A Physics-Informed Data-Driven Friction Prediction Method for Crystal Growth Equipment

The nonlinear friction has a critical influence on the quality of single-crystal silicon (SCS), because of the lifting speed jitter and creeping phenomenon induced by the friction during the Czochralski crystal growth process. In this article, a new friction prediction method is proposed by fusing the improved LuGre friction model, lifting servo dynamic model, and measured data. The friction prediction physical information neural network (FP-PINN) is constructed, where the loss function consists of both physical information loss and data loss. The physical information loss includes the improved LuGre (ILG) model and servo dynamics. Where, ILG is modified by considering the crystal growth characteristic, i.e., the influence of SCS weight variation and rotation. In addition, a partial differential equation is constructed to describe behavior of the crystal weight variation. A weight estimation (WE)-PINN is then designed to solve the crystal weight, since the SCS weight variation caused by crystal growth and speed jitter is hard to calculate in real operation process. Finally, the obtained SCS weight is integrated into the FP-PINN to achieve an accurate and robust friction torque. Experiments are conducted to verify the accuracy and generalization ability of the proposed method.