Analytical stability lobes including nonlinear process damping effect on machining chatter

Indentation of the tool edge and flank face into workpiece surface undulations has been recognized in the literature as the main source of process damping. This damping affects the process stability at low cutting speed greatly. Numerical simulations have allowed integrating the nonlinear indentation force into machining chatter models. It is shown in this paper that the indentation force requires very high discretization resolution for accurate numerical simulation. The objective of the current work is to develop the stability lobes analytically taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Plunge turning is utilized in the current work to illustrate the procedure of establishing the lobes analytically. Experimental cutting tests were conducted at three feedrates for sharp and worn tools and the results agreed well with the analytically established lobes.