A Novel Updated Full-Discretization Method for Prediction of Milling Stability

This paper presents an updated full-discretization method for milling stability prediction based on cubic spline interpolation. First, the mathematical model of the time-delay milling system considering regenerative chatter is represented by a dynamic delay differential equation. Then, in a single t...

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Bibliographic Details
Published in:	Micromachines (Basel) 2022-01, Vol.13 (2), p.160
Main Authors:	Ma, Junjin, Li, Yunfei, Zhang, Dinghua, Zhao, Bo, Wang, Geng, Pang, Xiaoyan
Format:	Article
Language:	eng
Subjects:	Accuracy Algorithms computational efficiency Delay delay-differential equation Differential equations Discretization Efficiency Eigenvalues Floquet theory Interpolation Mathematical analysis Mathematical models milling stability Numerical analysis Research methodology Stability lobes
Online Access:	Get full text
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Summary:	This paper presents an updated full-discretization method for milling stability prediction based on cubic spline interpolation. First, the mathematical model of the time-delay milling system considering regenerative chatter is represented by a dynamic delay differential equation. Then, in a single tooth passing period, the time is divided into a finite time intervals, the state item and the time-delay item are approximated in each time interval by cubic spline interpolation and third-order Newton interpolation, respectively. Afterward, a transition matrix is constructed to represent the transfer relationship of the teeth in a period. Finally, based on Floquet theory, the milling stability lobes can be obtained. Meanwhile, in order to improve computational efficiency, an optimized method is proposed based on the traditional algorithm and the proposed method has high precision without losing high efficiency. Finally, several milling experiments are conducted to verify the accuracy of the proposed method, and the results show that the predicted results agree well with the experimental results.
ISSN:	2072-666X 2072-666X