Chatter stability prediction of ball-end milling considering multi-mode regenerations

Ball-end milling has been commonly used in the manufacturing of complex surfaces and structures. In order to improve the machining efficiency and ensure the manufacturing quality, chatter has to be avoided. The stability of cylindrical end mills has been well studied by selecting the most flexible dominant mode. This paper models the chatter stability of ball-end milling cutter with multiple modes and solves it in discrete time domain. Firstly, the multiple degree-of freedom (DOF) vibration model of the tool-workpiece system is established in modal coordinates to decouple the delay differential equations (DDEs). Then, to complete the motion equations of ball-end milling cutter, the cutting force model considering regenerative effect is built by evaluating the dynamic thickness at each cutting point along the cutting edge. Finally, the stability lobe diagram (SLD) of ball-end milling is solved by full-discretization method in discrete time domain. The cutting tests carried out on a machining center verify the prediction accuracy and observe chatter phenomenon caused by different dominant modes.