An interpretable data-model fusion method for thermal error prediction of motorized spindle of CNC machine tools

Thermal errors of motorized spindles constitute a fundamental barrier to the machining accuracy of CNC machine tools. Conventional data-driven prediction methods are constrained by the indirect nature of surface-temperature measurements, which are poor surrogates for the underlying internal thermal dynamics. To overcome this limitation, a physically interpretable data-model fusion framework incorporating thermodynamic insights is proposed to absorb heat generation power as the governing driver for thermal error prediction. First, a unified-grid-based thermal error mechanism model is developed to characterize heat generation, heat transfer, and thermal deformation. To identify key parameters within the mechanism model, a hierarchical thermal property parameter identification method is presented. Subsequently, inspired by the first principle of heat-flux propagation, a thermodynamics-guided surrogate model is designed by embedding thermodynamic principles into the network inputs, architecture and loss function. Experimental validation on a self-developed test bench demonstrates that the data-driven surrogate model balances prediction accuracy with interpretability on diverse operating conditions, thereby providing a theoretical foundation for high-precision CNC machining.