The traditional stability analysis by only considering cutting depth-spindle speed lobe diagram is appropriate for parameters optimization and efficiency improvement of the five-axis ball-end milling. However due to the complicated cutter-workpiece engagement (CWE) of bull-nose end cutter in five-axis milling, the maximal cutting depth may not produce the maximal material removal rate (MRR). Thus, the traditional stability analysis is not suitable for the five-axis bull-nose end milling in parameters optimization, and this paper presents a new stability analysis method to analyze the effect of tool orientation on machining efficiency for five-axis bull-nose end milling. In the establishing of stability prediction model, coordinate transformation and vector projection method are adopted to identify the CWE and dynamic cutting thickness, and the geometrical relationship of frequency response function (FRF) coordinate system and cutting force coordinate system with variable tool orientation is derived to establish the conversion of FRF and cutting force in stability equation. Based on the CWE sweeping, the cutting area along the feed direction is calculated to realize the critical MRR analysis in the stability model. Based on the established stability prediction model, the effects of tool orientation on critical cutting depth and MRR considering the chatter constraint are analyzed and validated by the cutting experiments, respectively. The lead-tilt diagram, which not only gives the boundary of stability region but also describes the contour line for MRR, is proposed for the further tool orientation optimization.

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