Extraction of surface curvatures from tool path data and prediction of cutting forces in the finish milling of sculptured surfaces

To achieve higher accuracy in the prediction of cutting forces in finish milling process of sculptured parts, the curvatures of in-process workpiece surface are necessary to be taken into consideration in the calculation of cutter-workpiece engagement boundaries. These curvatures, however, are not readily available in tool path data, as the main existing source of geometrical information of the process. In this paper, first, a new straightforward algorithm is proposed to extract the principal curvatures and principal directions of the in-process workpiece surface from ball-end finish milling tool path data. These quantities, then, are employed to calculate the boundaries of engagement between the tool and workpiece geometries. In the next step, the cutting forces acting on a helical ball-end tool are formulated utilizing mechanistic approach and with the inclusion of radial run-out effect. By minimizing the square error between the predicted and experimentally measured cutting forces, the cutting force coefficients and radial run-out parameters are identified. Finally, the validity of the proposed force model is demonstrated by comparing the simulated forces with experimental measurements. The performed simulations show that the model can well capture the variation of milling forces along curved tool paths resulting from the variation of surface curvatures. Furthermore, it is shown that depending on the machining tolerance used in the tool path generation step, saw-tooth-like fluctuations may appear in the time history of milling forces originating from the approximation of curved paths by single steps (straight lines). All of the geometrical input parameters of the proposed force model are extracted from tool path data and hence it is quite flexible to be integrated into process modeling/optimization systems.