Ball-end milling stability and force analysis in the presence of inclination angles through a new algorithm with numerical chip thickness in edge-workpiece engagement

By studying the edge-workpiece engagement (EWE), and taking two inclination (lead and tilt) angles into account, the time-varying cutting areas and boundaries are determined, the instantaneous numerical chip thickness (NCT) within different EWEs at each point of the edge curve during the milling process of the ball end milling tool is solved, and the milling force and stability are calculated. The milling force and SLD of the model in this paper (NCT-EWE model) and the model in the literature (Altintas and Otzurk model) are compared. It is verified that the algorithm adopted in this paper has higher accuracy, and the algorithm is simple and fast. In addition, it is found that increasing the lead and tilt angles can reduce the milling force and improve the stability, and the free vibration in the stable region decreases gradually, while in the non-stable region, it increases. The algorithm in this paper has certain theoretical and application value for five-axis milling.