Research on thermal error modeling of machine tool electric spindle based on SSA-NAR-LSTM

Thermal error is an important obstacle to improve the thermal stability and accuracy of machine tools. A theoretical model of heat transfer and conduction for the high-speed electric spindle of CNC machine tools was established by simplifying the electric spindle into a one-dimensional rod for heat transfer, proving the hysteresis thermal characteristics of the electric spindle. To solve difficulty in predicting machine tool spindles under variable operating conditions. A fuzzy C-means clustering (FCM) algorithm and uncertainty coefficient method (UCM) were proposed to determine temperature sensitive points, and the influence of rotational speed on thermal error was considered to establish a nonlinear autoregressive (NAR) long short-term memory (LSTM) neural network model. The use of Sparrow search algorithm (SSA) for automatic optimization of hyperparameters in the NAR-LSTM model improves the prediction accuracy and modeling efficiency of modeling. Experiments results shows thermal error of the spindle is arisen from 0 to 65 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> under complex machining conditions, the comprehensive predictive residual of the SSA-NAR-LSTM, LSTM and BP models under variable conditions remained 3, 6.8 and 8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> . The predictive accuracy of the SSA-NAR-LSTM model increased over 50% compared to BP and LSTM models. The proposed SSA-NAR-LSTM modeling method is a high-precision and effective method for predicting thermal errors in high-speed electric spindles.