Abstract
This paper presents a method for predicting regenerative chatter onset conditions for uniform and stepped workpieces. The lateral deflections of flexible workpieces are modeled using the Timoshenko beam theory and three-node beam finite elements. The modal summation method is employed in conjunction with an adaptive remeshing scheme to determine the varying natural frequencies and varying mode shapes of workpieces during a cutting process, and to reduce the system equations of motion in terms of nodal variables to coupled equations of motion in terms of the modal coordinates. Various simulations were conducted and presented in this paper for understanding the gyroscopic and cross-coupling effect, and effects of other system and cutting process parameters on chatter onset conditions. Six experiments were carried out on an engine lathe for three uniform and three stepped workpieces to verify the theoretical chatter onset conditions. Good agreement in chatter onset conditions was observed between the simulations and the experiments.
