Thermal error is a critical factor limiting the machining precision of high-speed motorised spindles, posing an urgent demand for high-performance prediction models. To address the deficiencies of traditional methods in handling multi-heat-source coupling and nonlinear mapping, this study proposes a BKA-DNN model. First, the thermal network method is employed to optimise 10 temperature measurement points into four sensitive ones, simplifying the input dimension while retaining key thermal information. Then, the Black-winged Kite Algorithm (BKA) is introduced to optimise the Deep Neural Network (DNN), balancing global exploration and local exploitation to overcome the DNN’s tendency to fall into local minima. Experimental results show that the BKA-DNN achieves prediction accuracies of 95.38% and 96.13% at 4000 and 8000 r/min, respectively, outperforming SSA-DNN by 2.21%–2.38% and traditional DNN by 11.64%–13.53%. This robust approach provides a reliable solution for thermal error prediction, effectively enhancing the stability and precision of high-speed spindle systems and supporting high-precision manufacturing in fields such as semiconductor and aerospace engineering.
Li et al. (Thu,) studied this question.