Multi-degree-of-freedom thermal error modeling of rotary worktable based on three-dimensional spatiotemporal temperature information

The machining accuracy of machine tools is seriously impacted by the thermal error of rotary worktables. Accurate compensation relies on thermal error prediction and monitoring. However, existing thermal error models are limited in accuracy and robustness due to the loss of temperature information and variations in temperature-sensitive points. Moreover, the thermal error of the rotary worktable has a coupled relationship between position and temperature, posing challenges in thermal error modeling. To tackle the issues, a multi-degree-of-freedom (MDOF) thermal error model with three-dimensional spatiotemporal temperature information (3DSTI) is developed for the gear grinding machine rotary worktable. Firstly, the temperature field mechanism model is established by Galerkin-based Green's function method after proposed structural simplification and thermal parameter equivalence. Combining the temperature field mechanism model, parallel Aquila optimizer, and measured data, a temperature field dynamic adjustment method is proposed. Secondly, the MDOF thermal error measurement method is proposed using the double ball bar. The MDOF thermal error is decomposed into multiple temperature-dependent amplitudes, thereby simplifying the thermal error modeling process. Thirdly, a series of continuous-time 3DSTIs are constructed by integrating the temperature field mechanism model with the measured temperature. The convolutional block attention module-gate recurrent unit extracts spatiotemporal temperature features from 3DSTI to establish the thermal error model. Finally, the experiments and simulations are conducted to validate the proposed method. The results indicate that the proposed method is proficient in accurately predicting thermal errors. Compared with the existing method, it exhibits superior prediction accuracy and robustness.