高速铣削颤振系统稳定性及分岔的Chebyshev多项式数值分析(英文)

Prediction Chatter Stability and Bifurcation in Milling Machine

采用Chebyshev多项式法和Floquet理论相结合来预测铣床运行中的颤振和分岔。得到了稳定性极限形图,可以准确地预示机床的稳定性。通过系统的特征值分析得到此系统发生了倍周期分岔和Hopf分岔。系统由稳定的平衡点通过倍周期分岔收敛到稳定的极限环运动,由Hopf分岔转化到概周期运动。庞加莱截面的数值结果也证实了概周期运动的发生。

The shifted Chebyshev polynomials and Floquet theory are adopted for the prediction chatter stability and bifurcation in milling. The stability lobes diagram is obtained. The stability in milling can well be predicted by the lobes diagram. The muliti-periodic and Hopf bifurcations are detected by the Eigen-values analysis. The results showed that the stability solution of the system transform from the stable equilibrium point to the limit cycle oscillatory after multiple cycle bifurca- tion, and it transforms to the quasi-periodic oscillation after Hopf bifurcation. The numerical re- sults of the Poincare section prove that the occurrence of the quasi-periodic oscillation.