A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling

A new method for the prediction of chatter in milling is presented. The dynamics of the milling process are described by a set of differential-difference equations with time varying periodic coefficients. The stability of this system is examined using Fourier analysis and basic properties of the parametric transfer functions of linear periodic systems. The resulting characteristic equation is of infinite order and has constant coefficients. Its truncated version is used to determine the limit of stability employing standard techniques of control theory. The proposed method is applied to a theoretical example and a practical milling system.