This paper presents a numerical scheme to predict the milling stability based on the integral equation and numerical integration formulas. First, the milling dynamics taking the regenerative effect into account is represented in the form of integral equation. Then, the tooth passing period is precisely divided into the free vibration phase during which the analytical solution is available and the forced vibration phase during which an approximate solution is needed. To obtain the numerical solution of the integral equation during the forced vibration phase, the time interval of interest is equally discretized. Over each small time interval, Newton-Cotes integration formulas or Gauss integration formulas are employed to approximate the integral term in the integral equation. After establishing the state transition matrix of the system in one period, the milling stability is predicted by using Floquet theory. The benchmark examples are utilized to verify the proposed approach. The results demonstrate that it is highly efficient and accurate.
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June 2011
Research Papers
Numerical Integration Method for Prediction of Milling Stability
Ye Ding,
Ye Ding
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong
University, Shanghai 200240, China
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LiMin Zhu,
LiMin Zhu
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong
University, Shanghai 200240, China
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XiaoJian Zhang,
XiaoJian Zhang
State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology
, Wuhan 430074, China
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Han Ding
Han Ding
State Key Laboratory of Mechanical System and Vibration School of Mechanical Engineering, Shanghai Jiao Tong University
, Shanghai 200240, China
e-mail:
Search for other works by this author on:
Ye Ding
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong
University, Shanghai 200240, China
LiMin Zhu
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong
University, Shanghai 200240, China
XiaoJian Zhang
State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology
, Wuhan 430074, China
Han Ding
State Key Laboratory of Mechanical System and Vibration School of Mechanical Engineering, Shanghai Jiao Tong University
, Shanghai 200240, China
e-mail: J. Manuf. Sci. Eng. Jun 2011, 133(3): 031005 (9 pages)
Published Online: June 8, 2011
Article history
Received:
March 23, 2010
Revised:
April 13, 2011
Online:
June 8, 2011
Published:
June 8, 2011
Citation
Ding, Y., Zhu, L., Zhang, X., and Ding, H. (June 8, 2011). "Numerical Integration Method for Prediction of Milling Stability." ASME. J. Manuf. Sci. Eng. June 2011; 133(3): 031005. https://doi.org/10.1115/1.4004136
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