Chatter stability analysis of high speed machining by means of spectral decomposition modeling

A technique to study the stability of high speed milling machining process and the chatter vibration is proposed. The equation of motion of a one degree of freedom (dof) model of the milling machine-tool system is considered. The system is described by means of a linear, ordinary, time dependent parameter, Periodic Delay Differential Equation (PDDE). A spectral decomposition is then applied to the equation, by means of a generalized harmonic balance technique, so that a linear, ordinary, constant parameter, PDDE is attained. A non standard eigenvalue problem can then be solved in order to study the stability of the solution, making it possible to predict the occurrence of chatter vibration during milling. A numerical example is presented in order to test the proposed approach. The well known Semi-Discretization (SD) method is considered as reference for selecting stable and unstable configurations to be tested. The time solution obtained by means of direct integration of the original equation is used to show that the proposed model preserve the stability characteristics of the original model. Strengths and limits of the proposed approach are critically discussed and compared with the SD method.