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A rapid milling stability prediction method based on Gauss–Legendre quadrature rule.

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Title: A rapid milling stability prediction method based on Gauss–Legendre quadrature rule.
Authors: Wang, Kang1 (AUTHOR), Chen, Pin2 (AUTHOR), Ge, Shuyi1 (AUTHOR) gsy@fzu.edu.cn
Source: International Journal of Advanced Manufacturing Technology. Jun2026, Vol. 144 Issue 7/8, p4963-4979. 17p.
Subjects: Gaussian quadrature formulas, Delay differential equations, Self-induced vibration, State-space methods, Interpolation, Floquet theory
Abstract: Regenerative chatter is the primary reason of milling instability phenomena, which seriously affects the machining efficiency and accuracy. The stability region and unstable region can be predicted by the stability lobe diagram (SLD) to avoid milling chatter. An accurate and rapid approach for predicting milling stability is presented in this paper based on the five-point Gauss–Legendre quadrature formula (GLQF). Firstly, the delay-differential equation (DDE) of milling dynamics is expressed as a state-space formula. The state-space equation is then converted into an integral equation to obtain the relationship between two time points at each time interval. Next, the integral equation is solved algebraically using the five-point GLQF. Then the high-order Newton interpolation method is employed to approximate the state item and the delayed state item. The state transition matrix (STM) is constructed in the tool rotation period and the dimension of the STM is reduced. Then the Floquet theory is applied to forecast milling stability. Finally, the simulation and experiment results demonstrate that the presented approach not only converges more quickly but also significantly enhances computational efficiency. The method can be effectively used to anticipate and mitigate the chatter, which leads to more stable and efficient milling operations. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Advanced Manufacturing Technology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 194545526
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  Label: Title
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  Data: A rapid milling stability prediction method based on Gauss–Legendre quadrature rule.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Kang%22">Wang, Kang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Pin%22">Chen, Pin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ge%2C+Shuyi%22">Ge, Shuyi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gsy@fzu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Advanced+Manufacturing+Technology%22">International Journal of Advanced Manufacturing Technology</searchLink>. Jun2026, Vol. 144 Issue 7/8, p4963-4979. 17p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Gaussian+quadrature+formulas%22">Gaussian quadrature formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Delay+differential+equations%22">Delay differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Self-induced+vibration%22">Self-induced vibration</searchLink><br /><searchLink fieldCode="DE" term="%22State-space+methods%22">State-space methods</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Floquet+theory%22">Floquet theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Regenerative chatter is the primary reason of milling instability phenomena, which seriously affects the machining efficiency and accuracy. The stability region and unstable region can be predicted by the stability lobe diagram (SLD) to avoid milling chatter. An accurate and rapid approach for predicting milling stability is presented in this paper based on the five-point Gauss–Legendre quadrature formula (GLQF). Firstly, the delay-differential equation (DDE) of milling dynamics is expressed as a state-space formula. The state-space equation is then converted into an integral equation to obtain the relationship between two time points at each time interval. Next, the integral equation is solved algebraically using the five-point GLQF. Then the high-order Newton interpolation method is employed to approximate the state item and the delayed state item. The state transition matrix (STM) is constructed in the tool rotation period and the dimension of the STM is reduced. Then the Floquet theory is applied to forecast milling stability. Finally, the simulation and experiment results demonstrate that the presented approach not only converges more quickly but also significantly enhances computational efficiency. The method can be effectively used to anticipate and mitigate the chatter, which leads to more stable and efficient milling operations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Advanced Manufacturing Technology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1007/s00170-026-18041-5
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      – Code: eng
        Text: English
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        PageCount: 17
        StartPage: 4963
    Subjects:
      – SubjectFull: Gaussian quadrature formulas
        Type: general
      – SubjectFull: Delay differential equations
        Type: general
      – SubjectFull: Self-induced vibration
        Type: general
      – SubjectFull: State-space methods
        Type: general
      – SubjectFull: Interpolation
        Type: general
      – SubjectFull: Floquet theory
        Type: general
    Titles:
      – TitleFull: A rapid milling stability prediction method based on Gauss–Legendre quadrature rule.
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            NameFull: Wang, Kang
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            NameFull: Chen, Pin
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            NameFull: Ge, Shuyi
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 144
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              Value: 7/8
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            – TitleFull: International Journal of Advanced Manufacturing Technology
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