A novel stability prediction method for milling operations using the holistic-interpolation scheme

Abstract

Currently, accurate and efficient determination of chatter-free cutting conditions is becoming increasingly important. This paper proposes a semi-analytical stability prediction method for milling processes using the holistic-interpolation scheme. The dynamics considering regeneration effect for milling operations is formulated as delay differential equations with time-periodic coefficients. The period of milling dynamic system is divided into two time periods according to the value of the coefficient matrix. On each small time interval for the forced vibration time period, the holistic-interpolation method is utilized by approximating the state term, the delay term, and the time-periodic parameter matrix as a whole unit with the second-order Lagrange interpolating polynomials. Then the Floquet transition matrix can be semi-analytically constructed for milling stability prediction according to Floquet theory. Finally, the benchmark examples of milling models are utilized to validate the effectiveness of the proposed method, which shows that the proposed algorithm achieves both high computational accuracy and efficiency.