Stability Analysis of Milling Based on the Barycentric Rational Interpolation Differential Quadrature Method

Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature method (DQM). The dynamics of the milling process considering the regeneration effect is first modelled as a time-delay differential equation (DDE). When adjacent pitch angles of the milling cutter are symmetric, the milling dynamic equation contains a single time delay. Otherwise, when adjacent pitch angles are asymmetric, the dynamic equation contains multiple time delays. The barycentric rational interpolation DQM is then used to approximate the differential and delay terms of the milling dynamics equation, and to construct a state transition matrix between adjacent milling periods. Finally, the chatter stability lobe diagram (SLD) is obtained based on the Floquet theory. According to the SLD, the appropriate spindle speed can be selected to obtain the maximum stable axial depth of cutting, thereby effectively improving the material removal rate. The accuracy and efficiency of the proposed method have been validated by two widely used milling models, and the results show that the proposed method has good accuracy and computational efficiency.