Milling Force Prediction Model for Five-Axis Machining of Freeform Surface Considering Mesoscopic Size Effect

The core parts with the characteristic of freeform surface are widely used in the major equipment of various fields. Cutting force is the most important physical quantity in the five-axis CNC machining process of core parts. Not only in micro-milling, but also in macro-milling, there is also an obvious size effect, especially in medium- and high-speed milling, which is frequently ignored. In this paper, the milling force prediction model for five-axis machining of a freeform surface with a ball-end mill considering the mesoscopic size effect is established. Based on the characteristics of cutting thickness in macro-milling, a new dislocation density correction form is proposed, and a new experiment is designed to identify the dislocation density correction coefficient. Therefore, the shear stress calculated in this paper not only reflects the cutting dynamic mechanical characteristics but also considers the mesoscopic size effect. A linear function is proposed to describe the relationship between friction coefficient and cutting speed, cutter rake angle, and cutting thickness. Considering cutter run-out, the micro-element cutting force in the shear zone and plough zone are analyzed. The cutting geometry contact between the freeform surface and the ball-end mill is analyzed analytically by the space limitation method. Finally, the total milling force is obtained by summing all the force vectors of cutting edge micro-elements within the in-cut cutting edge. In the five-axis machining experiment of freeform surface, the theoretically predicted results of milling forces are in good agreement with the measured results in trend and amplitude.