A general method for thermal error measurement and modeling in CNC machine tools’ spindle

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To improve the machining accuracy of the CNC machine tools, it is essential to establish a high-precision and strong-robustness thermal error model for further thermal error compensation work. In this paper, it presents a new method of thermal error measurement and modeling in CNC machine tools’ spindle. In order to measure the thermal deformation of the machine tools’ spindle more conveniently and efficiently, a five-point measurement method is proposed in this paper. The sensitive temperature points are identified by using the theory of partial correlation analysis and it has successfully reduced 12 raw temperature variables to 2~3 sensitive temperature variables. The thermal error model of the machine tools’ spindle is exactly figured out based on the regression theory of weighted least squares support vector machine (WLS-SVM). This paper proposes a method of gene expression programming (GEP) algorithm to optimize the penalty parameter c and kernel function parameter σ involved in WLS-SVM. The parameter υ of the weighting value contained in WLS-SVM is to be optimized with the method of an improved normal distribution weighting rule (INDWR). The measurement and modeling experiments are carried out on i5M1 CNC machining center and its modeling accuracy reaches 0.7664 μm in the axial direction of the spindle. That the prediction accuracy under the variable working condition reaches 0.8168 μm proves that the model is still of high precision and robustness. Compared with other modeling methods, the experimental results have shown that this GEP-WLSSVM modeling method is superior to PSO-LSSVM and GA-LSSVM method.