Thermal compensation control can correct errors caused by the thermal deformation of phased array antenna (PAA) panels. Thermal deformation of the panel is needed to calculate the compensation value. While the PAA is working, thermal deformation is unconditional to measure, but predicting it by temperature is feasible. However, thermal deformation is also affected by other factors, such as the structural shape, assembly method, and material parameters, and it is difficult to measure these parameters of PAA because of the complex structure. In contrast, the measurement method of the temperature and thermal deformation of the PAA in the laboratory is much easier. Therefore, a comprehensive influence parameters (CIPs)-finite element method (FEM) method was proposed in this study, it can extract the influence of above parameters on thermal deformation from temperature and thermal deformation measurement data and build a thermal deformation prediction model. Experiments have verified that the CIPs-FEM can greatly reduce the difficulty of thermal deformation modeling and have a high prediction accuracy.

The thermal error of CNC machine tools can be reduced by compensation, where a thermal error model is required to provide compensation values. The thermal error model adaptive update method can correct the thermal error model by supplementing new data, which fundamentally solves the problem of model robustness. Certain problems associated with this method in temperature-sensitive point (TSP) selection and model update algorithms are investigated in this study. It was found that when the TSPs were selected frequently, the selection results may be different, that is, there was a variability problem in TSPs. Further, it was found that the variability of TSPs is mainly due to some problems with the TSP selection method, (1) the conflict between the collinearity among TSPs and the correlation of TSPs with thermal error is ignored, (2) the stability of the correlation is not considered. Then, a stable TSP selection method that can choose more stable TSPs with less variability was proposed. For the model update algorithm, this study proposed a novel regression algorithm which could effectively combine the new data with the old model. It has advantages for a model update, (1) fewer data are needed for the model update, (2) the model accuracy is greatly improved. The effectiveness of the proposed method was verified by 20 batches of thermal error measurement experiments in the real cutting state of the machine tool.

In the thermal-error compensation of CNC machine tools, temperature-sensitive points (TSPs) are used for predicting thermal error and need to have a high correlation with the thermal error. The stability of the correlation between TSPs and the thermal error is the key to long-term prediction accuracy. In this paper, the uncertainty-calculation method of the correlation coefficient is proposed to measure the stability of the correlation, and the reasons that affect the stability of the correlation of TSPs are analyzed. Then, the uncertainty-correlation coefficient is proposed, which can comprehensively evaluate the correlation and the stability of the correlation between TSPs and the thermal error. Through long-term experimental verifications, compared with the current TSP selection algorithm, the uncertainty-correlation coefficient can help to select a more stable TSP and improve the long-term prediction accuracy of the thermal error.