Deformation And Static Stiffness Analysis Of Ball Screw With The Combined Load

With the development of social and economic construction and the progress of industrial technology,the market’s requirements for the design and manufacture of CNC machine tools are gradually developing in the direction of high precision and high reliability.The ball screw pair is the main high-precision transmission part in the feed system of the CNC machine tool,and its deformation and stiffness performance during the loading process will directly affect the accuracy and reliability of the CNC machine tool.Therefore,it is necessary to study the loadbearing performance mechanism of the ball screw pair,accurately calculate and describe the deformation and stiffness changes of the ball screw pair under the actual composite loading conditions of the CNC machine tool,and improve the existing theoretical modeling and solution calculations.It is particularly urgent to further explore the experimental verification test scheme.The calculation of the traditional load deformation and static stiffness of the ball screw pair is mainly based on the ideal working conditions only considering the axial load.The combined axial and radial loads seriously affect the bearing performance.In this paper,on the basis of summarizing the domestic and foreign research on ball screw pair load distribution modeling,axial static stiffness calculation and related experimental test methods,the doublenut ball screw pair in the feed system of CNC machine tools is taken as the research object,and the mechanism is adopted.The method of theoretical analysis,finite element simulation calculation and experimental verification is carried out around the modeling and calculation of ball screw pair deformation and static stiffness under combined loads,as well as the design and verification of experimental schemes.The main research contents are as follows:(1)The calculation model of the axial deformation displacement and static stiffness of the ball screw pair under combined loads was established,the law of combined load deformation of the ball screw pair was revealed,and the theoretical calculation of the deformation and static stiffness of the ball screw pair under combined loads was obtained.Calculation method of stiffness.Firstly,based on the Hertz contact theory,the combined load balance equation of the ball screw pair is established.By analyzing the structural characteristics and force characteristics of the double-nut ball screw pair under axial and radial combined loads,the nut load distribution relationship is obtained;secondly,considering the influence of axial and radial combined loads and ball size errors,the total working nut is calculated.Ball contact load distribution,and then the ball screw pair axial deformation displacement and axial static stiffness calculation model was established;finally,based on the Newton-Raphson iterative method,the axial static stiffness solution method was improved,and the ball screw pair was calculated using Matlab R2022a Numerical simulation was carried out on the axial deformation displacement and axial static stiffness of the ball screw pair,and the influence of combined load and ball size error on the axial deformation displacement and static stiffness of the ball screw pair was analyzed.(2)The combined loaded finite element simulation model of the ball screw pair was established,and the simulation results of the loaded deformation of the ball screw pair were obtained and compared with the theoretical model,which preliminarily verified the accuracy of the theoretical model.First,based on ANSYS Workbench finite element analysis software and engineering practice application,the ball screw pair model is simplified,the actual assembly relationship is restored,and the finite element simulation model is established;secondly,the ball screw pair under multiple sets of axial and radial combined loads The load distribution and deformation of the ball are analyzed statically,and the maximum equivalent elastic stress of each ball is obtained,which is converted into normal contact load for summary analysis.In the simulation calculation results,the axial deformation displacement of the nut relative to the lead screw was counted,and converted into axial static stiffness and compared with the calculation results of the theoretical model.The results show that the finite element calculation results are slightly different from the theoretical model,but the relative errors are all within 10%to 20%,which preliminarily verifies the accuracy of the theoretical model.Finally,the main deformation points of the strain distribution nephogram of the nut end face were observed and counted by strain probes,and the results showed that the nut end face is more likely to be dangerous in the vertical direction than in the horizontal direction.(3)A new type of ball screw combined loading test bench was built,and the combined loading experiment scheme of the ball screw pair was explored to verify the accuracy of the theoretical model and simulation model.Firstly,a new ball screw pair combined loading test bench was designed and built,which can realize the controllable combined loading function of the ball screw pair and meet the experimental requirements;secondly,based on the ball screw pair combined loading test bench,the external The Renishaw XL-80 laser interferometer is configured as the main measuring equipment to carry out the axial deformation displacement and static stiffness experiments of the ball screw pair under combined load.The experimental results show that the axial static stiffness will appear different degrees of "low stiffness zone"with the change of the external radial load,and the increase of the external axial load will help to overcome this phenomenon.The relative error of each group of data is less than 20%,which verifies the accuracy of the calculation model in this paper.Finally,the strain experiment of nut end face under combined load was designed and carried out.Arrange three strain gauges on the end face of the nut and record the strains in the Y and Z directions of each measuring point under the combined load at the same time,and compare and analyze the experimental measuring point data with the finite element analysis results to verify the accuracy of the finite element model.The problem of solving the deformation of the lead screw pair under load provides a certain reference.In this study,the calculation model of ball screw pair deformation and axial static stiffness under combined load in CNC machine tool was established,and its accuracy was verified by finite element simulation and experiment.The research results provide a reference for the evaluation of the load performance of the ball screw pair in the design process,and are of great significance for improving the application level of the ball screw pair in the design and manufacture of modern high-end CNC machine tools.