A Legendre Polynomials Based Method for Stability Analysis of Milling Processes

Abstract

This paper presents a timedomain approach for a semianalytical prediction of stability in milling using the Legendre polynomials. The governing equation of motion of milling processes is expressed as a delaydifferential equation (DDE) with time periodic coefficients. After the DDE being reexpressed in statespace form, the state vector is approximated by a series of Legendre polynomials. With the help of the Legendre–Gauss–Lobatto (LGL) quadrature, a discrete dynamic map is formulated to approximate the original DDE, and utilized to predict the milling stability based on Floquet theory. With numerical examples illustrating the efficiency and accuracy of the proposed approach, an experimental example validates the method.