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The thermal drift modeling of spindle system based on a physical driven deformation methodology

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Abstract

Thermal error is one of the main factors that leads to the decline of CNC machine tool’s accuracy stability. The location of the typical thermal key points was determined by the finite element analysis model of the spindle system. The thermal experiments were conducted on a spindle of the milling machine tool. Furthermore, the distribution law of the spindle temperature field and the mechanism of its deformation were elaborated. On this basis, the temperature field model of each region of a spindle system was established based on the generation, conduction, and convection theory of heat, spindle speed, and motor load. A physical driven deformation modeling (PDDM) method was put forward for building the relationship between the axial thermal drift error and the temperatures of the key points of the spindle system. Then, with parameters identified using data of one speed, the influence of structural size uncertainty on prediction results was analyzed by the first-order second-moment (FOSM) method. The prediction residual errors of the suggested model with multiple size parameter fluctuation were provided. Finally, the effectiveness and robustness of the time-varying error model were verified by experiment and compensation.

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Abbreviations

A s :

Heat generation coefficient caused by spindle rotating

B s :

Convective heat transfer coefficient caused by spindle rotating

C s :

Heat dissipation coefficient

A m :

Heat generation coefficient caused by rotor operation

ω:

Spindle rotating speed

k I _i :

Heat conductivity coefficient (i.e., I–i:1–2,1–3)

L 1 :

Length of the spindle

L 2 :

Length of the spindle box

L 3 :

Width of the column

L 4 :

Length of the column

E tcz :

Tested axial thermal error

E ccz :

Calculated axial thermal error

T tI :

Tested temperature of section I

T cI :

Calculated temperature of section I

P :

Number of the motor load at time t

N :

Total test time

References

  1. Zhang Lx, Li Cq, Li Jp, Zhang K, Wu Yh (2017) Temperature rise prediction model of high-speed and high-precision motorized spindle. Int J Mech Eng 53(23):129–136. https://doi.org/10.1016/j.csite.2021.101056

    Article  Google Scholar 

  2. Ibaraki S, Inui H, Hong C, Nishikawa S, Shimoike M (2019) On-machine identification of rotary axis location errors under thermal influence by spindle rotation. Int J Precis Eng 55:42–47. https://doi.org/10.1016/j.precisioneng.2018.08.005

    Article  Google Scholar 

  3. Li Y, Wei WM, Su DX, Zhao WH, Zhang J, Wu WW (2018) Thermal error modeling of spindle based on the principal component analysis considering temperature-changing process. Int J Adv Manuf Techol 99(5–8):1341–1349. https://doi.org/10.1007/s00170-018-2482-z

    Article  Google Scholar 

  4. Li D, Feng P, Zhang J, Wu ZJ, Yu DW (2015) Method for modifying convective heat transfer coefficients used in the thermal simulation of a feed drive system based on the response surface methodology. Int J Numer Heat Tran Part A: Applications 69(1):51–66. https://doi.org/10.1080/10407782.2015.1037130

    Article  Google Scholar 

  5. Liu K, Han W, Wang YQ (2021) Review on thermal error compensation for axes of CNC machine tools. Int J Mech Eng 57:156–173

    Google Scholar 

  6. Shi H, Qu QQ, Mei XS, Tao T, Wang HT (2023) Robust modeling for thermal error of spindle of slant bed lathe based on error decomposition. Int J Case Stud Therm Eng 51:103564. https://doi.org/10.1016/j.csite.2023.103564

    Article  Google Scholar 

  7. Liu K, Liu Y, Sun MJ, Wu YL, Zhu TJ (2017) Comprehensive thermal growth compensation method of spindle and servo axis error on a vertical drilling center. Int J Adv Manuf Technol 88:2507–2516. https://doi.org/10.1007/s00170-016-8972-y

    Article  Google Scholar 

  8. 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 Tool Manufact 95:20–38. https://doi.org/10.1016/j.ijmachtools.2015.04.008

    Article  Google Scholar 

  9. Liu J, Ma C, Gui H, Wang S (2021) Thermally-induced error compensation of spindle system based on long short term memory neural networks. Int J Appl Soft Comput 102:107094. https://doi.org/10.1016/j.asoc.2021.107094

    Article  Google Scholar 

  10. Liu H, Miao E, Zhuang X, Wei X (2018) Thermal error robust modeling method for CNC machine tools based on a split unbiased estimation algorithm. Int J Precis Eng 51:169–75. https://doi.org/10.1016/j.precisioneng.2017.08.007

    Article  Google Scholar 

  11. Tan F, Yin M, Wang L, Yin G (2018) Spindle thermal error robust modeling using LASSO and LS-SVM. Int J Adv Manuf Technol 94(5–8):2861–2874. https://doi.org/10.1007/s00170-017-1096-1

    Article  Google Scholar 

  12. Zhang K, Yao X, Zhang Y, Yang J (2011) Thermal error modeling based on optimum selection of time series models. Modul Mach Tool Autom Manuf Techn 10:36–39

    Google Scholar 

  13. Liu K, Sun MJ, Zhu TJ, Wu YL, Liu Y (2016) Modeling and compensation for spindle’s radial thermal drift error on a vertical machining center. Int J Mach Tools Manuf 105:58–67. https://doi.org/10.1016/j.ijmachtools.2016.03.006

    Article  Google Scholar 

  14. Peng J, Yin M, Cao L, Liao QH, Wang L, Yin GF (2022) Study on the spindle axial thermal error of a five-axis machining center considering the thermal bending effect. Int J Precis Eng 75:210–226. https://doi.org/10.1016/j.precisioneng.2022.02.009

    Article  Google Scholar 

  15. Shi XJ, Yang X, Xiao MuYJ, Wang YZ, Wang WK (2019) Thermal error compensation model for a motorized spindle with shaft core cooling based on exponential function. Int J Adv Manuf Technol 103(9–12):4805–4813. https://doi.org/10.1007/s00170-019-04038-w

    Article  Google Scholar 

  16. Liu K, Chen F, Zhu TJ, Wu YJ, Sun MJ (2016) Compensation for spindle’s axial thermal growth based on temperature variation on vertical machine tools. Int J Adv Mech Eng 8(8):2071834861. https://doi.org/10.1177/1687814016657733

    Article  Google Scholar 

  17. Liu K, Li T, Hb Liu, Liu Y, Wang YQ (2020) Analysis and prediction for spindle thermal bending deformations of a vertical milling machine. Int J IEEE Trans Ind Inf 16(3):1549–1558. https://doi.org/10.1109/TII.2019.2926991

    Article  Google Scholar 

  18. Kang CM, Zhao CY, Liu K, Li TJ, Yang B (2018) Comprehensive compensation method for thermally induced error of a vertical drilling center. Int J Can Soc Mech Eng 43(1):92–101. https://doi.org/10.1139/tcsme-2018-0079

    Article  Google Scholar 

  19. Liu K, Song L, Liu H, Han W, Sun MJ, Yq Wang (2021) The influence of thermophysical parameters on the prediction accuracy of the spindle thermal error model. Int J Adv Manuf Technol. 115(1–2):617–626. https://doi.org/10.1007/s00170-021-07256-3

    Article  Google Scholar 

  20. Song L, Liu K, Zhao D, Zhang ZW, Yq Wang (2023) The spindle axial time-varying thermal error compensation method for horizontal boring and milling machine tool based on edge computing. Int J Adv Manuf Technol 128(5–6):2631–2638. https://doi.org/10.1007/s00170-023-11927-8

    Article  Google Scholar 

  21. Ma C, Zhao L, Mei X, 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(9–12):3071–3085. https://doi.org/10.1007/s00170-016-9254-4

    Article  Google Scholar 

  22. Kang CM, Zhao CY, Zhang JQ (2020) Thermal behavior analysis and experimental study on the vertical machining center spindle. Int J T Can Soc Mech Eng 44(3):344–351. https://doi.org/10.1139/tcsme-2019-0124

    Article  Google Scholar 

  23. Liu Y, Meng LL, Liu K, Zhang Y (2016) Chatter reliability of milling system based on first-order second-moment method. Int J Adv Manuf Technol 87(1–4):801–809. https://doi.org/10.1007/s00170-016-8523-6

    Article  Google Scholar 

  24. Dai Y, Pang J, Rui KK, Li WW, Wang QH, Li SK (2023) Thermal error prediction model of high-speed motorized spindle based on DELM network optimized by weighted mean of vectors algorithm. Int J Case Stud Therm Eng 47:103054. https://doi.org/10.1016/j.csite.2023.103054

    Article  Google Scholar 

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Acknowledgements

The authors thank the anonymous referees and editor for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Pharmaceutical Engineering, Shenyang Pharmaceutical University, Shenyang, 110016, China

    ChengMing Kang & YongXue Guo

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  1. ChengMing Kang
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  2. YongXue Guo
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Contributions

CMK: writing software and original draft preparation. YXG: conceptualization, methodology, and validation.

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Correspondence to ChengMing Kang.

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Kang, C., Guo, Y. The thermal drift modeling of spindle system based on a physical driven deformation methodology. Int J Adv Manuf Technol 130, 1207–1219 (2024). https://doi.org/10.1007/s00170-023-12720-3

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