Thermal error modeling of machine tool spindle based on the improved algorithm optimized BP neural network

  • Bo Li
  • Xitian TianEmail author
  • Min Zhang


Thermal error of the machine tool spindle is one of the main factors affecting the machining accuracy. For the complex operating environment of the machine tool, the difficulty of thermal error prediction modeling, and the low accuracy of the traditional thermal error prediction model, a spindle thermal error prediction model based on the improved particle swarm optimization (IPSO) optimize back propagation (BP) neural network is established in this paper. The temperature measurement points are clustered by SOM neural network, and the correlation analysis method is used to explore the correlation between the thermal sensitive points and the thermal error of the spindle. The S-type function is used to improve the inertia weight coefficient of the IPSO algorithm so as to improve the particle optimization effect. IPSO is used to optimize the parameters of BP neural network, such as the initial weights and thresholds. Compared with the GA-BP prediction model, the modeling efficiency, robustness, and accuracy of IPSO-BP neural network prediction model are all superior GA-BP prediction model. Taking the thermal error of the electric spindle of precision CNC machining center as the research object, the intelligent temperature sensor and the laser displacement sensor are used to obtain the machine tool temperature values and the spindle thermal error values. The prediction accuracy of the GA-BP model for the spindle thermal error was 93.1%, and the prediction accuracy of the IPSO-BP model was 96.5%. The results show that the IPSO-BP model can accurately predict the thermal error of the spindle under different working conditions. The model can obtain higher thermal error prediction accuracy and is more suitable for the thermal error compensation model.


Thermal error Artificial neural network IPSO-BP neural network CNC machine 



  1. 1.
    Ramesh R, Mannan MA, Poo AN (2000) Error compensation in machine tools-a review Part II: Thermal Errors. Int J Mach Tool Manu 40(9):1257–1284CrossRefGoogle Scholar
  2. 2.
    Bryan J (1990) International status of thermal error research. CIRP Ann Manuf Technol 39(2):645–656CrossRefGoogle Scholar
  3. 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 Tool Manu 95:20–38CrossRefGoogle Scholar
  4. 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):469–489CrossRefGoogle Scholar
  5. 5.
    Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8(3):240–255CrossRefGoogle Scholar
  6. 6.
    Chang BCH, Ratnaweera A, Halgamuge SK, Watson HC (2004) Particle swarm optimisation for protein motif discovery. Genet Program Evolvable Mach 5(2):203–214CrossRefGoogle Scholar
  7. 7.
    Wang HT, Li TM, Wang LP, Li FC (2015) Overview of thermal error modeling of machine tools. J Eng Mech 51(09):119–128CrossRefGoogle Scholar
  8. 8.
    Ma C, Zhao L, Mei XS, Shi H, Yang J (2017) Thermal error compensation of high-speed spindle system based on a modified BP neural network. Int J Adv Manuf Technol 89(9):3071–3085CrossRefGoogle Scholar
  9. 9.
    Liang XK, He ZJ (2013) Thermal error modeling of CNC machine tools based on fuzzy RBF neural network. Mach Des Res 29(5):71–74Google Scholar
  10. 10.
    Yang J, Shi H, Feng B, Zhao L, Ma C, Mei XS (2015) Thermal error modeling and compensation for a high-speed motorized spindle. Int J Adv Manuf Technol 77(5):1005–1017CrossRefGoogle Scholar
  11. 11.
    Guo QJ, Fan S, Xu RF, Cheng X, Zhao GY, Yang JG (2017) Spindle thermal error optimization modeling of a five-axis machine tool. Chin J Mech Eng 30(3):746–753CrossRefGoogle Scholar
  12. 12.
    Zhang Y, Yang JG, Jiang H (2012) Machine tool thermal error modeling and prediction by grey neural network. Int J Adv Manuf Technol 59(9):1065–1072CrossRefGoogle Scholar
  13. 13.
    Wilamowski BM (2009) Neural network architectures and learning algorithms. IEEE Ind Electron Mag 3(4):56–63CrossRefGoogle Scholar
  14. 14.
    Azorin-Lopez J, Saval-Calvo M, Fuster-Guillo A, Garcia-Rodriguez J, Mora-Mora H (2017) Constrained self-organizing feature map to preserve feature extraction topology. Neural Comput Applic 28(1):439–459CrossRefGoogle Scholar
  15. 15.
    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 Inst Mech Eng B J Eng 231(5):753–767CrossRefGoogle Scholar
  16. 16.
    Ma TH, Jiang L (2018) Modeling of thermal error of machine tools based on BP neural network optimized by hybrid particle swarm optimization algorithm. Chin J Construction Mach 16(03):221–224+230Google Scholar
  17. 17.
    Chao KH, Liao BJ, Hung CP (2013) Applying a cerebellar model articulation controller neural network to a photovoltaic power generation system fault diagnosis. Int J Photoenergy 2013(1):2–11Google Scholar
  18. 18.
    Gen M, Cheng R (2000) Genetic algorithms and engineering optimization. John Wiley & Sons, New YorkGoogle Scholar
  19. 19.
    Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. Proc 1st Int Conf Pittsburgh/PA 1985:93–100Google Scholar
  20. 20.
    Maddahi Y, Liao S, Fung WK, Sephri N (2016) Position referenced force augmentation in teleoperated hydraulic manipulators operating under delayed and lossy networks: a pilot study. Robot Auton Syst 83(5):231–242CrossRefGoogle Scholar

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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Institute of Intelligent ManufacturingNorthwestern Polytechnical UniversityXi’anChina

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