An accurate and fast milling stability prediction approach based on the Newton-Cotes rules. (1st July 2020)

• Record Type: Journal Article
• Authors: Li, Weitao; Wang, Liping; Yu, Guang
• Is Part Of: International journal of mechanical sciences. Volume 177(2020)
• Publication Date: 2020-07-01
• Subjects: Milling stability prediction -- Newton-Cotes rules -- Floquet theory -- Time delay; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2020.105469
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: An accuracy and fast method is proposed for milling stability prediction. The proposed method transforms the milling dynamics model in integral form into a set of algebra equations making the form of the state transition matrix quite simple. The proposed method predicts the milling stability more accurate than the zeroth-order SDM, the first-order SDM and the first-order FDM, and the proposed method consumes less computation time significantly than above three methods. 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. Graphical abstract: Image, graphical abstract