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Dynamic modeling for thermal error in motorized spindles

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This paper proposes a new modeling methodology to predict thermal error in motorized spindles. The dynamic model predicts thermal errors that are caused by deformation in the motorized spindle structure due to heat flow from internal sources. These thermally induced errors become more serious and dominate the total error when it comes to high speed and high precision. If these thermal errors can be predicted, they can be compensated in real time. In this paper, a new thermal errors model (ARX model) is presented which capitalizes on the notion that the motorized spindle thermoelastic system has very complicated dynamics. Furthermore, the selection principle of temperature key points, which are indispensable for building a robust thermal error model, is provided using the thermal error sensitivity technology. At last, an experiment on the thermal error in a motorized spindle is conducted to verify the effectiveness of the ARX model, the experimental results show that above 80 % of axial thermal errors are predicted for a variety of motorized spindle cycles and the dynamic model has good accuracy and robustness.

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  1. 1.

    DA. Krulewich (1998) Temperature integration model and measurement point selection for thermally induced machine tool errors. Mechantronics 8:395–412

  2. 2.

    Hsieh KH, Chen TR, Chang P, Tang CH (2013) Thermal growth measurement and compensation for integrated spindles. Int J Adv Manuf Technol 64(5–8):889–901

  3. 3.

    Chena JS, Chiou G (1995) Quick testing and modeling of thermally induced errors of CNC machine tools. Int J Mach Tools Manuf 35(7):1063–1074

  4. 4.

    Donmez MA, Blomquist DS, Hocken RJ, Liu CR, Barash MM (1996) General methodology for machine tool accuracy enhancement by error compensation. Precis Eng 8(4):187–196

  5. 5.

    Yang S, Yuan J, Ni J (1996) The improvement of thermal error modeling and compensation on machine tools by neural network. Int J Mach Tools Manuf 36(4):527–537

  6. 6.

    Yang J, Yuan J, Ni J (1999) Thermal error mode analysis and robust modeling for error compensation on a CNC turning center. Int J Mach Tools Manuf 39(4):1367–1381

  7. 7.

    Moriwaki T, Shamoto E (1998) Analysis of thermal deformation of an ultraprecision air spindle system. CIRP Ann-Manuf Technol 47(1):315–319

  8. 8.

    Huang YQ, Zhang J, Li X, Tian LJ (2014) Thermal error modeling by integrating GA and BP algorithms for the high-speed spindle. Int J Adv Manuf Technol 71(1):1669–1675

  9. 9.

    Li S, Zhang YA (1997) Study of pre-compensation for thermal errors of NC machine tools. Int J Mach Tools Manuf 37(12):1715–1719

  10. 10.

    Yang H, Ni J (2003) Dynamic modeling for machine tool thermal error compensation. J Manuf Sci Eng 125(5):245–254

  11. 11.

    Vejmelka M, Palus M, Susmakova K (2010) Identification of nonlinear oscillatory activity embedded in broadband neural signals. Int J Neural Syst 20(2):117–128

  12. 12.

    Puscasu G, Codres B (2011) Nonlinear system identification and control based on modular neural networks. Int J Neural Syst 21(4):319–334

  13. 13.

    Ljung L (1999) System identification: theory for the user. Prentice Hall PTR, Upper Saddle

  14. 14.

    Li YX, Yang JG, Gelvis T, Li YY (2008) Optimization of measuring points for machine tool thermal error based on grey system theory. Int J Adv Manuf Technol 35(7–8):745–775

  15. 15.

    Zhao HT, Yang JG, Shen JH (2006) Simulation of thermal behavior of a CNC machine tool spindle. Int J Mach Tools Manuf 46(6):1–8

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Correspondence to Baomin Wang.

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Wang, B., Mei, X., Wu, Z. et al. Dynamic modeling for thermal error in motorized spindles. Int J Adv Manuf Technol 78, 1141–1146 (2015). https://doi.org/10.1007/s00170-014-6716-4

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  • Motorized spindle
  • Thermal error
  • Dynamic model
  • System identification theory
  • ARX model