Dynamics and stability analysis of five-axis ball end milling with low radial immersion considering cutter runout

The inevitable cutter runout has an important influence on the cutter dynamic properties and transient cutting condition, whereas it is usually neglected in analyses of mechanics and dynamics in five-axis ball end milling for lack of efficient mechanism modeling methods. This paper presents a novel mechanical and dynamic model considering runout to develop stability analysis suitable in five-axis ball end milling with low radial immersion. Firstly, the mathematical modeling of the cutting edge trajectory is derived from the cutting process considering runout effect. The impact of runout on the motility pattern of the cutter center and cutting edge is clarified. Then, the optimized tool coordinate system independent on runout parameters is defined to decompose the cutter complex elliptical or quasi elliptical motion caused by runout into two regular circular motion combinations. One is the center of cutter rotates around spindle, and the other is the cutting edge of cutter rotates around cutter center. Taking advantage of this strategy, the mechanics and dynamics of five-axis ball end milling considering runout are determined. A new analytic method is developed to extract the cutter and workpiece engagement (CWE) for five-axis ball end milling considering runout effect based on the transient cutting force signal. The superiority of the proposed dynamic and CWE models are both immune from the runout parameters. Thereafter, generalized precise integration method (GPIM) is presented to deduce dynamic system with multiple time delays into the state transition matrix. The axial angle of cutting edge acts as a bridge between transition matrix and the limit cutting positions defined by the analytic CWE to develop stability analysis for five axis ball end milling. The accuracy and efficiency of the GPIM is validated by the classic benchmarks and experimentally verified examples. Finally, five-axis ball-end milling experiments are performed to confirm the effectiveness of the proposed me-chanical and dynamic models.