Skip to main content
SpringerLink
Log in

A thermal error modeling method for CNC lathes based on thermal distortion decoupling and nonlinear programming

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

CNC lathes often use hydraulic systems or motors to lock the turret, which causes the turret to have a high temperature rise and a large thermal deformation. The traditional measuring method couples the thermal distortions of the spindle and the turret together, which is not conducive to establishing the thermal error model. To solve this problem, a new measuring method was used in this research to decouple the thermal linear and angular distortions of the spindle and the turret. In addition, constraints on the model coefficients were proposed by studying the effects of long-term and short-term variations in ambient temperature on the thermal deformation of machine tools, thus transforming the thermal deformation modeling of the spindle and turret into nonlinear programming problems. After building the thermal deformation models of the spindle and the turret, the thermal distortion model of the whole machine tool was obtained by combining them. Finally, three experiments were designed to verify the validity of the established models, and the models were compared with those established using conventional methods. The experimental results showed that the models built based on thermal distortion decoupling and nonlinear programming had higher accuracy and robustness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Data availability

Not applicable.

Code availability

Not applicable.

References

  1. Bryan J (1990) International status of thermal error research. CIRP Ann Manuf Technol 39(2):645–656. https://doi.org/10.1016/s0007-8506(07)63001-7

    Article  Google Scholar 

  2. Mayr J, Jedrzejewski J, Uhlmann E, Alkan Donmez M, Knapp W, Härtig F, Wendt K, Moriwaki T, Shore P, Schmitt R, Brecher C, Würz T, Wegener K (2012) Thermal issues in machine tools. CIRP Ann Manuf Technol 61(2):771–791. https://doi.org/10.1016/j.cirp.2012.05.008

    Article  Google Scholar 

  3. Li Y, Zhao W, Lan S, Ni J, Wu W, Lu B (2015) A review on spindle thermal error compensation in machine tools. Int J Mach Tools Manuf 95:20–38. https://doi.org/10.1016/j.ijmachtools.2015.04.008

    Article  Google Scholar 

  4. Ge Z, Ding X (2018) Design of thermal error control system for high-speed motorized spindle based on thermal contraction of CFRP. Int J Mach Tools Manuf 125:99–111. https://doi.org/10.1016/j.ijmachtools.2017.11.002

    Article  Google Scholar 

  5. Grama SN, Mathur A, Badhe AN (2018) A model-based cooling strategy for motorized spindle to reduce thermal errors. Int J Mach Tools Manuf 132:3–16. https://doi.org/10.1016/j.ijmachtools.2018.04.004

    Article  Google Scholar 

  6. Weng L, Gao W, Zhang D, Huang T, Liu T, Li W, Zheng Y, Shi K, Chang W (2021) Analytical modelling method for thermal balancing design of machine tool structural components. Int J Mach Tools Manuf 164:1–20. https://doi.org/10.1016/j.ijmachtools.2021.103715

    Article  Google Scholar 

  7. Yue H, Guo C, Li Q, Zhao L, Hao G (2020) Thermal error modeling of CNC milling machine tool spindle system in load machining: based on optimal specific cutting energy. J Braz Soc Mech Sci Eng 42(9):456. https://doi.org/10.1007/s40430-020-02538-5

    Article  Google Scholar 

  8. Zimmermann N, Lang S, Blaser P, Mayr J (2020) Adaptive input selection for thermal error compensation models. CIRP Ann Manuf Technol 69(1):485–488. https://doi.org/10.1016/j.cirp.2020.03.017

    Article  Google Scholar 

  9. Liu H, Miao E, Wei X, Zhuang X (2017) Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm. Int J Mach Tools Manuf 113:35–48. https://doi.org/10.1016/j.ijmachtools.2016.11.001

    Article  Google Scholar 

  10. Miao E, Liu Y, Liu H, Gao Z, Li W (2015) Study on the effects of changes in temperature-sensitive points on thermal error compensation model for CNC machine tool. Int J Mach Tools Manuf 97:50–59. https://doi.org/10.1016/j.ijmachtools.2015.07.004

    Article  Google Scholar 

  11. Yan Z, Tao T, Du H, Shi H, Mei X (2022) An experiment-based multi-objective modeling method for thermal errors of slant bed CNC lathes. Int J Adv Manuf Technol 120(9-10):6565–6583. https://doi.org/10.1007/s00170-022-09158-4

    Article  Google Scholar 

  12. Liu J, Ma C, Wang S (2020) Data-driven thermally-induced error compensation method of high-speed and precision five-axis machine tools. Mech Syst Signal Process 138. https://doi.org/10.1016/j.ymssp.2019.106538

  13. Hu J, Zhou Z, Liu Q, Lou P, Yan J, Li R (2019) Key point selection in large-scale FBG temperature sensors for thermal error modeling of heavy-duty CNC machine tools. Front Mech Eng 14(4):442–451. https://doi.org/10.1007/s11465-019-0543-0

    Article  Google Scholar 

  14. Guo Q, Fan S, Xu R, Cheng X, Zhao G, Yang J (2017) Spindle thermal error optimization modeling of a five-axis machine tool. Chin J Mech Eng 30(3):746–753. https://doi.org/10.1007/s10033-017-0098-0

    Article  Google Scholar 

  15. Liu J, Ma C, Gui H, Wang S (2021) Thermally-induced error compensation of spindle system based on long short term memory neural networks. Appl Soft Comput 102:1–19. https://doi.org/10.1016/j.asoc.2021.107094

    Article  Google Scholar 

  16. Liu P, Du Z, Li H, Deng M, Feng X, Yang J (2021) Thermal error modeling based on BiLSTM deep learning for CNC machine tool. Adv Manuf 9(2):235–249. https://doi.org/10.1007/s40436-020-00342-x

    Article  Google Scholar 

  17. Miao E, Gong Y, Xu Z, Zhou X (2015) Comparative analysis of thermal error compensation model robustness of CNC machine tools. Journal of. Mech Eng 51(7). https://doi.org/10.3901/jme.2015.07.130

  18. Abdulshahed AM, Longstaff AP, Fletcher S (2017) A cuckoo search optimisation-based grey prediction model for thermal error compensation on CNC machine tools. Grey Syst: Theory Appl 7(2):146–155. https://doi.org/10.1108/gs-08-2016-0021

    Article  Google Scholar 

  19. Abdulshahed AM, Longstaff AP, Fletcher S, Potdar A (2016) Thermal error modelling of a gantry-type 5-axis machine tool using a Grey Neural Network Model. J Manuf Syst 41:130–142. https://doi.org/10.1016/j.jmsy.2016.08.006

    Article  Google Scholar 

  20. Liu J, Ma C, Gui H, Wang S (2022) Transfer learning-based thermal error prediction and control with deep residual LSTM network. Knowl-Based Syst 237:107704. https://doi.org/10.1016/j.knosys.2021.107704

    Article  Google Scholar 

  21. Liu K, Liu H, Li T, Liu Y, Wang Y (2019) Intelligentization of machine tools: comprehensive thermal error compensation of machine-workpiece system. Int J Adv Manuf Technol 102(9-12):3865–3877. https://doi.org/10.1007/s00170-019-03495-7

    Article  Google Scholar 

  22. Liu K, Song L, Han W, Cui Y, Wang Y (2022) Time-varying error prediction and compensation for movement axis of CNC machine tool based on digital twin. IEEE Trans Ind Inform 18(1):109–118. https://doi.org/10.1109/tii.2021.3073649

    Article  Google Scholar 

  23. Mareš M, Horejš O, Havlík L (2020) Thermal error compensation of a 5-axis machine tool using indigenous temperature sensors and CNC integrated Python code validated with a machined test piece. Precision Eng 66:21–30. https://doi.org/10.1016/j.precisioneng.2020.06.010

    Article  Google Scholar 

  24. Yang Y, Du Z, Feng X, Yang J (2021) Real-time thermal modelling approach of a machine tool spindle based on bond graph method. Int J Adv Manuf Technol 113(1-2):99–115. https://doi.org/10.1007/s00170-021-06611-8

    Article  Google Scholar 

  25. Dai Y, Zhan S, Wang J, Xuan L, Wang G (2021) Thermal error modeling of motorized spindle under variable pressure preload based on the bonding graph method. Chin J Sci Instrum 42(5):42–48. https://doi.org/10.19650/j.cnki.cjsi.J2107533

    Article  Google Scholar 

  26. Yang J, Yuan J, Ni J (1999) Thermal error mode analysis and robust modeling for error compensation on a CNC turning center. Int J Mach Tools Manuf 39(9):1367–1381

    Article  Google Scholar 

  27. Hou R, Du H, Yan Z, Yu W, Tao T, Mei X (2019) The modeling method on thermal expansion of CNC lathe headstock in vertical direction based on MOGA. Int J Adv Manuf Technol 103(2):3629–3641. https://doi.org/10.1007/s00170-019-03728-9

    Article  Google Scholar 

Download references

Funding

This research is financially supported by the National Key Research and Development Program of China (Grant No. 2018YFB1701205).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Xi’an Jiaotong University, Xianning West Road, Xi’an, 710049, People’s Republic of China

    Hongyang Du, Gedong Jiang, Tao Tao, Ruisheng Hou, Zongzhuo Yan & Xuesong Mei

  2. State Key Laboratory for Manufacturing Systems Engineering, Xianning West Road, Xi’an, 710049, People’s Republic of China

    Hongyang Du, Gedong Jiang, Tao Tao & Zongzhuo Yan

  3. School of Mechanical and Equipment Engineering, Hebei University of Engineering, Taiji Road, Handan, 056038, People’s Republic of China

    Ruisheng Hou

  4. Shaanxi Key Laboratory of Intelligent Robots, Xianning West Road, Xi’an, 710049, People’s Republic of China

    Xuesong Mei

Authors
  1. Hongyang Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gedong Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tao Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ruisheng Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zongzhuo Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xuesong Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Hongyang Du: methodology, writing; Gedong Jiang: data analysis; Tao Tao: funding acquisition, supervision; Ruisheng Hou: software; Zongzhuo Yan: validation; Xuesong Mei: conceptualization, supervision.

Corresponding author

Correspondence to Tao Tao.

Ethics declarations

Ethics approval

The article follows the guidelines of the Committee on Publication Ethics (COPE) and involves no studies on human or animal subjects.

Consent to participate

All authors voluntarily consent to participate in this research.

Consent for publication

All authors consent to publish this article.

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, H., Jiang, G., Tao, T. et al. A thermal error modeling method for CNC lathes based on thermal distortion decoupling and nonlinear programming. Int J Adv Manuf Technol 128, 2599–2612 (2023). https://doi.org/10.1007/s00170-023-12038-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-12038-0

Keywords

Search

Navigation