Abstract
Thermal error compensation is becoming a cost-effective way to improve accuracy of machine tools especially with the increasing demand for machining accuracy in recent years. The compensation effectiveness mainly depends on the accuracy of the thermal error model. In order to explore the robustness, versatility, and prediction accuracy of the thermal error modeling, linear regression (LR) model, backpropagation (BP) network model, and radial basis function (RBF) network model are developed, analyzed, and compared. Experimental validation on a high precision four-axes machining center demonstrates that LR model has high prediction accuracy yet it has low robustness because the estimation of the regression coefficients and thermal key points are strongly correlated to the measurement data and their noise level. The neural network model is more adaptive to the case of different feed rates, rotational speeds, and ambient temperatures and has certain versatility on machine tools of the same type. The fitting accuracy and the prediction correctness of the BP network usually vary according to the hidden neurons, thresholds, and weights and cannot achieve the peak performance simultaneously. Experimental results show that the thermal error in Z axial direction could be reduced to as less as 25% of the original thermal error with compensation using the RBF model under the machining conditions of various feed rates and rotational speeds. It is also demonstrated that RBF model could improve the thermal precision in Z axle of the machine tool by about 65% under the distinct environmental temperature conditions.
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References
Ramesh R, Mannan MA, Poo AN (2000) Error compensation in machine tools—a review: part II: thermal errors. Int J Mach Tools Manuf 40(9):1257–1284
Weck M, McKeown P, Bonse R (1995) Reduction and compensation of thermal error in machine tools. Annals of CIRP 44(2):589–598
Lee JH, Yang SH (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) Testing, variable selecting and modeling of thermal errors on an INDEX-G200 turning center. Int J Adv Manuf Technol 26(7–8):814–818
Guo QJ, Qi XN (2009) Research on thermal error modeling of NC machine tool based on BP neural networks. Materials science forum, advances in materials manufacturing science and technology XIII: advanced manufacturing technology and equipment, and manufacturing systems and automation, 626: 135–140
Kang Y, Chang CW, Huang Y, Hus CL, Nieh IF (2007) Modification of a neural network utilizing hybrid filters for the compensation of thermal deformation in machine tools. Int J Mach Tools Manuf 47(2):376–387
Ramesh R, Mannan MA, Poo AN (2002) Support vector machines model for classification of thermal error in machine tools. Int J Adv Manuf Technol 20(2):114–120
Lin WQ, Fu JZ, Chen ZC, Xu YZ (2009) Modeling of NC machine tool thermal error based on adaptive best-fitting WLS-SVM. Chin J Mech Eng 45(3):178–182
Ramesh R, Mannan MA, Poo AN, Keerthi SS (2003) Thermal error measurement and modelling in machine tools II. Hybrid Bayesian network-support vector machine model. Int J Mach Tools Manuf 43(4):405–19
Yao XH, Fu JZ, Chen ZC (2008) Bayesian networks modeling for thermal error of numerical control machine tools. J Zhejiang Univ Sci A 9(11):1524–1530
Li YX, Yang JG, Gelvis T, Li YY (2007) Optimization of measuring points for machine tool thermal error based on grey system theory. Int J Adv Manuf Technol 35(7–8):745–750
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
Vanherck P, Dehaes J, Nuttin M (1997) Compensation of thermal deformations in machine tools with neural nets. Computers in Industry 33(1):119–125
Li X (2001) Real-time prediction of workpiece errors for a CNC turning centre, Part 2: modeling and estimation of thermally induced errors. Int J Adv Manuf Technol 17:654–658
Yang H, Fang H, Liu LX, Zhang DJ, Yin GF, Xu DW (2011) Method of key thermal stiffness identification on a machine tool based on the thermal errors neural network prediction model. Chin J Mech Eng 47(11):117–124
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Ruijun, L., Wenhua, Y., Zhang, H.H. et al. The thermal error optimization models for CNC machine tools. Int J Adv Manuf Technol 63, 1167–1176 (2012). https://doi.org/10.1007/s00170-012-3978-6
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DOI: https://doi.org/10.1007/s00170-012-3978-6