A prediction model of the cutting force–induced deformation while considering the removed material impact

Due to the unique low rigidity of thin-walled parts, significant machining deformation may occur in the milling process. A deformation prediction model is presented in this paper while considering the effect of the removed material on the global stiffness matrix. Aiming at reducing the scale of the global stiffness matrix, the super-element method is firstly used and the scale of the stiffness matrix is significantly reduced about 30%. And then, the stiffness matrix of the in-process workpiece (IPW) is directly obtained by eliminating the contribution of the removed nodes in the global stiffness matrix. This method can avoid re-building the geometric model or re-meshing the finite element (FE) model in the machining process. To improve the inverse calculation efficiency of the stiffness matrix, a novel nodes re-sorting method is proposed based on the calculation order of the matrix blocks in LU decomposition and inverse calculation. Furthermore, the optimal stiffness direction is discussed and applying the cutting force in this direction can minimize the machining deformation. The simulation results verified the existence of the optimal stiffness direction. Finally, the simulation and experiment are carried out to validate the accuracy of the proposed model.