Numerical robust optimization of spindle speed for milling process with uncertainties

This work is motivated by the fact that the conventional cutting parameters optimization in milling process has been widely investigated based on the assumption that the dynamics of the milling system is deterministic. Since there are many uncertain factors in a practical milling process, nominal cutting parameters derived from the deterministic cutting parameters optimization formulation cannot guarantee the stability of milling process and cannot lead to actual maximization of material removal rate and minimization of surface location error at the shop floor level. We develop a robust spindle speed optimization formulation, in which the upper bound of surface location error and lower bound of Lobe diagram are adopted as the optimization object and the constraint condition, respectively. For a comparison, we also give a deterministic spindle speed optimization formulation, without uncertainties. Time finite element approach is employed as the conventional deterministic model to obtain the Lobe diagram and surface location error. The upper and lower bounds of Lobe diagram and surface location error due to the model parameters uncertainties are calculated using the sensitivity analysis. The optimization problems are solved by an augmented Lagrangian function method. Experiments of milling of blades with spindle speeds derived from the deterministic and robust optimization results are implemented. The robust optimization result leads to stable milling process, while the deterministic one does not. The experimental results validate the proposed method. The robust optimization formulation given in this paper is helpful to the decision making in a practical milling process.

► We develop a robust spindle speed optimization formulation in milling process.
► Upper bound of surface location error is adopted as an optimization object.
► Lower bound of Lobe diagram is adopted as the constraint condition.
► Experiments of milling of blades validate the proposed method.