A novel approach with smallest transition matrix for milling stability prediction
A novel approach with smallest transition matrix for milling stability prediction
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DOI：
10.1007/s11071-017-3649-0
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发表时间：
2017-07
影响因子：
5.6
通讯作者：
Tao Huang;Xiaoming Zhang;H. Ding
中科院分区：
文献类型：
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作者：
Tao Huang;Xiaoming Zhang;H. Ding
颤振的引入限制了铣削加工的效率。颤振预测是一种选择无颤振切削参数的离线策略。本文提出了一种新的铣削颤振预测方法，其目的是降低离散映射的转移矩阵的维数，其中转移矩阵的特征值决定了系统的稳定性，采用Floquet理论。将加权残数法应用于离散时间区间上的延迟微分方程时，引入了一个线性权函数。因此，位移项可以从状态向量中移除。当离散区间数一定时，该方法得到的过渡矩阵是时域方法中最小的。同时，在离散时间节点上自然满足加速度连续性条件，使该方法具有较好的精度。
The introduction of chatter limits the processing efficiency of milling. Chatter prediction is an off-line strategy to select chatter-free cutting parameters. This paper presents a novel method for prediction of milling chatter which aims to reduce the dimension of transition matrix of the discrete map, where the eigenvalues of the transition matrix determine the system stability by using Floquet theory. A linear weight function is introduced when the weighted residual method is applied to the delay differential equation on discrete time intervals. Thus the displacement item can be removed from the state vectors. When the number of discrete intervals is fixed, it is concluded that the transition matrix obtained by the proposed method is the smallest among the time-domain methods. Meanwhile, the acceleration continuity condition is naturally satisfied on discrete time nodes which endows the method with competitive accuracy.