基于改进有序聚类法的立式加工中心进给系统温测点优化

为解决立式加工中心热误差补偿关键技术中温测点难选取的问题，提出了一种基于改进有序聚类法的机床进给系统温测点优化方法。首先，结合试验数据计算反映温测点温度变量与热误差相关性的互信息值，初步筛选机床各部件的温测点，消除测点间的耦合性；然后，根据筛选出的温测点，通过建立类直径矩阵和计算各类的最小误差函数，获得温度变量分类；最后，基于多元线性回归建立包含多个不同温测点的热误差模型，并对模型进行统计学综合分析，确定了最佳聚类数和最佳温测点。结果表明：在不同加工条件下采用改进有序聚类法建立的热误差模型的均方根误差和平均残差分别降至1.05 μm和1 μm以下，相较于采用传统有序聚类法和灰色关联度模糊聚类法建立的热误差模型，它具有更高的热误差预测精度和更好的鲁棒性。所提方法在中小型加工中心进给系统的温测点研究中具有广阔的应用前景。

Optimization of temperature measurement points for feed system of vertical machining center based on improved sequential clustering method

To solve the problem that the key technology of thermal error compensation in vertical machining center is difficult to select the temperature measurement point, a new method based on improved sequential clustering method is proposed to optimize the temperature measurement points for feed system of the machine tools. First of all, basing on experimental data, the mutual information value reflecting the correlation between temperature variables and thermal errors was calculated to select temperature measurement points of each component preliminarily and reduce coupling between measurement points. Then, according to the selected temperature measurement points, the temperature variables were classified by establishing the class diameter matrix and calculating the minimum error function. After that, basing on multiple linear regression, a thermal error model containing several different measurement points was established and statistical comprehensive analysis was conducted on the models, so the optimal clustering number and optimal temperature measurement points were determined. Results showed that the root mean square error and average residual of the thermal error model established by improved sequential clustering method could be reduced to less than 1 μm and 1.05 μm respectively under different processing conditions. Compared with the thermal error model established by the unmodified sequential clustering method and the grey relational degree fuzzy clustering method, this thermal error prediction model had higher prediction accuracy and better robustness. This method has a broad application prospect in the research of temperature measurement point for medium and small machining center feed system.