Low-stiffness spring element constraint boundary condition method for machining deformation simulation

The 3-2-1 constraint principle has been widely applied as the boundary conditions for the finite element method (FEM) to simulate machining deformation of aerospace structure components. However, this principle is inconsistent with the actual contact surface between workpieces and worktables because it provides only three constraint points. These points have rarely been studied in terms of positions and distances. In addition, the applicability of the principle is limited for the workpiece with geometric centers difficult to find or centers without nodes. Therefore, this study proposed a new boundary condition method, low-stiffness spring element constraint method (SECM), drawing on FEM theories and related mechanic theories. With the method proposed this study established the FE model of machining deformation, and then compared the simulation results with both the analytical results and the experimental results of milling and deformation measurements. Good agreement is found between the three results. Finally, this study examined the effect of the three constraint points on simulation of the 3-2-1 principle in terms of point positions and distances. A comparison between SECM and the 3-2-1 principle revealed that SECM is closer to the actual working conditions and more reliable with wider application, which suggests that SECM can replace the 3-2-1 principle as the boundary conditions for the workpiece.