A second-order semi-discretization method for the efficient and accurate stability prediction of milling process

A second-order semi-discretization method for the efficient and accurate stability prediction of... Due to the high computational accuracy and good applicability with a low complexity of algorithm, semi-discretization method has a significant application for predicting milling stability, but to some extent it has some limitations in computational efficiency. Based on the Newton interpolation polynomial and an improved precise time-integration (PTI) algorithm, a second-order semi-discretization method for efficiently and accurately predicting the stability of the milling process is proposed. In the method, the milling dynamic system considering the regenerative effect is first approximated by a time-periodic delayed-differential equation (DDE) and then reformulated in state-space form. After discretizing the time period into a finite number of time intervals, the equation is integrated on each discrete time interval. In order to improve the approximation accuracy of the time-delay item, a second-order Newton interpolation polynomial is utilized instead of a linear function used in the original first-order semi-discretization method (SDM). Next, with a rapid matrix computation technique, an improved precise time-integration algorithm is employed to calculate the resulting exponential matrices efficiently. Finally, transition matrix of the system is constructed over the discretization period and the milling stability boundary is determined by Floquet theory. Compared with the typical discretization methods, the proposed method indicates a faster convergence rate. Further, two benchmark examples are given to validate the effectiveness of the proposed method from the aspects of computational efficiency and accuracy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The International Journal of Advanced Manufacturing Technology Springer Journals

A second-order semi-discretization method for the efficient and accurate stability prediction of milling process

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Publisher
Springer London
Copyright
Copyright © 2017 by Springer-Verlag London
Subject
Engineering; Industrial and Production Engineering; Media Management; Mechanical Engineering; Computer-Aided Engineering (CAD, CAE) and Design
ISSN
0268-3768
eISSN
1433-3015
D.O.I.
10.1007/s00170-017-0171-y
Publisher site
See Article on Publisher Site

Abstract

Due to the high computational accuracy and good applicability with a low complexity of algorithm, semi-discretization method has a significant application for predicting milling stability, but to some extent it has some limitations in computational efficiency. Based on the Newton interpolation polynomial and an improved precise time-integration (PTI) algorithm, a second-order semi-discretization method for efficiently and accurately predicting the stability of the milling process is proposed. In the method, the milling dynamic system considering the regenerative effect is first approximated by a time-periodic delayed-differential equation (DDE) and then reformulated in state-space form. After discretizing the time period into a finite number of time intervals, the equation is integrated on each discrete time interval. In order to improve the approximation accuracy of the time-delay item, a second-order Newton interpolation polynomial is utilized instead of a linear function used in the original first-order semi-discretization method (SDM). Next, with a rapid matrix computation technique, an improved precise time-integration algorithm is employed to calculate the resulting exponential matrices efficiently. Finally, transition matrix of the system is constructed over the discretization period and the milling stability boundary is determined by Floquet theory. Compared with the typical discretization methods, the proposed method indicates a faster convergence rate. Further, two benchmark examples are given to validate the effectiveness of the proposed method from the aspects of computational efficiency and accuracy.

Journal

The International Journal of Advanced Manufacturing TechnologySpringer Journals

Published: Mar 1, 2017

References

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