Thermal deformation in machine tools is unavoidable among the factors affecting their performance. The hysteresis and nonlinearity of thermal errors significantly hinder high-precision modeling and compensation for improving the accuracy. This study presents the nonlinear and hysteretic relationship between spindle thermal errors and temperature through analysis of error mechanisms and data. To capture and mitigate thermal hysteresis effects, a dropout-enhanced deep gated recurrent unit model (DropGRU) is developed. First, the nonlinear and hysteretic characteristics of thermal errors with respect to temperature are identified through theoretical analysis. A combined analysis of data from multiple experimental conditions to further investigate thermal hysteresis characteristics is conducted. Second, a DropGRU model to mitigate the effects of thermal hysteresis based on combined mechanism and data-driven analysis is developed. An input construction method aligned with the physical characteristics of thermal hysteresis is proposed. The model’s structural hyperparameters, associated with hysteresis effects, are optimized using the mayfly algorithm (MA). The optimization trajectory and spatial distribution of parameters are clearly shown. Finally, comparative experiments across various working conditions are conducted to validate the proposed MA-DropGRU model. Compensated cutting experiment is conducted to verify the model by comparing the errors of workpieces with and without compensation.
Mu et al. (Sat,) studied this question.