Skip to main content
SpringerLink
Log in

Integrated thermal error modeling and compensation of machine tool feed system using subtraction-average-based optimizer-based CNN-GRU neural network

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

A Correction to this article was published on 24 April 2024

This article has been updated

Abstract

The thermal error is a significant factor that influences the machining accuracy of machine tools, and error compensation is an economical and effective method for enhancing the accuracy of machine tools. However, establishing a precise thermal error prediction model is crucial for thermal error compensation. In this paper, the subtraction-average-based optimizer-based CNN-GRU neural network (SABO-CNN-GRU) is applied to integrated thermal error modeling. Through conducting a thermal characteristic experiment, temperature rise data and thermal error data were collected from the linear feed system of LXK300X helical groove CNC machine tool. The fuzzy c-means clustering and grey correlation analysis are employed to identify temperature-sensitive points in the linear feed system. By utilizing the temperature rise data from these sensitive points along with feed shaft thermal errors as data samples, and using the SABO algorithm to optimize the CNN-GRU prediction model, the thermal error prediction model of SABO-CNN-GRU is established. To validate its superiority and practicality, a comparative analysis is conducted with traditional thermal error prediction models based on CNN-GRU and SO-ELM. The results demonstrate that SABO-CNN-GRU model outperforms both models in terms of mean absolute error (MAE), root mean square error (RMSE), remaining prediction deviation (RPD), mean square error (MSE), and determination coefficient (R2) in accurately predicting results. Building upon this achievement, this paper develops a real-time thermal error compensation system which effectively reduces maximum thermal errors from 80.5 to 17.6 μm after implementing compensation measures. Effectively reducing the influence of thermal errors and improving the machining accuracy of machine tools.

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

Similar content being viewed by others

Change history

References

  1. Li Y, Zhao WH, Lan SH, Ni J, Wu WW, Lu BU (2015) A review on spindle thermal error compensation in machine tools. Int J Mach Tools Manufact 95:20–38

    Article  Google Scholar 

  2. Li Y, Yu ML, Bai YM, Hong ZY, Wu WW (2021) A review of thermal error modeling methods for machine tools. Appl Sci 11(11):5216

    Article  Google Scholar 

  3. Mayr J, Jedrzejewski J, Uhlmann E, Donmez MA, Knapp W, Haertig F, Wendt K, Moriwaki T, Shore P, Schmitt R, Brecher C, Wuerz T, Wegener K (2012) Thermal issues in machine tools. Cirp Ann manufact Technol 61(2):771–791

    Article  Google Scholar 

  4. Pang JW, Li S, Guo MT, Wang ZH, Xi JR, Yang XT (2012) Drilling of C/SiC composite micro holes with electroplated diamond bits. Diamond Abras Eng 61(2):771–791

    Google Scholar 

  5. Li C, Hu YX, Wei ZZ, Wu CJ, Peng YF, Zhang FH, Geng YQ (2024) Damage evolution and removal behaviors of GaN crystals involved in double-grits grinding. Int J Extreme Manufact 6(2):025103

    Article  Google Scholar 

  6. Piao YC, Li C, Hu YX, Cui HL, Luo XL, Geng YQ, Zhang FH (2024) Nanoindentation induced anisotropy of deformation and damage behaviors of MgF2 crystals. J Mater Res Technol 28:4615–4625

    Article  Google Scholar 

  7. Qu SS, Yao P, Gong YD, Chu DK, Yang YY, Li CW, Wang ZL, Zhang XP, Hou Y (2022) Environmentally friendly grinding of C/SiCs using carbon nanofluid minimum quantity lubrication technology. J Clean Product 366:132898

    Article  Google Scholar 

  8. Qu SS, Yao P, Gong YD, Yang YY, Chu DK, Zhu QS (2022) Modelling and grinding characteristics of unidirectional C-SiCs. Ceram Int 48:8314–8324

    Article  Google Scholar 

  9. Feng WL, Li ZH, Gu QY, Yang JG (2015) Thermally induced positioning error modelling and compensation based on thermal characteristic analysis. Int J Mach Tools Manufact 93:26–36

    Article  Google Scholar 

  10. Ramesh R, Manan MA, Poo AN (2000) Error compensation in machine tools-a review Part II: thermal errors. Int J Mach Tools Manufact 40(9):1257–1284

    Article  Google Scholar 

  11. Xu ZZ, Liu XJ, Choi CH, Lyu SK (2012) A study on improvement of ball screw system positioning error with liquid-cooling. Int J Precis Eng Manufact 13(12):2173–2181

    Article  Google Scholar 

  12. Sun LJ, Ren MJ, Hong HB, Yin YH (2017) Thermal error reduction based on thermodynamics structure optimization method for an ultra-precision machine tool. Int J Adv Manufact Technol 88(5-8):1267–1277

    Article  Google Scholar 

  13. Liang YC, Su H, Lu LH, Chen WQ, Sun YZ, Zhang P (2015) Thermal optimization of an ultra-precision machine tool by the thermal displacement decomposition and counteraction method. Int J Adv Manufact Technol 76(1-4):635–645

    Article  Google Scholar 

  14. Mori M, Mizuguchi H, Fujishima M, Ido Y, Mingkai N, Konishi K (2009) Design optimization and development of CNC lathe headstock to minimize thermal deformation. CIRP Ann Manufact Technol 58(1):331–334

    Article  Google Scholar 

  15. Tan F, Yin M, Wang L, Yin GF (2018) Spindle thermal error robust modeling using LASSO and LS-SVM. Springer London 94(5-8):2861-2874

  16. Chen TC, Chang CJ, Hung JP, Lee RM, Wang CC (2016) Real-time compensation for thermal errors of the milling machine. Appl Sci 6(4):101

    Article  Google Scholar 

  17. Liu JL, Ma C, Wang SL (2020) Data-driven thermally-induced error compensation method of high-speed and precision five-axis machine tools. Mechan system signal process 138:106538

    Article  Google Scholar 

  18. Guo QJ, Yang JG (2011) Application of projection pursuit regression to thermal error modeling of a CNC machine tool. Int J Adv Manufact Technol 55(5-8):623–629

    Article  Google Scholar 

  19. Zhang J, Li B, Zhou CX, Zhao WH (2016) Positioning error prediction and compensation of ball screw feed drive system with different mounting conditions. Proceed Instit Mechan Eng Part B-j Eng Manufact 230(12):2307–2311

    Article  Google Scholar 

  20. Tan F, Yin GF, Zheng K, Wang X (2021) Thermal error prediction of machine tool spindle using segment fusion LSSVM. Int J Adv Manufact Technol 116(1):99–114

    Article  Google Scholar 

  21. Shi H, Jiang CP, Yan ZZ, Tao T, Mei XS (2020) Bayesian neural network-based thermal error modeling of feed drive system of CNC machine tool. Int J Adv Manufact Technol 108:3031–3044

    Article  Google Scholar 

  22. Fu GQ, Gong HW, Gao HL, Gu TD, Cao ZQ (2019) Integrated thermal error modeling of machine tool spindle using a chicken swarm optimization algorithm-based radial basic function neural network. Int J Adv Manufact Technol 105(5-6):2039–2055

    Article  Google Scholar 

  23. Li B, Tian XT, Zhang M (2019) Thermal error modeling of machine tool spindle based on the improved algorithm optimized BP neural network. Int J Adv Manufact Technol 105(1-4):1497–1505

    Article  Google Scholar 

  24. Comesana MM, Febrero-Garrido L, Troncoso-Pastoriza F, Martinez-Torres J (2020) Prediction of building’s thermal performance using LSTM and MLP neural networks. Neural Netw Appl Sci 10(21):7439

    Google Scholar 

  25. Sajjad M, Khan ZA, Ullah A, Hussain T, Ullah W, Lee MY, Baik SW (2020) A novel CNN-GRU-based hybrid approach for short-term residential load forecasting. IEEE Access 8:143759–143768

    Article  Google Scholar 

  26. Wu LZ, Kong C, Hao XH, Chen W (2020) A short-term load forecasting method based on GRU-CNN hybrid neural network model. Mathemat Problems Eng 2020:1428104

    Google Scholar 

  27. Trojovský P, Dehghani M (2023) Subtraction-average-based optimizer: a new swarm-inspired metaheuristic algorithm for solving optimization problems. Biomimetics 8(2):149

    Article  Google Scholar 

  28. Li ZY, Li GL, Xu K, Tang XD, Dong X (2021) Temperature-sensitive point selection and thermal error modeling of spindle based on synthetical temperature information. Int J Adv Manufact Technol 113(3):1029–1043

    Article  Google Scholar 

  29. Guo QJ, Xu RF, Yang TY, He L, Cheng X, Li ZY, Yang JG (2016) Application of GRAM and AFSACA-BPN to thermal error optimization modeling of CNC machine tools. Int J Adv Manufact Technol 83(5-8):995–1002

    Article  Google Scholar 

  30. Miao EM, Gong YY, Dang LC, Miao JC (2014) Temperature-sensitive point selection of thermal error model of CNC machining center. Int J Adv Manufact Technol 74(5-8):681–691

    Article  Google Scholar 

  31. Pak U, Kim C, Ryu U, Sok K, Pak S (2018) A hybrid model based on convolutional neural networks and long short-term memory for ozone concentration prediction. Air Qual Atmosp Health 11(8):883–895

    Article  Google Scholar 

  32. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural comput 9(8):1735–1780

    Article  Google Scholar 

  33. Jia GJ, Zhang X, Wang XZ, Zhang XP, Huang ND (2023) A spindle thermal error modeling based on 1DCNN-GRU-Attention architecture under controlled ambient temperature and active cooling. Int J Adv Manufact Technol 127(3-4):1525–1539

    Article  Google Scholar 

  34. Yao Q, Lu DDC, Lei G A surface temperature estimation method for lithium-ion battery using enhanced GRU-RNN. IEEE Transact Transport Electrif 9(1):1103–1112

Download references

Funding

This research was supported by Project of Liaoning Province Applied Basic Research Program (Grant No. 2022JH2/101300214), General Project of Basic Scientific Research Projects for Higher Education Institutions of Liaoning Provincial Department of Education (Grant No. LJKMZ20220459), National Natural Science Foundation of China (Grant No. 52005346 and 52005347), Natural Science Foundation of Liaoning Province (Grant No. 2021-BS-149).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Shenyang University of Technology, NO.111 Shenliao West Road, Shenyang Economic and Technological Development District, Shenyang, 110870, People’s Republic of China

    Tongtong Yang, Xingwei Sun, Heran Yang, Yin Liu, Hongxun Zhao, Zhixu Dong & Shibo Mu

  2. Liaoning Province Key Laboratory of Complex Surface NC Manufacturing Technology, Shenyang University of Technology, NO.111 Shenliao West Road, Shenyang Economic and Technological Development District, Shenyang, 110870, People’s Republic of China

    Tongtong Yang, Xingwei Sun, Heran Yang, Yin Liu, Hongxun Zhao, Zhixu Dong & Shibo Mu

Authors
  1. Tongtong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingwei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Heran Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hongxun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhixu Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Shibo Mu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Tongtong Yang, Xingwei Sun and Heran Yang. The first draft of the manuscript was written by Tongtong Yang, Xingwei Sun and Yin Liu. Experimental tests were carried out by Hongxun Zhao, Zhixu Dong and Shibo Mu. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Heran Yang.

Ethics declarations

Conflicts of interest/Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

The authors consent to publish this article.

Additional information

Publisher’s note

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

The original online version of this article was revised: Figure 9 have the same image as in Figure 8 and has been revised.

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

Yang, T., Sun, X., Yang, H. et al. Integrated thermal error modeling and compensation of machine tool feed system using subtraction-average-based optimizer-based CNN-GRU neural network. Int J Adv Manuf Technol 131, 6075–6089 (2024). https://doi.org/10.1007/s00170-024-13369-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-024-13369-2

Keywords

Search

Navigation