Milling Stability Prediction: A New Approach Based on a Composited Newton–Cotes Formula

Abstract

Based on a composited Newton–Cotes formula, this paper proposes a numerical method to predict milling stability considering regenerative chatter and focusing on rate and prediction accuracy. First, the dynamic model of milling motion is expressed as state-space equations considering regenerative chatter, with the tooth passing period divided into a set of time intervals. Second, a composited Newton–Cotes formula is introduced to calculate the transition function map for each time interval. Third, the state transition matrix is constructed based on the above-mentioned transition function, and the prediction stability boundary is determined by the Floquet theory. Finally, simulation analysis and experimental verification are conducted to verify the effectiveness of the proposed method. The simulation results demonstrate that, for the milling model with a single degree of freedom (DOF), the convergence rate and prediction accuracy of the proposed method are higher than those of the comparison method. The experimental results demonstrate that, for the milling model with two DOFs, the machining parameters below the prediction stability boundary can avoid the chatter as much as possible, ensuring the machined surface quality.

Keywords

• dynamic model
• regenerative chatter
• milling stability prediction
• composite cotes formula
• Floquet theory