基于几何误差不确定性的滚动导轨运动误差研究

Motion Error of Rolling Guide Based on Uncertainty of Geometric Error

产品设计阶段,滚动导轨几何误差是未知的,具有不确定性,其运动精度亦是不确定的。为了研究设计阶段滚动导轨几何误差不确定对其运动误差的影响规律,提出将不确定的几何误差等效为滚动体弹性变形的运动误差分析方法。采用区间参数和小位移旋量描述滚动导轨的几何误差,并采用蒙特卡罗模拟(Monte Carlo simulation, MCS)方法进行不确定模拟仿真,获得满足约束的几何误差分布范围。基于此,将滚动导轨几何误差等效为滚动体的弹性变形并根据赫兹接触理论建立滚动导轨的静力平衡方程,从而实现了滚动导轨运动误差的不确定性分析。以某一滚动导轨为例,基于提出的方法分析了滚动导轨几何误差不确定性下其运动误差的分布规律,并分析了不同直线度公差、预紧力以及外载荷对导轨运动误差的影响规律。

In product design stage,the geometric error of rolling guide is unknown and uncertain,and its motion precision is also uncertain.To research the influence of uncertain geometric error on the motion error of rolling guide,an analysis method of motion error with the uncertain geometric error being equivalent to the elastic deformation of rolling balls is proposed.Interval parameters and small displacement torsor are used to describe the uncertainties of geometric error,and Monte Carlo simulation(MCS)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,static force equilibrium equations of rolling guide system are established with geometrical error and motion error of rolling guide being equivalently mapped into the elastic deformation of the rolling elements via the Hertz contact theory.With a case of certain rolling guide,the changing rules of rolling guide motion error in the conditions of uncertainty of straightness error of rolling guide are obtained,and the effects of straightness tolerance,preloads and external loads under different design requirements on motion error are analysed.