基于切比雪夫分割法的铣削稳定性分析

利用切比雪夫分割法离散延时微分方程中的时间周期项,然后采用二阶Newton差商方法求出每个时间元端点处铣刀的运动向量,进而得到铣削系统的传递矩阵,并用Floquet理论判断铣削系统的稳定性.利用以上方法,研究了一个两自由度铣削系统稳定性问题,得到了系统稳定性叶瓣图.结果表明:在同等计算精度的要求下,切比雪夫分割法比平均分割法所取的点数要少,计算效率较高;将时间周期分割成相同的份数,切比雪夫分割法计算精度高.

Milling Stability Analysis Based on Chebyshev Segmentation

Using the Chebyshev segmentation method to discrete the time period contained in delay differential equation， the Newton second-order difference quotient method was used to calculate the motion vector of cutter at each time endpoint， then the transfer matrix of milling system was obtained， and the system stability was determined by the Floquet theory. Using the above methods， a two-degrees of freedom milling system stability issues was investigated to get system stability lobe diagrams. The results showed that under the same calculation accuracy， the points needed to cut the time period by the Chebyshev segmentation are less than those by the average segmentation， and the computational efficiency of the Chebyshev segmentation is higher. When the time period is divided into the same parts， the stability lobe diagrams gotten by the Chebyshev segmentation method are more accurate than that of the other.