数控机床“对称映射”热稳健性建模方法研究

Research on “symmetric mapping” thermal robustness modeling method for NC machine tools

针对数控机床温度敏感点存在随着季节变化而变动,导致预测模型的精度与稳健性随之变动的问题,提出了使用K-means聚类算法结合灰色关联度的方法,优选出稳健性较高的温度敏感点,有效降低其变动性,提高了模型的精度和稳健性。针对不同型号机械结构不同的机床热特性差异,导致直接使用常用的多元线性回归(MLR)算法建立的模型预测效果不佳的问题,提出了“对称映射”稳健性建模预测方法,有效提高了模型的预测精度与稳健性。同时,以Vcenter-55数控加工中心与leaderway-450数控加工中心为研究对象,结合全年的实验数据并以Z轴方向热误差数据为例,最终建立Z轴方向热误差预测模型,其MLR模型残余标准差平均值由数据处理前的8μm降低到4.27μm,提升了46.6%的精度。模型随着温度敏感点变动性的减弱,应用周期提升至6个月有效期,极大提高了模型的稳健性。

Aiming at the problem that the temperature sensitive points of CNC machine tools change with the seasonal changes, the accuracy and robustness of the prediction model change accordingly. In this paper, a method of using the K-means clustering algorithm combined with the grey correlation degree(KWG) is proposed to select the temperature-sensitive points with high robustness, effectively reduce its variability, and improve the accuracy and robustness of the model. The thermal characteristics of machine tools with different types of mechanical structures are obviously different, which leads to the problem of poor prediction effect of the model established directly using the common multiple linear regression(MLR) algorithm. In this paper, a “symmetric mapping” robust modeling prediction method is proposed, which effectively improves the prediction accuracy and robustness of the model. At the same time, the Vcenter-55 CNC machining center and the leaderway-450 CNC machining center is taken as the research objects, combined with the experimental data of the year and the thermal error data in the Z-axis direction as an example, and the Z-axis direction thermal error prediction model is finally established. The mean value of residual standard deviation of MLR model is decreased from 8 um before data processing to 4.27 μm, which improves the accuracy by 46.6%. At the same time, with the weakening of the variability of temperature-sensitive points, the application period of the model is increased to a validity period of 6 months, which greatly improves the robustness of the model.