{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:31:29Z","timestamp":1787027489634,"version":"build-2736575974"},"reference-count":24,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,15]],"date-time":"2026-08-15T00:00:00Z","timestamp":1786752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52275462"],"award-info":[{"award-number":["52275462"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["51805404"],"award-info":[{"award-number":["51805404"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52575529"],"award-info":[{"award-number":["52575529"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["52275462"],"award-info":[{"award-number":["52275462"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["51805404"],"award-info":[{"award-number":["51805404"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["52575529"],"award-info":[{"award-number":["52575529"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Xi\u2019an City Science and Technology Plan Project","award":["25GXKIRC00075"],"award-info":[{"award-number":["25GXKIRC00075"]}]},{"DOI":"10.13039\/501100015401","name":"Key Research and Development Projects of Shaanxi Province","doi-asserted-by":"publisher","award":["2025CY-YBXM-119"],"award-info":[{"award-number":["2025CY-YBXM-119"]}],"id":[{"id":"10.13039\/501100015401","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["2025SYS-SYSZD-039"],"award-info":[{"award-number":["2025SYS-SYSZD-039"]}]},{"DOI":"10.13039\/501100003512","name":"National Foreign Expert Projects","doi-asserted-by":"publisher","award":["H20250181"],"award-info":[{"award-number":["H20250181"]}],"id":[{"id":"10.13039\/501100003512","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Micro curved-surface parts are widely used in the aerospace, defense, biomedical, and automotive industries, and their growing adoption imposes increasingly stringent performance requirements. Five-axis micro-milling can achieve precision machining of parts with complex shapes. In the micro-milling process, the cutting force is a critical parameter, as it is the main factor causing machining deformation, vibration, and tool wear. Therefore, this study develops a prediction model for five-axis micro-milling forces in the machining of micro complex curved-surface parts. First, four coordinate systems were established for the five-axis milling process, and the transformation relationships among them were derived. A cutter\u2013workpiece engagement (CWE) extraction method based on solid modeling was also introduced. Then, an instantaneous undeformed chip thickness (IUCT) model was established, taking into account tool runout, elastic recovery of the machined surface, minimum chip thickness, and the local radius of the micro ball-end mill. On this basis, a five-axis micro-milling force prediction model was developed. Finally, five-axis micro-milling experiments were conducted on a micro-impeller and a micro-spherical part, and the cutting forces at different cutter location (CL) points were measured. For the micro-impeller blade, the average percentage errors in the X, Y, and Z directions at all selected CL points were below 11.2%; for the micro-spherical part, the corresponding errors were below 14.4%. These results show good agreement between the predicted and measured values, verifying the effectiveness of the proposed model.<\/jats:p>","DOI":"10.3390\/mi17080961","type":"journal-article","created":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T13:42:17Z","timestamp":1786974137000},"page":"961","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Five-Axis Micro Ball-End Milling Force Prediction for Micro Curved-Surface Parts"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5615-8278","authenticated-orcid":false,"given":"Zhenghu","family":"Yan","sequence":"first","affiliation":[{"name":"School of Mechatronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yicheng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuai","family":"Wang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jingdiao Software Technology Co., Ltd., Xi\u2019an 710119, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenxi","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruisi","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107863","DOI":"10.1016\/j.ijmecsci.2022.107863","article-title":"CWE Identification and Cutting Force Prediction in Ball-End Milling Process","volume":"239","author":"Qin","year":"2023","journal-title":"Int. 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