{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T21:02:17Z","timestamp":1762376537548,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,3,9]],"date-time":"2019-03-09T00:00:00Z","timestamp":1552089600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 107-2221-E-197-031","MOST 107-2622-E-197-007"],"award-info":[{"award-number":["MOST 107-2221-E-197-031","MOST 107-2622-E-197-007"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The internal temperature is an important index for the prevention and maintenance of a spindle. However, the temperature inside the spindle is undetectable directly because there is no space to embed a temperature sensor, and drilling holes will reduce its mechanical stiffness. Therefore, it is worthwhile understanding the thermal-feature of a spindle. This article presents a methodology to identify the thermal-feature model of an externally driven spindle. The methodology contains self-made hardware of the temperature sensing and wireless transmission module (TSWTM) and software for the system identification (SID); the TSWTM acquires the temperature training data, while the SID identifies the parameters of the thermal-feature model of the spindle. Then the resulting thermal-feature model is written into the firmware of the TSWTM to give it the capability of accurately calculating the internal temperature of the spindle from its surface temperature during the operation, or predicting its temperature at various speeds. The thermal-feature of the externally driven spindle is modeled by a linearly time-invariant state-space model whose parameters are identified by the SID, which integrates the command \u201cn4sid\u201d provided by the System ID Toolbox of MATLAB and the k-fold cross-validation that is common in machine learning. The present SID can effectively strike a balance between the bias and variance of the model, such that both under-fitting and over-fitting can be avoided. The resulting thermal-feature model can not only predict the temperature of the spindle rotating at various speeds but can also calculate the internal temperature of the spindle from its surface temperature. Its validation accuracy is higher than 98.5%. This article illustrates the feasibility of accurately calculating the internal temperature (undetectable directly) of the spindle from its surface temperature (detectable directly).<\/jats:p>","DOI":"10.3390\/s19051209","type":"journal-article","created":{"date-parts":[[2019,3,12]],"date-time":"2019-03-12T03:49:31Z","timestamp":1552362571000},"page":"1209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Thermal-Feature System Identification for a Machine Tool Spindle"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0183-8182","authenticated-orcid":false,"given":"Yuh-Chung","family":"Hu","sequence":"first","affiliation":[{"name":"Department of Mechanical and Electro-Mechanical Engineering, National ILan University, Yilan 26047, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping-Jung","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Applied Mechanics, National Taiwan University, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pei-Zen","family":"Chang","sequence":"additional","affiliation":[{"name":"Institute of Applied Mechanics, National Taiwan University, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"771","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_2","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1016\/S0890-6955(00)00010-9","article-title":"Error compensation in machine tools\u2014A review. Part II: Thermal errors","volume":"40","author":"Ramesh","year":"2000","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1016\/S0890-6955(99)00005-X","article-title":"A thermal model for high speed motorized spindles","volume":"39","author":"Bossmanns","year":"1999","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1115\/1.1349555","article-title":"A power flow model for high speed motorized spindles\u2014Heat generation characterization","volume":"123","author":"Bossmanns","year":"2001","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.applthermaleng.2015.04.064","article-title":"Simulation and experimental study on the thermally induced deformations of high-speed spindle system","volume":"86","author":"Ma","year":"2015","journal-title":"Appl. Therm. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1007\/s00170-014-6519-7","article-title":"Mathematical modeling and experimental testing of high-speed spindle behavior","volume":"77","author":"Zivkovic","year":"2015","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/23080477.2016.1214062","article-title":"An Experimental and Numerical Study of the Thermal Issues of a High-speed Built-in Motor Spindle","volume":"4","author":"Huang","year":"2016","journal-title":"Smart Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"73","DOI":"10.4236\/eng.2015.72007","article-title":"Thermal behavior of externally driven spindle: Experimental study and modelling","volume":"7","author":"Brecher","year":"2015","journal-title":"Engineering"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Lo, Y.-C., Hu, Y.-C., and Chang, P.-Z. (2018). Parameter estimation of the thermal network model of a machine tool spindle by self-made Bluetooth temperature sensor module. Sensors, 18.","DOI":"10.3390\/s18020656"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1080\/13873950600605250","article-title":"Modelling and system identification of active magnetic bearing systems","volume":"13","author":"Cho","year":"2007","journal-title":"Math. Comput. Model. Dyn. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Eguia, T.J.A., Shen, R., Tan, S.X., Pacheco, E.H., and Tirumala, M. (2009, January 20\u201323). Architecture level thermal modeling for multi-core systems using subspace system method. Proceedings of the IEEE 8th International Conference on ASICON\u201909, Changsha, China.","DOI":"10.1109\/ASICON.2009.5351305"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1109\/63.76809","article-title":"Thermal parameter estimation using recursive identification","volume":"6","author":"Skibinski","year":"1991","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kerezov, A., Kulkarni, A., and Nihtianov, S. (2015, January 9\u201312). Wireless temperature sensor for harsh industrial environments. Proceedings of the IECON 2015-41st Annual Conference of the IEEE Industrial Electronics Society, Yokohama, Japan.","DOI":"10.1109\/IECON.2015.7392721"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Qian, Y., Luo, Z., Liu, Z., Zhao, H., Li, C., Song, Y., Nan, D., and Wei, J. (2014, January 18\u201320). Application of rtd sensor in the real time measurement and wireless transmission. Proceedings of the 2014 Fourth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC), Harbin, China.","DOI":"10.1109\/IMCCC.2014.140"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1177\/0954405414567929","article-title":"Review of industrial temperature measurement technologies and research priorities for the thermal characterisation of the factories of the future","volume":"230","author":"Maropoulos","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part B J. Eng. Manuf."},{"key":"ref_16","first-page":"439","article-title":"An examination and validation of the theoretical resistivity-temperature relationship for conductors","volume":"7","author":"Lacy","year":"2013","journal-title":"World Acad. Sci. Eng. Technol. Int. J. Electr. Comput. Energ. Electron. Commun. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zvizdi\u0107, D., and \u0160estan, D. (2013). Hysteresis of thin film iprts in the range 100 c to 600 c. AIP Conf. Proc., 445\u2013450.","DOI":"10.1063\/1.4819582"},{"key":"ref_18","unstructured":"Analog Devices (2019, January 02). Datasheet of ADG1606\/ADG1607 4.5\u03a9 RON, 16-Channel, Differential 8-Channel, \u00b15 v, +12 v, +5 v, and +3.3 v Multiplexer. Available online: http:\/\/pdf1.alldatasheet.com\/datasheet-pdf\/view\/310835\/AD\/ADG1606.html."},{"key":"ref_19","unstructured":"Analog Devices (2019, January 02). Datasheet of AD7794\/AD7795 6-Channel, Low Noise, Low Power, 24-\/16-bit \u2211-\u0394 ADC with On-Chip In-Amp and Reference. Available online: https:\/\/www.analog.com\/media\/en\/technical-documentation\/data-sheets\/ad7794_7795.pdf."},{"key":"ref_20","unstructured":"(2019, January 02). 1502A Thermometer Readout User\u2019s Guide. Available online: https:\/\/cdn.testequity.com\/documents\/pdf\/1502A-ug.pdf."},{"key":"ref_21","unstructured":"Tangirala, A.K. (2014). Principles of System Identification: Theory and Practice, CRC Press."},{"key":"ref_22","unstructured":"Ljung, L. (1987). System Identification: Theory for the User, Prentice-Hall."},{"key":"ref_23","first-page":"1","article-title":"Automatic control systems","volume":"2","author":"Golnaraghi","year":"2010","journal-title":"Complex Var."},{"key":"ref_24","unstructured":"Ljung, L. (1995). System Identification Toolbox: User\u2019s Guide, Citeseer."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1214\/09-SS054","article-title":"A survey of cross-validation procedures for model selection","volume":"4","author":"Arlot","year":"2010","journal-title":"Stat. Surv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s11222-009-9153-8","article-title":"Estimation of prediction error by using k-fold cross-validation","volume":"21","author":"Fushiki","year":"2011","journal-title":"Stat. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/S1526-6125(07)70111-1","article-title":"Model-based design of motorized spindle system to improve dynamic performance at high speed","volume":"9","author":"Lin","year":"2007","journal-title":"J. Manuf. Process."},{"key":"ref_28","first-page":"1","article-title":"Thermal-mechanical behavior analysis of motorized spindle based on a coupled model","volume":"10","author":"Liu","year":"2018","journal-title":"Adv. Mech. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1209\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:37:38Z","timestamp":1760186258000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,9]]},"references-count":28,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19051209"],"URL":"https:\/\/doi.org\/10.3390\/s19051209","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,3,9]]}}}