Analytical prediction of three dimensional chatter stability in milling

The chip regeneration mechanism during chatter is influenced by vibrations in three directions when milling cutters with ball end, bull nose, or incli ned cutting edges are used. A three dimensional chatter stability is modele d analytically in this article. The dynamic milling system is formulated as a function of cutter geometry, the frequency response of the machine tool structure at the cutting zone in three Cartesian directions, cutter engagem ent conditions and material property. The dynamic milling system with nonli nearities and periodic delayed differential equations is reduced to a three dimensional linear stability problem by approximations based on the physic s of milling. The chatter stability lobes are predicted in the frequency do main using the proposed analytical solution, and verified experimentally in milling a Titanium alloy with a face milling cutter having circular insert s.