An accurate and fast milling stability prediction approach based on the Newton-Cotes rules

Abstract

Regenerative chatter is the main factor causing milling instability. The stability prediction of milling process is a useful method to suppress chatter, improve machining efficiency and surface equality of the workpiece. An accurate and fast milling stability prediction approach based on the Newton-Cotes rules is proposed in this study. First, the milling dynamics model based on regenerative chatter is expressed as state-space equations, where the tooth passing period is divided into a set of time intervals equally. Then, the relationship between the responses at two time points on each time interval is derived by expressing the state-space equations in the form of integral equations. Next, the integral equations are transformed into algebraic equations based on the Newton-Cotes rules, and a discrete map over the tooth passing period is obtained via these algebraic equations. Finally, a transition matrix connecting the current state and the delayed state is established by the discrete map to predict the milling stability according to the Floquet theory. A typical benchmark example is demonstrated and two milling cases are utilized to verify the validity. Both of them show that the proposed method converges fast with high computational efficiency.