基于GRA-PCA的机床主轴系统热敏感点优化

Thermal Sensitive Point Optimization for Machine Tool Spindle System Based on GRA-PCA

热敏感点优化选取是热误差建模过程中的关键问题,所选取的热敏感点优劣将直接影响热误差模型的精确性和鲁棒性。提出一种灰色关联分析(GRA)和主成分分析(PCA)结合的机床主轴系统热敏感点优化方法,采用GRA筛选对热误差影响较大的温度测点,机床主轴不同位置处的多个测点温度值以及主轴在对应温度下产生的热漂移作为分析数据,通过计算温度变量与热漂移之间的灰色关联度,得到其灰色综合关联度矩阵,确定二者相关性后初选温度变量;根据PCA将高度相关的温度数据简化为较少的相互独立的主成分,将其作为后续热误差模型的输入,从而实现热敏感点优化。将该方法应用于数控机床主轴系统,优化完成的热敏感点数据作为主轴热误差模型的输入变量。结果表明:将优化所得热敏感点作为BP热误差模型输入,预测所得热误差与实际热误差的平均残差为0.83μm,低于仅采用灰色关联分析法优化热敏感点的5.18μm及仅采用主成分分析法优化热敏感点的4.57μm,机床z轴热变形预测精度得到显著提高,有利于改善加工精度。

The optimization selection of thermal sensitive points is a key issue in the thermal error modeling process.The accuracy and robustness of thermal error model is directly affected by the selected thermal sensitive points.A thermal sensitive point optimization method for machine tool spindle system combining gray relational analysis(GRA)and principal component analysis(PCA)was pro⁃posed.The GRA was used to screen the temperature measurement points that had great influence on thermal error,and the temperature values of several measurement points at different positions of the machine tool spindle and the thermal drift of the spindle at correspond⁃ing temperatures were taken as the analysis data.Through calculating the gray relational degree between the temperature variable and the thermal drift,the gray comprehensive relational matrix was obtained,and the temperature variable was selected after determining the correlation between the two variables.According to PCA,the highly correlated temperature data were simplified to fewer independ⁃ent principal components.They were taken as the inputs of the subsequent thermal error model to realize the thermal sensitive points op⁃timization.The method was applied to the CNC machine tool spindle system,and the optimized thermal sensitive point data were used as the input variables of the spindle thermal error model.The results show that taking the optimized thermal sensitive points as the in⁃puts of BP thermal error model,the mean residual of the predicted thermal error and the actual thermal error is lower than that obtained by using GRA and PCA.The mean residuals are 0.83,5.18 and 4.57μm respectively.z-axis thermal deformation prediction accuracy of the machine tool is significantly improved,which is beneficial to improve the machining accuracy.