Chatter stability prediction for five-axis ball end milling with precise integration method

The differential dynamic equation (DDE) considering regenerative chatter effect is derived from an ideal cutting model. At the same time, the ball end mill-workpiece engagement (BWE) in five-axis milling is efficiently extracted by the semi-analytical method, where the machining residual left on the finished surface is taken into account. The explicit precise integration method (PIM) is adopted to translate the DDE into a time series expression, ensuring stability prediction without any discretization error loss. With the relationship of cutter edge and BWE at different instants, the stability lobe diagram (SLD) is constructed by Floquet theory, which is subsequently testified in the five-axis NC machine tool. The experimental results keep good agreement with estimations, validating the proposed method. Compared with traditional method in dynamic cutting forces modeling, the proposed approach is more close to actual processing. In contrast to Runge-Kutta based complete discretization method, PIM shows higher superiority no matter in convergence rate or calculation accuracy. Lastly, the influences of different inclination angles on stability are revealed, which can give a reference to selection of suitable process parameters for higher productivity.