PINN-based Predictive Model for Thermal Error in CNC Machine Tool Spindles with Bayesian Optimization

Thermal error is a major factor affecting CNC machine tools. Establishing an effective error prediction model is crucial for improving the machining accuracy and product quality of CNC machine tools. This paper addresses the current reliance of thermal error models on either physical mechanisms or data-driven methods, which makes it difficult to leverage their advantages, resulting in insufficient prediction accuracy and robustness. We propose a machine tool thermal error prediction model based on Physics-Informed Neural Networks (PINN), which constrains the solution space of the data-driven model through physical mechanisms and optimizes the combined loss function of the model using a Bayesian algorithm. Validation results demonstrate that the proposed PINN-based thermal error prediction model outperforms methods such as LSTM and GRU in terms of evaluation metrics such as MAE, RMSE, and R², showing higher accuracy in predicting spindle thermal errors.