Milling stability prediction based on the hybrid interpolation scheme of the Newton and Lagrange polynomials

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The stability lobe diagram (SLD) is commonly used to determine the suitable cutting parameters of the machining system in order to achieve a chatter-free machining process. An improved full-discretization method (FDM) is proposed to predict the SLD based on the hybrid interpolation scheme of the Newton and Lagrange polynomials. In order to solve the SLD, a third-order Newton polynomial is employed to interpolate the state term of the physical space equation of the system. Meanwhile, to investigate the influence of the interpolation order on predicting the SLD, the delayed term is estimated using the Lagrange polynomials of orders one to four successively. Subsequently, after constructing the transition matrix, a series of calculation for the stability prediction are carried out by applying Floquet theory. The calculated results from these constructed methods demonstrate that the FDM with a second-order Lagrange polynomial is optimal, and further has better computational performance compared with some existing discretization methods. Lastly, the influences of the dynamic parameters on chatter stability are analyzed based on the proposed FDM. When the stiffness and damping ratio increase, the limit cutting depth will be enhanced. The increasing natural frequency not only causes an obvious shift of the lobes to the right, but also raises the limit cutting depth to some extent. These theoretical analyses can guide the prediction and improvement of the chatter stability of a machining system.