两自由度轧机非线性扭振系统的振动特性及失稳研究

建立了含有非线性刚度和非线性摩擦阻尼的两自由度轧机非线性扭振动力学方程，研究了该非线性方程在电机加载力矩作用下的振动特性。首先通过坐标变换消除恒定加载力矩影响，得到轧机在稳态点附近的等效非线性扭振方程。其次采用平均法得到轧机受外部周期激励时的主共振幅频方程，并应用奇异性理论得到系统的转迁集以及系统出现各种分岔行为的条件。最后以某轧机实际参数为例，研究了不同非线性因素对轧机传动系统的幅频特性影响以及轧机出现失稳振动的条件，这为研究和抑制轧机传动系统的扭振提供了理论基础

Vibration characteristics of 2 DOF nonlinear torsional vibration system of rolling mill and its conditions of instability

A kind of 2 DOF nonlinear torsional vibration equation of rolling mill which considers nonlinear stiffness and nonlinear friction damping was established,and its vibration characteristics under torsional loading of motor were studied.The equivalent torsional vibration equation under torsional loading of motor was obatined by means of coordinate transformation.Then the main resonance amplitude-frequency equation of system under extrnal periodic excitation was obtained by averaging method.The transition set of system and its different bifurcation behaviors were analyzed by using singularity theory.According to actual parameters of rolling mill,the amplitude-frequency resonance characteristics under different nonlinear factors were studied and the instability conditions of self-excited vibration were elicited.The results supply theoretical bases for suppressing torsional vibration of rolling mill.