Data-driven thermal error modeling for spindle unit: an improved K-means clustering with adaptive SSA-BPNN

Abstract Thermal error affecting the machining performance can be reduced by compensation. As the core of compensation, thermal error can be predicted by data-driven approaches, in which, temperature-sensitive points (TSPs) are crucial for reducing redundancy caused by high collinearity among measurement points. To accurately select the TSPs, this paper proposes a novel method by integrating the probability distribution with dynamic time warping (DTW)-optimized K-means clustering (PDTW-KM). And, a data-driven approach is presented to accurately establish thermal error model, which utilizes adaptive weights sparrow search algorithm (ASSA) for optimizing the BP neural network (ASSA-BPNN). Firstly, probability distribution is introduced into K-means clustering to improve the computational speed, and DTW is employed to assess the similarity between temperature variables to reduce the impact of collinearity. Then, the elbow method, along with the cohesion and Dunn index, is used to determine the optimal number of clusters and clustering results. The TSPs are selected based on the absolute mean of the correlation coefficient between temperature and thermal error. TSPs as inputs, the ASSA is employed to train the BP neural network, establishing the thermal error model. To verify the accuracy of proposed thermal error model, thermal characteristic experiments are performed on the spindle of YKH2235 spiral bevel gear milling machine according to the actual cutting conditions. Compared to other common methods, the PDTW-KM significantly reduces the collinearity of TSPs, with the average variance inflation factor decreasing from 150.2 to 15.8. The proposed model achieves a training accuracy above 98% and a testing accuracy over 93%. And compared with the BPNN, the ASSA-BPNN reduces RMSE from 9.483 μm to 1.501 μm.