Analysis of stability in high speed milling machining by means of spectral decomposition

A method to study the chatter stability of a high speed milling machining process is presented. Identification of the chatter-free machining parameters maximizing the metal removal rate is also studied in order to improve the milling process productivity. Starting from the equations of motion of a general machine-tool-workpiece system, resulting in a set of linear, ordinary, time dependent parameter, Periodic Delay Differential Equations (PDDEs), a spectral decomposition technique is applied. A new set of linear, ordinary, constant parameter, PDDEs is derived by applying a spectral decomposition and a generalized harmonic balance technique. The stability of the solution can be studied in advance by solving a non standard eigenvalue problem, making it possible to predict the occurrence of chatter vibration during milling. The proposed approach makes it possible to obtain a straightforward formula for the sensitivity of the real component of eigenvalues with respect to the variation of a technological parameter. A comparison with the well known Semi-Discretization (SD) method is carried out. The SD method is revisited so that a closed formula for the sensitivity of eigenvalues with respect to the variation of a technological parameter is introduced. A numerical example is presented in order to test the proposed approach. Finally strengths and limits of the proposed approach are critically discussed and a comparison with the SD method is carried out.