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research-article

Derived nodes approach for improving accuracy of machining stability prediction

[+] Author and Article Information
Le Cao

PHD candidate, State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
clhuststu@hust.edu.cn

Xiao-Ming Zhang

Professor, State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
zhangxm.duyi@gmail.com

Tao Huang

Postdoctor, State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
nuaaht@163.com

Han Ding

Professor, State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
famt@hust.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4038947 History: Received October 11, 2017; Revised December 15, 2017

Abstract

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 equtions. 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 with higher-order polynomials due to the Runge phenomenon. In this study the derivative continuity of piecewise polynomials at the joint nodes is 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.

Copyright (c) 2017 by ASME
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