Research on Prediction Method of Stability Lobe Diagram for Ball-end Mill Based on Engagement

The equations for the boundaries of ball-end mill-workpiece engagement (BWE) are precisely established by a semi-analytical method at first. The differential dynamic equation derived from the ideal 2-Dof milling system is solved by the complete discrete method. Based on the cutter within a tooth passing period considered as arc path cutting, the instantaneous cutting positions required in the numerical solution are identified by the relationship of cutter edge and BWE. The stability lobe diagram is constructed by Floquet theory, which is subsequently verified on a three-axis NC machine tool. The experimental results are in good agreement with the predicted results, indicating the validity of this method. In contrast to traditional method, the proposed method shows higher prediction precision. The influence laws of different parameters on stability are analyzed at last, which can give a help for the actual machining.