Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.