Efficient cutting force modelling for flat end milling under hard milling conditions

Direct machining of hardened steel using flat end mills is a key enabling technology in die and mould manufacturing, eliminating grinding processes and improving productivity. Hard milling is typically performed under finishing conditions, characterized by small axial depth of cut and feed, which create a unique cutting environment where the influence of nose radius geometry, bottom cutting-edge engagement and progressive flank wear becomes more pronounced, thereby altering the cutting mechanics compared to conventional milling. In mechanistic force modelling, cutting force coefficients are critical parameters, and their accurate identification is essential for reliable force prediction. In this study, an approximation method is proposed for flat end milling cutters to extract cutting force coefficients under practical oblique cutting conditions, incorporating the influence of tool macro- and micro-geometry. With proper consideration of tool geometry, cutting force coefficients can be accurately identified using a minimal set of experiments, thereby reducing calibration effort. The proposed approach utilizes instantaneous cutting force measurements from a single experimental set, significantly reducing experimental cost and calibration time. Furthermore, the model is extended to account for force generation due to flank wear, including wear along the main cutting edge, nose radius and bottom cutting edge. The validity of the proposed method is experimentally demonstrated over a wide range of cutting conditions, with mean errors within − 4.99 ± 12.5 % under finishing conditions.