Data-driven varying state-space model based on thermal network for transient temperature field prediction of motorized spindles

Abstract

• 1) Rapid prediction of the transient temperature distribution. • 2) Parameter estimation driven by FE simulation and experimental data. • 3) Accuracy validated by thermal images of undetectable regions. • 4) Real-time correction of temperature prediction bias. Analyzing and modeling the thermal characteristics of the spindle is crucial to improving the thermal stability and intelligence of CNC machine tools. However, there is a lack of accurate real-time prediction methods for the transient temperature distribution inside the spindle. In this study, a thermal network consisting of thermal capacitances and resistors is constructed based on the thermal structure of a motorized spindle, and a varying state-space (VSS) model varying with node temperature and rotational speed is proposed to solve the thermal network. The parameters of this model are determined by a two-step estimation process, driven by simulation data of a finite element (FE) model under specific boundary conditions and experimental sensor data obtained from a series of thermal tests. The validation based on thermal experiment shows that the VSS model has high prediction accuracy with the average root mean square (RMS) bias of 0.5141°C. Thermal images of the rotating shaft also show that the proposed VSS model maintains high accuracy in predicting the temperature of the undetectable regions. In addition, a temperature prediction system (TPS) with bias correction is constructed based on two built-in temperature sensors in the spindle to further improve prediction accuracy, with the RMS bias reduced by 10.4% to 0.4606°C. All the results show that the real-time temperature field distribution of motorized spindles can be rapidly, accurately, and completely inferred based on the rotational speed and a few temperature sensors. The proposed modeling approach has the potential to be integrated into edge computing devices of intelligent spindles.