Abstract
A great challenge in a thermal error compensation process is to select proper temperature variables and to establish accurate thermal error models. In this paper, a new approach for building an effective mathematic thermal error for machine tools is presented. Fuzzy clustering analysis is conducted to identify temperature variables, and then screen the representative variable as an independent variable meanwhile eliminate the coupling among the variables. Cluster validity is forwarded to measure the reasonability of the clustering and the classification accuracy for the temperature variables. Furthermore, a mathematical model using the robust regression analysis is built to reveal the relationship between these temperature variables and thermal deformation. To evaluate the performance of our proposed model, a verification experiment is carried out. Pt-100 thermal resistances and Eddy current sensors are used to monitor the temperature and thermal shift fluctuation respectively. Fuzzy clustering analysis is utilized to classify 32 temperature variables to four clusters. A robust regression thermal error model is proposed based on the four key temperature points. The result shows that four representative temperature variables are precise predictors of the thermal errors of the machine tools. The proposed method is shown to be capable of improving the accuracy of the machine tools effectively.
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Mehrabi MG, O’Neal G, Min BK, Pasek Z, Koren Y, Szuba P (2002) Improving machining accuracy in precision line boring. J Intel Man 13(5):379–389
Bryan J (1990) International status of thermal error research. CIRP Ann-Manuf Tech 39(2):645–656
Weck M, McKeown P, Bonse R, Herbst U (1995) Reduction and compensation of thermal errors in machine tools. CIRP Ann-Manuf Techn 44(2):589–598
Wang SM, Liu YL, Kang Y (2002) An efficient error compensation system for CNC multi-axis machines. Int J Mach Tool Man 42(11):1235–1245
Ni J (1997) CNC machine accuracy enhancement through real-time error compensation. J Manuf Sci E-T Asme 119(4B):717–725
Yuan JX, Ni J (1998) The real-time error compensation technique for CNC machining systems. Mechatron 8(4):359–380
Tseng PC, Ho JL (2002) A study of high-precision CNC lathe thermal errors and compensation. Int J Adv Manuf Technol 19(11):850–858
Lei WT, Hsu YY (2003) Accuracy enhancement of five-axis CNC machines through real-time error compensation. Int J Mach Tool Man 43(9):871–877
Wu CH, Kung YT (2006) Thermal analysis and compensation of a double-column machining centre. P I Mech Eng B-J Eng 220(2):109–117
Chen JS (1996) Neural network-based modelling and error compensation of thermally-induced spindle errors. Int J Adv Manuf Technol 12(4):303–308
Lee DS, Choi JY, Choi DH (2003) ICA based thermal source extraction and thermal distortion compensation method for a machine tool. Int J Mach Tool Man 43(6):589–597
Lo CH, Yuan JX, Ni J (1999) Optimal temperature variable selection by grouping approach for thermal error modeling and compensation. Int J MachinTool Man 39(9):1383–1396
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):745–750
Yan JY, Yang JG (2009) Application of synthetic grey correlation theory on thermal point optimization for machine tool thermal error compensation. Int J Adv Manuf Technol 43(11–12):1124–1132
Wang KC, Tseng PC (2010) Thermal error modeling of a machine tool using data mining scheme. J Adv Mech Des Syst 4(2):516–530
Guo QJ, Yang JG, Wu H (2010) Application of ACO-BPN to thermal error modeling of NC machine tool. Int J Adv Manuf Technol 50(5–8):667–675
Ramesh R, Mannan MA, Poo AN (2000) Error compensation in machine tools—a review Part I: geometric, cutting-force induced and fixture-dependent errors. Int J Adv Manuf Technol 40(9):1235–1256
Wang YD, Zhang GX, Moon KS, Sutherland JW (1998) Compensation for the thermal error of a multi-axis machining center. J Mater Process Tech 75(1–3):45–53
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(5–8):623–629
Li JW, Zhang WJ, Yang GS, Tu SD, Chen XB (2009) Thermal-error modeling for complex physical systems: the-state-of-arts review. Int J Adv Manuf Technol 42(1–2):168–179
Yang ZY, Sun ML, Li WQ, Liang WY (2011) Modified Elman network for thermal deformation compensation modeling in machine tools. Int J Adv Manuf Technol 54(5–8):669–676
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
Schwammle V, Jensen ON (2010) A simple and fast method to determine the parameters for fuzzy c-means cluster analysis. Bioinformatics 26(22):2841–2848
Huang KY (2010) Applications of an enhanced cluster validity index method based on the Fuzzy C-means and rough set theories to partition and classification. Eepert Syst Appl 37(12):8757–8769
Wen W, Hao ZF, Yang XW (2010) Robust least squares support vector machine based on recursive outlier elimination. Soft Comput 14(11):1241–1251
Sadaaki M, Hidetomo I, Katsuhiro H (2008) Algorithms for fuzzy clustering: methods in c-means clustering with applications. Springer, Berlin Heidelberg
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Han, J., Wang, L., Wang, H. et al. A new thermal error modeling method for CNC machine tools. Int J Adv Manuf Technol 62, 205–212 (2012). https://doi.org/10.1007/s00170-011-3796-2
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DOI: https://doi.org/10.1007/s00170-011-3796-2