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Improved precise integration method for chatter stability prediction of two-DOF milling system

  • Hongkun Li
  • Yuebang DaiEmail author
  • Zhenfang Fan
ORIGINAL ARTICLE
  • 61 Downloads

Abstract

The motivation of this paper is to update the precise integration method (PIM) by a second-order Taylor formula and make detailed contrasts with the existing PIM, the semi-discretization method (SDM) to exhibit the necessity of developing this improved PIM (IPIM). The dynamics of two-degree of freedom (DOF) milling process with consideration of regeneration effect is first governed by a time periodic delay differential equation (DDE). With time period being evenly divided into a limited set of intervals, the integral non-homogeneous element is approximated by the second-order Taylor formula in every small time segment. After decomposing the exponential factor into a real term with 2N order algorithm, the transition matrix representing the specific machining system state is established in one whole tooth passing period to search for the chatter-free borderline. To investigate the characteristics of the proposed method in convergence rate, prediction accuracy, and computational efficiency, the benchmark example used in the literatures is introduced to develop a battery of comparisons with PIM and SDM. Finally, the experimental verification is also conducted in a CNC machine tool to further confirm the operability of the proposed IPIM, and the results indicate the method is of availability.

Keywords

Milling process Stability lobe diagram Improved precise integration method 

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Notes

Funding information

This work received financial support from the National Natural Science Foundation of China (51575075) and Collaborative Innovation Center of Major Machine Manufacturing in Liaoning.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringDalian University of TechnologyDalianChina

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