Investigation of Rényi entanglement entropy in nonlinear micro/macro milling chatter identification

Chatter detection is crucial for both micro- and macro-milling, as chatter can cause detrimental damage on machining process and machined surface. Compared to macro-milling, micro-milling is more susceptible to external non-Gaussian noise interference, making it extremely difficult to extract chatter features and identify chatter modes at the micrometer scale due to the lower chatter component which is usually drowned out by noise. In this paper, an adaptive iterative reduction algorithm and a chatter quantification index: Rényi entanglement entropy, are proposed. With the physical significance of Rényi entanglement entropy elucidated, the application of Rényi entanglement entropy has been successfully expanded from the microscopic quantum entanglement field to the macroscopic nonlinear milling systems by redefining the state probability vector, probability and probability density matrix. Firstly, the adaptive iterative signal-to-noise separation algorithm is designed to increase the sensitivity of quantification indicator to chatter features. Then, to apply Rényi entanglement entropy to nonlinear micro- and macro-milling systems, the milling system is regarded as a mixed state without prior information, and the method considering causality for calculating state probability vectors and probability density matrices are presented. Finally, the relevance relation among subsystems is analyzed, and the physical significance of Rényi entanglement entropy in micro- and macro-milling systems is discussed. In addition, the relationships between parameter τ and chatter identification, feature space are analyzed. The research results demonstrate that the proposed Rényi entanglement entropy algorithm is effective in identification of multiple quasi-periodic chatter modes and can quantify the degree of cross-correlation among several subsystems in macroscopic nonlinear milling systems.