再生型颤振系统的Hopf分岔分析与控制

Analysis and Control of Hopf Bifurcation for Regenerative Chatter System

考虑一类单自由度的非线性再生型切削颤振系统,利用多尺度法分析系统时滞参数对解稳定性的影响,并在此基础上采用非线性位移反馈控制抑制Hopf分岔引起的颤振.理论分析和数值模拟结果验证了所给控制方法在切削颤振控制模型中的有效性.

We considered a class of retarded one-degree-of-freedom nonlinear system,namely,the regenerative model of chatter in a lathe machine tool.The time-delay influence on the stability of the system solutions was analyzed with the aid of multiple scales.Nonlinear displacement feedback control can be used to suppress the self-sustained oscillation caused by Hopf bifurcation.The results of the theory analysis and numerical simulation show that the designed controller is valid for the cutting chatter system.