Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method

LI Zhongqun; PENG Yuerong

doi:10.16080/j.issn1671-833x.2016.23/24.030

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Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method

更新时间：2025-10-30

- Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method
- Aeronautical Manufacturing Technology Vol. 59, Issue 23/24, (2016)
- 作者机构：
  
  湖南工业大学机械工程学院,株洲,412007
- 作者简介：
- 基金信息：
- DOI：10.16080/j.issn1671-833x.2016.23/24.030
  CLC：
- Published：2016
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李忠群，彭岳荣，夏磊，朱帆. 基于三阶龙格库塔法的铣削稳定性半解析法预测*[J]. 航空制造技术, 2016, 59(23/24): 30-33. LI Zhongqun, PENG Yuerong, XIA Lei, ZHU Fan. Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method. Aeronautical Manufacturing Technology, 2016, 59(23/24): 30-33.

LI Zhongqun, PENG Yuerong. Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method[J]. Aeronautical Manufacturing Technology, 2016, 59(23/24).
李忠群，彭岳荣，夏磊，朱帆. 基于三阶龙格库塔法的铣削稳定性半解析法预测*[J]. 航空制造技术, 2016, 59(23/24): 30-33. LI Zhongqun, PENG Yuerong, XIA Lei, ZHU Fan. Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method. Aeronautical Manufacturing Technology, 2016, 59(23/24): 30-33. DOI： 10.16080/j.issn1671-833x.2016.23/24.030.

LI Zhongqun, PENG Yuerong. Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method[J]. Aeronautical Manufacturing Technology, 2016, 59(23/24). DOI： 10.16080/j.issn1671-833x.2016.23/24.030.

摘要

针对使用再生颤振理论建立的铣削动力学模型，提出了一种基于三阶龙格库塔法用于预测铣削稳定性的半解析方法。首先，以状态空间方程的形式表示动力学微分方程；其次，利用三阶龙格库塔法推导出传递矩阵；最后利用 Floquet 理论判断特定切削状态下的稳定性，进而获得铣削稳定性叶瓣图。通过与半离散法的仿真结果进行对比发现，基于三阶龙格库塔法的铣削稳定性求解方法具有更高的预测精度和计算效率。

Abstract

In order to solve the dynamic model of milling process set up using regenerative chatter theory

a new semi-analytical approach based on three-order Runge-Kutta method was proposed in the paper. Firstly

the dynamic differential equation was represented by the form of the state space equation. Secondly

the state transition matrix was deduced using the three-order Runge-Kutta method. Lastly

the stability under current cutting condition was determined according to the Floquet theory

and as a result

the stability lobe diagram (SLD) of milling process can be obtained. It was shown that the proposed semi-analytical approach based on three-order Runge-Kutta method has higher convergence rate and computation accuracy

when compared with the simulation results of the classical semi-discretization method.

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