轧机主传动非线性延时系统的Hopf分岔研究

Hopf Bifurcation for Nonlinear Delay System of Rolling Mill Main Drive

针对传统轧机主传动系统模型忽略位移延时的缺点,在考虑轧辊与轧件间的非线性摩擦力、阻尼、刚度和系统延时的基础上,建立了轧机主传动非线性延时系统的数学模型。分析了系统的局部稳定性和Hopf分岔的存在性,从理论上得到了系统产生Hopf分岔的延时临界值,通过采用1150型初轧机的实验数据进行对比仿真,证明了实验系统所建模型的正确。从得到的轧机主传动位移延时反馈系统的时间历程图、相图以及分岔图,验证了时延就是一个分岔参数,当时延的取值超过临界值时,轧机主传动位移延时反馈系统产生了Hopf分岔,从而得出了从生产工艺的角度加大轧制速度可以避免延时产生的不良影响,为进一步研究、控制轧机主传动系统提供了新思路。

In order to overcome the shortcoming of ignoring the displacement delay for the traditional rolling mill main drive system,a model of nonlinear displacement delayed feedback system in the rolling mill main drive system is derived that considers friction,damping,stiffness and delay.The local stability of the system and the existence of Hopf bifurcation are analyzed,and the delay threshold is drawn theoretically.The correctness of the model is verified by simulating and contrasting between the blooming mill experimental data of 1 150.The time-history chart,phase diagram and bifurcation diagram of the displacement delay feedback system in the rolling mill main drive system are achieved simultaneously,and time delay is proved to be a bifurcation parameter.When the time delay exceeds the threshold,the system generates Hopf bifurcation.In conclusion,delayed adverse effects in the production process can be avoided by increasing the rolling speed,which suggests a new idea for further study on how to control the rolling mill drive system.