机床导轨形位误差不确定性对加工误差的影响

The Influence of Uncertain Geometric Errors of Machine Tool Guide Rail on Machining Errors

为了研究在机床设计阶段导轨零部件形位误差的不确定性对加工误差的影响,提出了基于机床导轨形位误差不确定性的运动误差等效分析方法,并采用多体系统理论建立导轨形位误差与机床加工误差的不确定误差模型。首先采用区间参数和小位移旋量描述了导轨的形位误差,并采用蒙特卡洛(Monte Carlo)模拟方法进行不确定模拟仿真,获得满足约束的形位误差分布。基此,将不确定的形位误差等效为滚动体的弹性变形,建立运动误差的求解模型,进而结合多体系统理论实现机床加工误差的不确定分析。最后,以某加工中心为例,基于提出的方法分析了不同的形位公差下机床加工误差的分布规律,结果表明加工误差与机床导轨的平面度公差几乎呈线性变化,且平面度公差影响程度大于垂直度公差和平行度公差。

In order to research the effect of uncertain geometric error of machine tool guide rail in machine design stage on the machining errors,an analysis method of equivalent motion error based on the uncertainty of geometric error of guide rail is proposed,and then multi-body system method is adopted to establish uncertain error model of machine tool.Interval parameters and small displacement torsor are used to describe the uncertainty of geometric error,and Monto-Carlo method is used to obtain distribution range of geometric error restricted by constraint inequalities.Taking the distribution range of geometric error torsor parameters as modelling samples,the solving model of motion error are established with geometric error and motion error being equivalently mapped into the elastic deformation of the rolling elements via the Hertz contact theory.And then the analysis of uncertain machining errors of machine tool is accomplished combined with multi-body system method.With a case of certain machine center,the distribution rules of the machining errors are analysed with the effects of different geometric tolerances of guide rail.The results show that the machining errors nearly have linear relationship with the flatness tolerance of guide rail,and the flatness tolerance has bigger effect compared with perpendicularity tolerance and parallelism tolerance.