling of thin-walled parts","volume":"297","author":"Li","year":"2021","journal-title":"J. Mater. Process. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1177\/0954405418780163","article-title":"Error compensation in the five-axis flank milling of thin-walled workpieces","volume":"233","author":"Si","year":"2019","journal-title":"Proc. Inst. Mech. Eng. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106111","DOI":"10.1016\/j.ijmecsci.2020.106111","article-title":"A hybrid driven approach to integrate surrogate model and Bayesian framework for the prediction of machining errors of thin-walled parts","volume":"192","author":"Sun","year":"2021","journal-title":"Int. J. Mech. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2537","DOI":"10.1007\/s00170-022-08798-w","article-title":"Study on deformation and compensation for micromilling of thin walls","volume":"120","author":"Li","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103543","DOI":"10.1016\/j.ijmachtools.2020.103543","article-title":"Controlling of compliant grinding for low-rigidity components","volume":"152","author":"Yang","year":"2020","journal-title":"Int. J. Mach. Tool Manuf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"102398","DOI":"10.1016\/j.rcim.2022.102398","article-title":"Integrated profile and thickness error compensation for curved part based on on-machine measurement","volume":"79","author":"Zhang","year":"2023","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"041010","DOI":"10.1115\/1.4048955","article-title":"A data-driven machining error analysis method for finish machining of assembly interfaces of large-scale components","volume":"143","author":"Fan","year":"2021","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"101928","DOI":"10.1016\/j.rcim.2019.101928","article-title":"A closed-loop error compensation method for robotic flank milling","volume":"63","author":"Xiong","year":"2020","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.precisioneng.2020.03.002","article-title":"An integrated error compensation method based on on-machine measurement for thin web parts machining","volume":"63","author":"Ge","year":"2020","journal-title":"Precis. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.cirp.2011.03.123","article-title":"Predictive compliance based model for compensation in multi-pass milling by on-machine probing","volume":"60","author":"Guiassa","year":"2011","journal-title":"CIRP Ann."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"021006","DOI":"10.1115\/1.4051793","article-title":"Online first-order machining error compensation for thin-walled parts considering time-varying cutting condition","volume":"144","author":"Zhao","year":"2022","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103401","DOI":"10.1016\/j.cad.2022.103401","article-title":"An efficient prediction method for the dynamic deformation of thin-walled parts in flank milling","volume":"152","author":"Ge","year":"2022","journal-title":"Comput.-Aided Des."},{"key":"ref_19","first-page":"4","article-title":"Investigation into the Flow of Gas-Solids during Dry Dust Collectors Exploitation, as Applied in Domestic Energy Facilities\u2013Numerical Analyses","volume":"25","author":"Kostrzewski","year":"2023","journal-title":"Eksploat. I Niezawodn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1007\/s00170-020-05616-z","article-title":"State of the art in milling process of the flexible workpiece","volume":"109","author":"Fei","year":"2020","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"216224","DOI":"10.1115\/1.2831014","article-title":"Prediction of Milling Force Coefficients From Orthogonal Cutting Data","volume":"118","author":"Budak","year":"1996","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"106284","DOI":"10.1016\/j.ymssp.2019.106284","article-title":"Cutting force modeling and accurate measurement in milling of flexible workpieces","volume":"133","author":"Kiran","year":"2019","journal-title":"Mech. Sys. Signal. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1016\/j.ijmachtools.2009.05.006","article-title":"Deformation prediction and error compensation in multilayer milling processes for thin-walled parts","volume":"49","author":"Chen","year":"2009","journal-title":"Int. J. Mach. Tool Manuf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1007\/s00170-022-09962-y","article-title":"Adaptive sampling method for thin-walled parts based on on-machine measurement","volume":"122","author":"Wu","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/j.cirp.2019.05.005","article-title":"On-machine and in-process surface metrology for precision manufacturing","volume":"68","author":"Gao","year":"2019","journal-title":"CIRP Ann."},{"key":"ref_26","unstructured":"Piegl, L., and Tiller, W. (2012). The NURBS Book, Springer Science and Business Media."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/2\/613\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:49:33Z","timestamp":1760104173000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/2\/613"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,18]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["s24020613"],"URL":"https:\/\/doi.org\/10.3390\/s24020613","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,18]]}}}