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.
Spindle thermal error modeling Multiple variables Multiple regression model Back propagation network model Standardized regression coefficients
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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):814–818CrossRefGoogle Scholar
Chen J, Yuan J, Ni J (1996) Thermal error modelling for real-time error compensation. Int J Adv Manuf Technol 12(4):266–275CrossRefGoogle Scholar
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):114–120CrossRefGoogle Scholar
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):745–750CrossRefGoogle Scholar
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):654–658CrossRefGoogle Scholar
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):669–676CrossRefGoogle Scholar
Harris TA (1991) Rolling bearing analysis. Wiley, New YorkGoogle Scholar
Lienhard JH, Lienhard J (2000) A heat transfer textbook. Phlogiston Press, Cambridge, MassachusettszbMATHGoogle Scholar
Bossmanns B, Tu JF (1999) A thermal model for high speed motorized spindles. Int J Mach Tools Manuf 39(9):1345–1366CrossRefGoogle Scholar
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 2319-2323Google Scholar
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):1167–1176CrossRefGoogle Scholar
Mize CD, Ziegert JC (2000) Neural network thermal error compensation of a machining center. Precis Eng 24(4):338–346CrossRefGoogle Scholar