Plunge milling time optimization via mixed-integer nonlinear programming

• A new approach to minimize time machining through Mixed-Integer Nonlinear Programming.
• Mathematical formulation of cutting parameter optimization for plunge milling.
• Machine-tool and cutter-related constraints taking into account control laws.
• Optimal cutting parameters obtained, tailored to each elementary tool trajectory.
• Gains as high as 55% are obtained when compared with standard industrial methods.

Plunge milling is a recent and efficient production mean for machining deep workpieces, notably in aeronautics. This paper focuses on the minimization of the machining time by optimizing the values of the cutting parameters. Currently, neither Computer-Aided Manufacturing (CAM) software nor standard approaches take into account the tool path geometry and the control laws driving the tool displacements to propose optimal cutting parameter values, despite their significant impact. This paper contributes to plunge milling optimization through a Mixed-Integer NonLinear Programming (MINLP) approach, which enables us to determine optimal cutting parameter values that evolve along the tool path. It involves both continuous (cutting speed, feed per tooth) and, in contrast with standard approaches, integer (number of plunges) optimization variables, as well as nonlinear constraints. These constraints are related to the Computer Numerical Control (CNC) machine tool and to the cutting tool, taking into account the control laws. Computational results, validated on CNC machines and on representative test cases of engine housing, show that our methodology outperforms standard industrial engineering know-how approaches by up to 55% in terms of machining time.