An Adams-Moulton-based method for stability prediction of milling processes

Abstract

Machining chatter has detrimental effects on surface quality, tool life, and machining efficiency. Therefore, it is of vital significance to predict and avoid this undesirable phenomenon. This paper presents an Adams-Moulton-based method for the stability prediction of milling operations. Generally, delay differential equations with time-periodic coefficients are applied to model the milling dynamics that include the regenerative effect. To begin with, the tooth-passing period is divided into free vibration time period and forced vibration time period. Subsequently, the Adams-Moulton method is utilized to construct the transition matrix over one period through dividing the forced vibration time period equally into small time intervals. Finally, the milling stability can be obtained by examining the eigenvalues of the transition matrix based on Floquet theory. A comparison with the first-order semi-discretization method and the Simpson-based method is conducted to evaluate the convergence rate and the computation efficiency of the proposed algorithm. The results verify that the proposed method is highly accurate and efficient; thus, it is practical for workshop technicians to select chatter-free machining parameters.