An efficient full-discretization method for prediction of milling stability
An efficient full-discretization method for prediction of milling stability
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一种有效的全离散化铣削稳定性预测方法
DOI：
10.1016/j.ijmachtools.2012.07.008
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发表时间：
2012-12-01
影响因子：
14
通讯作者：
Wu, Baohai
中科院分区：
文献类型：
--
作者：
Liu, Yilong;Zhang, Dinghua;Wu, Baohai
本文提出了一种有效的全离散化方法来预测铣削稳定性。动态铣削过程以具有单个离散时间延迟的状态空间形式表示。将时间周期均匀地离散成有限的间隔集合后，在每个小的时间离散化步骤中，首先用三个相邻的离散状态值来近似时滞项，并通过线性插值方法来表示时滞项。同时，利用状态项的可导性，考虑状态空间方程的独特结构，可以得到状态项在每个区间开始和结束时的导数，从而可以利用Hermite插值更精确、更紧凑地逼近状态项。最后，确定单个周期内的转移矩阵，以通过 Floquet 理论预测铣削稳定性。估计该方法的收敛速度并与其他方法进行比较。利用两个基准示例来验证所提出的方法在低主轴转速和高主轴转速域中预测铣削稳定性的有效性。结果表明，该方法具有较高的计算效率。 (C) 2012 Elsevier Ltd. 保留所有权利。
This paper presents an efficient full-discretization method for the prediction of milling stability. The dynamic milling process is represented in state-space form with a single discrete time delay. After discretizing the time period equally into a finite set of intervals, in each small time discretization step, the time-delayed item is first approximated with three neighboring discrete state values, and the time-periodic item is represented by the linear interpolation method. Meanwhile, by utilizing the derivability of the state item and considering the unique structure of the state-space equation, the derivatives of the state items at the start and end of each interval could be obtained, with which the state item could then be more precisely and compactly approximated by using Hermite interpolation. Finally, the transition matrix over a single period is determined to predict the milling stability via the Floquet theory. The rate of convergence of the proposed method is estimated and compared with other methods. Two benchmark examples are utilized to verify the effectiveness of the proposed method for the prediction of milling stability both in low and high spindle speed domains. The results show that the proposed method has high computational efficiency. (C) 2012 Elsevier Ltd. All rights reserved.