Analysis on milling stability performed under the conditions of positive and negative process stiffness

This paper aims at discussing chatter characteristics performed by a one-dimensional milling system having positive process stiffness and negative process stiffness. In this study, a dynamic model of the milling system is established first. An analytical form showing the critical chatter conditions including axial depth of cut, chatter frequency, critical spindle speed, etc. is formed. The analysis of process function shows that positive process stiffness occurs under most cutting conditions. However, process stiffness becomes negative when a one-dimensional milling system carries out low radial depth of cut in the direction of the feed (down milling) or semi-groove milling in the direction against the feed (up milling). Further analysis is made to explore chatter characteristics performed by the milling systems with positive process stiffness and negative process stiffness respectively. Finally, the prediction equation calculating critical chatter conditions of these two types of milling system, the range of rotation speed with high cutting stability and the range of rotation speed with low cutting stability is proposed.