single-au.php

IJAT Vol.19 No.5 pp. 758-773
doi: 10.20965/ijat.2025.p0758
(2025)

Research Paper:

Comprehensive Analysis of Temperature-Sensitive Points Across Machine Tool Structures Using Highly Redundant Temperature Data and Sparse Modeling

Shun Tanaka*,† ORCID Icon, Toru Kizaki** ORCID Icon, Yuta Teshima** ORCID Icon, and Naohiko Sugita*,** ORCID Icon

*The Research into Artifacts, Center for Engineering, Graduate School of Engineering, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Corresponding author

**Department of Mechanical Engineering, Graduate School of Engineering, The University of Tokyo
Tokyo, Japan

Received:
January 31, 2025
Accepted:
June 9, 2025
Published:
September 5, 2025
Keywords:
CNC machine tools, thermal error compensation, temperature-sensitive points, large-scale array of temperature sensors interconnected in series, least absolute shrinkage and selection operator
Abstract

Thermal influences account for up to 75% of errors in precision machining, highlighting the critical requirement for effective thermal error compensation. In this study, we employed a large-scale array of temperature sensors interconnected in series together with least absolute shrinkage and selection operator (LASSO) regression to determine the optimal number and placement of temperature sensors for precise thermal error estimation. Temperature data from 307 points were collected under six operational patterns on a three-axis horizontal machining center and subjected to correlation analysis. Distinct correlation map trends emerged for each pattern, underscoring the difficulty of removing highly correlated coefficients. Further, by tuning the LASSO regularization parameter, we reduced the sensor count by 76% while keeping the root mean square error below 10 µm, thereby shifting the priority of sensor locations. These findings demonstrate a practical, data-driven pathway for deploying minimal yet highly informative sensor sets, enabling cost-effective and physically interpretable thermal error compensation in next generation precision machine tools.

Cite this article as:
S. Tanaka, T. Kizaki, Y. Teshima, and N. Sugita, “Comprehensive Analysis of Temperature-Sensitive Points Across Machine Tool Structures Using Highly Redundant Temperature Data and Sparse Modeling,” Int. J. Automation Technol., Vol.19 No.5, pp. 758-773, 2025.
Data files:
References
  1. [1] C. Liu, P. Zheng, and X. Xu, “Digitalisation and servitisation of machine tools in the era of Industry 4.0: A review,” Int. J. Prod. Res., Vol.61, No.12, pp. 4069-4101, 2023. https://doi.org/10.1080/00207543.2021.1969462
  2. [2] R. A. Laghari and S. Mekid, “Comprehensive approach toward IIoT based condition monitoring of machining processes,” Measurement, Vol.217, Article No.113004, 2023. https://doi.org/10.1016/j.measurement.2023.113004
  3. [3] G. Zhang, R. Ouyang, B. Lu, R. Hocken, R. Veale, and A. Donmez, “A displacement method for machine geometry calibration,” CIRP Ann., Vol.37, No.1, pp. 515-518, 1988. https://doi.org/10.1016/s0007-8506(07)61690-4
  4. [4] G. Zhang, R. Veale, T. Charlton, B. Borchardt, and R. Hocken, “Error compensation of coordinate measuring machines,” CIRP Ann., Vol.34, No.1, pp. 445-448, 1985. https://doi.org/10.1016/s0007-8506(07)61808-3
  5. [5] C. Hong and S. Ibaraki, “Observation of thermal influence on error motions of rotary axes on a five-axis machine tool by static R-test,” Int. J. Automation Technol., Vol.6, No.2, pp. 196-204, 2012. https://doi.org/10.20965/ijat.2012.p0196
  6. [6] H. Tachiya, H. Hirata, T. Ueno, Y. Kaneko, K. Nakagaki, and Y. Ishino, “Evaluation of and compensation for thermal deformation in a compact CNC lathe,” Int. J. Automation Technol., Vol.6, No.2, pp. 137-146, 2012. https://doi.org/10.20965/ijat.2012.p0137
  7. [7] K. Wegener, S. Weikert, and J. Mayr, “Age of compensation – challenge and chance for machine tool industry,” Int. J. Automation Technol., Vol.10, No.4, pp. 609-623, 2016. https://doi.org/10.20965/ijat.2016.p0609
  8. [8] M. Mareš, O. Horejš, and J. Hornych, “Thermal error minimization of a turning-milling center with respect to its multi-functionality,” Int. J. Automation Technol., Vol.14, No.3, pp. 475-483, 2020. https://doi.org/10.20965/ijat.2020.p0475
  9. [9] S. Ibaraki and K. Kawano, “On thermal positioning error of a planar robot arm over entire workspace,” Int. J. Automation Technol., Vol.17, No.5, pp. 504-511, 2023. https://doi.org/10.20965/ijat.2023.p0504
  10. [10] R. Ramesh, M. A. Mannan, and A. N. Poo, “Error compensation in machine tools – A review,” Int. J. Mach. Tools Manuf., Vol.40, No.9, pp. 1257-1284, 2000. https://doi.org/10.1016/s0890-6955(00)00010-9
  11. [11] J. Bryan, “International status of thermal error research (1990),” CIRP Ann., Vol.39, No.2, pp. 645-656, 1990. https://doi.org/10.1016/s0007-8506(07)63001-7
  12. [12] J. Mayr, J. Jedrzejewski, E. Uhlmann, M. Alkan Donmez, W. Knapp, F. Härtig, K. Wendt, T. Moriwaki, P. Shore, R. Schmitt, C. Brecher, T. Würz, and K. Wegener, “Thermal issues in machine tools,” CIRP Ann., Vol.61, No.2, pp. 771-791, 2012. https://doi.org/10.1016/j.cirp.2012.05.008
  13. [13] Y. Teshima, S. Tanaka, T. Kizaki, and N. Sugita, “Sensor placement strategy based on reduced-order models for thermal error estimation in machine tools,” CIRP J. Manuf. Sci. Technol., Vol.55, pp. 403-410, 2024. https://doi.org/10.1016/j.cirpj.2024.10.015
  14. [14] M. Gebhardt, M. Ess, S. Weikert, W. Knapp, and K. Wegener, “Phenomenological compensation of thermally caused position and orientation errors of rotary axes,” J. Manuf. Process., Vol.15, No.4, pp. 452-459, 2013. https://doi.org/10.1016/j.jmapro.2013.05.007
  15. [15] J. Mayr, M. Gebhardt, B. B. Massow, S. Weikert, and K. Wegener, “Cutting fluid influence on thermal behavior of 5-axis machine tools,” Procedia CIRP, Vol.14, pp. 395-400, 2014. https://doi.org/10.1016/j.procir.2014.03.085
  16. [16] B. Bossmanns and J. F. Tu, “A thermal model for high speed motorized spindles,” Int. J. Mach. Tools Manuf., Vol.39, No.9, pp. 1345-1366, 1999. https://doi.org/10.1016/s0890-6955(99)00005-x
  17. [17] R. Neugebauer, S. Ihlenfeldt, and C. Zwingenberger, “An extended procedure for convective boundary conditions on transient thermal simulations of machine tools,” Prod. Eng., Vol.4, No.6, pp. 641-646, 2010. https://doi.org/10.1007/s11740-010-0263-0
  18. [18] P. Hernandez-Becerro, J. Mayr, and K. Wegener, “Reduced thermo-mechanical model of a rotary table of a 5-axis precision machine tool,” ASPE Spring Topical Meeting Design and Control of Precision Mechatronic Systems (ASPE 2020) (virtual), 2020. https://doi.org/10.3929/ETHZ-B-000424410
  19. [19] X. Min, J. Shuyun, and C. Ying, “An improved thermal model for machine tool bearings,” Int. J. Mach. Tools Manuf., Vol.47, No.1, pp. 53-62, 2007. https://doi.org/10.1016/j.ijmachtools.2006.02.018
  20. [20] Y. Li, W. Zhao, S. Lan, J. Ni, W. Wu, and B. Lu, “A review on spindle thermal error compensation in machine tools,” Int. J. Mach. Tools Manuf., Vol.95, No.99, pp. 20-38, 2015. https://doi.org/10.1016/j.ijmachtools.2015.04.008
  21. [21] J. S. Chen, J. X. Yuan, J. Ni, and S. M. Wu, “Real-time compensation for time-variant volumetric errors on a machining center,” J. Eng. Ind., Vol.115, No.4, pp. 472-479, 1993. https://doi.org/10.1115/1.2901792
  22. [22] Z. Ge and X. Ding, “Thermal error control method based on thermal deformation balance principle for the precision parts of machine tools,” Int. J. Adv. Manuf. Technol., Vol.97, Nos.1-4, pp. 1253-1268, 2018. https://doi.org/10.1007/s00170-018-1992-z
  23. [23] X. Gao, Z. Qin, Y. Guo, M. Wang, and T. Zan, “Adaptive method to reduce thermal deformation of ball screws based on carbon fiber reinforced plastics,” Materials, Vol.12, No.19, Article No.3113, 2019. https://doi.org/10.3390/ma12193113
  24. [24] M. A. Donmez, M. H. Hahn, and J. A. Soons, “A novel cooling system to reduce thermally-induced errors of machine tools,” CIRP Ann., Vol.56, No.1, pp. 521-524, 2007. https://doi.org/10.1016/j.cirp.2007.05.124
  25. [25] X. Shi, K. Zhu, W. Wang, L. Fan, and J. Gao, “A thermal characteristic analytic model considering cutting fluid thermal effect for gear grinding machine under load,” Int. J. Adv. Manuf. Technol., Vol.99, Nos.5-8, pp. 1755-1769, 2018. https://doi.org/10.1007/s00170-018-2562-0
  26. [26] C.-W. Wu, C.-H. Tang, C.-F. Chang, and Y.-S. Shiao, “Thermal error compensation method for machine center,” Int. J. Adv. Manuf. Technol., Vol.59, Nos.5-8, pp. 681-689, 2012. https://doi.org/10.1007/s00170-011-3533-x
  27. [27] H. Yang and J. Ni, “Dynamic modeling for machine tool thermal error compensation,” J. Manuf. Sci. Eng., Vol.125, No.2, pp. 245-254, 2003. https://doi.org/10.1115/1.1557296
  28. [28] E.-M. Miao, Y.-Y. Gong, P.-C. Niu, C.-Z. Ji, and H.-D. Chen, “Robustness of thermal error compensation modeling models of CNC machine tools,” Int. J. Adv. Manuf. Technol., Vol.69, Nos.9-12, pp. 2593-2603, 2013. https://doi.org/10.1007/s00170-013-5229-x
  29. [29] C. Ma, H. Gui, and J. Liu, “Self learning-empowered thermal error control method of precision machine tools based on digital twin,” J. Intell. Manuf., Vol.34, No.2, pp. 695-717, 2023. https://doi.org/10.1007/s10845-021-01821-z
  30. [30] A. M. Abdulshahed, A. P. Longstaff, S. Fletcher, and A. Potdar, “Thermal error modelling of a gantry-type 5-axis machine tool using a Grey Neural Network Model,” J. Manuf. Syst., Vol.41, pp. 130-142, 2016. https://doi.org/10.1016/j.jmsy.2016.08.006
  31. [31] Y. Wang, Y. Cao, X. Qu, M. Wang, Y. Wang, and C. Zhang, “A review of the application of machine learning techniques in thermal error compensation for CNC machine tools,” Measurement, Vol.243, Article No.116341, 2025. https://doi.org/10.1016/j.measurement.2024.116341
  32. [32] Q. Cheng, Z. Qi, G. Zhang, Y. Zhao, B. Sun, and P. Gu, “Robust modelling and prediction of thermally induced positional error based on grey rough set theory and neural networks,” Int. J. Adv. Manuf. Technol., Vol.83, Nos.5-8, pp. 753-764, 2016. https://doi.org/10.1007/s00170-015-7556-6
  33. [33] Y. Liu, E. Miao, H. Liu, and Y. Chen, “Robust machine tool thermal error compensation modelling based on temperature-sensitive interval segmentation modelling technology,” Int. J. Adv. Manuf. Technol., Vol.106, Nos.1-2, pp. 655-669, 2020. https://doi.org/10.1007/s00170-019-04482-8
  34. [34] D. S. Lee, J. Y. Choi, and D.-H. Choi, “ICA based thermal source extraction and thermal distortion compensation method for a machine tool,” Int. J. Mach. Tools Manuf., Vol.43, No.6, pp. 589-597, 2003. https://doi.org/10.1016/s0890-6955(03)00017-8
  35. [35] S. Kumar and D. S. Srinivasu, “Optimal number of thermal hotspots selection on motorized milling spindle to predict its thermal deformation,” Mater. Today, Vol.62, pp. 3376-3385, 2022. https://doi.org/10.1016/j.matpr.2022.04.267
  36. [36] D. E. Farrar and R. R. Glauber, “Multicollinearity in regression analysis: The problem revisited,” Rev. Econ. Stat., Vol.49, No.1, pp. 92-107, 1967. https://doi.org/10.2307/1937887
  37. [37] E. Miao, Y. Liu, H. Liu, Z. Gao, and W. Li, “Study on the effects of changes in temperature-sensitive points on thermal error compensation model for CNC machine tool,” Int. J. Mach. Tools Manuf., Vol.97, pp. 50-59, 2015. https://doi.org/10.1016/j.ijmachtools.2015.07.004
  38. [38] N. Zimmermann, S. Lang, P. Blaser, and J. Mayr, “Adaptive input selection for thermal error compensation models,” CIRP Ann., Vol.69, No.1, pp. 485-488, 2020. https://doi.org/10.1016/j.cirp.2020.03.017
  39. [39] C. Chen, H. Dai, C. Lee, T. Hsieh, W. Hung, and W. Jywe, “The development of thermal error compensation on CNC machine tools by combining ridge parameter selection and backward elimination procedure,” Int. J. Adv. Manuf. Technol., Vol.130, Nos.5-6, pp. 2423-2442, 2024. https://doi.org/10.1007/s00170-023-12778-z
  40. [40] F. Tan, M. Yin, L. Wang, and G. Yin, “Spindle thermal error robust modeling using LASSO and LS-SVM,” Int. J. Adv. Manuf. Technol., Vol.94, Nos.5-8, pp. 2861-2874, 2018. https://doi.org/10.1007/s00170-017-1096-1
  41. [41] T. Kizaki, S. Tsujimura, Y. Marukawa, S. Morimoto, and H. Kobayashi, “Robust and accurate prediction of thermal error of machining centers under operations with cutting fluid supply,” CIRP Ann., Vol.70, No.1, pp. 325-328, 2021. https://doi.org/10.1016/j.cirp.2021.04.074
  42. [42] S. Tanaka, T. Kizaki, K. Tomita, S. Tsujimura, H. Kobayashi, and N. Sugita, “Robust thermal error estimation for machine tools based on in-process multi-point temperature measurement of a single axis actuated by a ball screw feed drive system,” J. Manuf. Process., Vol.85, pp. 262-271, 2023. https://doi.org/10.1016/j.jmapro.2022.11.037
  43. [43] R. Ramesh, M. A. Mannan, and A. N. Poo, “Thermal error measurement and modelling in machine tools,” Int. J. Mach. Tools Manuf., Vol.43, No.4, pp. 391-404, 2003. https://doi.org/10.1016/s0890-6955(02)00263-8
  44. [44] R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Series B Stat. Methodol., Vol.58, No.1, pp. 267-288, 1996. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Sep. 05, 2025