Machining process dynamics can be described by state-space delayed differential equations (DDEs). To numerically predict the process stability, diverse piecewise polynomial interpolation is often utilized to discretize the continuous DDEs into a set of linear discrete equations. The accuracy of discrete approximation of the DDEs generally depends on how to deal with the piecewise polynomials. However, the improvement of the stability prediction accuracy cannot be always guaranteed by higher-order polynomials due to the Runge phenomenon. In this study, the piecewise polynomials with derivative-continuous at joint nodes are taken into consideration. We develop a recursive estimation of derived nodes for interpolation approximation of the state variables, so as to improve the discretization accuracy of the DDEs. Two different temporal discretization methods, i.e., second-order full-discretization and state-space temporal finite methods, are taken as demonstrations to illustrate the effectiveness of applying the proposed approach for accuracy improvement. Numerical simulations prove that the proposed approach brings a great improvement on the accuracy of the stability lobes, as well as the rate of convergence, compared to the previous recorded ones with the same order of interpolation polynomials.
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June 2018
Research-Article
Derived Nodes Approach for Improving Accuracy of Machining Stability Prediction
Le Cao,
Le Cao
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
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Xiao-Ming Zhang,
Xiao-Ming Zhang
Professor
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mails: zhangxm.duyi@gmail.com;
cheungxm@hust.edu.cn
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mails: zhangxm.duyi@gmail.com;
cheungxm@hust.edu.cn
Search for other works by this author on:
Tao Huang,
Tao Huang
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Search for other works by this author on:
Han Ding
Han Ding
Professor
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Search for other works by this author on:
Le Cao
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Xiao-Ming Zhang
Professor
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mails: zhangxm.duyi@gmail.com;
cheungxm@hust.edu.cn
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mails: zhangxm.duyi@gmail.com;
cheungxm@hust.edu.cn
Tao Huang
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
Han Ding
Professor
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China
1Corresponding author.
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 11, 2017; final manuscript received December 15, 2017; published online February 9, 2018. Assoc. Editor: Julian Rimoli.
J. Vib. Acoust. Jun 2018, 140(3): 031017 (8 pages)
Published Online: February 9, 2018
Article history
Received:
October 11, 2017
Revised:
December 15, 2017
Citation
Cao, L., Zhang, X., Huang, T., and Ding, H. (February 9, 2018). "Derived Nodes Approach for Improving Accuracy of Machining Stability Prediction." ASME. J. Vib. Acoust. June 2018; 140(3): 031017. https://doi.org/10.1115/1.4038947
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