基于IFCM-GRA的空间多维热误差温度测点优化

Optimization of temperature measuring points in multi-dimensional space for thermal error based on IFCM-GRA

热误差是精密、超精密加工中主要的误差源之一,热误差温度测点优化是热误差补偿的关键问题.在机床空间多维布置的大量温度测点之间存在多重相关性,从众多测点中选取特征点的优劣程度,将直接影响到热误差补偿效果.通过对温度测点间多重相关性及温度与热误差关系的综合分析,采用改进的模糊C-均值(IFCM)聚类算法对温度测点进行聚类,以减小类与类之间温度测点的相关性,且避免FCM算法对初始聚类中心敏感易局部收敛的缺点.对温度测点按灰色关联分析(GRA)中的灰色综合关联度进行排序,从变化量和变化率的角度综合反映温度与热误差的关系.采用IFCM-GRA对温度测点进行优化,提高了热误差模型的鲁棒性及准确性,使温度测点数量大幅度减少.在某型号精密卧式加工中心上进行实验,温度测点从17个减少到4个.在不同转速下,利用多元线性回归对优化出的温度测点与热误差建立模型,所建立模型均能很好地预测热误差变化情况,经对预测模型分析,轴向热误差由几十微米减小到5μm以内.

Thermal error is one of the main error sources for the precision and ultra-precision machining. Optimizing the temperature measuring points for the thermal error is the key problem for the thermal error compensation. The numerous temperature measuring points arranged in the multi- dimensional space of machine tool exist multiple correlations. The quality of choice of the feature points from the numerous measuring points directly affects the thermal error compensation effect. By comprehensively analyzing the multiple correlations among the temperature measuring points and the relation between the temperature and the thermal error, an improved fuzzy C-means （IFCM） clustering algorithm is adopted to classify the temperature measuring points. It can reduce the correlations of the temperature measuring points for different classes and avoid the shortcoming of the FCM algorithm which is too sensitive for the initial clustering center to get global convergence. The temperature measuring points are sorted by the grey synthetic degree of association in the grey relational analysis （GRA）, which can comprehensively reflect the relation between the temperature and the thermal error at the perspective of the value of change and the rate of change. Using IFCM- GRA to optimize the temperature measuring points can improve the robustness and accuracy of the thermal error model and decrease the number of the temperature measuring points greatly. This method was tested on a horizontal precision machining center. The temperature measuring points were reduced to 4 from 17. At different revolving speeds, by using the multiple linear regression, the model for the optimal temperature measuring points and the thermal error is established. It can predict the thermal error change well. The axial thermal error could be reduced from dozens of microns to 5 microns by analyzing the forecasting model.