Cutting force and nonlinear chatter stability of ball-end milling cutter

Ball-end milling cutters are one of the most widely used cutters in the automotive, aerospace, die, and machine parts industries. Milling chatter reduced the surface quality and production efficiency, resulting in noise. It is particularly important to model the cutting force and analyze the flutter stability of ball-end milling cutters. In this study, a simplified milling force model of ball-end milling cutter with three degrees of freedom was established based on Merchant bevel cutting theory. The model simplified the milling force coefficient. The expressions of instantaneous milling area considering the vibration displacements in X, Y, and Z directions were derived. The nonlinear dynamic cutting force model of ball-end milling cutter with three degrees of freedom was proposed. The nonlinear chatter vibration mechanical model of ball-end milling cutter with three degrees of freedom was developed by introducing the time delay term, and the stability analysis is carried out by the stability lobe diagram. The proposed models were experimentally verified.