An improved numerical integration method to predict the milling stability based on the Lagrange interpolation scheme

To predict the milling stability accurately and efficiently, an improved numerical integration method (INIM) is proposed based on Lagrange interpolation scheme. First, dynamic model considering regenerative chatter can be described as a delay linear differential equation. The tooth passing period of cutter divided into free forced vibration stages. Then, stage equally discretized, INIMs are built scheme within discretized intervals to construct state transition matrix. Finally, convergence rates lobes for benchmark systems calculated discussed by using existing methods, respectively. comparison results reveal that second-order INIM shows higher computational efficiency accuracy compared with related discretization in meantime, it more accurate under just slightly loss time cost NIMs.