Second-order full-discretization method for milling stability prediction

Abstract

This paper proposes a second-order full-discretization method for milling stability prediction based on the direct integration scheme. The model of the milling dynamics taking the regenerative effect into account in the state-space form is firstly represented in the integral form. After the time period being equally discretized into a finite set of intervals, the full-discretization method is developed to handle the integration term of the system. On each small time interval, the second-degree Lagrange polynomial is employed to interpolate the state item, and the linear interpolation is utilized to approximate the time-periodic and time delay items, respectively. Then, a discrete dynamical map is deduced to establish the state transition matrix on one time period to predict the milling stability via Floquet theory. The rate of convergence of the method is discussed, and the benchmark example is utilized to verify the effectiveness of the presented algorithm. The MATLAB code of the algorithm is attached in the Appendix.