Effective and fast prediction of milling stability using a precise integration-based third-order full-discretization method

Chatter stability prediction is of great practical importance for stable machining because regenerative chatter in the milling process will result in poor surface quality and low machining efficiency. Full-discretization method and its variants have been demonstrated to be effective for the prediction of milling stability. However, the main shortcoming of such methods is that they can predict milling stability but involve inverse matrix calculation, which would lead to increases in computational complexity and reductions in numerical stability. In addition, there may not necessarily exist good inverse matrix for these methods. This study proposes a precise integration-based third-order full-discretization method that can be both accurate and efficient in milling stability prediction without the need of any inverse matrix calculation. The performance evaluation performed by the simulation demonstrates that the proposed method outperforms the conventional methods with respect to stability prediction accuracy and speed. Extensive simulation is also carried out to investigate the effects of interpolation order for the simplified state term on the performance of the proposed method. Three demonstrative examples are employed to demonstrate how the proposed method can function effectively in the prediction of milling chatter stability. Although a chatter stability prediction tool for the milling process is the particular application presented here, the proposed method can be applied to other machining processes, such as turning, boring, and drilling.