A unified stability prediction method for milling process with multiple delays

A unified method for predicting the stability lobes of milling process with multiple delays is presented. The characteristics of delays in milling are analyzed by considering the effects of the runout and the pitch angles of the cutter. The cutter is divided into a finite number of axial elements so that the contributions of different delays and the influence of the helix angle can be considered in the governing equation. The stability lobes are obtained through the following steps. First, transform the infinite time domain into certain time discretization intervals. Second, an explicit relation between the current time interval and the previous time interval is obtained based on the governing equation. Third, a transition matrix related to every discretized time interval is constructed with the aid of the above relation. Finally, according to Floquet theory, the chatter-free axial depth of cut is derived from the eigenvalues of the transition matrix. Both numerical and experimental tests demonstrate that the proposed method is effective for milling process with multiple delays, whether with runout or with variable pitch angles. The proposed method is also applied to examine the asymptotic stability trends for different cutting condition parameters such as radial immersions, feed directions, feeds per tooth and helix angles when cutter runout occurs. Some new phenomena for certain combinations of parameters are shown and explained. It is found that feed per tooth has great effect on the stability lobes when cutter runout occurs.