Investigation of chatter stability of cutting process with a rotating tapered cutter bar considering internal and external damping

The damping of cutting system is an important factor influencing stability in boring and milling process. However, systematical and thorough studies of the influencing mechanism of damping, especially on the chatter stability of rotating cutter bar, are still absent. The damping of a cutting system mainly consists of external damping and internal damping. This study focuses on these damping effects on chatter stability of the cutting system with a rotating tapered cutter bar. The partial differential equation of motion of the cutter bar is derived based on the Hamilton principle combined with the Euler-Bernoulli beam theory. It is assumed that the cutter bar is tapered, and its free ends acts on a two-dimensional regenerative cutting force with time-delay effect. The damping mechanisms of external and internal are described by the viscous damping model and the strain-rate-dependent Kelvin-Voigt model, respectively. The partial differential equation of motion is discretized as an ordinary differential equation using the Galerkin method. The Campbell diagram and the decay rate plots including critical rotating speed and instability threshold of the cutter bar are obtained by free vibration analysis. Also, the chatter stability lobes in the cutting process are plotted and the predicted results of stability in frequency domain are compared with those in time domain. The results indicate that the structural parameters of a cutter bar, including the rotation, the ratio of internal and total damping, damping ratio, and taper and aspect ratios have significant effects on cutter bar dynamics and chatter stability of cutting process. In particular, a new chatter instability is observed for the cutting system in higher rotating speed ranges due to the effects of rotation and internal damping. The onset rotating speed of the new chatter instability equals to the instability threshold of rotor system of cutter bar. Finally, the present model is validated by comparing both stability prediction given by previous study and natural frequencies and decay rates by ANSYS FE code.