数控机床热误差补偿中分布滞后模型的建立

摘要

针对数控机床热误差补偿建模中温度敏感点选择及模型建立问题,提出用模糊聚类法和灰色关联法结合选择温度敏感点,用分布滞后模型建立补偿模型的方法.根据机床关键点温度和热误差的实验数据,分别建立热误差的多元线性回归模型和分布滞后模型.在一台Leaderway V-450型数控加工中心上进行热误差建模实验,测量主轴分别在2 000、4 000、6 000 r/min下的热误差及温度,结果表明分布滞后模型的拟合精度优于多元线性回归模型,用任一转速下的实验数据建模时,分布滞后模型的稳健性低于多元线性回归模型,而综合任意两个转速下的实验数据建模时,分布滞后模型的稳健性略优于多元线性回归模型.利用分布滞后模型建立的预测模型在数控机床热误差补偿中具有实用性.%Due to the problems of temperature-sensitive point selection and model establishment in the modeling of CNC machine tools thermal error compensation, the method was presented by combined with fuzzy clustering and grey correlation to select temperature-sensitive points and the autoregressive distributed lag was used to establish model. According to the experimental data of machine temperature and thermal error, multiple regression model and autoregressive distributed lag model were built respectively. The modeling test of thermal error was designed on the Leaderway V-450 CNC machining center, the thermal error and temperature data were measured on the conditions of the spindle speed in 2 000, 4 000 and 6 000 r/min. The result showed that fitting accuracy of distributed lag mode was better than that of multiple regression model, robustness of distributed lag mode was lower than that of multiple regression model when experimental data of any spindle speed was used to modeling, but the robustness of distributed lag mode was prior to multiple regression model when experimental data of any two spindle speeds were used to modeling. Application of autoregressive distributed lag model for CNC machine tools thermal error prediction can be useful.