Enhanced modeling of instantaneous uncut chip thickness and cutter workpiece engagement region in 5 axis ball end milling: Case of the tilt orientation

An accurate prediction of milling force is a critical component of assessing tool life and machined surface quality, particularly in five-axis ball end milling. An algorithm is designed to calculate the precise boundaries of the cutter workpiece engagement regions (CWER) considering the various tool tilt orientations. This work presents an enhanced cutting force model for ball-end milling, based on a new instantaneous uncut chip thickness (IUCT) model that is limited by the CWER model's determined constraints. We developed in this work a detailed analytical demonstration of the different parameters based on a geometric analysis of the contact between the tool and the workpiece. The provided model of IUCT takes into consideration the effects of tilt angle in ball-end milling including the local effect of tilt cutting tool inclination on the chip shape and CWER, making it more accurate compared to the published models of prior studies. The created model includes both up-and-down milling, following, and slot milling with positive and negative tilt angles, among other possible situations of the tool-workpiece interaction. The cutting force components are determined analytically using a mechanistic approach for every elementary cutting edge. The cutting geometry, shear force, and edge force are all considered in this process. Experiments using multi-axis milling have been used to validate the suggested model under different conditions. With a mean error of 4.7 %, a strong connection was found between the experimental outcomes and the analytical forecast.