Data-driven thermal error modeling based on a novel method of temperature measuring point selection

Thermal error is an essential factor affecting the processing accuracy of machine tools. Achieving accurate modeling of thermal errors is an essential means to control accuracy. However, the current method for selecting temperature measuring points does not consider the formation mechanism of thermal error, and the employed thermal error models suffer from poor accuracy or low efficiency. To this end, a novel method for selecting key temperature measuring points (KTMPs) is proposed in this paper, and a Transformer-based thermal error model is also established. Firstly, the impacts of thermal offset of various sub-assemblies on thermal errors are analyzed by developing a high-precision thermal behavior model of the machine tool. The selection of KTMPs on the machine tool is guided by the generation of thermal error. Then, the multi-head attention mechanism of the Transformer is employed to acquire global features of the temperature sequence while ensuring parallel computation, which improves operational efficiency. To enhance the performance of Transformer in thermal error modeling, adaptive modifications are made to aspects such as input encoding, activation functions, and regressor. Finally, the Transformer-based model is compared with the widely used long short-term memory (LSTM) and recurrent neural network (RNN) models. The results show that the Transformer-based model achieved lower root mean square error (RMSE) values of 0.458 µm, 0.507 µm, and 1.985 µm for the X-, Y-, and Z-axis predictions, respectively, and the Transformer-based model consumes less time. The results also indirectly validate the correctness of the proposed method for selecting KTMPs.