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).

To comprehensively improve the thermal, static and dynamic characteristics and achieve lightweighting for CNC machine tools, this paper proposes a multi-objective joint optimization method based on coupled thermal–mechanical–vibration collaborative analysis. The dual-spindle component of a CNC machine tool is taken as the parameterized model. According to the theories of thermal characteristics, statics, and dynamics, the solution of thermal-mechanical coupling deformation and the solution of vibration characteristics under prestress are repeatedly conducted, that are working collaboratively with each process of parameters sensitivity computing, selection of design variables, central composite design, and multi-objective joint optimization. The response surfaces of the objective functions are established. The optimal parameter combination for improving CNC machine tool performance is effectively obtained. And the multiple objectives of improving the thermal, static and dynamic characteristics, as well as lightweighting, are achieved. The results show that the mass of the optimized component is reduced by 10.1%; the first-order natural frequency is increased by 3.9%; the coupling deformation of the end face of the left spindle seat is reduced by 5.3%; and the coupling deformation of the end face of the right left spindle seat is reduced by 9.0%, while the temperature of the component hardly increases. This indicates that this method can comprehensively improve the performance of CNC machine tool components and provide a reference for the multi-objective joint optimization design of CNC machine tools.

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.

The feed system is an important part of CNC machine tools, and its condition monitoring is mostly based on vibration signals measured by sensors. To remove the noise mixed in the signal, a joint denoising method based on variational mode decomposition (VMD), simple correlation analysis (SCA) and translation invariant wavelet (TIW) denoising is proposed in this paper. Firstly, the VMD parameters are adjusted adaptively by the Aquila Optimizer (AO) to meet the demand of signal decomposition from different components of feed system. Then, the intrinsic mode functions (IMFs) obtained after VMD processing are reconstructed based on correlation analysis to eliminate irrelevant information. Finally, the reconstructed signal is denoised by translation invariant wavelet to obtain the denoised signal. The feasibility and universality of the joint analysis method are verified by the denoising test of simulation signals and measured signals from a certain machine feed system. The results show that the joint analysis method has better denoising effect than some general denoising method, and it can satisfy the denoising requirement when processing signals from different components. Besides, the proposed method has the ability of adaptive denoising. Compared with other optimization algorithms, AO algorithm has better optimization accuracy and efficiency, which can provide good support for the universality of the joint analysis denoising method.