Abstract
When a thermal error model of a machine tool is established, selecting the appropriate temperature measurement point is a very difficult problem. This paper proposes a novel method for constructing a linear virtual temperature. The proposed method can overcome the problem of selecting the temperature measurement point. First, temperature-thermal expansion hysteresis characteristics are used to divide the temperature measurement points into two groups. Each temperature variable is then chosen through a principal component analysis (PCA). Finally, using two temperature-variable weights and the correlative coefficient thermal displacement as the maximum optimal indexes, two temperature-weighted coefficients are calculated, and a linear virtual-temperature variable related to the thermal error linearity is then formed. In establishing the proposed thermal error model, the linear virtual temperature formed can serve as a system input variable. The proposed method was tested on a three-axis milling machine to determine the spindle Z-axial thermal error, and the results show that the root mean square error (RMSE) is reduced by 11 % and the sum of the squares of the error (SSE) is reduced by 39 % in comparison with a direct application of a temperature variable when establishing such a model. In the proposed method, only two temperature measurement points are used to establish a model, through which the complexity in determining the optimal measurement points through a traditional method, along with the number of temperature measurement points required, is greatly reduced.
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References
Ramesh R, Mannan M, Poo A (2003) Thermal error measurement and modelling in machine tools: Part I. Influence of varying operating conditions. Int J Mach Tools Manuf 43(4):391–404
Li J, Zhang W, Yang G, Tu S, Chen X (2009) Thermal-error modeling for complex physical systems: the-state-of-arts review. Int J Adv Manuf Technol 42(1):168–179
Mayr J, Jedrzejewski J, Uhlmann E, Alkan Donmez M, Knapp W, Hartig F, Wendt K, Moriwaki T, Shore P, Schmitt R (2012) Thermal issues in machine tools. CIRP Ann Manuf Technol 61(2):771–791
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
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
Yang JG, Ren YQ, Liu GL, Zhao HT, Dou XL, Chen WZ, He SW (2005) Variable selecting and modeling of thermal errors on an INDEX-G200 turning center. Int J Adv Manuf Technol 26(7–8):814–818
Han J, Wang L, Wang H, Cheng N (2012) A new thermal error modeling method for CNC machine tools. Int J Adv Manuf Technol 62(1–4):205–212
Yang H, Ni J (2005) Adaptive model estimation of machine-tool thermal errors based on recursive dynamic modeling strategy. Int J Mach Tools Manuf 45(1):1–11
Zhang T, Ye WH, Liang RJ, Lou PH, Yang XL (2013) Temperature variable optimization for precision machine tool thermal error compensation on optimal threshold. Chin J Mech Eng 26(1):158–165
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
En-ming M, Ya-yun G, Lian-chun D, Ji-chao M (2014) Temperature-sensitive point selection of thermal error model of CNC machining center. Int J Adv Manuf Technol 74(5–8):681–691
Wang H, Wang L, Li T, Han J (2013) Thermal sensor selection for the thermal error modeling of machine tool based on the fuzzy clustering method. Int J Adv Manuf Technol 69(1–4):121–126
Zhu J, Ni J, Shih AJ (2008) Robust machine tool thermal error modeling through thermal mode concept. J Manuf Sci Eng Trans ASME 130(6):61006
Xia C, Fu J, Xu Y, Chen Z (2014) Machine tool selected point temperature rise identification based on operational thermal modal analysis. Int J Adv Manuf Technol 70(1–4):19–31
Ma Y (2001) Sensor placement optimization for thermal error compensation on machine tools. University of Michigan
Mian N, Fletcher S, Longstaff A, Myers A (2012) An efficient offline method for determining the thermally sensitive points of a machine tool structure. In Proceedings of the 37th International Matador Conference, Springer
Yang H, Ni J (2003) Dynamic modeling for machine tool thermal error compensation. J Manuf Sci Eng Trans ASME 125(2):245–254
Yang H, Ni J (2005) Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error. Int J Mach Tools Manuf 45(4):455–465
Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24(6):417
Jolliffe I (2005) Principal component analysis. Wiley Online Library
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Zhang, C., Gao, F., Meng, Z. et al. A novel linear virtual temperature constructing method for thermal error modeling of machine tools. Int J Adv Manuf Technol 80, 1965–1973 (2015). https://doi.org/10.1007/s00170-015-7167-2
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DOI: https://doi.org/10.1007/s00170-015-7167-2