Abstract
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.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Gomez-Acedo E, Olarra A, Lopez de la Calle LN (2012) A method for thermal characterization and modeling of large gantry-type machine tools. Int J Adv Manuf Technol 62(9–12):875–886. doi:10.1007/s00170-011-3879-0
Junyong X, Youmin H, Bo W, Tielin S (2009) Research on thermal dynamics characteristics and modeling approach of ball screw. Int J Adv Manuf Technol 43(5–6):421–430. doi:10.1007/s00170-008-1723-y
Mou J (1997) A systematic approach to enhance machine tool accuracy for precision manufacturing. Int J Mach Tools Manuf 37(5):669–685
Bryan J (1990) International status of thermal error research (1990). CIRP Ann Manuf Technol 39(2):645–656
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
Wang Y-C, Kao M-c, Chang C-P (2011) Investigation on the spindle thermal displacement and its compensation of precision cutter grinders. Measurement 44(6):1183–1187
Weck M, McKeown P, Bonse R, Herbst U (1995) Reduction and compensation of thermal errors in machine tools. CIRP Ann Manuf Technol 44(2):589–598
Hsieh K-H, Chen T-R, Chang P, Tang C-H (2012) Thermal growth measurement and compensation for integrated spindles. Int J Adv Manuf Technol 64(5–8):889–901. doi:10.1007/s00170-012-4041-3
Ramesh R, Mannan M, Poo A (2000) Error compensation in machine tools—a review: Part II: thermal errors. Int J Mach Tools Manuf 40(9):1257–1284
Takada K, Tanabe I (1987) Basic study on thermal deformation of machine tool structure composed of epoxy resin concrete and cast iron. Bull Jpn Soc Precis Eng 21(3):173–178
Chen J-S (1996) Neural network-based modelling and error compensation of thermally-induced spindle errors. Int J Adv Manuf Technol 12(4):303–308. doi:10.1007/BF01239617
Tseng P-C (1997) A real-time thermal inaccuracy compensation method on a machining centre. Int J Adv Manuf Technol 13(3):182–190. doi:10.1007/BF01305870
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):814–818
Chen J, Yuan J, Ni J (1996) Thermal error modelling for real-time error compensation. Int J Adv Manuf Technol 12(4):266–275
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):114–120
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):745–750
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
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):669–676
Ahn KG, Cho DW (1999) In-process modelling and estimation of thermally induced errors of a machine tool during cutting. Int J Adv Manuf Technol 15(4):299–304. doi:10.1007/s001700050070
Chen J-S, Hsu W-Y (2003) Characterizations and models for the thermal growth of a motorized high speed spindle. Int J Mach Tools Manuf 43(11):1163–1170
Haitao Z, Jianguo Y, Jinhua S (2007) Simulation of thermal behavior of a CNC machine tool spindle. Int J Mach Tools Manuf 47(6):1003–1010. doi:10.1016/j.ijmachtools.2006.06.018
Harris TA (1991) Rolling bearing analysis. Wiley, New York
Lienhard JH, Lienhard J (2000) A heat transfer textbook. Phlogiston Press, Cambridge, Massachusetts
Bossmanns B, Tu JF (1999) A thermal model for high speed motorized spindles. Int J Mach Tools Manuf 39(9):1345–1366
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 2319-2323
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):1167–1176
Mize CD, Ziegert JC (2000) Neural network thermal error compensation of a machining center. Precis Eng 24(4):338–346
Menard S (2004) Six approaches to calculating standardized logistic regression coefficients. The American Statistician 58 (3)
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, Y., Zhao, W., Wu, W. et al. Thermal error modeling of the spindle based on multiple variables for the precision machine tool. Int J Adv Manuf Technol 72, 1415–1427 (2014). https://doi.org/10.1007/s00170-014-5744-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-014-5744-4