The effect of harmonic force components on regenerative stability in end milling

In a systematic manner, this paper investigates the effects of harmonic force components on the regenerative stability of an end milling process. By representing the milling force pulsation in a Fourier series expansion form, the dynamic force components and the average forces due to bi-directional dynamic feed rates are both included in the generalized system dynamics formulation. In the resulting expression for the stability criterion, the spectral features of the milling forces are integrated with the dynamics of the structure, showing the significance or insignificance of the dynamic components of the milling forces in affecting the stability of the milling process. Key system parameters discussed include the magnitude of the average and harmonic forces, the cutter helix angle and the spindle speed. It is shown that a low helix angle and a smaller number of cutting flutes increase the effect of dynamic forces on the system stability. The significance of the harmonic forces is exemplified by the special cutting conditions where the average force becomes zero and the stability limits would be infinite as predicted by models using the average force alone. Improvements in the accuracy of stability lobes resulting from the inclusion of the dynamic forces and the validity of the presented model in general will be illustrated by numerical simulation and verified by experiments as well as by comparison with published results.