{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T23:42:13Z","timestamp":1778802133263,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T00:00:00Z","timestamp":1712534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"publisher","award":["No. 958357"],"award-info":[{"award-number":["No. 958357"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Large machine tools are critically affected by ambient temperature fluctuations, impacting their performance and the quality of machined products. Addressing the challenge of accurately measuring thermal effects on machine structures, this study introduces the Machine Tool Integrated Inverse Multilateration method. This method offers a precise approach for assessing geometric error parameters throughout a machine\u2019s working volume, featuring a low level of uncertainty and high speed suitable for effective temperature change monitoring. A significant innovation is found in the capability to automatically realise the volumetric error characterisation of medium- to large-sized machine tools at intervals of 40\u201360 min with a measurement uncertainty of 10 \u00b5m. This enables the detailed study of thermal errors which are generated due to variations in ambient temperature over extended periods. To validate the method, an extensive experimental campaign was conducted on a ZAYER Arion G\u2122 large machine tool using a LEICA AT960\u2122 laser tracker with four wide-angle retro-reflectors under natural workshop conditions. This research identified two key thermal scenarios, quasi-stationary and changing environments, providing valuable insights into how temperature variations influence machine behaviour. This novel method facilitates the optimization of machine tool operations and the improvement of product quality in industrial environments, marking a significant advancement in manufacturing metrology.<\/jats:p>","DOI":"10.3390\/s24072380","type":"journal-article","created":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T12:01:22Z","timestamp":1712577682000},"page":"2380","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Novel Methodology for Measuring Ambient Thermal Effects on Machine Tools"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0917-4691","authenticated-orcid":false,"given":"Fernando","family":"Ega\u00f1a","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Tekniker, Basque Research and Technology Alliance (BRTA), C\/I\u00f1aki Goenaga 5, 20600 Eibar, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4157-5666","authenticated-orcid":false,"given":"Unai","family":"Mutilba","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tekniker, Basque Research and Technology Alliance (BRTA), C\/I\u00f1aki Goenaga 5, 20600 Eibar, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7152-4117","authenticated-orcid":false,"given":"Jos\u00e9 A.","family":"Yag\u00fce-Fabra","sequence":"additional","affiliation":[{"name":"I3A, Universidad de Zaragoza, C\/Mar\u00eda de Luna 3, 50018 Zaragoza, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eneko","family":"Gomez-Acedo","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tekniker, Basque Research and Technology Alliance (BRTA), C\/I\u00f1aki Goenaga 5, 20600 Eibar, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.precisioneng.2020.01.001","article-title":"Mapping and compensation of geometric errors of a machine tool at different constant ambient temperatures","volume":"63","author":"Gross","year":"2020","journal-title":"Precis. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"771791","DOI":"10.1016\/j.cirp.2012.05.008","article-title":"Thermal issues in machine tools","volume":"61","author":"Mayr","year":"2012","journal-title":"CIRP Ann. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.cirp.2021.04.084","article-title":"Direct measurement of thermo-elastic errors of a machine tool","volume":"70","author":"Brecher","year":"2021","journal-title":"CIRP Ann."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.cirp.2013.05.009","article-title":"Machine tools for large parts","volume":"62","author":"Uriarte","year":"2013","journal-title":"CIRP Ann. Manuf. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.procir.2015.06.087","article-title":"Traceable measurements on machine tools-Thermal influences on machine tool structure and measurement Uncertainty","volume":"33","author":"Schmitt","year":"2015","journal-title":"Procedia CIRP"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/j.precisioneng.2012.10.006","article-title":"Efficient estimation by FEA of machine tool distortion due to environmental temperature perturbations","volume":"37","author":"Mian","year":"2013","journal-title":"Precis. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"104017","DOI":"10.1016\/j.ijmachtools.2023.104017","article-title":"Machine tool calibration: Measurement, modeling, and compensation of machine tool errors","volume":"187","author":"Gao","year":"2023","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/S0007-8506(07)63001-7","article-title":"International Status of Thermal Error Research (1990)","volume":"39","author":"Bryan","year":"1990","journal-title":"CIRP Ann. Manuf. Technol."},{"key":"ref_9","unstructured":"(2020). Test Code for Machine Tools\u2014Part 3: Determination of Thermal Effects (Standard No. ISO 230-3:2020)."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wei, X., Ye, H., and Feng, X. (2022). Year-Round Thermal Error Modeling and Compensation for the Spindle of Machine Tools Based on Ambient Temperature Intervals. Sensors, 22.","DOI":"10.3390\/s22145085"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wei, X., Ye, H., Zhou, J., Pan, S., and Qian, M. (2023). A Regularized Regression Thermal Error Modeling Method for CNC Machine Tools under Different Ambient Temperatures and Spindle Speeds. Sensors, 23.","DOI":"10.3390\/s23104916"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/S0007-8506(07)60148-6","article-title":"Error mapping of CMMs and machine tools by a single tracking interferometer","volume":"54","author":"Schwenke","year":"2005","journal-title":"CIRP Ann. Manuf. Technol."},{"key":"ref_13","first-page":"79","article-title":"Concept of a Virtual Metrology Frame Based on Absolute Interferometry for Multi Robotic Assembly","volume":"Volume 435","author":"Schmitt","year":"2014","journal-title":"Precision Assembly Technologies and Systems, Proceedings of the 7th IFIP WG 5.5 International Precision Assembly Seminar, IPAS 2014, Chamonix, France, 16\u201318 February 2014"},{"key":"ref_14","unstructured":"Schwenke, H. (2016, January 18). Large parts with critical tolerances: Concepts and possible solutions for traceable CMM measurements on machine tools. Proceedings of the Traceable in-Process Dimensional Measurement Final Workshop, Braunschweig, Germany."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.cirp.2016.04.067","article-title":"Measurement of thermal influence on a two-dimensional motion trajectory using a tracking interferometer","volume":"65","author":"Ibaraki","year":"2016","journal-title":"CIRP Ann. Manuf. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.cirp.2019.04.093","article-title":"A new measurement method for machine tool thermal deformation on a two-dimensional trajectory using a tracking interferometer","volume":"68","author":"Mori","year":"2019","journal-title":"CIRP Ann."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.precisioneng.2021.09.009","article-title":"Absolute multilateration-based coordinate measurement system using retroreflecting glass spheres","volume":"73","author":"Guillory","year":"2022","journal-title":"Precis. Eng."},{"key":"ref_18","first-page":"110735","article-title":"Calibration and uncertainty budget analysis of a high precision telescopic instrument for simultaneous laser multilateration","volume":"190","author":"Acero","year":"2022","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.cirp.2008.09.008","article-title":"Geometric error measurement and compensation of machines\u2014An update","volume":"57","author":"Schwenke","year":"2008","journal-title":"CIRP Ann. Manuf. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.precisioneng.2023.01.015","article-title":"Characterization and uncertainty analysis of volumetric error variation with temperature","volume":"81","author":"Ibabe","year":"2023","journal-title":"Precis. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.cirp.2018.04.008","article-title":"Integrated multilateration for machine tool automatic verification","volume":"67","author":"Mutilba","year":"2018","journal-title":"CIRP Ann."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.cirp.2021.04.025","article-title":"Machine tool integrated inverse multilateration uncertainty assessment for the volumetric characterisation and the environmental thermal error study of large machine tools","volume":"70","author":"Mutilba","year":"2021","journal-title":"CIRP Ann."},{"key":"ref_23","unstructured":"Ega\u00f1a, F., Yag\u00fce-Fabra, J.A., Mutilba, U., and Eguskiza, J. (June, January 30). The MIIM method for the environmental thermal error study of large machine tools: A real case study. Proceedings of the Euspen\u2019s 22nd International Conference & Exhibition, Geneva, Switzerland."},{"key":"ref_24","unstructured":"(2017). Testing and Calibration Laboratories (Standard No. ISO\/IEC-17025)."},{"key":"ref_25","first-page":"6909","article-title":"From the Traditional Multilateration to the Integrated Multilateration Approach: A Roadmap towards the Automatization of Volumetric Error Mapping Process for Large Machine Tools","volume":"2023","author":"Mutilba","year":"2023","journal-title":"MM Sci. J."},{"key":"ref_26","unstructured":"(2008). GUM 1995 with Minor Corrections. Evaluation of Measurement Data\u2014Guide to the Expression of Uncertainty in Measurement (Standard No. JCGM 100:2008)."},{"key":"ref_27","unstructured":"(2005). Test Code for Machine Tools\u2014Part 9: Estimation of Measurement Uncertainty for Machine Tool Tests according to Series ISO 230, Basic Equations (Standard No. ISO\/TR 230-9:2005)."},{"key":"ref_28","unstructured":"(2008). Evaluation of Measurement Data\u2014Supplement 1 to the \u201cGuide to the Expression of Uncertainty in measurement\u201d\u2014Propagation of Distributions Using a Monte Carlo Method (Standard No. JCGM 101:2008)."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"085111","DOI":"10.1063\/1.4928159","article-title":"Precision measurement of refractive index of air based on laser synthetic wavelength interferometry with Edl\u00e9n equation estimation","volume":"86","author":"Yan","year":"2015","journal-title":"Rev. Sci. Instrum."},{"key":"ref_30","unstructured":"(2022, September 05). Statistics and Machine Learning Toolbox\u2122 User\u2019s Guide. MathWorks, Inc. (Available Online with MathWorks Account). Available online: https:\/\/es.mathworks.com\/help\/stats\/index.html?s_tid=CRUX_topnav."},{"key":"ref_31","unstructured":"Jollife, I.T. (2002). Principal Component Analysis, Springer."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"20150202","DOI":"10.1098\/rsta.2015.0202","article-title":"Principal component analysis: A review and recent developments","volume":"374","author":"Jollife","year":"2016","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_33","unstructured":"Potdar, A.A., Longstaff, A.P., Fletcher, S., and Mian, S. (2015). Laser Metrology and Machine Performance XI, LAMDAMAP 2015, EUSPEN."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5429","DOI":"10.1007\/s00170-020-04932-8","article-title":"Sensor placement methodology for spindle thermal compensation of machine tools","volume":"106","author":"Tsai","year":"2020","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Li, Y., Shi, H., Ji, S., and Liang, F. (2021). Thermal Positioning Error Modeling of Servo Axis Based on Empirical Modeling Method. Micromachines, 12.","DOI":"10.3390\/mi12020201"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.1007\/s00170-022-09930-6","article-title":"Failure mode classification for condition-based maintenance in a bearing ring grinding machine","volume":"122","author":"Ahmer","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/7\/2380\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:25:09Z","timestamp":1760106309000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/7\/2380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,8]]},"references-count":36,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["s24072380"],"URL":"https:\/\/doi.org\/10.3390\/s24072380","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,8]]}}}