具位移时滞反馈机床颤振系统的稳定性和分支分析

Stability and bifurcation analysis of a machine tool chatter system with displacement delay feedback

研究了具位移时滞反馈机床颤振系统模型.从对系统线性化方程的特征方程根的分布分析入手,讨论了系统平衡点的稳定性,确定了系统的线性稳定性区域,发现当系统中的时滞经过一系列临界值时,系统经历了Hopf分支.然后,利用中心流形理论和规范型方法分析了分支周期解的稳定性和Hopf分支的分支方向.最后,数值模拟验证了理论结果.

Mathematical model of a machine tool chatter system with displacement delay feedback is studied.Stability of equilibrium is discussed by analyzing the characteristic equation of linearized system of original system at equilibrium.Regions of linear stability of equilibrium are given;it is found that Hopf bifurcation exists when delay passes through a sequence of critical values.Then,using center manifold theorem and normal form method,direction and stability of Hopf bifurcation are determined.Finally,some numerical simulations are carried out supporting the analytic results..