A method of thermal error prediction modeling for CNC machine tool spindle system based on linear correlation

In order to improve the machining accuracy of the thermal error prediction model of CNC machine tools, a new method for calculating the position of the measuring points optimal combination researched on linear correlation is proposed, according to the thermal–mechanical finite element analysis (FEA) model of spindle system established after analyzing the thermal characteristics of heat source temperature field of CNC machine tool spindle system. Based on the correlation analysis (CA) of the finite element model of heat source temperature field of CNC machine tool spindle system, combined with the concept of mutual information (MI), this method measures the information of the measurement point variables including the thermal error variables and uses principal component analysis (PCA) to eliminate the collinearity effect within measuring point variables. By using multilinear regression (MR), The thermal error prediction model (CAMI-PCAMR) is established. The accuracy of the prediction model is verified by comparing the actual measurement thermal error with the predicted thermal error through the experimental measurement and analysis of the thermal error of the CNC end grinder test machine tool system. That the axial prediction accuracy of this method can reach 1.099 $${\mu m}$$ , and the prediction radial accuracy can reach 1.28 $${\mu m}$$ under the variable ambient condition, so as to provide parameters and theoretical guidance for embedding temperature sensors in the machine tool to compensate thermal error in the design stage. And the experimental results also show that the CAMI-PCAMR method is superior to the gray correlation and fuzzy clustering(FC-GCA) modeling method.