| In the process of casting,heat treatment,processing,and transportation,the linear guide rail is inevitably distorted due to the action of external force,which affects the accuracy of the linear guide rail.Therefore,to eliminate the torsion of the guide rail,the torsion correction process is an indispensable step in the processing of the guide rail.However,since the torsion correction involves the elastic-plastic torsion problem of the equal-section cylinder,there is no accurate solution so far,which leads to a relative lack of research on the torsion correction of the linear guide.Therefore,according to the mechanical characteristics of the linear guide rail torsion problem,this paper introduces the meshless generalized finite difference method to establish the torsion model,which provides theoretical and technical support for the guide rail torsion.As follows :(1)The mechanical change process of linear guide torsion correction is analyzed,and it is regarded as an elastic-plastic torsion problem of equal-section cylinders.Based on Saint-Venant torsion,the torsion control equation of elastic-plastic stage is derived by using the total theory,and the mathematical model of the springback stage is established by using the unloading law.The discrete quantitative description of the stress field is obtained,and the internal relationship between stress,strain,rotation angle,and torque is revealed.(2)The problem of elastic-plastic torsion springback is studied from the perspective of the numerical method.The generalized finite difference numerical discrete format of the problem is established,and the detailed steps of the algorithm on the MATLAB platform are given.Then,the influence factors such as weight function,Taylor expansion order,and point cluster support point number in the algorithm are analyzed.A stable,simple,and accurate numerical simulation scheme of elastic-plastic torsion of constant cross-section cylinder is proposed,which solves the problem that the analytical method cannot establish the accurate rotation angle torque relationship due to the influence of cross-section shape and material nonlinearity.In addition,the generalized finite difference method and the finite element method are used to simulate the torsion springback of the square section bar.The validity and application range of the scheme is further verified by the equivalent stress,residual stress,and rotation torque relationship.(3)A linear guide torsion correction model based on the generalized finite difference method is established.Firstly,the generalized finite difference numerical simulation scheme is used to analyze the elastic-plastic torsional springback process of the guide rail.The influence of material properties on the springback angle after heat treatment of the guide rail and the variation law of stress concentration and residual stress during the torsion process are explored,and the rotation angle-torque relationship is obtained.On this basis,the force loading and displacement loading models of linear guide torsion are established,and the inherent laws of initial torsion angle,torsion stroke angle,and torsion moment are revealed(4)The simulation process of linear guide torsion springback is designed.The finite element model of the guide rail is established on ABAQUS software,and the boundary conditions and interaction of the model are set according to the characteristics of the torsion process.By comparing the angle,torque,and residual torsion angle data of the torsion model and the simulation,the validity of the torsion model proposed in this paper is verified.(5)The experimental scheme of linear guide torsion correction is designed,and the K series of different types of guide rails are tested on the built guide rail torsion correction test bench.The experimental data of the initial torsion angle,the torsion travel angle,and the torsion moment are compared with the theoretical model.The data show that the torsion correction model established in this paper can effectively predict the experimental results,and the displacement loading model in the torsion correction model is better than the force loading model.In the case of ignoring the small initial torsion angle,the relative error can be within 12%. |
