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

  • Hongkun Li
  • Yuebang DaiEmail author
  • Zhenfang Fan


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.


Milling process Stability lobe diagram Improved precise integration method 


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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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