An efficient and accurate chatter prediction method of milling processes with a transition matrix reduction scheme

Efficient and accurate chatter prediction is essential for selection of chatter-free process parameters in order to improve machining productivity and surface quality of the workpiece. This paper proposes a five-point Gaussian quadrature-based chatter prediction method of milling processes together with a transition matrix reduction scheme to improve the computational accuracy and efficiency. The five-point Gauss–Legendre quadrature rule is utilized to approximate the equations of motion of milling systems represented in the form of integral equation. By this means, the convergence rate of the chatter prediction method can be improved. Since the transition matrix describing the relation between the states of current and previous tooth or spindle period is used to evaluate chatter stability, its dimension has a significant effect on the computational efficiency. In this paper, it is theoretically proved that the dimension of the transition matrix constructed by numerical integration-based methods can be reduced by half. Based on this, an efficient scheme is firstly proposed to further decrease the computational time. Typical benchmark examples are employed to verify the proposed method. The results demonstrate that the proposed method with the transition matrix reduction scheme is more efficient and accurate than the existing methods. Meanwhile, experimental validation shows the proposed method can predict the milling chatter accurately.