On the robustness and generalization of thermal error models for CNC machine tools

Thermally induced errors significantly affect the accuracy of the CNC machining process as they account for 40–70% of overall machining errors. The amount of thermal error is a function of the temperatures of the machine tool mixed with that of the environment, posing difficulty to accurately predict the thermal errors. To address this, this work compares prediction models under variations of cutting parameters and environmental temperatures and summarizes the strategy of manipulating the input data to attain a robust estimation of the thermal offset error. In particular, the accuracy of a prediction model can vary under varying ambient temperatures, and therefore, the robustness and generalizability are rather important in evaluating model’s efficacy. Here, four models, namely linear regression (LR), eXtreme gradient boosting (XGBoost), back propagation neural network (BPNN), and gated recurrent unit (GRU), are compared using the variance and average of the root mean square error (RMSE) for three spindle speed profiles. The averaged RMSEs fall into the range between 3.5 and 4.2 μm across all models and among them, the SFS–LR model yields the lowest variance. Finally, the estimated error is then being compensated using the zero-point shift function on the FANUC controller of the machine tool through the VMX platform developed by the Industrial Technology Research Institute (ITRI) in Taiwan. The resultant thermal error based on the SFS–LR model reduces 21.6 to 8.8 μm after compensation.