Stability analysis for milling operations using an Adams-Simpson-based method

Abstract

The onset of chatter vibration in milling operations will result in poor surface finish and low machining productivity. Hence, it is of crucial importance to predict and eliminate this undesirable instability. In this paper, an Adams–Simpson-based method is developed for the stability analysis of milling processes. The regenerative chatter for milling operations can be described by delay differential equations with time-periodic coefficients. After dividing the forced vibration time interval equally into small time intervals, the Adams–Moulton method and the Simpson method are adopted to construct the Floquet transition matrix over one tooth passing period. On this basis, the milling stability can be obtained by using the Floquet theory. The accuracy and efficiency of the proposed method are verified through two benchmark examples, in which comparisons with the first-order semi-discretization method and the Adams–Moulton-based method are conducted. The results demonstrate that the proposed method has both high computational efficiency and accuracy, thus it is of high industrial application value.