On the accurate calculation of milling stability limits using third-order full-discretization method

Based on third-order Newton's Interpolation theory, this paper proposed one method to compute milling stability. The machining is first considered as a dynamic process expressed by a mathematical equation, and this equation integrates the regenerative effect utilizing a time delay item. The time period is discretized as a series of small elements. Then, in each time element, the third-order Newton's interpolation algorithm is used to approximate the state item of the equation. The time-period and time-delay items are expressed by liner-interpolation. After equation items are expressed using the interpolation method on the time period, a matrix denoting the machining system is built. Taking advantage of the matrix, the stability of milling process is investigated, and the convergence feature of the proposed method is also analyzed. Finally, examples of 1-dof and 2-dof dynamic systems are conducted and the comparison results show that the method is effective.

► The convergence rate of the proposed method is faster compared with literatures.
► The precision of the introduced method is closer to ideal value computed by the literature's algorithm than other methods.
► 1-dof and 2-dof dynamic milling systems' stability lobs are predicted using the presented method.