Stability prediction in milling based on linear multistep method

  • Yonggang Mei
  • Rong Mo
  • Huibin Sun
  • Bingbing He
  • Neng Wan


On the basis of linear multistep method, the stability of milling process is investigated in this paper. The dynamics of milling process considering the regeneration effect is modeled as a delay differential equation (DDE) with periodic coefficient. The Floquet theory is adopted to predict the stability of milling by calculating the spectral radius of the transition matrix over one principal period. Two high-order starting methods for the Milne-Simpson method are introduced firstly. The effects of different starting methods on the convergence rate of the algorithm are studied. Subsequently, a Milne-Simpson-based predictor-corrector method (SSM) is proposed to further improve the numerical stability and convergence rate. The accuracy and computational efficiency of SSM are verified through two benchmark milling models. The simulation results demonstrate that the proposed method has excellent numerical stability and higher convergence rate compared with the Simpson-based method (SBM) and Adams-Simpson-based method (ASM).


Stability prediction Linear multistep method Milne-Simpson Starting method Predictor-corrector 


Funding information

This research received financial support from the National Natural Science Foundation of China (NSFC, nos.: 51875475 and 51775445).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Yonggang Mei
    • 1
  • Rong Mo
    • 1
  • Huibin Sun
    • 1
  • Bingbing He
    • 2
  • Neng Wan
    • 1
  1. 1.Department of Mechanical EngineeringNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.College of Mechanical & Electrical EngineeringShaanxi University of Science & TechnologyXi’anPeople’s Republic of China

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