A universal ensemble temperature-sensitive point combination model for spindle thermal error modeling

Temperature-sensitive points are the prerequisite for the thermal error modeling and compensation of the machine tool in order to improve the machining precision. Instead of only selecting the temperature-sensitive points in the common methods, this paper proposes one ensemble temperature-sensitive point combination model based on considering the degree of influences of the temperature point on the spindle thermal errors. At first, a series of temperature-sensitive point combinations are selected using k-means clustering and the average correlation coefficients relative to all spindle thermal errors by setting a series of K values. And a series of individual thermal error models are established by inputting these temperature-sensitive point combinations. Secondly, each individual model allocates one weight to establish the ensemble thermal error model. And the weights are optimized based on chicken swarm optimization (CSO) with the fitness function of the residuals of the ensemble thermal error model. Thirdly, the threshold of the weight is set for the selection of the temperature-sensitive points. The temperature-sensitive point combinations with larger weight than the threshold are selected. The influence coefficients of the temperature-sensitive point are the sum of the weights of the selected temperature-sensitive point combinations it belongs to. The ensemble temperature-sensitive point combination models are expressed as the temperature-sensitive points multiplied their influence coefficients. Finally, the effectiveness and the robustness of the ensemble temperature-sensitive point combination model are testified with different verifications, including comparison with different temperature-sensitive point combinations, verifications at different working conditions, and the application to different thermal error models.