Trajectories of forces and displacements in stable and unstable milling

Abstract

Analyzing the characteristics of force and tool vibration trajectories during stable and unstable milling processes provides information such as the shape, orientation, and sense of rotation of these trajectories; such information facilitates positively identifying machine chatter. This paper presents analytical models for determining the forces and tool tip displacement during stable and unstable milling with axis-symmetrical structural dynamics. The trajectory of nominal milling forces under both stable and unstable cutting conditions was demonstrated to run clockwise in an elliptical path, with the dynamic forces during chatter running counterclockwise. The tool tip displacements demonstrated the same trajectory pattern as the milling forces. Both the nominal and dynamic forces had similar modal directions, pointing to the right and left sides of the x axis for up and down-millings, respectively. The predictions of the force and tool tip displacement trajectories in stable milling and during chatter were verified using numerical simulations and validated in experiments.