Pareto multi-objective optimization of cutter orientation for 5-axis ball-end milling

To improve the machining quality of free-form surfaces, machining deformation and chatter should be considered in 5-axis ball-end milling. In this paper, a Pareto multi-objective optimization method for cutter orientation is presented. Firstly, the cutting force is calculated by the differential element method. To improve the computational efficiency of cutting force, the proposed cutting force model considers the influence of surface curvature on the cutter workpiece engagement (CWE) region and gives an analytical calculation method. Then, the deformation and chatter of 5-axis ball-end milling are studied. The static deflection corresponding to different cutter orientations is calculated based on the large-scale sparse matrix inversion algorithm. The chatter-free stability region is calculated based on the 3-dimensional semi-discretization method (SDM). It was found experimentally that the smaller the eigenvalue of the SDM transition matrix is, the more stable the machining is and the better the surface quality is. On this basis, the minimum eigenvalue is proposed as optimization criteria for chatter. Finally, a non-dominated sorting genetic algorithm (NSGA-II) is used to obtain the Pareto optimal region of the cutter orientations. The optimization model takes the minimum value of static deflection and stability eigenvalue as optimization objectives. For each key cutter location point, the feasible region of the cutter orientations with high precision and surface quality is obtained based on NSGA-II. Furthermore, based on the optimization results at the key cutter location points, Dijkstra algorithm and quaternion interpolation algorithm were used to optimize the cutter orientations of the whole free-form surface, which ensured the kinematics performance of the 5-axis machine. The experimental results are in good agreement with the simulation results, which shows that the theoretical model is effective. The results provide a theoretical basis for the comprehensive optimization of machining deformation and chatter of thin-walled parts with the free-form surface.