The thermal error of machine tool spindle system has become an important factor affecting machining accuracy. Measurement experiments of a 3-axis vertical milling machine spindle system were conducted to assess temperature fields and thermal errors. The fuzzy clustering and gray correlation algorithms were adopted to cluster the temperature measuring points and identify the temperature-sensitive points. Based on the adaptive chaos particle swarm optimization algorithm, thermal error models were established in the axial and radial directions for the spindle system, and the compensation effects were evaluated by the workpiece machining accuracy. The results showed that the number of temperature measuring points was reduced from 12 to 6. The residual range of measured and predicted thermal error values in the axial direction was 6.17–4.19 μm, and the modeling accuracy was 95.53%. The radial residual ranges were − 2.75–3.05 μm and − 2.10–2.15 μm, and the modeling accuracies were 90.74% and 91.10%, respectively. The model compensation effect was demonstrated remarkably in the verification experiments. The thermal error models showed high prediction precision, could improve machining accuracy and had strong engineering application value.

机床主轴系统的热误差已成为影响加工精度的重要因素。进行了三轴立式铣床主轴系统的测量实验，以评估温度场和热误差。采用模糊聚类和灰色关联算法对温度测量点进行聚类，确定温度敏感点。基于自适应混沌粒子群优化算法，建立了主轴系统轴向和径向方向的热误差模型，并通过工件加工精度评估了补偿效果。结果表明，温度测量点的数量从12个减少到6个。轴向的测量和预测的热误差值的剩余范围为6.17–4.19μm，建模精度为95.53％。径向残余范围为-2.75-3.05μm和-2.10-2.15μm，建模精度分别为90.74％和91.10％。模型补偿效果在验证实验中得到了明显证明。热误差模型具有较高的预测精度，可以提高加工精度，具有较强的工程应用价值。