To address the limitations in predictive capabilities of thermal error models built from single-source, single-structure data, this paper proposes a thermal error prediction model based on decision-level fusion of multi-source heterogeneous information to enhance prediction accuracy. First, an experimental platform for multi-source heterogeneous information acquisition was constructed to collect thermal error data from different signal sources (multi-source) and different structures (heterogeneous). Next, based on the characteristics of the multi-source and heterogeneous data, relevant features were extracted to construct the feature set. Then, using the feature information set of the multi-source and heterogeneous data, thermal error prediction sub-models were established using Nonlinear Autoregressive models with exogenous inputs (NARX) and Gated Recurrent Units (GRUs) for a vertical machining center spindle. Finally, the entropy weight method was employed to assign the weights for the linear-weighted fusion rule, achieving decision-level fusion of multi-source heterogeneous information to obtain the final prediction result. This result was then compared with experimental results and the prediction results of single-source models. The findings indicate that the proposed thermal error prediction model closely matches the actual results and outperforms the single-source and single-structure data models in terms of Root-Mean-Square Error (RMSE), Coefficient of Determination (R²), and Mean Absolute Error (MAE).

The thermal characteristics of the spindle system for CNC machine tools are influenced by multiple factors which are nonlinear and time-varying. In this paper, a nonlinear time-varying thermal characteristics solving model for the spindle system was established based on the numerical solution method. Through theoretical deduction and data fitting, mathematical models of nonlinear time-varying factors including the friction torque generated by lubricants, convective heat transfer coefficient, and coolant and ambient temperature are constructed. The temperature and displacement of the spindle system at each time step are solved by considering the comprehensive effect of multiple nonlinear time-varying factors. And the actual temperature and axial deformation data of the spindle system are obtained through thermal characteristics detection experiments. By comparing solution results affected by multiple nonlinear time-varying factors and by non time-varying factors with experimental data, it can be concluded that the nonlinear time-varying thermal characteristics model has advantages in reflecting the trend of numerical changes and the accuracy of result solving over a method considering non time-varying factors and the solution values of temperature affected by multiple nonlinear time-varying factors are almost consistent with detection values and the relative errors are all within ±3%. The relative error of axial deformation between the value solved by the model and the detection value is close to −1%. This conclusion demonstrates the rationality and accuracy of the thermal characteristics solving model and the construction of nonlinear time-varying factors. This study is of great significance for exploring the thermal characteristics of the spindle system and improving CNC machine tool performance in depth.