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Thermal error modeling of the spindle based on multiple variables for the precision machine tool

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Abstract

Thermal error, especially the one caused by the thermal expansion of spindle in axial direction, seriously impacts the accuracy of the precision machine tool. Thermal error compensation based on the thermal error model with high accuracy and robustness is an effective and economic way to reduce the impact and enhance the accuracy. Generally, thermal error models are built only on temperatures at some points in the spindle system. However, the thermal error is also closely related to other working parameters. Through the theoretical analysis, the simulation, and the experimental testing in this paper, it is found out that thermal error is determined by multiple variables, such as the temperature, the spindle rotation speed, the historical spindle temperature, the historical thermal error, and the time lag between the present and previous times. In order to examine the performance of thermal error models based on multiple variables, two common methods are used for modeling—the multiple regression method and the back propagation network. The data for modeling are collected from experiments conducted on the spindle of a precision machine tool under various working conditions. The modeling results demonstrate that models established based on the multiple variables have better accuracy and robustness. It also turns out that data filtering before modeling can further improve the performance of the models. Therefore, models based on multiple variables with good accuracy and robustness can be very useful for the further thermal error compensation. In addition, by taking relative importance analysis of multiple variables based on standardized regression coefficients, the influence of each variable to the thermal error is revealed. The ranking of coefficients can also be used as a new criterion for the optimal temperature variable selection in the future research.

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References

  1. Gomez-Acedo E, Olarra A, Lopez de la Calle LN (2012) A method for thermal characterization and modeling of large gantry-type machine tools. Int J Adv Manuf Technol 62(9–12):875–886. doi:10.1007/s00170-011-3879-0

    Article  Google Scholar 

  2. Junyong X, Youmin H, Bo W, Tielin S (2009) Research on thermal dynamics characteristics and modeling approach of ball screw. Int J Adv Manuf Technol 43(5–6):421–430. doi:10.1007/s00170-008-1723-y

    Article  Google Scholar 

  3. Mou J (1997) A systematic approach to enhance machine tool accuracy for precision manufacturing. Int J Mach Tools Manuf 37(5):669–685

    Article  Google Scholar 

  4. Bryan J (1990) International status of thermal error research (1990). CIRP Ann Manuf Technol 39(2):645–656

    Article  Google Scholar 

  5. Lee J-H, Yang S-H (2002) Statistical optimization and assessment of a thermal error model for CNC machine tools. Int J Mach Tools Manuf 42(1):147–155

    Article  Google Scholar 

  6. Wang Y-C, Kao M-c, Chang C-P (2011) Investigation on the spindle thermal displacement and its compensation of precision cutter grinders. Measurement 44(6):1183–1187

    Article  Google Scholar 

  7. Weck M, McKeown P, Bonse R, Herbst U (1995) Reduction and compensation of thermal errors in machine tools. CIRP Ann Manuf Technol 44(2):589–598

    Article  Google Scholar 

  8. Hsieh K-H, Chen T-R, Chang P, Tang C-H (2012) Thermal growth measurement and compensation for integrated spindles. Int J Adv Manuf Technol 64(5–8):889–901. doi:10.1007/s00170-012-4041-3

    Google Scholar 

  9. Ramesh R, Mannan M, Poo A (2000) Error compensation in machine tools—a review: Part II: thermal errors. Int J Mach Tools Manuf 40(9):1257–1284

    Article  Google Scholar 

  10. Takada K, Tanabe I (1987) Basic study on thermal deformation of machine tool structure composed of epoxy resin concrete and cast iron. Bull Jpn Soc Precis Eng 21(3):173–178

    Google Scholar 

  11. Chen J-S (1996) Neural network-based modelling and error compensation of thermally-induced spindle errors. Int J Adv Manuf Technol 12(4):303–308. doi:10.1007/BF01239617

    Article  MathSciNet  Google Scholar 

  12. Tseng P-C (1997) A real-time thermal inaccuracy compensation method on a machining centre. Int J Adv Manuf Technol 13(3):182–190. doi:10.1007/BF01305870

    Article  MathSciNet  Google Scholar 

  13. Yang J, Ren Y, Liu G, Zhao H, Dou X, Chen W, He S (2005) Testing, variable selecting and modeling of thermal errors on an INDEX-G200 turning center. Int J Adv Manuf Technol 26(7–8):814–818

    Article  Google Scholar 

  14. Chen J, Yuan J, Ni J (1996) Thermal error modelling for real-time error compensation. Int J Adv Manuf Technol 12(4):266–275

    Article  Google Scholar 

  15. Ramesh R, Mannan M, Poo A (2002) Support vector machines model for classification of thermal error in machine tools. Int J Adv Manuf Technol 20(2):114–120

    Article  Google Scholar 

  16. Li Y, Yang J, Gelvis T, Li Y (2008) Optimization of measuring points for machine tool thermal error based on grey system theory. Int J Adv Manuf Technol 35(7–8):745–750

    Article  Google Scholar 

  17. Li X (2001) Real-time prediction of workpiece errors for a CNC turning centre, Part 2. Modelling and estimation of thermally induced errors. Int J Adv Manuf Technol 17(9):654–658

    Article  Google Scholar 

  18. Yang Z, Sun M, Li W, Liang W (2011) Modified Elman network for thermal deformation compensation modeling in machine tools. Int J Adv Manuf Technol 54(5–8):669–676

    Article  Google Scholar 

  19. Ahn KG, Cho DW (1999) In-process modelling and estimation of thermally induced errors of a machine tool during cutting. Int J Adv Manuf Technol 15(4):299–304. doi:10.1007/s001700050070

    Article  Google Scholar 

  20. Chen J-S, Hsu W-Y (2003) Characterizations and models for the thermal growth of a motorized high speed spindle. Int J Mach Tools Manuf 43(11):1163–1170

    Article  Google Scholar 

  21. Haitao Z, Jianguo Y, Jinhua S (2007) Simulation of thermal behavior of a CNC machine tool spindle. Int J Mach Tools Manuf 47(6):1003–1010. doi:10.1016/j.ijmachtools.2006.06.018

    Article  Google Scholar 

  22. Harris TA (1991) Rolling bearing analysis. Wiley, New York

    Google Scholar 

  23. Lienhard JH, Lienhard J (2000) A heat transfer textbook. Phlogiston Press, Cambridge, Massachusetts

    MATH  Google Scholar 

  24. Bossmanns B, Tu JF (1999) A thermal model for high speed motorized spindles. Int J Mach Tools Manuf 39(9):1345–1366

    Article  Google Scholar 

  25. Li Y, Zhao W Axial thermal error compensation method for the spindle of a precision horizontal machining center. In: Mechatronics and Automation (ICMA), 2012 International Conference on, 2012. IEEE, pp 2319-2323

  26. Ruijun L, Wenhua Y, Zhang HH, Qifan Y (2012) The thermal error optimization models for CNC machine tools. Int J Adv Manuf Technol 63(9–12):1167–1176

    Article  Google Scholar 

  27. Mize CD, Ziegert JC (2000) Neural network thermal error compensation of a machining center. Precis Eng 24(4):338–346

    Article  Google Scholar 

  28. Menard S (2004) Six approaches to calculating standardized logistic regression coefficients. The American Statistician 58 (3)

    Article  MathSciNet  Google Scholar 

  29. Lo C-H, Yuan J, Ni J (1999) Optimal temperature variable selection by grouping approach for thermal error modeling and compensation. Int J Mach Tools Manuf 39(9):1383–1396

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory for Manufacturing System Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710054, China

    Yang Li, Wanhua Zhao, Wenwu Wu & Bingheng Lu

  2. Department of Industrial and Manufacturing Systems Engineering, University of Michigan–Dearborn, Dearborn, MI, 48128-1491, USA

    Yubao Chen

  3. School of Mechanical Engineering, Xi’an Jiaotong University, No. 28 Xianning Road, Beilin District, Xi’an, Shaanxi Province, 710049, China

    Wanhua Zhao

Authors
  1. Yang Li
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  2. Wanhua Zhao
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  3. Wenwu Wu
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  4. Bingheng Lu
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  5. Yubao Chen
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Correspondence to Wanhua Zhao.

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Li, Y., Zhao, W., Wu, W. et al. Thermal error modeling of the spindle based on multiple variables for the precision machine tool. Int J Adv Manuf Technol 72, 1415–1427 (2014). https://doi.org/10.1007/s00170-014-5744-4

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  • DOI: https://doi.org/10.1007/s00170-014-5744-4

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