非线性时滞弹性关节机械臂系统稳定性与Hopf分岔  

Stability and Hopf Bifurcation of Nonlinear Flexible Joint Manipulator with Time Delay

作　　者：顾强强 蒋扇英 GU Qiangqiang;JIANG Shanying(School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai 201418,China)

机构地区：[1]上海应用技术大学机械工程学院,上海201418

出　　处：《机床与液压》2021年第11期12-16,21,共6页Machine Tool & Hydraulics

基　　金：国家自然科学基金青年科学基金项目(11502147)。

摘　　要：以非线性时滞弹性关节机械臂系统为研究对象,引入时滞建立系统动力学方程。利用多尺度法对非线性弹性关节机械臂系统进行理论分析,得到系统发生Hopf分岔的规范型。讨论时滞参数对系统Hopf分岔的影响,并对其周期解的稳定性以及产生的唯一极限环进行分析;通过数值计算对理论分析结果进行验证。结果表明:数值计算的结果与理论分析的结果具有较好的吻合度,验证了多尺度方法的有效性和可行性。The nonlinear flexible joint manipulator system with time delay was taken as the research object and the time delay was introduced to establish the system dynamics equation.The nonlinear flexible joint manipulator system was analyzed theoretically by using the multi-scale method,and the normative type of Hopf bifurcation occurred in the system was obtained.The effect of time delay parameters on the system Hopf bifurcation was discussed,and the stability of its periodic solution and the generated unique limit cycle were analyzed;the results of theoretical analysis were verified by numerical calculation.The results show that the results of numerical calculation agree well with the results of theoretical analysis,which verifies the validity and feasibility of the multi-scale method.

关 键 词：非线性 时滞 弹性关节机械臂 多尺度法 稳定性 HOPF分岔 

分 类 号：O326[理学—一般力学与力学基础]