Abstract: 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.

Key words: geometric error, Monte Carlo simulation method, motion error, rolling guide, uncertainty