A full-discretization method for prediction of milling stability
A full-discretization method for prediction of milling stability
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DOI：
10.1016/j.ijmachtools.2010.01.003
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发表时间：
2010-05-01
影响因子：
14
通讯作者：
Ding, Han
中科院分区：
文献类型：
--
作者：
Ding, Ye;Zhu, LiMin;Ding, Han
本文提出了一种基于直接积分法的铣削稳定性预测的全离散化方法。将考虑再生效应的动态铣削过程的基本数学模型表示为具有单离散时滞的线性时间周期系统，并通过离散时间周期的直接积分法计算系统的响应。然后，使用全离散化方法求解响应的Duhamel项。在每一个小的时间间隔内，所涉及的系统状态，时间周期和时间延迟项同时近似的线性插值。在得到一个时间区间上状态转移的离散映射后，构造了系统转移矩阵的封闭形式表达式。然后根据Floquet理论预测铣削稳定性。通过对一自由度和二自由度铣削模型的基准算例验证了算法的有效性。结果表明，该方法在不损失任何数值精度的前提下，具有较高的计算效率。算法的代码也附在附录中。皇冠版权所有（C）2010由爱思唯尔有限公司出版。保留所有权利。
This paper presents a full-discretization method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-discretization method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.