Skip to main content
Log in

Thermal positioning error modeling of machine tools using a bat algorithm-based back propagation neural network

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

Abstract

Thermal error of a machine tool is one of the main reasons affecting the machining accuracy. Heat production and heat transfer of a machine tool are too complicated to predict the generated thermal error accurately. According to the nonlinear and time-varying characteristics of thermal error, the back propagation (BP) neural network is perfectly suitable for thermal error modeling, which has been extensively used to map the nonlinear relationship. However, traditional BP neural network usually has poor prediction performance under different operating conditions. Therefore, a new swarm intelligent optimization algorithm, bat algorithm (BA), is introduced to optimize BP neural network and improve its performance. The focus of this paper is the application of the combined algorithm (bat algorithm-based back propagation neural network) to solve the problem of thermal error modeling. Thermal positioning error experiments were conducted on a three-axis experiment bench. The experimental results show that thermal positioning error model built by BA-BP neural network is more stable and has high prediction accuracy and strong robustness, which can provide a candidate method for thermal error modeling.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Schwenke H, Knapp W, Haitjema H, Weckenmann A, Schmitt R, Delbressine F (2008) Geometric error measurement and compensation of machines—an update. CIRP Ann Manuf Technol 57(2):660–675. https://doi.org/10.1016/j.cirp.2008.09.008

    Article  Google Scholar 

  2. 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 

  3. Li Y, Zhao WH, Lan SH, Ni J, Wu WW, Lu BH (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. Ma C, Mei XS, Yang J, Zhao L, Shi H (2015) Thermal characteristics analysis and experimental study on the high-speed spindle system. Int J Adv Manuf Technol 79(1–4):469–489. https://doi.org/10.1007/s00170-015-6821-z

    Article  Google Scholar 

  5. Mian NS, Fletcher S, Longstaff AP, Myers A (2013) Efficient estimation by FEA of machine tool distortion due to environmental temperature perturbations. Precis Eng 37:372–379. https://doi.org/10.1016/j.precisioneng.2012.10.006

    Article  Google Scholar 

  6. Fan KG (2016) Research on the machine tool’s temperature spectrum and its application in a gear form grinding machine. Int J Adv Manuf Technol 90(9–12):3841–3850. https://doi.org/10.1007/s00170-016-9722-x

    Google Scholar 

  7. Chen JS, Yuan J, Ni J (1996) Thermal error modeling for real-time error compensation. Int J Adv Manuf Technol 12(4):266–275. https://doi.org/10.1007/BF01239613

    Article  Google Scholar 

  8. Wu CW, Tang CH, Chang CF, Shiao YS (2011) Thermal error compensation method for machine center. Int J Adv Manuf Technol 59(5–8):681–689. https://doi.org/10.1007/s00170-011-3533-x

    Google Scholar 

  9. Ramesh R, Mannan MA, Poo AN (2002) Support vector machines model for classification of thermal error in machine tools. Int J Adv Manuf Technol 20(2):114–120. https://doi.org/10.1007/s001700200132

    Article  Google Scholar 

  10. Miao EM, Gong YY, Niu PC, Ji CZ, Chen HD (2013) Robustness of thermal error compensation modeling models of CNC machine tools. Int J Adv Manuf Technol 69(9–12):2593–2603. https://doi.org/10.1007/s00170-013-5229-x

    Article  Google Scholar 

  11. Yang J, Zhang DS, Feng B, Mei XS, Hu ZB (2014) Thermal-induced errors prediction and compensation for a coordinate boring machine based on time series analysis. Math Probl Eng 2014:1–13. https://doi.org/10.1155/2014/784218

    Google Scholar 

  12. Dai H, Wang S, Xiong X (2017) Thermal error modelling of motorised spindle in large-sized gear grinding machine. Proc IMechE B J Eng Manuf 231(5):768–778. https://doi.org/10.1177/0954405417696335

    Article  Google Scholar 

  13. Zhang T, Ye WH, Shan YC (2016) Application of sliced inverse regression with fuzzy clustering for thermal error modeling of CNC machine tool. Int J Adv Manuf Technol 85(9):1–11. https://doi.org/10.1007/s00170-015-8135-6

    Google Scholar 

  14. Lei MH, Jiang GD, Yang J, Mei XS, Xia P, Zhao L (2017) Thermal error modeling with dirty and small training sample for the motorized spindle of a precision boring machine. Int J Adv Manuf Technol 2017:1–16. https://doi.org/10.1007/s00170-017-0531-7

    Google Scholar 

  15. Ma C, Zhao L, Mei XS, Shi H, Yang J (2016) Thermal error compensation of high-speed spindle system based on a modified BP neural network. Int J Adv Manuf Technol 85(9–12):1–11. https://doi.org/10.1007/s00170-016-9254-4

    Google Scholar 

  16. Huang YQ, Zhang J, Li X, Tian LG (2014) Thermal error modeling by integrating GA and BP algorithms for the high-speed spindle. Int J Adv Manuf Technol 71(9):1669–1675. https://doi.org/10.1007/s00170-014-5606-0

    Article  Google Scholar 

  17. Ma C, Zhao L, Mei XS, Shi H, Yang J (2017) Thermal error compensation based on genetic algorithm and artificial neural network of the shaft in the high-speed spindle system. Proc IMechE B J Eng Manuf 231(5):753–767. https://doi.org/10.1177/0954405416639893

    Article  Google Scholar 

  18. Guo QJ, Yang JG, Wu H (2010) Application of ACO-BPN to thermal error modeling of NC machine tool. Int J Adv Manuf Technol 50(5):667–675. https://doi.org/10.1007/s00170-010-2520-y

    Article  Google Scholar 

  19. 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 Manuf Technol 83(5):995–1002. https://doi.org/10.1007/s00170-015-7660-7

    Article  Google Scholar 

  20. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization[J]. IEEE T Evolut Comput 1(1):67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  21. Yang, XS (2010) A new metaheuristic bat-inspired algorithm. Nature Inspired Cooperative Strategies for Optimization Studies in Computational Intelligence, vol 284, pp 65–74 Springer, Berlin

  22. Chen JS, Yuan JX, Ni J, Wu SM (1993) Real-time compensation for time-variant volumetric errors on a machining center[J]. J Ind Eng 115(4):472–479. https://doi.org/10.1115/1.2901792

    Article  Google Scholar 

  23. Yan JY, Yang JG (2008) Application of synthetic grey correlation theory on thermal point optimization for machine tool thermal error compensation. Int J Adv Manuf Technol 43(11–12):1124–1132. https://doi.org/10.1007/s00170-008-1791-z

    Google Scholar 

  24. Han J, Wang LP, Cheng NB, Wang HT (2011) Thermal error modeling of machine tool based on fuzzy c-means cluster analysis and minimal-resource allocating networks. Int J Adv Manuf Technol 60(5–8):463–472. https://doi.org/10.1007/s00170-011-3619-5

    Google Scholar 

  25. Zhang T, Ye WH, Liang RJ, Lou PH, Yang XL (2013) Temperature variable optimization for precision machine tool thermal error compensation on optimal threshold. Chin J Mech Eng 26(1):158–165. https://doi.org/10.3901/cjme.2013.01.158

    Article  Google Scholar 

  26. Wang HT, Wang LP, Li TM, Han J (2013) Thermal sensor selection for the thermal error modeling of machine tool based on the fuzzy clustering method. Int J Adv Manuf Technol 69(1–4):121–126. https://doi.org/10.1007/s00170-013-4998-6

    Article  Google Scholar 

  27. Miao EM, Gong YY, Dang LC, Miao JC (2014) Temperature-sensitive point selection of thermal error model of CNC machining center. Int J Adv Manuf Technol 74(5–8):681–691. https://doi.org/10.1007/s00170-014-6009-y

    Google Scholar 

Download references

Acknowledgments

This work is supported by the National Key Basic Research and Development Program (973 Program) of China (grant no. 2011CB706702), Natural Science Foundation of China (grant no. 51135006 and 51305161), Jilin province science and technology development plan item (grant no. 20130101042JC).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ji Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Zhao, J. & Ji, S. Thermal positioning error modeling of machine tools using a bat algorithm-based back propagation neural network. Int J Adv Manuf Technol 97, 2575–2586 (2018). https://doi.org/10.1007/s00170-018-1978-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-018-1978-x

Keywords

Navigation