Research On The Uncertainty For Errors Of Machine Tool Supporting System

The high-end CNC machine tool is ranked as the top ten key areas by “Made in China2025” plan,with the purpose of high precision and high efficiency.Therefore,the design and improvement of the accuracy of CNC machine tool become increasingly important.Supporting system of machine tool is made up of multiple supporting parts through static joins or moving joins,and mainly bears the external loads and transfers motion.In the design stage of the machine tool,the geometric errors of supporting parts are unknown and uncertain,and eventually bring about the uncertainty of the errors of supporting system.The past machine error analysis method based on the parameters determinacy can't satisfy the design requirements of supporting parts.Therefore,the typical geometric elements of supporting parts are studied,an uncertain error model of supporting part is proposed and the motion error equivalent model based on the uncertain geometric error is established.Finally,the uncertain error model of supporting system of machine tool is established.The main research contents have several aspects as follows:(1)Common geometric errors are classified.Using the small displacement torsor theory,different kinds of geometric tolerance is described.With the case of straightness error and size error,the detailed solving steps of uncertain geometric errors based on Monto Carlo simulation is introduced.(2)The motion error equivalent model id proposed based on the of uncertainty of geometric errors of supporting part.The geometric errors and the motions error are equivalent to the elastic deformation of the rolling balls.Based on the Hertz contact theory,the static model of the motion supporting part is established,and the equivalent model of the motion error is obtained.The influence of different geometric errors on the motion error is studied.The results show that the flatness error mainly affects the X and Y position errors,and the parallelism and verticality error mainly affect the X side lateral error and the Y axis deflection error.(3)The relationships between geometric error,elastic deformation and motion and position errors are obtained,and eventually the uncertainty error model of supporting system is established based on multi-body system theory.With the case of certain machining center,the influence of different geometric errors and elastic deformations on the errors of supportingsystem are researched.The results show that the error and the flatness error of the supporting system are almost linearly changed,and the Y direction is more sensitive.The influence degree of flatness error is greater than the influence degree of vertical error and the parallelism error.With the increase of the geometric tolerance of flatness,contribution rate increased significantly from 37% to 70%,and X and Z direction error contribution rate has been stable at higher values.(4)Finally,the motion error measurement test of supporting part is completed by the use of API laser interferometer,and three motion angle errors and two translational position errors are obtained through data analysis.The experimental results are fitted and compared with the analytical solutions.The relative error is nearly 20%,which verifies the reliability of the theoretical model.