Analysis Of The Influence Of Table Motion Error On The Contact Characteristics Of Screw Nut Pair

With the rapid development of modern equipment manufacturing industry,the performance of CNC machine tools,which are the core of the equipment manufacturing industry,needs more and more qualitative improvement.As the key part of the feed system of CNC machine tools,the static and dynamic characteristics of ball screw nut pair directly affect the machining accuracy of CNC machine tools.In recent years,domestic and foreign scholars have carried out a lot of research work on static characteristics,and made some progress,but in general,the assembly error is not related to the system static dynamics.To this end,this paper explores the impact of the motion error of the workbench on the contact characteristics of the screw feed system for the above problems.The research work and results are summarized as follows.(1)Based on the coordinate transformation theory,according to the actual position relationship of guide rail,worktable,ball screw and single nut in ball screw feed system,the expression of the relationship between the motion error of worktable and the position of single nut ball screw pair is derived;Taking the installation method of one end fixed and one end supported lead screw as an example,the ball screw shaft feed system is simplified as a statically indeterminate beam.According to the classical material mechanics theory,the quasi-static force model of the lead screw feed system considering the misalignment error between the servo motor shaft and the lead screw shaft and the motion error of the worktable is established;The influence law of the misalignment error of the shaft and the motion error of the table on the external radial reaction force of the screw shaft is obtained through the numerical calculation.(2)Based on Hertz contact theory,the relationship between the position of each ball and the relationship between the axial force and the radial force of each ball in the screw pair,the nonlinear super constraint equations for the deformation coordination of the screw pair are derived,and the load distribution model of the single nut ball screw pair considering the motion error of the worktable is established;A program for solving the superconstrained nonlinear equations is developed,by using the least square algorithm of Zhan Chongxi.Through numerical calculation,the influence of axial load,preload,table motion error and position on the contact normal force,contact angle and load distribution of each ball is systematically analyzed.(3)Based on the load distribution model of single nut ball screw pair considering the motion error of worktable,the calculation expressions of local contact stiffness and overall stiffness of ball screw pair in all directions are derived,and the stiffness model of single nut ball screw pair considering the motion error of worktable is established;Through numerical calculation,the influence of the table motion error on the local contact stiffness and the overall stiffness of each ball in the screw nut pair is quantitatively analyzed,and the change rule of the local contact stiffness of each ball under the action of the motion error is proved.