Mechanical vibrations in milling, also known as 'chatter' result in lessened productivity, poorer product surface finish, and decreased cutting life of the tool. Thus, it is desirable to predict and avoid the onset of this instability. In this paper, an efficient method is proposed to predict the chatter stability for milling operation with variable pitch or variable helix cutters. In order to consider the variation in pitch angle for the cutting tool along the tool axis, which is depending upon the helix angles selected, the cutter is divided into a finite number of axial elements. Any slice assumes time-averaged cutting force coefficients. 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. The proposed technique has been verified with the comparison with other methods. The results show that the proposed method has high computational efficiency. It is suited to quickly optimize the cutting conditions or calculate optimal geometries of milling tools.
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