Prediction of cutting forces from an analytical model of oblique cutting, application to peripheral milling of Ti-6Al-4V alloy

In this work, a predictive machining theory, based on an analytical thermomechanical approach of oblique cutting (Moufki et al., Int J Mech Sci 42:1205–1232, 2000; Moufki et al., Int J Mach Tools Manuf 44:971–989, 2004), is applied to the peripheral milling process. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening are considered. In the primary shear zone, thermomechanical coupling and inertia effects are accounted for. Due to the fact that the reference frame associated to the primary shear zone moves with the tool rotation, an analysis of the inertial effects has been performed. As the heat conductivity of Ti-6Al-4V is low, the thermomechanical process of chip formation is supposed to be adiabatic; thus, the problem equations are reduced to a system of two non-linear equations which are solved numerically by combining the Newton–Raphson method and Gaussian quadrature. The present analytical approach leads to a three-dimensional cutting force model for end milling operations. Calculated and experimental results extracted from the literature are compared for several operations: full immersion, up-milling and down-milling and for different cutting conditions. Although the present model was established for stationary conditions and for continuous chips, it gives acceptable predictions for machining titanium alloy for which the chips are usually segmented. The proposed model appears as an interesting alternative to the mechanistic approach which requires many experimental tests to determine the milling cutting force coefficients.