预测铣削稳定性的Hamming线性多步法

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (22) : 67-74.

论文

智红英1 ,闫献国2,杜娟2,曹启超2

作者信息 +

Prediction of the milling stability based on the Hamming linear multistep method

ZHI Hongying1, YAN Xianguo2,DU Juan2,CAO Qichao2

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摘要

针对铣削加工过程中产生的振动现象，提出了一种 Hamming 线性多步法（HAMM）来预测铣削加工过程中的稳定性。考虑再生颤振的铣削加工动力学方程可以表示为时滞线性微分方程，将刀齿周期划分为自由振动阶段和强迫振动阶段，对强迫振动阶段进行离散，运用HAMM方法构建状态传递矩阵，利用 Floquet 理论，判定系统的稳定性，获得系统的稳定性叶瓣图。Matlab软件仿真结果表明，HAMM方法是预测铣削稳定性的一种有效方法。随着离散数的增加，HAMM方法的收敛速度要快于一阶半离散法（1st-SDM）和二阶全离散法（2nd-FDM），离散数较少的HAMM方法能达到和离散数较多的1st-SDM方法和2nd-FDM方法的局部离散误差。此外，在单自由度和双自由度动力学模型下，由三种方法的稳定性叶瓣图可以看出，HAMM方法预测铣削稳定性的精度均好于1st-SDM方法和2nd-FDM方法，计算效率远远高于1st-SDM方法和2nd-FDM方法。实验结果表明，HAMM方法是一种有效的预测铣削稳定性的方法。

Abstract

To address the vibration phenomenon in milling process, the Hamming linear multistep method (HAMM) was proposed to predict the stability of milling process.The dynamic equation for milling process with regenerative chatter was expressed as a delay linear differential equation .The cutter tooth cycle was divided into forced and free vibration stages.The forced vibration stage was discretized and the HAMM was used to construct a state transition matrix.The stability of the system was determined based on the Floquet theory, and the corresponding stability lobe diagrams were obtained.The matlab simulation results show that the HAMM is an effective method to predict the stability of milling.With the increase of discretization number, the convergence rate of HAMMis faster than that of the first-order semi-discretization method(1st-SDM) and second-order full-discretization method(2nd-FDM).The HAMM with less discretization number can already reach the local discrete error of 1st-SDM and 2nd-FDM with more discretization numbers.In addition, for one and two degree-freedom dynamic models, the stability lobes diagrams by the three methods show that the prediction accuracy of the HAMM is better than that of the 1st-SDM and 2nd-FDM, and the computation efficiency of the HAMM is much higher than that of the 1st-SDM and 2nd-FDM.The experimental results also show that the HAAM method is effective for predicting the milling stability.

导出引用

智红英1,闫献国2,杜娟2,曹启超2 . 预测铣削稳定性的Hamming线性多步法[J]. 振动与冲击, 2018, 37(22): 67-74

ZHI Hongying1, YAN Xianguo2,DU Juan2,CAO Qichao2. Prediction of the milling stability based on the Hamming linear multistep method[J]. Journal of Vibration and Shock, 2018, 37(22): 67-74

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