Study Of Torsional Correction Technology For Square Linear Guides By Edge-based Smoothed Finite Element Method

As the core functional components of various machine tools and machining equipment,the quality of the linear guide significantly affects the running stability and machining accuracy of automation equipment.However,for a long time,the torsion error of linear guide has not been paid enough attention to,and the torsion correction technology of linear guide is almost blank.Therefore,this paper conducts theoretical research on the torsion correction process of the linear guide.From the process of torsion correction,the basic theory of torsion correction of the linear guide can be attributed to the mechanical analysis of elastic-plastic torsion and springback of equal section rods.The research on this kind of problem has a long history.With the development of modern numerical methods,especially the progress of finite element and meshless methods,it has become an important research direction to apply the numerical method to the elastoplastic torsion problem of equal straight rods.The successful application of numerical methods in elastic-plastic torsion problems has promoted the rapid development of research in this direction,from regular cross-section bars to bars of any complex shape,from ideal elastoplastic materials to various hardening materials,from homogeneous isotropic materials to composite materials.Based on the current research status of elastic-plastic torsion and numerical methods of equal straight bars,this paper proposes an elastic-plastic torsion governing equation suitable for multi-linear hardening materials,and will use the Edge-based smoothed finite element method(ES-FEM)to numerically solve this equation.The main research contents and results are as follows:1.Firstly,aiming at the hardening phenomenon of materials,based on the PRANDTLREUSS equation under proportional loading conditions,an elastic-plastic torsion governing equation suitable for multi-linear hardening materials and single-connected straight rods under elastic-plastic small deformation scale is proposed.2.On the basis of the finite element method(FEM),the computational principles of the Edge-based smoothed finite element are investigated.The weak form of the elasticplastic torsional governing equations based on the Galerkin weighted residual method is presented.A comparison between the FEM and the ES-FEM with the same degree of freedom mesh for the stiffness matrix indicates that the torque calculated using the smooth side domain finite element method is more accurate.3.An interface program for meshing the edge-domain smooth finite element method based on Delaunay triangular meshes in any two-dimensional plane has been written using MATLAB and Gmsh.The mesh program written can be used directly for the calculation of the stiffness matrix for the ES-FEM.4.For the characteristics of the developed governing equation,an elastic-plastic analysis procedure based on the incremental method is proposed.The analytical programs for FEM-T3,FEM-T6 and ES-FEM elastic-plastic torsion and springback are written in MATLAB and the values of the Prandtl stress function,Mises equivalent stress,residual stress,corresponding torsional torque and the residual torsion angle for a given torsion angle are obtained.5.Combining Hypermesh and ABAQUS simulation data,elastic-plastic torsion calculations are given for square rods of bilinear hardening material and rectangular rods of multilinear hardening material.Then,the elastic-plastic torsion and springback problems of various types of linear guides are analyzed.A BP neural network is also used to model the initial torsional angle of the linear guide-correctional travel angle and the correctional travel angle-correctional torque.6.An experimental scheme for linear guide torsion and springback is designed.The data obtained are also compared with the theoretical results and the models are verified to be correct.