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Thermal error prediction of motorized spindle for five-axis machining center based on analytical modeling and BP neural network

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Abstract

To ensure the stability of precision of the motorized spindle for five-axis machining center, the thermal error of five-axis machining center was investigated, and the temperature rise-thermal deformation model of a thin-wall ring type rotary elastomer was built on the basis of thermo-elastic property. Thus, a model of radial thermal error was con-structed. The relationship between radial error and axial error was also investigated in this paper and the total radial errors were gotten. In addition, the thermal error of the motorized spindle of five-axis machining center was measured by the ball bar in the experiment of thermal error. The motorized spindle total radial error was achieved by this experiment and radial total error analytical model. Finally, a BP neural network algorithm was introduced for thermal error prediction of five-axis machining center, and the precision of prediction of these models was compared and analyzed. The analysis shows that this method is practical and effective.

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Abbreviations

σ r :

Radial normal stress

σ θ :

Radian normal stress; is shear stress.

E :

Elastic modulus of the material

μ :

Poisson ratio of the material

α :

Linear expansion coefficient of the material

μ 1 :

Bearing’s radial thermal error

μ 2 :

Radial thermal error caused by axial deformation

Δ :

Axial thermal error

μ r :

Radial total thermal error

δ X :

x direction measurement thermal error

δ y :

y direction measurement thermal error

δ z :

z direction measurement thermal error

References

  1. Y. Li, W. Zhao and S. Lan, A review on spindle thermal error compensation in machine tools, Int. J. Mach. Tools & Manuf., 95 (2015) 20–38.

    Article  Google Scholar 

  2. B. Bossmanns and J. F. Tu, A thermal model for high speed motorized spindles, Int. J. Mach. Tools & Manuf., 39(9) (1990) 1345–1366.

    Article  Google Scholar 

  3. J. Lee, D. H. Kim and C. M. Lee, A study on the thermal characteristics and experiments of high-speed spindle for machine tools, International J. of Precision Eng. and Manuf., 16(2) (2015) 293–299.

    Article  Google Scholar 

  4. Z. F. Liu, M. H. Pan and A. P. Zhang, Thermal characteristic analysis of high-speed motorized spindle system based on thermal contact resistance and thermal-conduction resistance, Int. J. Adv. Manuf. Technol., 76(9) (2015) 1913–1926.

    Article  Google Scholar 

  5. A. Zivkovic, M. Zeljkovic and S. Tabakovic, Mathematical modeling and experimental testing of high-speed spindle behavior, Int. J. Adv. Manuf. Technol., 77(5) (2015) 107–1086.

    Google Scholar 

  6. H. Su, L. Lu and Y. Liang, Thermal analysis of the hydrostatic spindle system by the finite volume element method, Int. J. Adv. Manuf. Technol., 71(9–12) (2014) 1949–1959.

    Article  Google Scholar 

  7. C. Ma, J. Yang and L. Zhao, Simulation and experimental study on the thermally induced deformations of high-speed spindle system, Applied Thermal Engineering, 86 (2015) 251–268.

    Article  Google Scholar 

  8. C. Ma, X. Mei and J. Yang, Thermal characteristics analysis and experimental study on the high-speed spindle system, J. of Zhejiang University, 79(1–4) (2015) 469–489.

    Google Scholar 

  9. Y. Li, W. Zhao, W. Wu and B. Lu, Boundary conditions optimization of spindle thermal error analysis and thermal key points selection based on inverse heat conduction, Int. J. Adv. Manuf. Technol., 90(9–12) (2017) 2803–2812.

    Article  Google Scholar 

  10. Y. Cui, H. Li, T. Li and L. Chen, An accurate thermal performance modeling and simulation method for motorized spindle of machine tool based on thermal contact resistance analysis, Int. J. Adv. Manuf. Technol., 96(2) (2018) 1–13.

    Google Scholar 

  11. L. Zhang, W. Gong, K. Zhang, Y. Wu, D. An and H. Shi, Thermal deformation prediction of high-speed motorized spindle based on biogeography optimization algorithm, Int. J. Adv. Manuf. Technol., 97(5–8) (2018) 1–11.

    Google Scholar 

  12. Z. F. Liu, M. H. Pan, A. P. Zhang, Y. S. Zhao, Y. Yang and C. Y. Ma, Thermal characteristic analysis of high-speed motorized spindle system based on thermal contact resistance and thermalconduction resistance, Int. J. Adv. Manuf. Technol., 76 (2015) 1913–1926.

    Article  Google Scholar 

  13. T. Liu, W. G. Gao, D. W. Zhang, Y. F. Zhang, W. F. Chang, C. M. Liang and Y. L. Tian, Analytical modeling for thermal errors of motorized spindle unit, Int. J. Mach. Tool Manu., 112 (2016) 53–70.

    Article  Google Scholar 

  14. Q. Li and H. Li, A general method for thermal error measurement and modeling in CNC machine tools’ spindle, Int. J. Adv. Manuf. Technol., 103(5–8) (2019) 2739–2749.

    Article  Google Scholar 

  15. A. Statham, Assessing the thermal distortion caused by spindle rotation of a machining centre using the draft standard ISO/DIS 230-3, Laser Metrology & Machine Performance III (2014).

  16. Z. S. Yan, W. H. Lin and C. H. Liu, Measurement of the thermal elongation of high speed spindles in real time using a cat’s eye reflector based optical sensor, Sensors & Actuators A Physical, 221(10) (2015) 154–160.

    Article  Google Scholar 

  17. K. Liu, T. Li, H. Liu, Y. Liu and Y. Wang, Analysis and prediction for spindle thermal bending deformations of a vertical milling machine, IEEE Transactions on Industrial Informatics, 16(3) (2020) 1549–1558.

    Article  Google Scholar 

  18. X. Qi, D. Zhang and H. Zhang, The control system design of thermal experimental platform for high-speed spindle based PLC, International Conference on Digital Manufacturing & Automation, IEEE Computer Society (2010) 639–642.

  19. H. Lu, Q. Wu and S. Wu, A new spindle rotation error measurement system based on three point method, Conference on Industrial Electronics and Applications, IEEE (2016) 2003–2008.

  20. S. D. Ashok and G. L. Samuel, Modeling, measurement, and evaluation of spindle radial errors in a miniaturized machine tool, Int. J. Adv. Manuf. Technol., 59(5–8) (2012) 445–461.

    Article  Google Scholar 

  21. C. W. Wu, C. F. Chang and Y. S. Shiao, Thermal error compensation method for machine center, Int. J. Adv. Manuf. Technol., 59(5–8) (2012) 681–689.

    Article  Google Scholar 

  22. Y. Li, W. Zhao and W. Wu, Thermal error modeling of the spindle based on multiple variables for the precision machine tool, Int. J. Adv. Manuf. Technol., 72(9–12) (2014) 1415–1427.

    Article  Google Scholar 

  23. K. Liu, T. Li and T. Li, Thermal behavior analysis of horizontal CNC lathe spindle and compensation for radial thermal drift error, Int. J. Adv. Manuf. Technol., 95(1–4) (2018) 1293–1301.

    Article  Google Scholar 

  24. T. M. Li, F. C. Li, Y. Jiang and H. T. Wang, Thermal error modeling and compensation of a heavy gantry-type machine tool and its verification in machining, Int. J. Adv. Manuf. Technol., 92 (2017) 3073–3092.

    Article  Google Scholar 

  25. B. M. Wang, X. S. Mei, Z. X. Wu and F. Zhu, Dynamic modeling for thermal error in motorized spindles, Int. J. Adv. Manuf. Technol., 78 (2015) 1141–1146.

    Article  Google Scholar 

  26. J. Yang, H. Shi, B. Feng, L. Zhao, C. Ma and X. S. Mei, Thermal error modeling and compensation for a high-speed motorized spindle, Int. J. Adv. Manuf. Technol., 77 (2015) 1005–1017.

    Article  Google Scholar 

  27. Q. Yin, F. Tan, H. Chen and G. Yin, Spindle thermal error modeling based on selective ensemble bp neural networks, The Int. J. Adv. Manuf. Technol., 101(5–8) (2019) 1699–1713.

    Article  Google Scholar 

  28. B. Jian et al., Predicting spindle displacement caused by heat using the general regression neural network, Int. J. Adv. Manuf. Technol., 104(9–12) (2019) 4665–4674.

    Article  Google Scholar 

  29. B. L. Jian, Y. S. Guo, C. H. Hu, L. W. Wu and H. T. Yau, Prediction of spindle thermal deformation and displacement using back propagation neural network, Sensors and Materials, 32(1) (2020) 431–445.

    Article  Google Scholar 

  30. W. Tian, G. Wang, L. Yang and W. Gao, The application of a regularization method to the estimation of geometric errors of a three-axis machine tool using a double ball bar, Journal of Mechanical Science and Technology, 32(10) (2018) 4871–4881.

    Article  Google Scholar 

  31. Z. Zhao, J. Zhang, Y. Wang, Z. Wang and C. Quan, Dynamic thermal behavior and thermal error prediction of spindle due to periodic jump motions in a large precision die-sinking edm machine, Journal of Mechanical Science and Technology, 33(7) (2019) 3397–3405.

    Article  Google Scholar 

  32. B. Rengui, Q. Pingz and Y. Can, Elasto-plastic analysis for static and dynamic performance of rolling element bearings, J. of Jishou University (Natural Sciences Edition), 40(5) (2019) 37–44.

    Google Scholar 

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Authors and Affiliations

  1. School of Intelligent Manufacturing, Changchun Sci-Tech University, Changchun, 130600, China

    Yang Liu, Xiaofeng Wang, Xiaogang Zhu & Ying Zhai

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  1. Yang Liu
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  2. Xiaofeng Wang
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  3. Xiaogang Zhu
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  4. Ying Zhai
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Corresponding author

Correspondence to Xiaofeng Wang.

Additional information

Xiaofeng Wang is a Post Doctor of Jilin University. He received his Ph.D. in Mechanical Engineering from Jilin University. His research interests include manufacturing equipment reliability and thermal balance design of precision machine tools.

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Liu, Y., Wang, X., Zhu, X. et al. Thermal error prediction of motorized spindle for five-axis machining center based on analytical modeling and BP neural network. J Mech Sci Technol 35, 281–292 (2021). https://doi.org/10.1007/s12206-020-1228-7

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  • DOI: https://doi.org/10.1007/s12206-020-1228-7

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