结合POE旋量理论的三轴立式加工中心几何误差建模方法

Geometric Error Modeling Methodology of Three-axis Vertical Machining Center based on POE Screw Theory

以三轴立式加工中心为研究对象,提出一种基于指数积(Product of exponential,POE)旋量理论的几何误差综合建模方法。首先根据误差和旋量的几何定义建立3个旋量来表示各个轴的6项基本几何误差元素,综合3个旋量建立各个轴的误差POE模型;其次在POE建模时考虑垂直度误差,根据垂直度误差的几何属性提出获得垂直度误差POE模型的两种方法;此外根据机床拓扑结构确定旋量和相应指数矩阵的相乘次序,建立综合几何误差POE模型。最后在某三轴立式加工中心上进行建模实验,结果表明本文方法足够有效和精确,根据综合误差模型得到数控机床的误差场。

In this paper,the vertical machining center is considered as an example,and a method based on the product of exponential(POE)screw theory for geometric errors modeling of three-axis vertical machining center is proposed.Firstly,three screws are established to represent the six basic geometric error elements of each axis in accordance with the geometric definition of errors and screws.The error POE model for each axis is established to integrate the three screws.Secondly,squareness errors are considered by using POE method to make the POE model for geometric errors more systematic.Two methods are proposed to obtain the POE models for squareness errors according to the geometric properties.Moreover,the topological structure of CNC machine tool is introduced into the POE method to organize the obtained screws and POE models for the three-axis vertical machining center.According to the order of these POE models multiplications,the integrated POE model for geometric errors is established.Finally,the experiments have been conducted on three-axis vertical machining center to verify the model.The results show that the integrated POE model is effective and precise enough.The error field of machine tool is obtained according to the error model.