A stability prediction method research for milling processes based on implicit multistep schemes

  • Yi WuEmail author
  • Youpeng You
  • Jianjun Jiang


Chatter suppression during milling operations is of great significant for tool life, surface quality, and cutting efficiency. Based on the Hamming and Simpson methods, a Hamming–Simpson–based method is presented in this paper for accurately and efficiently determining the milling stability. The milling dynamic model with consideration of the regeneration effect is expressed by delay differential equations (DDEs) with time-periodic coefficients. After separating the tooth-passing period into two different phases, the two linear multistep methods are simultaneously adopted to estimate the state term by discretizing the forced vibration phase into time intervals of equal length. Subsequently, the state transition matrix can be determined over one period and the chatter-free borderline can be searched according to the Floquet theory. On this basis, the precision and efficiency of the Hamming–Simpson–based method are analyzed in detail through comparing with the three benchmark methods. Analysis results indicate that the Hamming method is required to convert variables which may affect the prediction accuracy. To overcome this shortcoming and promote the computational accuracy, a three-step implicit multistep exponential fitting method is applied to predict chatter stability; meanwhile, the Simpson method is responsible for the correction of the prediction. The effectiveness of the proposed method has been comparatively analyzed through two benchmark examples. Numerical simulations illustrate that the proposed method exhibits better prediction accuracy and computational efficiency.


Milling process Convergence rate Implicit multistep schemes Floquet theory Chatter prediction 


Funding information

This work was partially supported by the Natural Science Foundation of Jiangsu Province Outstanding Youth Fund (Grant No. BK20160084) and the Fundamental Research Funds for the Central Universities (Grant No. NS2016056).


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Copyright information

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

Authors and Affiliations

  1. 1.College of Mechanical and Electrical EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of Safety and Environment EngineeringHunan Institute of TechnologyHengyangChina

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