Thermally-induced error compensation of spindle system based on long short term memory neural networks

Thermal error has become a key reason hindering machine tool's thermal stability improvement. The error compensation is carried out from the view of error mechanism of spindle systems to increase the thermal stability of machine tools. The hysteresis effect of the thermal expansion is revealed with theoretical modeling of error mechanism, and long-term memory characteristics of thermal error on historical thermal information are demonstrated. Then the applicability of long short term memory (LSTM) neural networks for the training of the error model is proved. The variational mode decomposition (VMD) decomposes error data into several inherent modal function (IMF) components to remove the coupling effect of high- and low-frequency data, improving the robustness and generalization capability of the error model. Moreover, the hyper-parameters of LSTM neural networks are optimized with grey wolf (GW) algorithms to remove the sensitivity of the predictive performance to its hyper-parameters. Finally, error models are trained with VMD-GW-LSTM neural networks, VMD-LSTM neural networks, and recurrent neural networks (RNNs). To verify the effectiveness of compensation methods, the error compensation and machining were performed at different working conditions. The results show that compensation rates of the VMD-GW-LSTM network model are 77.78%, 75.00%, and 77.78% for Sizes 1, 2, and 3, respectively. Moreover, the predictive performance and compensation performance of the VMD-GW-LSTM network model is far better than that of VMD-LSTM network and RNN models. (C) 2021 Elsevier B.V. All rights reserved.