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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]
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Database: Engineering Source
Description
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]
ISSN:02683768
DOI:10.1007/s00170-026-18041-5