A semi-analytical method for stability analysis of milling thin-walled plate

Abstract

In this paper, a partial differential difference equation is setup to describe the dynamics of a thin-walled plate during milling processes. A semi-analytical method is developed to study the stability, with the emphasis on the varying dynamics and higher-order vibration modes. In this method, the thin-walled plate is divided into a series of subdomains to accommodate the computing requirements of higher-order vibration modes. The classical Kirchhoff plate theory is employed to formulate the theoretical model. Continuity conditions on the interface between two adjacent subdomains are imposed by means of a modified variational principle. The expressions of the transfer functions for each vibration mode are derived at an arbitrary point in the plate. Based on these expressions, the stability limit of the plate is determined by using a frequency method. It is found that the proposed method has a high computational efficiency for the stability analysis of the plate in milling process. The effect of higher-order vibration modes on the stability of the plate are examined, and the physical insights into the chatter in milling process are also discussed.