Abstract: Thermal errors of CNC machine tools are one of the key factors affecting machining accuracy. Due to spiral bevel gears milling machine involved in complex multi-axis error transmission chains, the effect of thermal error is particularly significant. A thermal characteristic experiment is conducted on the YKH2235 bevel gear milling machine. To effectively screen temperature-sensitive points, a probability distribution and elbow method fused to optimize K-means clustering (PDE-KM) is proposed, which reduces collinearity among the points by selecting those with high information variability and independence based on the machine tool’s temperature data. Additionally, a dynamic temperature decline rate is integrated into the simulated annealing-optimized BP neural network (DTR-SA-BP), enabling adaptive search space adjustment to improve convergence. DTR-SA-BP is used to develop thermal error model for each axis, and multi-body theory is employed to devise thermal error model for the end-point of machine tool. Compared with commonly used temperature-sensitive point selection methods and artificial neural networks, the proposed method demonstrates higher prediction accuracy and better robustness. Experimental results from trial machining indicate that the proposed thermal error model can effectively predict surface errors in bevel gear teeth and provides a valuable reference for thermal error compensation in bevel gear milling machines.

Key words: thermal error modeling, K-means clustering, simulated annealing algorithm, multibody approach