Solution and analysis of chatter stability for end milling in the time-domain

In this paper, the instantaneous undeformed chip thickness is modeled to include the dynamic modulation caused by the tool vibration while the dynamic regenerative effects are taken into account. The numerical method is used to solve the differential equations governing the dynamics of the milling system. Several chatter detection criteria are applied synthetically to the simulated signals and the stability diagram is obtained in time-domain. The simulation results in time-domain show a good agreement with the analytical prediction, which is validated by the cutting experiments. By simulating the chatter stability lobes in the time-domain and analyzing the influences of different spindle speeds on the vibration amplitudes of the tool under a fixed chip-load condition, conclusions could be drawn as follows: In rough milling, higher machining efficiency can be achieved by selecting a spindle speed corresponding to the axial depth of cut in accordance with the simulated chatter stability lobes, and in finish milling, lower surface roughness can be achieved by selecting a spindle speed well beyond the resonant frequency of machining system.