Abstract
In order to achieve effective control of thermal error compensation of computer numerical control (CNC) machine tools, the prediction accuracy and robustness of the compensation model is particularly important. In this paper, the temperature of sensitive points and thermal error of the spindle in Z direction are measured. Using a combination of fuzzy clustering analysis and gray correlation method to select temperature-sensitive points and then using multiple linear regression of least squares and least absolute estimation methods, distributed lag model, and support vector regression machine to establish prediction models of the relationship between temperature of sensitive points and the thermal error. Also, the temperature values of sensitive points and the thermal error in the experimental conditions of different ambient temperatures and different spindle speeds are measured. By comparing the prediction accuracy of various prediction models under different experimental conditions verify the robustness of the models. Experimental results show that when the modeling data are less, the prediction accuracy of multiple linear regression of least squares and least absolute estimation methods and distributed lag model is declined, and their robustness are poor, while support vector regression model has good prediction accuracy and its robustness remains strong when changing the experimental conditions. However, when modeling data are rich, the prediction accuracy of various algorithms is improved, but the robustness of support vector regression model is volatile. The robustness analysis of different models provides a useful reference for the thermal error compensation model, selection of CNC machine tools, and has good engineering applications.
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References
Bryan J (1990) International status of thermal error research. Ann CIRP 39(2):645–656
Aronson RB (1996) War against thermal expansion. Manuf Eng 116(6):45–50
LO CH, Yuan JX, Ni J (1995) An application of real-time error compensation on a turning center. Int J Mach Tools Manuf 35(1):61–67
Yang JG, Deng WG, Ren YQ, Li YS, Dou XL (2004) Grouping optimization modeling by selection of temperature variables for the thermal error compensation on machine tools. Chin J Mech Eng 15(6):478–481
Yan JY, Yang JG (2009) Application of synthetic gray correlation theory on thermal point optimization for machine tool thermal error compensation. Int J Adv Manuf Technol 43(11):1124–1132
Guo QJ, Yang JG (2011) Application of projection pursuit regression to thermal error modeling of a CNC machine tool. Int J Adv Manuf Technol 55(8):623–629
Kim SK, Cho DW (1997) Real-time estimation of temperature distribution in a ball-screw system. Int J Mach Tools Manuf 37(4):451–464
YANG S, YUAN J, NI J (1996) The improvement of thermal error modeling and compensation on machine tools by CMAC neural network. Int J Mach Tools Manuf 36(4):527–537
Zeng HL, Sun Y, Zhang HY (2009) Thermal error compensation on machine tools using rough set artificial neural networks. World Congress on Computer Science and Information Engineering CSIE2009, Los Angles, USA
Chen C, Zhang CY, Chen H (2011) Selection and modeling of temperature variables for the thermal error compensation in servo system. The Tenth International Conference on Electronic Measurement & Instruments ICEMI2011, Cheng Du, China, 16–18 Aug 2011
Yang JG, Ren YQ, Zhu WB, Huang ML, Pan ZH (2003) Research on on-line modeling method of thermal error compensation model for CNC machines. Chin J Mech Eng 39(3):81–84
Vapnik VN (1998) Statistical learning theory. Wiley, New York
Deng NY, Tian YJ (2009) Support vector machine—theory, algorithms, and expansion. Press of Science, Bei Jing
MIAO EM, GONG YY, CHENG TJ, CHEN HD (2013) Application of support vector regression to thermal error modeling of machine tools. Opt Precis Eng 21(4):980–986
Wang FC, Hu ST, Zhang YF (2007) The coefficient estimation of least absolute deviation regression and implementation in MATLAB. J Inst Disaster-Prev Sci Technol 9(4):85–89
Lin SL, Liu Z (2007) Parameter selection in SVM with RBF kernel function. J Zhe Jiang Univ Technol 35(2):163–167
Duan K, Keerthi S, Poo A (2003) Evaluation of simple performance measures for tuning SVM hyper parameters. Neurocomputing 51:41–59
Han J, Wang LP, Wang HT, Cheng NB (2012) A new thermal error modeling method for CNC machine tools. Int J Adv Manuf Technol 62(3):205–212
Miao EM, Niu PC, Fei YT, Yan Y (2011) Selecting temperature-sensitive points and modeling thermal errors of machine tools. J Chin Soc Mech Eng 32(6):559–565
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Miao, EM., Gong, YY., Niu, PC. et al. Robustness of thermal error compensation modeling models of CNC machine tools. Int J Adv Manuf Technol 69, 2593–2603 (2013). https://doi.org/10.1007/s00170-013-5229-x
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DOI: https://doi.org/10.1007/s00170-013-5229-x