高速切削过程中颤振现象的二自由度非光滑模型分析  

ANALYSIS ON CHATTER VIBRATION OF A TWO-DEGREE-OF-FREEDOM NON-SMOOTH SYSTEM IN HIGH-SPEED CUTTING PROCESS

作　　者：刘喻 张思进[1] 殷珊 Liu Yu;Zhang Sijin;Yin Shan(College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,China;The State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学机械与运载工程学院,长沙410082 [2]湖南大学湖南大学汽车车身先进设计制造国家重点实验室,长沙410082

出　　处：《动力学与控制学报》2018年第4期350-355,共6页Journal of Dynamics and Control

摘　　要：研究了一类二自由度模型在高速切削过程中的颤振运动.首先建立了二自由度切削运动模型,得到了四维的非线性分段方程,然后研究切削力中的动态分量对切削颤振的影响,应用特征值法解析建立了系统发生Hopf分岔的临界条件.结果表明,当分岔参数经过某一临界值时发生Hopf分岔.最后,通过数值方法对该系统进行了数值模拟,从而验证了该临界条件的有效性.The chatter dynamics of a two-degree-of-freedom model in the high-speed cutting process was analyzed. A set of four-dimensional piecewise equations with the segment of cutting force were constructed for the model at first. Afterwards,the influence of the dynamic component of the cutting force on the cutting chatter was studied,and the condition of the chatter was derived by analyzing the associated characteristic transcendental equation. It reveals that the Hopf＇s bifurcation occurred at a positive steady state as bifurcating parameters pass a sequence of critical values. And the results of the analytical calculations are verified by full numerical simulations.

关 键 词：颤振 高速切削 非光滑系统 HOPF分岔 

分 类 号：O242.1[理学—计算数学] TG506.1[理学—数学]