Analytical Chatter Stability of Milling With Rotating Cutter Dynamics at Process Damping Speeds

Abstract

This paper presents a chatter stability prediction method for milling flexible workpiece with end mills having asymmetric structural dynamics. The dynamic chip thickness regenerated by the vibrations of the rotating cutter and the fixed workpiece is transformed into the principle modal directions of the rotating tool. The process damping is modeled as a linear function of vibration velocity. The dynamics of the milling system is modeled by a time delay matrix differential equation with time varying directional factors and speed dependent elements. The periodic directional factors are averaged over a spindle period, and the stability of the resulting time invariant but speed dependent characteristic equation of the system is investigated using the Nyquist stability criterion. The stability model is verified with time domain numerical simulations and milling experiments.