Ma Junjin, Li Yunfei, Zhang Dinghua, Zhao Bo, Wang Geng, Pang Xiaoyan
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China.
Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi'an 710072, China.
Micromachines (Basel). 2022 Jan 21;13(2):160. doi: 10.3390/mi13020160.
This paper presents an updated full-discretization method for milling stability prediction based on cubic spline interpolation. First, the mathematical model of the time-delay milling system considering regenerative chatter is represented by a dynamic delay differential equation. Then, in a single tooth passing period, the time is divided into a finite time intervals, the state item and the time-delay item are approximated in each time interval by cubic spline interpolation and third-order Newton interpolation, respectively. Afterward, a transition matrix is constructed to represent the transfer relationship of the teeth in a period. Finally, based on Floquet theory, the milling stability lobes can be obtained. Meanwhile, in order to improve computational efficiency, an optimized method is proposed based on the traditional algorithm and the proposed method has high precision without losing high efficiency. Finally, several milling experiments are conducted to verify the accuracy of the proposed method, and the results show that the predicted results agree well with the experimental results.
本文提出了一种基于三次样条插值的铣削稳定性预测全离散化方法。首先，考虑再生颤振的时滞铣削系统数学模型由动态延迟微分方程表示。然后，在单个齿通过周期内，将时间划分为有限个时间间隔，状态项和时滞项在每个时间间隔内分别通过三次样条插值和三阶牛顿插值进行近似。之后，构建一个转移矩阵来表示一个周期内各齿的传递关系。最后，基于弗洛凯理论得到铣削稳定性叶瓣。同时，为提高计算效率，在传统算法基础上提出了一种优化方法，该方法在不损失高效性的前提下具有高精度。最后，进行了多次铣削实验以验证所提方法的准确性，结果表明预测结果与实验结果吻合良好。
