Prediction of multiple dominant chatter frequencies in milling processes

Chatter frequencies of milling operations and their strengths are analysed using the semi-discretization method. It is known that milling processes, being parametrically excited systems, are theoretically associated with infinitely many chatter frequencies that are given as a base frequency plus an integer multiplier of the tooth passing frequency (or the characteristic frequency of the cutter) according to the Floquet theory [1]. The dominant vibration frequencies that are usually associated with chatter frequencies are, however, hidden among the infinitely many harmonics. In this paper, it is shown that the amplitudes corresponding to the individual frequency harmonics can be determined in a simple way by analysing the eigenvectors of the Floquet transition matrix obtained by the semi-discretization method without increasing the computational cost. The method can be used to determine the dominant frequency components that help in the identification of the interactions between different modes and the spindle speed.