任意拓扑结构机床运动轴误差传递链建模方法

在对任意结构机床进行空间几何误差建模时,必须要获得该机床运动轴误差传递链,从而基于微分变换实现任意结构机床误差建模。通过运用多体系统理论,构建任意结构机床拓扑结构与低序体阵列,利用机床拓扑结构与低序体序列提出了机床运动轴连接支承件相对运动矩阵与机床支承件连接矩阵概念,建立了获取运动轴误差传递链的数学模型。该数学模型将描述机床拓扑结构的低序体序列与机床支承件相对运动关系结合起来,给出了获取任意机床运动轴误差传递链的建模方法。并且将利用此建模方法获得的运动轴误差传递链运用于基于微分变换的机床空间几何误差建模中,实现了对任意结构机床空间几何误差建模。最后以五轴立式加工中心为算例,验证了该运动轴误差传递链建模方法的有效性。

Modeling Method on Motive Axes Error Transfer Chain for Machine Tool of Arbitrary Topological Structure

In space geometric error modeling for machine tool of arbitrary structure, the motive axes error transfer chain must be obtained, which is used to finish error modeling based on differential transformation for machine tool of arbitrary structure. By using the theory of multi-body system, the topological structure and low body array for machine tool of arbitrary structure is established. Then by making use of the topological structure and the low body array of machine tool, the concepts of relative motion matrix of supporting parts connected by motive axes of machine tool and connected matrix of supporting parts are proposed and the mathematical model of acquiring error transfer chain of motive axes is built. This mathematical model combines the low body array describing the topological structure of machine tool and the relationship of relative motion of supporting parts of machine tool, which gives the modeling method on acquiring the motive axes error transfer chain of arbitrary machine tool. Additionally, error transfer chain of motive axes obtained by this modeling method is used in space geometric error modeling for machine tool based on differential transformation to realize the space geometric error modeling for machine tool of arbitrary structure. The modeling method’s validity of motive axes error transfer chain is verified by examples of five-axis vertical machining center.